1 © 2014 IOP Publishing Ltd Printed in the UK

Journal of Physics D: Applied Physics

W R Lempert and I V Adamovich

Printed in the UK

433001

JPD

© 2014 IOP Publishing Ltd

2014

47

J. Phys. D: Appl. Phys.

D

0022-3727

10.1088/0022-3727/47/43/433001

43

Journal of Physics D: Applied Physics

1. Introduction

Accurate characterization of high-pressure nonequilibrium molecular plasmas, at high specific energy loadings and highly transient conditions, is critical for the fundamental understanding of the kinetics of pulsed breakdown, energy partition in pulsed electric discharges, molecular energy trans-fer processes, plasma chemical reactions and nonequilibrium high-enthalpy flows. Quantitative insight into these processes is necessary for the development of engineering applications of high-pressure nonequilibrium plasmas, such as plasma

assisted combustion, plasma flow control, and molecular gas lasers. Time-resolved and spatially-resolved measure-ments of rotational/translational temperature, vibrational level populations of molecules, species number densities and electric fields in these plasmas are of particular importance for these applications. Coherent anti-Stokes Raman scattering (CARS) and spontaneous Raman spectroscopy are two pow-erful laser diagnostic techniques that have been widely used for these non-intrusive measurements, providing high spatial resolution, time resolution and spectral resolution. Broadband CARS and Raman diagnostics are particularly attractive since

Coherent anti-Stokes Raman scattering and spontaneous Raman scattering diagnostics of nonequilibrium plasmas and flows

Walter R. Lempert and Igor V. Adamovich

Departments of Mechanical & Aerospace Engineering and Chemistry & Biochemistry The Ohio State University Columbus, OH 43210, USA

E-mail: lempert.1@osu.edu

Received 6 June 2014, revised 24 July 2014Accepted for publication 18 August 2014Published 9 October 2014

AbstractThe paper provides an overview of the use of coherent anti-Stokes Raman scattering (CARS) and spontaneous Raman scattering for diagnostics of low-temperature nonequilibrium plasmas and nonequilibrium high-enthalpy flows. A brief review of the theoretical background of CARS, four-wave mixing and Raman scattering, as well as a discussion of experimental techniques and data reduction, are included. The experimental results reviewed include measurements of vibrational level populations, rotational/translational temperature, electric fields in a quasi-steady-state and transient molecular plasmas and afterglow, in nonequilibrium expansion flows, and behind strong shock waves. Insight into the kinetics of vibrational energy transfer, energy thermalization mechanisms and dynamics of the pulse discharge development, provided by these experiments, is discussed. Availability of short pulse duration, high peak power lasers, as well as broadband dye lasers, makes possible the use of these diagnostics at relatively low pressures, potentially with a sub-nanosecond time resolution, as well as obtaining single laser shot, high signal-to-noise spectra at higher pressures. Possibilities for the development of single-shot 2D CARS imaging and spectroscopy, using picosecond and femtosecond lasers, as well as novel phase matching and detection techniques, are discussed.

Keywords: CARS, Raman scattering, four-wave mixing, nonequilibrium plasmas, nonequilibrium flows

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Topical Review

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0022-3727/14/433001+26$33.00

doi:10.1088/0022-3727/47/43/433001J. Phys. D: Appl. Phys. 47 (2014) 433001 (26pp)

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2

they do not require high long-term temporal stability of the laser beams and provide simultaneous access to a manifold of vibrational levels of multiple molecular species, although this reduces the signal-to-noise ratio. Over the last 20–30 years, these techniques have been applied for nonequilibrium plasma and flow thermometry, quantifying vibrational excitation of molecular species in these environments, identification of dominant energy transfer processes controlling vibrational level populations and energy thermalization, and measure-ments of vibrational energy transfer rates.

The objectives of the present work are to provide an over-view of recent experimental results that used these diagnostic techniques to characterize nonequilibrium molecular plasmas and nonequilibrium high-enthalpy flows, and to discuss the current state of the art. This work is not pretending to be a comprehensive review of the use of CARS and Raman scat-tering for other applications such as combustion diagnostics, high-resolution spectroscopy and condensed matter diagnos-tics. This paper is organized as follows: section 2 presents a brief overview of theoretical background of CARS (sections 2.1–2.3), four-wave mixing (section 2.4), and spontaneous Raman spectroscopy (section 2.5); section 3 discusses details of the experimental implementation of these techniques and data reduction; section  4 reviews experimental results (sec-tion 4.1—vibrational CARS for vibrational level population measurements and thermometry in nonequilibrium plasmas and afterglow, section  4.2—vibrational CARS for vibra-tional level populations and thermometry in nonequilibrium high-enthalpy flows; section  4.3—pure rotational CARS thermometry in nonequilibrium plasmas and afterglow, sec-tion 4.4—CARS / 4-wave mixing for electric field measure-ments in nonequilibrium plasmas, section 4.5—spontaneous Raman spectroscopy for vibrational level populations and thermometry in nonequilibrium plasmas and afterglow, sec-tion  4.6—brief overview of kinetic modeling); finally, sec-tion 5 discusses future prospects.

2. Theoretical background: polarization theory of coherent anti-Stokes Raman scattering

CARS is a well-known optical four-wave mixing diagnostic technique which has been used extensively in combustion, gas discharges, and aerospace applications for measurements of rotational/translation temperature and, to a lesser extent, of the vibrational distribution function [1]. Recently, its use has become more prevalent in studies of nonequilibrium molecu-lar plasmas, particularly air or nitrogen containing plasmas. Of particular relevance are studies of nanosecond pulsed dis-charge plasmas, which have generated much recent interest due to their significant potential for a wide variety of applica-tions such as plasma assisted combustion, plasma medicine and plasma aerodynamic flow control [2].

2.1. Principle of CARS

Referring to the energy level diagram of figure 1, the CARS technique can be visualized as a pair of two-photon processes.

In the first process, a pair of optical waves, termed ‘pump’ and ‘Stokes’, are brought incident to a polarizable medium contain-ing, most often, diatomic molecular species. The interaction of the pump/Stokes beam pair with the medium results in the establishment of a polarization (dipole moment per unit vol-ume) which oscillates coherently (i.e. spatially and temporally phased) at the difference frequency between the two waves, ωv = ω0 − ω1, with the induced polarization being maximum if ωv is equal to a resonant frequency (vibrational or rotational fre-quency) for one of the species within the medium. In the sec-ond process, a third wave, known as the ‘probe’ wave, which is often but not necessarily at the same frequency as the pump wave (ω0), induces ordinary Raman scattering from the coher-ent oscillating polarization. Since the individual scatterers within the medium have a well-established phase relationship, the resulting Raman scattering from each individual molecule adds coherently in what is known as the phase matching direc-tion. The result is the creation of a fourth laser-like beam at the anti-Stokes frequency, ω3 = 2ω0 − ω1. In common practice, the Stokes wave is spectrally broad, typically derived from what is known as a ‘modeless’ pulsed dye laser, which enables an entire molecular Raman spectrum to be acquired simultane-ously, in some cases including the spectra of multiple spe-cies. If signal levels are sufficient, the Raman spectrum can be obtained essentially instantaneously from a single simultane-ous firing of the short pulsed laser beams, most often gener-ated using Q-switched (nanosecond duration) lasers, but more recently the use of picosecond and even femtosecond lasers has become more common. In scanning CARS, the dye laser is slowly scanned across the spectrum, providing a high spec-tral resolution. In this case, high temporal stability of the laser beams becomes critical.

2.2. CARS beam generation

The classical polarization theory of CARS has been well established for more than 40 years. The summary below is based on the formulation given by Eckbreth [1], which is in turn based principally on the formulations given by Harvey [3], Nibler and Knighten [4], and Yariv [5]. The starting point for the classical polarization theory description of CARS is the definitions of the electric displacement and polarization vectors, which for a linear process are given as

ε= +→ → →D E P ,0 (1)

Figure 1. Energy level diagram for the basic CARS process.

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ε χ= +→ →[ ]D E1 ,0 1 (2)

ε χ=→ →P E ,0 1 (3)

where χ1 is the linear susceptibility. Basically, equations (1) and (2) state that when an electric field is incident upon a medium, the medium responds by creating a macroscopic polarization (dipole moment per volume, in C m−2). If the field oscillates, such as in an electromagnetic wave, then the polar-ization will also oscillate. More generally, as the intensity of the applied field is increased, the induced polarization can be expressed as a series expansion,

ε χ χ χ= + + +→ → → →( )P E E E ... ,0 1 2

23

3(4)

where for an isotropic medium, such as a plasma, all χeven are equal to zero by symmetry. CARS is a third order non-linear process where χ3 has units of m−1 V−2. In its more general form, taking into account the varying possible polarizations of the applied fields and the resulting polarization, the compo-nents of the polarization vector are written as

ω ε χ ω ω ω ω ω ω ω= → → →P E r E r E r( ) ( , , , ) ( ) ( ) ( ) ,i ijkl j k l(3)

3 0(3)

3 0 1 2 0 1 2(5)

where the indices i, j, k, l represent polarization directions of the incident and CARS (ω3) fields, and repeated indices indi-cate performing a summation. As will be shown below, the application of what are known as pump and Stokes waves, ω0 and ω1 respectively, will result in the creation of a coherent oscillating polarization at the difference frequency, ω0 − ω1. This coherent oscillating dipole will ‘launch’ a wave at the anti-Stokes frequency, ω3 = 2ω0  −  ω1, which originates by substitution of the third order polarization,

→P ,

3 into the wave equation, which for the CARS wave at ω3 is given as

ωω ε

εω μ ω ω∇ + = −

→ → → → → →⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟E r

cE r P r( ) ( ) ( ) .2

332

20

3 0 32 3

3 (6)

Assuming a plane wave solution, and what is known as the ‘slowly varying wave’ approximation, the CARS ‘beam’ intensity generated over a length l is given as

ω

εχ=

Δ

Δ

⎛

⎝⎜

⎞

⎠⎟

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

( )I

n n n cI I l

sin,

kl

klCARS32

12

2 34

02 1

22 CARS

2 2 2

2

2

(7)

where I1 represents the intensity of the pump and probe beams,

I2 is the intensity of the Stokes beam, and Δ ≡ − −→ → → →k k k k2 1 2 3

represents what is known as the ‘phase matching’ condition where the magnitude of the wave vectors ki are given as

πλ

=kn2

,ii

i(8)

where ni is the refraction index of the medium at the wave-length λi. Physically, the phase matching condition repre-sents the constraint that in order to grow coherently, the fields created at each spatial location along the beam propagation direction must be in phase with the propagating field gener-ated at ‘downstream’ locations. This requires a zero mismatch

between the phase velocity of the generated CARS beam and the effective phase velocity of the pump/Stokes/probe beam combination. The simplest phase matching condition is to use collinear beams, since the dispersion in the refrac-tion index in weakly ionized plasma will be small. However, as will be discussed below, a much higher spatial resolution can be achieved by arranging the beams in what is known as the ‘folded BoxCARS’ configuration, in which the beams are crossed at appropriate angles in 3D.

2.3. Physical origin of the CARS susceptibility

The CARS medium is generally modeled as an ensemble of damped harmonic oscillators which are ‘driven’ by a polariz-ability-based driving force. Defining x(t) as the time-depen-dent internuclear separation for an individual dipole, and ignoring the spatial dependence of x and the driving force, we have:

Γ ω+ + =x

t

x

tx

F t

m

d

d

d

d

( ),v

2

22 (9)

where Γ is the damping coefficient, ωv is the vibrational reso-nant frequency, and F is the driving force given, on a per mol-ecule basis, as

ε α= ∂

∂⎜ ⎟⎜ ⎟

⎛⎝

⎞⎠

⎛⎝

⎞⎠F t

xE t( )

2( ) ,0

0

2 (10)

Note that the force is averaged over the period of the optical frequency, which is much faster than the molecular response, and α∂ ∂x( / )0 is the polarizability derivative with respect to vibration, evaluated at the equilibrium internuclear separation.

Now consider a field given by the superposition of two oscillations, again ignoring the explicit spatial dependence and focusing only on the time dependence.

= + +ω ωE t E E( )1

2[ e e ] c.c.i t i t

1 21 2 (11)

In equation  (11), ‘c.c’ stands for complex conjugate. Substitution of equations (10) and (11) into equation (9) will give

ε αω ω ω Γ ω ω

= ∂∂ − − + −

+ω ω−

⎜ ⎟⎜ ⎟⎛⎝

⎞⎠

⎛⎝

⎞⎠

⎡

⎣⎢

⎤

⎦⎥x t

m x

E E

i( )

8

*e

( ) ( )c.c.

i t

v

0

0

1 2( )

21 2

21 2

1 2

(12)

The vibrational term for the Raman third order polariza-tion, P3(t), is given by

ε α= ∂∂

⎜ ⎟⎛⎝

⎞⎠P t N

xx t E t( ) ( ) ( )3

00

(13)

where N is the number density of dipoles. Substitution of equations (11) and (12) into equation (13), after some algebra, will give

ε α

ε αω ω ω Γ ω ω

= ∂∂

+ +

× ∂∂ − − + −

+

ω ω

ω ω−

⎜ ⎟

⎜ ⎟

⎛⎝

⎞⎠

⎡

⎣⎢⎢

⎛⎝

⎞⎠

⎛

⎝⎜

⎞

⎠⎟⎤

⎦⎥⎥

P t Nx

E E

m x

E E e

i

( )1

4[ e e c.c.]

4

*

( ) ( )c.c. .

i t i t

i t

v

30

01 2

0

0

1 2( )

21 2

21 2

1 2

1 2

(14)

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From equation (14), it is apparent that there will be oscil-lations at ω1, ω2, 2ω1 − ω2, and 2ω2 − ω1. Focusing on the CARS term, ω3 = 2ω1 − ω2, and defining the amplitude of the third order polarization as

ω ω≡ +ωP t P( , )1

2( ) e c.c.,i t3

33

33 (15)

we arrive at the amplitude of the oscillating polarization at ω3, given as

ωε

ω ω ω Γ ω ω=

− − + −

α∂∂( )

PN E E

m i( )

*

8 [ ( ) ( )].

x

v

33

02

0

2

12

2

21 2

21 2

(16)

As discussed above, when the third order polarization is substituted into equation (6), the wave equation, the result is to ‘launch’ an electromagnetic wave at ω3 = 2ω1 − ω2. If the phase matching condition for the four waves is met, than the wave at ω3 will grow into an intense CARS ‘beam.’ Finally, defining the CARS susceptibility as

ω ε χ ω ω≡P E E( ) ( ) ( ) ,33 0 CARS 1

21 2 2 (17)

we have

χε

ω ω ω Γ ω ωχ=

− − + −+

α∂∂( )N

m i8 [ ( ) ( )],

x

vCARS

02

0

2

21 2

21 2

nr(18)

where χnr is the contribution to the CARS susceptibility due to what is known as the ‘non-resonant background’, which is typi-cally small compared to the resonant susceptibility, particularly in plasmas, but is non-negligible. The CARS resonant suscepti-bility can also be expressed in terms of the spontaneous Raman cross section for the transition of interest, with the result

χπ ε ω

ω ω ω ω Γ ω ω=

−

ℏ − − + −

σΩ

∂∂( )c N N

i

4 ( )

[ ( ) ( )],

l u v

vCARS

20

4

24 2

1 22

1 2

(19)

where Nl − Nu is the population difference between the lower and upper levels of the targeted transition.

2.4. CARS / 4-wave mixing for electric field measurements

Recently, the use of a four-wave mixing technique, very simi-lar to CARS, has been developed into a diagnostic technique for determination of spatially and temporally resolved electric field. The basis of the technique, first described and demon-strated in [6], is illustrated and compared to vibrational CARS in figure 2. By application of an external electric field, an elec-tric dipole can be induced in an otherwise non-polar molecule. Introduction of strong collinear pump and Stokes fields, from an appropriate pair of laser beams, creates the same coherent oscillating polarization that is the basis of vibrational CARS. However, in this case, the oscillating molecules now have a small field-induced dipole moment and as such they radiate at the vibrational frequency, which is in the IR portion of the spec-trum. The result is a coherent CARS-like signal in the infrared whose intensity depends quadratically on the external electric field strength. Most reported CARS measurements of electric field, including the initial work of [6], have been performed

using hydrogen as the active species [7–9], although some mea-surements have also been reported in nitrogen [10, 11].

In practice, the ordinary vibrational CARS signal is obtained simultaneously with the electric field signal since it is the ratio of the two signals which results in the electric field measurement. This can be seen by comparing the IR and CARS signal beam intensities, which are given as

χ≺I I I E ,IR IR2

Pump Stokes Ext2 (20)

χ≺I I I I ,CARS CARS2

Pump Stokes Probe (21)

where EExt is the electric field to be measured, and χi are the third order susceptibilities for the CARS and E-field CARS processes. Taking the ratio of the IR and CARS signal intensi-ties, noting that for E-field CARS the ‘green’ beam serves as both the pump and probe, and rearranging gives

=⎛⎝⎜

⎞⎠⎟E A

I I

I,Ext

IR Pump

CARS(22)

where A is a constant which is determined by calibration in sub-breakdown dc field. Thus, by monitoring the intensities of the pump, CARS, and IR beams the electric field can be determined.

2.5. Spontaneous Raman spectroscopy

Spontaneous Rayleigh/Raman scattering is a linear (χ1) pro-cess (see equation  (2)), which can be explained, classically, as the result of an incident electromagnetic wave inducing an oscillating electric dipole moment, p(t), which is given by the product of the polarizability, α, of the medium and the time-varying incident electric field, E(t),

α= ⋅p t E t( ) ( ) . (23)

The polarizability is customarily expanded with respect to the vibrational normal coordinates (or ‘normal modes’, Q) of the molecule, as follows,

α α α= + ∂∂

+ ⋯⎛⎝⎜

⎞⎠⎟

QQ ,0

0(24)

where α0 and α∂ ∂Q( / )0 are evaluated at the equilibrium inter-nuclear displacement. Assuming a harmonic oscillation with

Figure 2. Vibrational and electric field CARS energy level diagrams.

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natural frequency, ωk, and sinusoidal applied electric field, E, with frequency ω1 and amplitude E0, the induced electric dipole moment is given as

α ωα ω ω ω ω

=

+ ∂∂

− + +⎛⎝⎜

⎞⎠⎟

p t E t

Q

Q Et t

( ) cos ( )

2[cos ( ) cos ( ) ]k k

0 0 1

0

0 01 1 (25)

The first term in equation (25) contributes to Rayleigh and pure rotational Raman scattering, whereas the second term represents vibrational Raman scattering.

For quantized transitions between rotational–vibrational quantum states, the analogous quantum mechanical expres-sion for what is known as the polarizability matrix element is

α α α

α′ = ′ =

+ ∂∂

′

⎛⎝⎜

⎞⎠⎟

QQ

" "J"v" J'v J"v" J'v'

J"v" J'v' ,

J v J v, 0

0

(26)

where J″, v″, J′, and v′ are rotational and vibrational quan-tum numbers labeling the initial and final states, respectively, and the brackets indicate integration. In equation (26), the first term represents Rayleigh and pure rotational Raman scatter-ing, both of which vanish unless v″ = v′, due to orthogonal-ity of the vibrational wave functions, and the second term is responsible for vibrational Raman scattering.

For pure rotational Raman scattering, the scattering inten-sity, I, is given as [12]

πε

νγ

Δ= = ±∼∥ ±

⎡

⎣⎢

⎤

⎦⎥I b N J

4( )

45I 2s J J J L

2

02

42,

002

(27)

πε

νγ

Δ= = ±∼⊥ ±

⎡

⎣⎢

⎤

⎦⎥I b N J

( )

15I 2s J J J L

2

02

42,

002

(28)

Symbols ″′b ,J J, known as the Plazeck–Teller symbols, are the part of the polarizability matrix elements which arise from summation over the magnetic sublevels, mJ.

For vibrational scattering, assuming harmonic oscillator wave functions, the scattering intensities are given as

πε

νγ

Δ Δ= + = =∼∥

⎡

⎣⎢

⎤

⎦⎥I a b N( )

4( )

45I v   1, J   0s J J J L

2

02

410

2,

102

(29)

πε

νγ

Δ Δ= = =∼⊥

⎡

⎣⎢

⎤

⎦⎥I b N I

( )

15v   1, J   0s J J J L

2

02

4,

102

(30)

πε

νγ

Δ Δ= = = ±∼∥ ±

⎡

⎣⎢

⎤

⎦⎥I b N v J

4( )

45I  1, 2s J J J L

2

02

42,

102

(31)

πε

νγ

Δ Δ= = = ±∼±⊥

⎡

⎣⎢

⎤

⎦⎥I b N v J

( )

15I  1, 2s J J J L

2

02

42,

102

(32)

In equations (27)–(32), symbols ‖ and ⊥ correspond to the scattering polarized parallel and perpendicular, respectively, to the incident laser polarization direction. NJ is the number

density of scatterers in the level J, IL the irradiance (power density) of the incident laser beam, and a00 and γ00 represent matrix elements for the mean and anisotropic parts of the polarizability tensor, respectively, given as

α α α= + +a1

3( )xx yy zz (33)

γ α α α α α α

α α α

= − + − + −

+ + +

⎡⎣⎤⎦( )

1

2( ) ( ) ( )

6

xx yy yy zz zz xx

xy yz zx

2 2 2

2 2 21

2(34)

Similarly, γa /10 10 represent the corresponding polarizabil-ity derivative components. For linear molecules which behave as rigid rotors (or more precisely, for symmetric top wave functions with the quantum number K = 0), the Plazeck–Teller symbols, ″′b ,J J, have the following form [12],

= + ++ ++b

J J

J J

3 ( 1) ( 2)

2 (2 1) (2 3),J J2, (35)

= −+ −−bJ J

J J

3 ( 1)

2 (2 1) (2 1),J J2, (36)

= +− +

bJ J

J J

( 1)

(2 1) (2 3).J J, (37)

In nonequilibrium plasmas, a variety of anharmonicity effects also need to be taken into account including the anhar-monic correction to the vibrational matrix element (second term in equation  (26) [13]), centrifical distortion [14], and rotation–vibration interaction [15]. This is discussed in more detail in [16].

3. Experimental details and spectral analysis

3.1. Broadband CARS

Figure 3 shows the major elements of a basic broadband CARS apparatus. The key elements are (i) the pump laser, most often

Figure 3. Generic broadband CARS experimental setup.

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the second harmonic output (532 nm) of a Q-switched (nsec duration) Nd:YAG laser, although the use of picosecond lasers is becoming more common; (ii) a broadband dye laser, which generates the Stokes beam, and which is typically pumped by the same laser that provides the CARS pump (and often probe) beams; (iii) beam delivery and capture optics, and (iv) a grat-ing spectrometer/imaging camera combination (in this case an electron multiplying charge-coupled device (CCD) camera), also known as an optical multichannel analyzer (OMA). Note that typical gratings have more spectral resolution than can be afforded by scientific grade digital cameras and so the spectral resolution can be increased by the incorporation of an image magnification system using a pair of lenses (typically com-mercial camera lenses).

The most important element of a broadband CARS system is the ‘modeless’ broadband dye laser, an example of which, taken from Roy et al [17], is shown in figure 4. The dye laser, which in this case produces picosecond duration pulses (nano-second versions are similar) consists of a transversely pumped ‘oscillator’ cell, followed by a transversely pumped pre-amplifier, and a longitudinally pumped final amplifier. Note that in this case the oscillator beam is created from amplified spontaneous emission, as there is no actual optical cavity. This is the basis of the ‘modeless’ design. Figure 4 also shows the insertion of a variable angle of incidence transmission filter between the pre-amplifier and final amplifier. When used in combination with a very broad dye mixture [18], consisting of a solution of Pyrromethene 597 and Pyrromethene 650 dyes, this enables tuning of the broadband spectral output. Figure 5 shows the spectral output, as determined from the non-res-onant background (NRB) spectrum of argon, along with the Stokes wavelengths for v = 0 to v = 10 transitions of N2, when a 552 nm edge dichroic filter is inserted oriented at an angle of 10° with respect to the laser beam propagation axis. The Stokes beam is centered near 600 nm, with a FWHM of approximately 11 nm. The band center is purposefully tuned

such that there is greater output at higher vibrational levels in order to compensate, somewhat, for the reduced population of these higher levels in the experiment.

Figure 6 illustrates what is known as the ‘folded BoxCARS’ phase matching geometry, in which the pump/Stokes and the probe beams are arranged on a single lens in an isosceles tri-angular geometry. The CARS beam is then formed opposite to the Stokes beam. This geometry provides high spatial resolu-tion, with a typical cylindrical probe volume with dimensions of 50–100 microns in diameter and ~0.5–1.0 mm in length, depending upon the focal length of the lens.

CARS is most often used for determination of the rotational/translational temperature and vibrational distribution function of N2, although the technique can also be readily applied to other major species. Determination of the rotational/transla-tional temperature is most often performed using either the v = 0 to v = 1 Q-branch (ΔJ = 0) transition or the pure rota-tional transition, Δv = 0, ΔJ = ±2. In general, the vibrational Q-branch is preferred for relatively high temperatures (higher

Figure 4. Modeless picosecond broadband dye laser with a variable angle of incidence transmission filter placed between the preamplifier and final amplifier. Reproduced with permission from [17], Copyright 2005 Optics Letters.

Figure 5. Modeless broadband dye laser spectral output when a solution of Pyrromethene 597 and Pyrromethene 650 is used in combination with a dichroic absorption filter [19].

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than ~600–700 K), whereas at temperatures on the order of room temperature there are advantages to using pure rota-tional CARS. At low densities (less than ~50 Torr), pure rota-tional CARS is also advantageous since the spacing between the individual pure rotational transitions are much larger than for the Q-branch. This mitigates Stark broadening effects when high pulse energies are used.

As evident from equations (7) and (19), inference of rota-tional/translational temperature is based on the spontaneous Raman spectrum of the targeted species, most often the N2 molecule. For Q-branch transitions, the individual rotational lines are weakly separated due to what is known as rotation-vibration interaction. Specifically, to within the first term in the Dunham expansion,

α= − + +⎜ ⎟⎡⎣⎢

⎛⎝

⎞⎠

⎤⎦⎥E v J B v J J( , )

1

2( 1) ,e e (38)

where Be is the equilibrium rotational constant, αe is the vibration–rotation interaction constant, which accounts for the v-dependence of the molecular moment of inertia of the molecule, and J is the rotational angular momentum quantum number. In terms of transition frequency, the individual J tran-sitions within the v = 0 to v = 1 Q-branch are given as

ν ν= + − +J B B J J( ) ( ) ( 1) ,0 1 0 (39)

where for N2 ν0 ≈ 2330 cm−1 and B1 − B0 ≈ − 0.017 cm−1 (or approximately 1% of B0). Physically, the effect of increasing vibration is to slightly increase the internuclear separation which leads to an increase in the moment of inertia, I = μRe

2, of the molecule. Since the rotational energy levels are given as

= ℏ +E JI

J J( )2

( 1) ,2

(40)

an increase in Re leads to a decrease in rotational energy. Figure 7 shows an example Q-branch spectrum obtained in a repetitively pulsed nanosecond H2-air plane-to-plane dielec-tric barrier discharge at an equivalence ratio of ϕ = 0.4 and 92 Torr total pressure, along with a least squares fit with an inferred rotational/translational temperature of 1250  ±  35 K [20]. The spectrum was obtained ~3.5 μs after the end of a 120-pulse ‘burst’ at a pulse repetition rate of 10 kHz. The spectrum represents an average of 100 individual laser shots and the individual rotational lines are clearly partially resolved. The weaker broad feature centered at ~2298 cm−1 is the v = 1 → 2 Q-branch.

Note that for pure rotational CARS, with selection rule ΔJ = ±2, the spacing between individual transitions in the ground vibrational level, assuming rigid rotor wave functions, is 4B0, which is on the order of 8 cm−1 for N2. This is significantly higher compared to line spacing in Q-branch vibrational CARS, (B1 − B0)J(J + 1), unless high rotational levels, J ~ 20, are populated, which occurs at rotational temperatures Trot ~ BJ2/2 ~ 600 K. Thus, line spacing in pure rotational CARS spectra is sufficient to be readily resolvable with relatively low resolution grating spectrometers.

One of the most powerful features of CARS is the abil-ity to determine the vibrational distribution function. The spectroscopic basis for this is the ability to resolve transitions originating in different vibrational levels, which is the result of the anharmonicity in the molecular potential. Specifically, the vibrational energy, considering the molecule as a simple harmonic oscillator plus the first anharmonicity correction term, can be approximated as

ω ω= + − +⎜ ⎟ ⎜ ⎟⎛⎝

⎞⎠

⎛⎝

⎞⎠E v v x v( )

1

2

1

2e e evib

2

(41)

where for N2 in the ground electronic state ωe = 2358.6 cm−1 and ωexe = 14.32 cm−1. Figure 8 gives example spectra from a highly vibrationally non-equilibrium nanosecond pulse pin-to-pin discharge in N2 at P = 100 Torr, at three differ-ent times relative to the leading edge of the discharge current pulse. The pulse duration is ~100 ns. Measurable population is observed for vibrational levels as high as v = 9, whereas the measured rotational/translational temperature does not exceed ~500 K [19].

Inference of the vibrational distribution function from the raw spectra consists of the following steps. First, the raw spectrum is divided by the non-resonant background signal in order to normalize it, principally, to the broadband dye laser spectral output. Second, the square root of the normalized spectrum is least squares fit to a set of spectral lineshapes, one for each vibrational level detected. Numerical integration of these individual spectral components is then divided by v + 1, the assumed harmonic oscillator dependence of the spontane-ous Raman cross section, which is a very good approxima-tion for N2 vibrational levels. The result is a set of vibrational population differences, N(vi)  −  N(vi+1), see equation  (19). Assuming a zero population in levels exceeding the maximum level with a detectable population, vmax, allows straightfor-ward inference of the relative population of vibrational levels

vi, ∑==

f v N v N v( ) ( ) / ( ) .i i

k

v

k

0

max

3.2. Spontaneous Raman scattering

The experimental procedure for spontaneous Raman scatter-ing is considerably simpler than that for CARS, which is a large factor in its relative popularity as a diagnostic method. Basically, a single, generally linearly polarized, ‘probe’ laser beam is brought incident to the measurement volume, scatter-ing from which, typically at 90° with respect to the laser propa-gation direction, is imaged onto the entrance slit of a grating spectrometer. The use of a single laser beam considerably

Figure 6. Schematic of the folded BoxCARS phase matching geometry.

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simplifies alignment. The resulting spectrum is then spectrally analyzed in a manner that is essentially identical to that of the square root of the CARS spectrum. Spectral resolution, how-ever, is typically lower compared to CARS, in spite of the fact that similar resolution spectrometers are typically employed. This is due to the fact that for spontaneous Raman scattering there is an inherent trade-off between the entrance slit dimen-sion, which dictates the spectral resolution, and the level of the detected signal. This is not an issue for CARS since the coherent scattering can be readily focused to a near diffrac-tion limited spot at the spectrometer entrance slit location. As such, CARS Q-branch spectra are at least partially spectrally resolved, enabling accurate rotational/translational tempera-ture measurements, something which is more challenging for

spontaneous Raman scattering, where the temperature needs to be inferred from an unresolved rotational envelope, if the spec-trometer instrument function is known accurately. Also, CARS signal scaling as a square of the number density, compared to linear scaling of spontaneous Raman scattering signal, is an advantage for measurements in high pressure environments.

Spatial resolution in spontaneous Raman measurements is also typically somewhat lower compared to that realiz-able with CARS under identical conditions (mostly dictated by the scatterer number density), since signal levels are typi-cally lower and as such, significant spatial averaging is often employed. Spontaneous scattering is also more susceptible to contamination from spontaneous plasma emission and stray laser scattering. However, spatially-resolved measurements are possible when signal-to-noise is sufficiently high, using line-wise Raman spectra obtained by imaging the measure-ment region onto the spectrometer slit [21, 22]. This provides a significant advantage compared to CARS, where spatially resolved measurements require displacing the probed volume across the plasma or the flow, either by moving the test cell / flow channel relative to the laser beams, or by moving the beams if the position of the cell cannot be changed.

4. CARS and spontaneous Raman scattering stud-ies of nonequilibrium molecular plasmas and flows

4.1. Vibrational CARS: vibrational populations and rotational temperature in plasmas and afterglow

As illustrated in figure 8, CARS is ideally suited for the deter-mination of vibrational distributions of major molecular spe-cies. Early work in this field was done in low-pressure direct current (dc) discharges in nitrogen (P ~ 10 Torr), where vibra-tional levels of the ground electronic state N2 were measured by Shaub et al [23] (v = 0–7) and Smirnov and Fabelinskii [24] (v = 0–6). In high peak current pulsed discharges in nitro-gen, operated at pressures of up to P = 100 Torr, Valyansky

Figure 7. Sample vibrational Q-branch CARS spectrum of N2 in a repetitively pulsed nsec plane-to-plane dielectric barrier discharge in a H2/air mixture (equivalence ratio φ = 0.4) at P = 92 Torr [20].

Figure 8. Experimental CARS spectra of nanosecond pulse pin-to-pin discharge in N2 at P = 100 Torr captured 100 ns, 1 μs and 10 μs after the beginning of the discharge current pulse (pulse duration ~100 ns [19]).

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et al [25] and Devyatov et al [26] measured N2 vibrational level populations up to v = 5. Devyatov et al used a broad-band CARS system with collinear phase-matching for time-resolved measurements of N2 vibrational level populations v = 0–4 in a 200 ns duration pulsed discharge in nitrogen at 60 Torr, between two circular electrodes. They detected a significant rise in relative populations of vibrational levels v = 1–3 after the discharge pulse, for time delays ranging from a few μs to a few tens of μs. This rise could not be explained by near-res-onant vibration–vibration (V–V) transfer, one of the dominant processes resulting in overpopulating high vibrational levels in vibrationally excited nitrogen (anharmonic V–V pumping [27, 28]), which conserves vibrational quanta. This effect, in combination with an observed rise in the total energy stored in the vibrational mode of nitrogen N2(v = 0–4), by about 30% over several μs after the pulse (see figure 9), led the authors to the conclusion that the energy pooling process N2(A3Σ) + N2(A3Σ)  →  N2(C3Π) + N2(X1Σ,v) was adding additional vibrational quanta to the nitrogen vibrational mode. Although in this work the rotational structure of vibrational bands was not fully resolved, temperature rise estimated from the rota-tional envelope was insignificant, within ΔT ~ 50 K. At this low temperature and on this time scale, V–T relaxation and gas dynamic expansion are very unlikely to affect N2 vibrational populations.

In a related work by Vereschagin et al [29], a narrowband scanning CARS system, employing a tunable dye laser and collinear phase matching, was used to measure time-resolved N2(v = 0–5) vibrational populations and N2 rotational temper-ature, Trot = 320  ±  10 K, after a ~100 ns duration pulsed dis-charge in nitrogen at 115 Torr, between two plane electrodes. In this work, the rise of v = 2 and v = 3 populations after the discharge pulse has not been reported [25], in spite of specific energy loading in the discharge being higher than in the work by Devyatov et al [26]. Note that although the use of scan-ning narrowband CARS provides high spectral resolution, it also requires high temporal stability of the laser beams. In both these experiments [26, 29], a well-pronounced ‘bimodal’ structure of the N2 vibrational distribution was detected, with the first level vibrational temperature,

= −

( )T

E E

ln,

N

N

vib(0,1)1 0

0

1

(42)

being significantly lower compared to the slope of the distri-bution for the higher vibrational levels,

= −

−−

−( )T

E E

ln.v v

v v

N

N

vib( 1, )1

v

v

1 (43)

In the work by Vereschagin et al [29], Tvib(0,1) = 1740  ±  200 K and Tvib(1,5) = 7290   ±  350 K were measured 50 ns after the beginning of current rise (see figure 10). This effect occurs since the electron temperature in the discharge is very high, Te ~ 1 eV, and the time scale for vibrational excitation by electron impact is much shorter compared to the one for V–V energy exchange processes, such as

= + = ↔ = + =v v v vN ( 0) N ( 2) N ( 1) N ( 1) .2 2 2 2 (44)

For this reason, on time scales shorter compared to the char-acteristic time for V–V energy exchange (several microseconds), the vibrational level populations represent the nascent distribu-tion created by electron impact. The difference between the two vibrational temperatures gradually decreased in the afterglow due to V–V exchange, Tvib(0,1) = 2130  ±  200 K and Tvib(1,5) = 4429  ±  350 K 6 μs after the discharge pulse. These results are in good agreement with kinetic modeling calculations [29], which have been used to validate the theoretically predicted V–V energy transfer rates for N2–N2 [30]. Note that the use of vibrational populations measured in a pulsed discharge for V–V rate model validation is somewhat complicated because of ‘indiscriminant’ excitation of multiple vibrational levels, up to v ~ 10, by electron impact. Inference of V–V energy transfer rates becomes considerably more straightforward and accurate when a selective excitation of v = 1, with subsequent V–V pumping / relaxation, is used (see section 4.5).

Massabieaux et al [31] used a high-resolution, narrowband scanning N2 CARS system in BoxCARS (for v = 0–3) and collinear (for v ≥ 1) phase matching geometries for measure-ments of rotational temperature and N2(v = 0–15) vibrational level populations in a low-pressure dc discharge and afterglow in nitrogen (P = 2–4 torr). Figures 11 and 12 plot a rotation-ally resolved Q-branch of the 3 → 4 vibrational band, as well as a vibrational population distribution in the discharge at

Figure 9. Time dependence of total vibrational energy stored in first four N2 vibrational levels. Reproduced with permission from [26], Copyright 1986 JETP.

Figure 10. Experimental and predicted N2 vibrational level populations in the pulsed discharge in nitrogen at P = 115 Torr, 50 ns after the beginning of the current rise. Reproduced with permission from [29], Copyright 1997 Springer.

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Trot = 500  ±  30 K and Tvib(0,1) = 4000  ±  200 K. The quasi-steady-state vibrational distribution measured in these experi-ments is markedly non-Boltzmann, exhibiting significant overpopulation of high vibrational levels, in good agreement with theory of anharmonic V–V pumping [27, 28] and kinetic modeling calculations.

Dreier et al [32] have used both broadband and narrowband CARS systems to measure N2(v = 0–3) populations and N2 vibrational temperature, Tvib = 2130  ±  110 K, in a N2–CO–He mixture excited in a low-pressure microwave discharge (P = 5.3 mbar). Similarly, Kishimoto et al [33] used both broadband and narrowband CARS systems in a folded BoxCARS con-figuration for measurements of spatial distributions of N2(v = 0–2) populations and N2 rotational temperature, respectively, in a N2–CO2–He mixture in a radio frequency (RF)-excited capillary waveguide CO2 laser resonator at P = 100 mbar. As expected, measurements without laser generation demon-strated a significantly higher N2 first level vibrational tem-perature, Tvib(0,1) = 2010 K compared to its value with laser generation, Tvib(0,1) = 1620 K, at peak rotational temperature of Trot = 575 K. Doerk et al [34] used a narrowband CARS sys-tems in a folded BoxCARS configuration for measurements of spatial distributions of N2(v = 0–2) vibrational populations, N2 rotational temperature, as well as CO and O2 number den-sities in dc-excited and microwave-excited N2–CO2–He laser mixtures, at pressures of 3–7 kPa. It was shown for nitrogen excited in the microwave discharge, the second level N2 vibra-tional temperature exceeds the first level vibrational tempera-ture, Tvib(1,2) > Tvib(0,1).

Ershov et al [35] described the use of broadband CARS in Unstable Resonator Enhanced Detection (USED-CARS) phase matching geometry for time-resolved measurements of N2 first level vibrational temperature in a 40 μs pulse dis-charge in nitrogen at P = 6 Torr. The vibrational temperature increased during the discharge pulse, up to Tvib(0,1) = 4000 K.

These results also illustrated that the use of the vibrational temperature of N2(C3Π) state, obtained from UV/visible emis-sion spectroscopy, as an estimate of the ground electronic state, N2(X1Σ), was inadequate.

Baeva et al [36] used a narrowband scanning CARS sys-tem in a folded BoxCARS phase matching configuration to measure time-resolved and spatially-resolved N2 vibrational temperature and rotational temperature, as well as NO number density, in a plane-to-plane and a knife edge / plane dielec-tric barrier discharges in N2–O2–NO mixtures powered by μs duration pulses. At these conditions the peak N2 vibrational temperature remains fairly low, Tvib(0,1) = 1400 K at 20 kPa and Tvib(0,1) = 800 K at 98 kPa, at near room temperature, both due to fairly low discharge energy loading per molecule and due to the high value of the reduced electric field, E/N ~ 170–220 Td, which is in good agreement with kinetic modeling calculations. Time-resolved and spatially-resolved CARS measurements conducted by the same group in a low-pressure microwave discharge in N2 (P = 5 mbar) demonstrated sig-nificant vibrational nonequilibrium, with the peak N2 vibra-tional temperature exceeding Tvib(0,1) = 3000 K at a rotational temperature of Trot = 450 K [37]. As shown in figure 13, N2 vibrational temperature keeps increasing after the micro-wave discharge pulse ~200 μs long. This trend, reproduced by kinetic modeling calculations, is consistent with the first level N2 vibrational temperature behavior in the afterglow, observed by Devyatov et al [26] and by Vereschagin et al [29]. In a microwave discharge in O2 (P = 10 mbar), however, vibrational nonequilibrium was much less pronounced, with the O2 vibrational temperature reaching Tvib(0,1) = 1000 K at a rotational temperature of Trot = 900 K [39].

Broadband H2 vibrational CARS spectra have been used extensively for rotational temperature measurements, due to large spacing between individual rotational lines of the Q-branch of 0 → 1 vibrational band (Bornemann et al [40],

Figure 11. Rotationally resolved Q-branch of the 3 → 4 N2 vibrational band. Nitrogen, P = 4 torr, I = 80 mA. Reproduced with permission from [31], Copyright 1987 EDP Sciences.

Figure 12. N2(v=0–15) vibrational distribution in the discharge. Solid lines: experimental data, dashed line and symbols: modeling calculations (see details in [31]). Nitrogen, P = 4 torr, I = 80 mA.

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Kornas et al [41], planar BoxCARS geometry, high-pressure arc discharges in hydrogen; Kaminski and Ewart [42], col-linear phase matching geometry, low-pressure microwave discharge in a H2–CH4–Ar mixture; Tuesta et al [43], folded BoxCARS geometry, low-pressure microwave graphene discharge reactor in H2, H2–CH4, and H2–N2 mixtures; Shakhatov et al [44], Shakhatov et al [45], collinear and pla-nar BoxCARS geometries, low-pressure capacitively coupled and inductively coupled RF discharges in hydrogen). In [46], both vibrational and rotational temperatures of hydrogen have been measured versus discharge pressure in the range 0.5–8 Torr, Tvib(0,1) = 4250 K–2800 K, Trot =525–750 K, dem-onstrating strong vibrational nonequilibrium which became more pronounced as the pressure was reduced. A similar trend was observed in narrowband scanning CARS (in collinear and planar BoxCARS geometries) measurements of N2 rotational and vibrational temperatures in diffuse glow and contracted discharges in nitrogen at P = 2–20 Torr [46]. In these meas-urements, strong vibrational nonequilibrium was detected at a quasi-steady-state at low pressures (Trot = 395–600 K, Tvib(0,1) = 2850–5300 K), and discharge contraction at higher pres-sures resulted in a significantly higher rotational / translational temperatures, Trot =1000–1350 K. Vibrational and rotational level populations of H2 and D2 (v = 0–3) in low-pressure dis-charges (P = 55 μbar) have been measured by Pealat et al [47] using a narrowband scanning CARS system, demonstrating strong vibrational and rotational disequilibrium (up to Tvib(0,1) = 2390 K at T = 530 K in hydrogen). Significantly higher H2 vibrational–rotational level populations, up to v = 13 (close to dissociation limit), have been measured in a low-pressure hydrogen plasma (P = 1.5 Pa) by vacuum UV LIF [48], where the VUV beam was generated in a high-pressure hydrogen Raman cell using Stimulated Anti-Stokes Raman Scattering (SARS). Extreme disequilibrium, including total population inversion for v = 9–10, caused by electronic to vibrational (E–V) energy transfer from excited electronic states of H2, such as B1Σg

+, C1Πu, has been detected.

More recently, Filimonov and Borysow [49] used broad-band CARS in USED-CARS phase matching geometry for time-resolved measurements of vibrational level populations of nitrogen, N2(v = 0–6). This work used a ~1 μs duration pulsed dc discharge in 5 torr of N2. The authors observed sig-nificant vibrational loading during the discharge pulse, as can be seen in figure  14. Similar to earlier results by Devyatov et al [26] and Vereschagin et al [29], it can be seen that vibra-tional levels v > 1 are characterized by a much higher vibra-tional temperature, Tvib(2–6), than the first level vibrational temperature, Tvib(0,1). Specifically, immediately after the end of the discharge pulse, Tvib(0,1) ~ 2200 K, while Tvib(2–6) ~ 6000 K (see figure 14). In the afterglow, Tvib(0,1) continues to grow slightly, as Tvib(2–6) decreases, and the two vibrational temperatures converge with each other, as well as with Trot after ~50–100 μs, where Trot ~ Tvib ~ 3500 K. However, an unexpected result is the occurrence of a second disequilib-rium phase, from 100 μs < Δt < 10 ms, when Trot again falls significantly below Tvib. It is expected that if the vibrational and rotational temperatures were equilibrated at T ~ 3500 K, V–T energy exchange processes should dominate, and barring external influence, the gas should remain in V–T equilibrium while it cools and eventually reaches T ~ 300 K. The authors attributed the second nonequilibrium stage to vibrational exci-tation by superelastic collisions with free electrons, which have an electron temperature that greatly exceeds the heavy species rotational/translational temperature. The authors fur-ther claim that a lack of strong coupling between vibration and rotation results in a rotational temperature substantially below the electron and vibrational temperatures.

In a similar study Messina et al [50] performed time-resolved broadband CARS, planar BoxCARS phase match-ing geometry measurements of N2 rotational/translational and vibrational temperatures in atmospheric pressure ns pulse pin-to-pin discharges in air and in methane-air mixtures. Vibrational levels v = 0–2 were detected, with partial rota-tional resolution. While the voltage waveforms used in this case had a relatively short full width at half maximum, FWHM ~ 70 ns, a relatively long tail ~200 ns was also present. Results from two discharge cases in air are shown in figure 15, where a very significant nonequilibrium is readily observed. For both

Figure 13. Calculated and measured temporal evolution of N2 vibrational temperature in a pulsed microwave discharge in nitrogen. P = 5 mbar, Trot = 450 K; pulse duration 200 μs, pulse repetition rate 10 Hz [38].

Figure 14. Temporal evolution of vibrational and rotational/translational temperatures in a 1 μs duration N2 pulsed dc discharge at P = 5 Torr [49].

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discharge energy loading conditions, the authors note an initial high first level vibrational temperature during the discharge, Tvib(0,1) ~ 1400 K and 2200 K for the lower and higher energy loading case, respectively, which rapidly relax ~100 ns–1 μs after the discharge pulse to Tvib ~ 1000 K. Approximately 20–50 μs after the discharge pulse, the vibrational temperature reaches a secondary maximum, Tvib(0,1) ~ 2000 K and Tvib(0,1) ~ 1800 K for the lower and higher energy loading conditions, respectively. In the lower energy loading case, Trot is below ~400 K for the entire time, while for the higher energy loading case Trot is ~450–500 K immediately after the pulse, reaching a maximum of ~900 K at a time nearly coincident with the peak in the vibrational temperature.

Figure 16 shows results of time-resolved N2(v = 0–9) vibra-tional populations measurements in a ~2 mm diameter diffuse filament pin-to-pin nanosecond pulsed discharge in air, ini-tially at approximately room temperature and P =  100 Torr [19]. These measurements, as well as time-resolved N2 rota-tional/translational temperature measurements, were done

by a psec broadband CARS system, described in section 3.1, using a folded BoxCARS phase matching geometry provid-ing spatial resolution in the direction of the laser beams of approximately 0.5 mm. Rotational temperature was inferred from partially resolved Q-branch of N2 0 → 1 band, such as shown in figure 7. Radial distribution of N2 first level vibra-tional temperature across the plasma filament after the dis-charge pulse has also been measured. Typical vibrational CARS spectrum, with 0 → 1 to 9 → 10 bands readily identi-fied, is shown in figure 8. These results have been simulated using a state-specific ‘master equation’ kinetic model, which incorporates electron impact excitation processes, as well as vibration–translation (V–T) and vibration–vibration (V–V) processes, for N2 levels up to v = 45, and radial diffusion [19].

From figure 16, it can be seen that N2 vibrational popu-lations t = 50 ns–1 μs after the beginning of discharge cur-rent rise (current pulse duration of ~100 ns) exhibit the same well-pronounced bimodal structure as in previous work by Devyatov et al [26] and Vereschagin et al [29] (e.g. see

Figure 15. Temporal evolution of rotational and vibrational temperatures produced by a single ~200 ns duration discharge pulse in atmospheric pressure air. Reproduced with permission from [50], Copyright 2007 Elsevier.

Figure 16. Comparison between experimental and predicted time dependent N2 vibrational level populations in pin-to-pin single filament nanosecond pulsed discharge in air at P = 100 Torr [19].

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figure 10). The kinetic model predictions are in good agree-ment with the experiments for these short time delays after the beginning of the discharge pulse, indicating that vibra-tional excitation by electron impact is modeled correctly. At t = 1–50 μs, the experimental data demonstrate and the model predicts a significant increase of the v = 1 population, due to the V–V exchange process of equation (44), which results in a rise of first level N2 vibrational temperature (see figure 17). However, at t = 1–10 μs, all vibrational level populations v > 0, v = 1–9, continue to increase, a trend not reproduced by the model, which predicts significant depopulation of vibrational levels v > 2 on this time scale (see figure 16). Also, over this period of time, the total number of vibrational quanta per N2 molecule predicted by the model,

∑==

=

Q vf ,v

v

v0

9

(45)

remains nearly constant. This indicates that V–T relaxation at these conditions over this time scale remains insignificant and the predicted v = 3–9 depopulation is primarily due to N2–N2 V–V exchange, which conserves vibrational quanta. The trend observed in the experiment, however, is a significant N2(v = 2,3) overpopulation which occurs without depopulating lev-els v = 4–8, resulting in significant increase of N2 vibrational quanta per molecule (see figure  17). The effect of N2(v = 1–9) rise 1–10 μs after the discharge pulse in nitrogen was even more pronounced, such that the number of vibrational quanta per N2 molecule after the discharge increased by more than a factor of two [19]. Again, this increase could not be reproduced by the kinetic model incorporating only electron impact, V–T, V–V, and radial diffusion processes. This sug-gested that overpopulation of high vibrational levels after the pulse occurred either by V–V exchange with higher vibrational levels, v > 8, which have not been detected in the experiment,

or by an additional energy transfer process into N2(X,v) from other molecular energy modes, similar to the conclusion of Devyatov et al [26]. Indeed, postulating that 30% of energy defect during quenching of excited electronic states N2(C3Π), N2(B3Π), and N2(aʹ1Σ), as well as during N2(A3Σ) energy pooling reactions goes into vibrational energy mode of the ground electronic state, N2(X1Σ,v) (E–V processes), improved the agreement between the experiment and model predictions.

However, interpreting the apparent increase of vibrational quanta per molecule as an indication of the effect of E–V energy transfer requires some caution. In the experiments [19, 51], time-resolved rotational/translational temperature measurements demonstrated very rapid heating of the gas in the discharge filament, up to ΔT ~ 200 K on the time scale of t ~ 0.1–1 μs (see figure 18), which is shorter compared to the acoustic time scale, tacoustic ~ d/a ~ 5 μs, where d ~ 2 mm is the filament diameter and a ~ 0.4 mm μs−1 is the speed of sound. This suggests that rapid heating, caused primarily by quench-ing of N2 excited electronic states, would result in significant pressure overshoot in the filament, with subsequent gasdy-namic expansion. Indeed, qualitative evidence of this expan-sion was detected in phase-locked schlieren images, which demonstrated compression waves originating in the discharge filament propagating in the radial direction after the discharge pulse [51]. The subsequent ‘slow’ heating, up to T ~ 850 K on the time scale of ~10–500 μs, detected in air but missing in nitrogen (see figure 18), is most likely caused by V–T relaxa-tion of nitrogen by O atoms, N2(v) + O → N2(v − 1) + O.

Qualitatively, gasdynamic expansion of the discharge fila-ment after the discharge pulse is likely to result in CARS signal collection predominantly from the near-centerline region, which is most strongly vibrationally excited by the discharge. Although 95% of the signal comes from a region approximately 0.5 mm long in the direction of the laser beams [19], the filament diam-eter (full width at half maximum of broadband plasma emission)

Figure 17. ‘First level’ vibrational temperature, rotational temperature and number of vibrational quanta per N2 molecule in the ns pulse filament discharge in nitrogen [19].

Figure 18. Comparison of translational–rotational temperatures on the filament centerline versus delay time after the discharge pulse in nitrogen and air. Reproduced with permission from [51], Copyright 2013 JSME.

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is comparable, ≈2 mm. At these conditions, the effect of gasdy-namic expansion and subsequent probing of the most excited region of the filament might be interpreted as additional vibra-tional excitation after the discharge pulse. Additional work, with better resolution in the radial direction (e.g. probing of a filament discharge sustained between two hollow cylindrical electrodes, to provide optical access in the axial direction) is needed to quantify the possible contribution of this effect.

Experimental demonstration of two-stage energy thermali-zation in nanosecond pulse discharges and afterglow in air (see figure 18) may have significant implications for plasma flow control. Specifically, compression waves generated by heat-ing on sub-acoustic time scale may well be a dominant factor causing turbulent transition in boundary layer and generat-ing coherent structures in flows forced by nanosecond pulse, surface dielectric barrier discharges [52]. In addition, ‘slow’ heating in near-surface filamentary discharges may well result in the formation of transient low-density regions in the bound-ary layer and contribute to flow instability development. At this time, the mechanism by which transient perturbations created by nanosecond pulse discharges affect the flow in the boundary layer is not fully understood.

The same ps CARS system as used in [19] was employed to measure time-resolved N2 rotational and ‘first level’ vibra-tional temperatures in a repetitively pulsed, plane-to-plane geometry, double dielectric barrier, nanosecond discharge used for ignition of hydrogen air mixtures [20]. The results have shown the vibrational temperature in air and H2-air to be quite low, Tvib ~ 800–1000 K, consistent with earlier experi-ments in a barrier discharge powered by microsecond dura-tion pulses [36]. The results also demonstrated a significant rotational temperature overshoot during ignition of hydrogen, with subsequent gradual reduction due to heat transfer to the test section walls and convective cooling of the flow.

4.2. Vibrational CARS: vibrational and rotational temperatures in nonequilibrium flows

CARS diagnostics has been used rather extensively for ther-mometry, velocimetry, species concentration measurements,

and to some extent for vibrational temperature measurements in nonequilibrium high-enthalpy flows. In these flows, nonequi-librium may be produced by rapid supersonic expansion of a high-temperature flow heated in a shock tube used as a nozzle plenum, by a high-power electric discharge, or by a strong shock (either a propagating shock wave in a shock tube or a station-ary shock standing in a supersonic test section). An overview of CARS measurements in hypersonic flows is given by Taran [53], and a comprehensive review of the use of CARS spectroscopy in a more general field of reacting flows is given by Roy et al [54].

Scanning narrowband and broadband CARS systems, as well as dual-line CARS have been used in previous experi-ments in nonequilibrium flows. An early work in this field is by Slenszka et al [55] who used narrowband scanning H2 CARS in folded BoxCARS geometry for rotational tempera-ture measurements in a free expansion of hydrogen jet exit-ing from an RF heated nozzle, at nozzle temperatures of T = 300–2500 K, detecting significant vibrational-rotational nonequilibrium. Grisch et al [56] used narrowband dual-line N2 CARS in folded BoxCARS geometry to measure 2D distributions of N2 rotational temperature and number den-sity in Mach 10 nitrogen flow, in a shock wave—boundary layer interaction region behind compression corner. Pulford et al [57] and Boyce et al [58] used single-shot broadband N2 CARS spectra, also in folded BoxCARS geometry, for measurements of N2 rotational and vibrational temperatures in a pulsed free piston supersonic shock tunnel flow facility, both in freestream and in a bow shock layer in front of a blunt body. In these experiments, significant vibrational nonequilib-rium was detected in freestream, Trot = 850  ±  100 K, Tvib(0,1) = 1985  ±  200 K, while the flow in the shock layer was near equilibrium, Trot = 3730   ±  400 K, Tvib(0,1) = 4000   ±  200 K [58]. Broadband CARS has also been used to determine vibra-tional relaxation rates of diatomic molecules, inferred from vibrational and rotational temperatures measured in a super-sonic expansion in a shock tunnel, such as has been done by Kozlov et al [59] for vibrational relaxation of CO by H atoms.

More recently, Grisch et al [60] used narrowband scanning N2 CARS spectra taken in folded BoxCARS geometry (see figure 19) to measure spatially resolved nitrogen first level

Figure 20. N2 rotational and vibrational temperature distributions downstream from the bow shock. Reproduced with permission from [60], Copyright 2000 AIAA.

Figure 19. Nitrogen CARS spectrum of (0,1) and (1,2) vibrational bands recorded in the freestream. Reproduced with permission from [60], Copyright 2000 AIAA.

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vibrational temperature and rotational temperature distribu-tions in free stream and across the shock layer in a hyper-sonic nitrogen flow heated by an arc discharge in the wind tunnel plenum. These measurements demonstrated signifi-cant vibrational nonequilibrium both in the free stream (Tvib ~2500 K > Trot ~ 300 K) and in the shock layer (Tvib ~ 2700–2800 K < Trot ~ 4300–4500 K, see figure 20), and suggested rotational nonequilibrium (deviation of rotational populations from Bolzmann distribution). Note that, in spite of a longer flow residence time along the stagnation line, vibrational relaxation behind the shock remains slow, such that vibra-tional nonequilibrium persists through most of the shock layer (see figure 20). Recent work by Osada et al [61] used broad-band N2 CARS to measure rotational temperatures behind a strong propagating shock wave in a shock tube, Trot and Tvib.

CARS diagnostics has also been used to study dynamics of supersonic combustion in non-premixed fuel-air flows. Magre et al [62, 63] used broadband H2 and N2 CARS in planar BoxCARS geometry for temperature measurements in a Mach 2 supersonic mixing layer of hydrogen and air, to obtain temperatures in fuel reach and fuel lean regions. Vereschagin et al [64] used broadband N2 CARS in axisym-metric BoxCARS geometry for tempetature measurements in Mach 3 supersonic combustor with preheated free stream flow, both in subsonic (ram, T = 600–900 K) and supersonic (scram, T = 1200–1600 K) regimes. Cutler et al [65] and O’Byrne et al [66] employed dual-pump CARS diagnostics in planar BoxCARS phase matching geometry, using two different broadband pump beams and a single broadband Stokes beam, to take N2 and O2 CARS spectra simultaneously in a super-sonic combustor. The measurements have been done in four different planes upstream and downstream of H2 injection into a Mach 2 flow, yielding 2D temperature distributions, as well as N2 and O2 mole fraction distributions, across the flow [66]. Additional data obtained using this approach include distribu-tions of N2, O2, and H2 mole fractions, rotational tempera-ture, as well as N2 and O2 vibrational temperatures at multiple

planes across the flow, demonstrating modest vibrational non-equilibrium [67–69].

Strong vibrational and electronic nonequilibrium in super-sonic expansion flows can also be produced by exciting the flow in the nozzle plenum by an electric discharge operated at a low temperature. This approach has been previously used in electrically excited gasdynamic lasers, such as CO laser [70] and oxygen–iodine laser [71, 72]. Recently, broadband psec vibrational CARS diagnostics has been used to meas-ure vibrational and rotational temperatures of molecular gas mixtures excited in a plenum of a Mach 5 plasma wind tunnel by two fully overlapped electric discharges, a repetitive nano-second pulse discharge (to sustain ionization) and transverse dc discharge (to load energy into the plasma) [73–75]. The ‘pulser–sustainer’ discharge configuration consists of orthog-onal plane-to-plane electrode pairs, one of which is excited with a ~30 kV, 100 kHz repetitively pulsed 5 ns pulsed power supply, and the other with a 4.5 kV dc power supply. The high peak E/N, ~320 Td, of the pulsed discharge produces volume ionization whereas the dc discharge, with E/N of ~50 Td, efficiently loads N2 vibrational mode. In these experiments, the degree of vibrational nonequilibrium was controlled by injecting various ‘relaxer’ species, such as N2, O2, NO, H2, and CO2, into a nitrogen flow excited in the ‘pulser–sustainer’ discharge in the nozzle plenum. CARS measurements have been done in the plenum, free stream, and behind a bow shock in a Mach 5 plasma wind tunnel [74, 75]. Figure  21 shows v = 0 and v = 1 N2 Q-branch CARS spectra obtained in 300 Torr N2 discharges. The black (dashed) spectrum illus-trates the significant vibrational non-equilbrium produced by the pulser–sustainer discharge, whereas the blue (solid) spec-trum illustrates the rapid relaxation of this non-equilibrium by addition of a small quantity of CO2 (1 Torr partial pressure) a few cm downstream of the discharge, resulting in a rotational/translational temperature rise.

CARS measurements were also performed just upstream and downstream of a bow shock standing in front of a

Figure 21. N2 CARS spectra obtained in the plenum of a Mach 5 plasma wind tunnel, with flow excited by a pulser-sustainer discharge at 300 Torr total pressure, in nitrogen (dashed line) and 1 torr CO2 partial pressure injection (solid line). Reproduced with permission from [75], Copyright 2013 Springer.

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cylindrical model located in the Mach 5 section  of the flow (see figure 22). The free stream static pressure and temperature were 1.2 Torr (measured with a pressure tap) and 50 K (calcu-lated assuming isentropic flow expansion), respectively. The increase in density behind the bow shock is clearly observable. In these experiments, the measurement spatial resolution in the axial (flow) direction, both in front and behind the shock, was ~0.05 mm, much lower compared to shock stand-off distance of ~1 mm. This made possible measuring N2 vibrational tem-perature at several locations across the shock layer between the how shock and the model. From figure 22, it can be seen that that no measurable N2 vibrational relaxation occurs down-stream of the bow shock, consistent with the results obtained by Grisch et al [60] at a much higher stagnation temperature (see figure 20). These measurements demonstrated significant potential of CARS diagnostics for studies of molecular energy transfer kinetics in nonequilibrium expansion flows.

4.3. Pure rotational CARS: rotational temperatures in plasmas and afterglow

As discussed in section 3.1, the use of pure rotational, broad-band N2 and O2 CARS for temperature measurements in low-temperature, low-pressure plasmas has the advantage of higher spectral resolution, due to significant rotational line spacing (e.g. see figure 23), which also mitigates Stark broadening effects when high laser pulse energies are used. Time-resolved temperature was measured during a repeti-tively pulsed, double dielectric barrier, plane-to-plane geom-etry, nanosecond discharge in ethylene–air [76], hydrogen–air [77], as well as H2–O2–Ar and C2H4–O2–Ar mixtures [78], as a function of the number of discharge pulses in a burst. In these experiments, it was demonstrated that heating rate in low temperature ethylene–air and hydrogen–air plasmas is much faster than in air plasmas (e.g. see figure 24), primarily due to

energy release from exothermic reactions of radicals gener-ated in the plasma with fuel. At sufficiently high equivalence ratios, radical generation in the repetitively pulsed discharge resulted in ignition, detected both from significant rotational temperature overshoot, in good agreement with plasma chem-istry kinetic model (see figure  24), and from OH (A  →  X) transient emission.

More recently, pure rotational, broadband N2 and O2 psec CARS diagnostics have been used for time-resolved measure-ments of the rotational temperature in single-pulse, diffuse fil-ament nanosecond pulse discharge in air, H2–air and C2H4–air between two spherical electrodes, at P = 40 torr [79]. In these experiments, estimated discharge pulse energy loading per molecule was significantly higher compared to the plane-to-plane geometry dielectric barrier discharge, ~0.1 eV/molecule compared to ~0.1 meV/molecule. This resulted in significant

Figure 23. Experimental and synthetic rotational CARS spectra in ethylene–air (φ = 1) at P = 40 torr after a burst of 400 ns discharge pulses at 40 kHz (burst duration 10 ms [76]).

Figure 22. (a) Estimated number density and (b) the first level N2 vibrational temperature in free stream and behind the Mach 5 bow shock. Reproduced with permission from [75], Copyright 2013 Springer.

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heating and vibrational excitation after a single discharge pulse, and made possible studying kinetic mechanisms of energy conversion and thermalization in highly transient plas-mas, with high temporal and spatial resolution. The results of these measurements confirmed existence of a ‘two-stage’ energy thermalization mechanism in air and fuel–air plasmas, first detected by psec vibrational CARS measurements in air [19, 51]. Figure 25 compares experimental and predicted time-resolved rotational temperature during and after a nanosecond pulse discharge in air. It can be seen that although a significant fraction of discharge input energy, ~35%, is rapidly (within ~1 μs) converted to heat, the rest of the energy is thermalized much slowly, on the time scale of ~100–200 μs, which is fol-lowed by gradual cooling of the plasma filament by radial diffusion. As discussed in section 4.1, the ‘slow’ and ‘rapid’ heating in the afterglow are primarily due to quenching of N2 excited electronic states and N2 vibrational relaxation by O atoms, respectively. The use of high spectral, spatial, and tem-poral resolution, pure rotational broadband psec CARS ther-mometry in the nanosecond pulse discharge afterglow helped isolating these two kinetic mechanisms, with high accuracy.

4.4. CARS / 4-wave mixing: electric field in pulsed plasmas

CARS / 4-wave diagnostics has been used for electric field measurements in nanosecond pulse duration electric discharges [8–10, 80]. As a representative example of the use of CARS / 4-wave diagnostics for electric field measurements in the plasma, figure 26 shows applied voltage, current, and electric field in a plane-to-plane H2 discharge with gap of 1.2 mm and a pressure of 175 Torr [80]. The discharge is sustained by a ~10 ns duration volt-age pulse with a peak voltage of 1.3 kV. It can be seen that prior to breakdown, the field in the plasma closely follows the applied field. However, at the onset of breakdown, indicated by the rapid rise in discharge current, space charge formation near the cathode results in partial shielding of the plasma, such that the field in the

plasma becomes lower than the applied field by approximately 20 percent. Finally, after breakdown the field in the quasi-steady-state plasma remains lower compared to the applied field because of cathode layer formation and cathode voltage fall. This behavior was reproduced by kinetic modeling of the discharge dynamics using a Particle-in-Cell / Monte Carlo model [81].

Similar measurements have been conducted in nitrogen. Figure 27 compares experimental electric field in a plane-to-plane discharge in N2 at P = 0.25–0.35 bar [82] with kinetic modeling calculations, using a drift-diffusion, quasi-one-dimensional discharge model [83]. It can be seen that the model predictions are in good overall agreement with the experimen-tal measurements, although the model overpredicts the rate of voltage drop during breakdown and somewhat underpredicts the quasi-steady-state electric field in the plasma (thus over-predicting the cathode voltage fall). The slower rate of voltage reduction during breakdown, measured in the experiment, may be in part due to the finite duration of the laser pulse (~5 ns).

Recently, a psec broadband CARS system for highly tran-sient electric field measurements has been developed at Ohio

Figure 24. Comparison of experimental and predicted temperatures in air and hydrogen–air at different equivalence ratios versus number of pulses in the burst. Reproduced with permission from [77], Copyright 2011 Elsevier.

Figure 25. Experimental and predicted N2 rotational temperature, as well as predicted N2 vibrational temperature, during and after a nanosecond pulse filament discharge in air at P = 40 Torr. Reproduced with permission from [79], courtesy of S Sheche.

Figure 26. Applied voltage, current and measured electric field on the centerline of a nsec pulse, plane-to-plane discharge in hydrogen. Electrode gap is 1.2 mm [80].

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State [84]. The two main advantages of the psec laser pulse dura-tion system are higher peak laser intensity, resulting in higher signal-to-noise, and higher temporal resolution of the electric field measurements, if the jitter of the high-voltage plasma generator and the optical diagnostics system is low. Psec dura-tion CARS systems are potentially capable of resolving rapidly varying electric field across the front of propagating ionization waves, at the conditions where ionization may well be affected by non-local effects. The capability of measuring the electric fields at these highly transient conditions would provide new insight into kinetics of ionization in strong electric fields.

4.5. Spontaneous Raman scattering: vibrational populations and temperature in plasmas and afterglow

The main advantages of using spontaneous Raman spectros-copy for measurements of vibrational level populations of molecular species are (i) linear dependence of Raman signal intensity on the population, compared to quadratic depen-dence of CARS signal on the population difference (see equa-tion (19)), making possible measurements of high vibrational level populations; (ii) capability of taking simultaneous mea-surements of vibrational populations along the laser beam path (i.e. obtaining ‘line images’ of the populations), and (iii) simultaneous measurements of vibrational level populations of multiple species. One of the disadvantages is relatively low spectra resolution, compared to CARS spectra. Early sponta-neous Raman spectroscopy N2 vibrational level populations measurements, v = 0–15, in afterglow of a pulsed discharge in nitrogen at P = 230 torr were made by Akishev et al [85]. These results exhibited markedly non-Boltzmann distribu-tion of vibrational level populations, with first level vibra-tional temperature of Tvib = 2500 K. More recently, spatially resolved measurements of nitrogen vibrational populations, N2(v = 0–8), have been performed in a short-lived afterglow of a microwave discharge in nitrogen [86], exhibiting a slowly evolving V–V pumped plateau in N2 vibrational distribution.

Spontaneous Raman measurements of vibrational level populations of three diatomic species, N2, O2, and CO, have been made in high-pressure (up to 1 bar) mixtures of these gases where CO in relatively low vibrational levels, v < 10, was vibrationally excited by resonance absorption of the CO laser radiation (10–20 W c.w [87–89].),

ν+ ↔ +v h vCO ( ) CO ( 1) . (46)

High vibrational levels of CO, as well as vibrational levels of N2 and O2, not accessible to laser excitation, were popu-lated by V–V energy transfer, such as

+ ↔ − + +v w v wCO ( ) CO ( ) CO ( 1) CO ( 1) . (47)

+ ↔ − + +v w v wCO ( ) O ( ) CO ( 1) O ( 1) ,2 2 (48)

+ ↔ − + +v w v wCO ( ) N ( ) CO ( 1) N ( 1) ,2 2 (49)

As shown in the theory of anharmonic V–V pumping [27, 28], these processes favor overpopulation of vibrational levels with smaller energy spacing, such as high vibrational levels of carbon monoxide and vibrational levels of oxygen, since O2 has a significantly smaller vibrational quantum compared to that of CO. N2 vibrational level populations, on the other hand, are expected to be lower than those of CO since N2 vibrational quantum is somewhat larger than that of CO. Indeed, in opti-cally pumped CO/N2 mixtures at steady state, CO vibrational levels up to v = 37 were detected, compared to v = 5 of N2 (see figures 28 and 29). At these conditions, first level vibrational temperatures were Tvib(CO) = 3500 K and Tvib(N2) = 2200, with CO exhibiting strikingly non-Boltzmann V–V pumped vibrational distribution (see figure 29). In these experiments, rotational/translational temperature was estimated from the rotational structure of N2 S-branch Raman spectrum Trot = 420–640 K [88], and from the ratio of Q branch vibrational bands intensities in N2 Raman spectra taken with CO pump laser turned on and off, Ttrans  ≈  500 K [87]. In optically pumped, steady-state CO/N2/O2 mixtures, N2(v = 0–5), CO(v = 0–8), and O2(v = 0–12) have been detected (see figure 30). As expected, O2 vibrational level populations exceeded those of CO and N2 (see figure 31). These experimental results are

Figure 27. Experimental and predicted electric field, as well as applied voltage / gap on the centerline of a nsec pulse, plane-to-plane discharge in nitrogen. Electrode gap is 1.2 mm [82].

Figure 28. Spontaneous Raman spectrum of optically pumped 394/16 Torr mixture of N2 /CO. Vibrational quantum number increases with decreasing wavelength, as indicated. Reproduced with permission from [88], Copyright 2001 American Institute of Physics.

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in good agreement with master equation kinetic modeling cal-culations (see figures 29 and 31).

In a related work [90–92], stimulated Raman scattering, such as

ω ω ω= + ℏ + ℏ → = + ℏv vN ( 0) N ( 1) 2 ,p s p2 2 (50)

was used to selectively excite v = 1 populations of N2, O2, and H2, with subsequent decay of the v = 1 population and excita-tion of v > 1 populations monitored using time-resolved sponta-neous Raman spectroscopy. Figure 32 plots Raman-pumped N2 spectra at two different time delays after the pump laser pulse, with several vibrational bands clearly identified. Time-resolved vibrational level populations inferred from these spectra, N2(v = 0–6), O2(v = 0–5), and H2(v = 0–5) were used to infer rates of V–V energy transfer in these species at room temperature.

Partially resolved spontaneous Raman spectra have been used to infer spatial distributions of rotational temperatures, vibra-tional temperatures, and number densities of N2 and O2 in non-equilibrium high-temperature air plasma flows generated in an inductively coupled plasma wind tunnel [93]. Unlike LIF, spon-taneous Raman scattering (SRS) measurements in high pressure plasmas are not affected by quenching, the signal is proportional to the flow density, and multiple species (such as N2 and O2) can be probed at the same time. SRS measurements in large-scale wind tunnels also have an advantage compared to CARS meas-urements since spatially resolved distributions of flow param-eters can be obtained by adjusting a single laser beam. These experiments demonstrated significant vibrational–rotational nonequilibrium (Tvib(N2) = 5200 K, Trot(N2) = 2500 K), as well as significant nitrogen dissociation fraction (with approximately 40% of N2 molecules dissociated), in the freestream. Vibrational nonequilibrium also persisted in the boundary layer, with rota-tional temperature approaching the surface temperature (Twall = 300 K), while vibrational temperature near the wall remained fairly high (Tvib(O2) = 1400–1700 K, Tvib(N2) = 2000–2300 K), with approximately half of N2 and O2 molecules dissoci-ated. These measurements are complementary to NO LIF and

emission spectroscopy data taken at the same conditions [94, 95]. Spatially resolved 1D SRS imaging have also been used for simultaneous measurements of instantaneous (single laser shot) and mean distributions of major species concentrations (N2, O2, H2, CO, CO2, H2O and CxHy), fuel–air mixture fraction, and temperature in premixed and partially premixed turbulent flames [96, 97], as well as for high-speed (10 kHz acquisition rate) 1D SRS imaging of major species (N2, O2, H2, and CH4) in a turbulent CH4–H2 jet issuing into air [98].

Recently, spontaneous Raman spectroscopy has been used for studies of a pin-to-plane nanosecond pulse filament dis-charge in atmospheric pressure air, by Lo et al [21, 22, 99]. Time-resolved and spatially resolved measurements of N2 vibrational levels up to v = 20, O2 vibrational levels up to v = 13, number densities of N2, O2, and O atoms, and rotational

Figure 29. Experimental (symbols) and predicted (lines) CO and N2 vibrational level populations on the centerline of the pump CO laser beam at the conditions of figure 28. Reproduced with permission from [88], Copyright 2001 American Institute of Physics.

Figure 30. Experimental Raman spectrum of the optically pumped 700/15/40 torr mixture of N2./O2 /CO. Reproduced with permission from [88], Copyright 2001 American Institute of Physics.

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temperature during and after the discharge pulse have been performed. Spatial resolution of these measurements in the radial direction was approximately 0.18 mm. Rotational–translational temperature was inferred from the unresolved envelope of the vibrational bands. Figure 33 shows an example of N2 Raman spectrum taken 100 ns on the discharge centerline after the current pulse rise, with vibrational levels up to v = 16 clearly identified. The vibrational level population measure-ment results exhibit trends similar to those obtained by CARS [19, 26, 29], e.g. see figures 10 and 16. Specifically, temporal evolution of vibrational populations of N2 and O2 required two vibrational temperatures, Tvib(0,1) and Tvib(1,v), characterizing population of levels v = 1 and v > 1, respectively, defined as in section 4.1. Similar to figures 10 and 16, immediately after the discharge pulse Tvib(1,v)(N2) was found to exceed Tvib(0,1)(N2), Tvib(1,v) = 6510  ±  75 K and Tvib(0,1) = 4060  ±  55 K, at a rela-tively low rotational temperature of Trot = 850  ±  40 K, with subsequent equilibration on the time scale of ~100 μs after the pulse (see figure 34). Vibrational excitation of O2 was signifi-cantly lower compared to that of N2, with fewer vibrational levels identified. Radial distributions of Tvib(1,v), Tvib(0,1), and Trot, measured in this work, demonstrated strong vibrational nonequilibrium over a region ≈3 mm in diameter, with high Tvib(1,v) region extending beyond this diameter.

Time evolution of N2 vibrational level populations in a nanosecond pulse discharge in nitrogen between two spheri-cal electrodes were also measured using spontaneous Raman spectroscopy at a somewhat lower pressure of P = 100 torr by Roettgen et al [100], at the conditions similar to previous work by Montello et al [19]. In [100], the electrode geometry and the pulsed plasma generator were the same as in [19], but dis-charge pulse energy was approximately 30% higher. In these experiments, spontaneous Raman spectra were collected from a line segment across the entire discharge filament, 2.1 mm in diameter, and N2(v = 0–12) vibrational level populations were

inferred from the spectra. The results were consistent with pre-vious CARS measurements [19] and demonstrated significant vibrational nonequilibrium, with first level N2 vibrational tem-perature at the end of the discharge pulse of Tvib(0,1) = 2000 K, increasing considerably in the afterglow to exceed Tvib(0,1) = 4000 K. As in several previous studies (e.g. [26, 29]), the vibrational distribution at the end of the pulse was bimodal, with vibrational temperatures of levels v > 1 being higher than the first level vibrational temperatures, Tvib(v  −  1,v) < Tvib(0,1). Consistent with the results of CARS measurements [19], N2(v) vibrational level populations inferred from spontaneous Raman spectra also show a rise of the number of vibrational quanta per N2 molecule in the afterglow (by about 70% ~1–10 μs after the pulse). Thus, both sets of data exhibit two similar trends after the pulse, (i) significant rise of Tvib(0,1), and (ii) significant apparent increase of vibrational quanta per molecule.

The fact that CARS data set was taken at a significantly higher spatial resolution than the filament diameter (~0.5 mm versus ~3 mm), and spontaneous Raman data set was taken from the entire filament, suggests that these trends are not caused by gasdynamic expansion of the filament. In fact, the first trend that appears to be well understood has been observed previously at the low-temperature conditions when gas dynam-ics expansion was not a factor, and is in good agreement with kinetic modeling calculations [19], predicting Tvib(0,1) rise and Tvib(v − 1,v) reduction in the afterglow due to the downward V–V exchange process of equation (44), as shown in figure 17. The second trend, which suggests additional energy input into N2(X,v) vibrational mode after the discharge, remains a mat-ter of discussion. Using the assumption that 30% of energy defect during quenching of excited electronic states N2(C3Π), N2(B3Π), and N2(a’1Σ) and during N2(A3Σ) energy pooling reactions goes into vibrational energy mode of the ground elec-tronic state, N2(X1Σ,v [19]) provides relatively good agreement between the experimental results and the kinetic modeling pre-dictions [100], as shown in figure 35.

However, detailed spatially-resolved measurements of vibrational level populations across the discharge filament in air, using line-wise Raman spectra [21, 22] suggested that gasdynamic expansion may still play a role in the kinetics of vibrational energy transfer in the afterglow of a nanosecond pulse discharge filament. These results have shown that, after the discharge pulse, Tvib(0,1)(N2) rise away from the centerline, ~1–10 μs after the pulse, is more pronounced compared to the centerline (compare temporal distributions of Tvib(0,1)(N2) in figures 34 and 36). The authors have concluded that this effect cannot be explained by V–V and V–T energy transfer, although previous kinetic modeling calculations [19] (see figure 17) prove otherwise, demonstrating significant Tvib(0,1) due to the downward V–V energy transfer of equation (44). In [21], this effect has been attributed to hydrodynamics expansion of the filament, due to rapid heating during and after the discharge pulse. This conclusion appears consistent with time-resolved radial pressure distributions, inferred from temperature and major species number density measurements [22], which show significant pressure overshoot on the fila-ment centerline near the plane electrode (up to P = 3.5 atm), strong compression wave propagating in the radial direction,

Figure 31. Experimental (symbols) and calculated (solid lines) centerline VDFs of N2, O2 and CO corresponding to the data of figure 30. Reproduced with permission from [88], Copyright 2001 American Institute of Physics.

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and subsequent rarefaction in the filament region (see fig-ure 37). Compression waves generated by a nanosecond pulse discharge filament have been detected by phase-lock schlieren imaging in [51, 101]. The discharge energy balance calculated based on these experimental results demonstrates significant input energy fractions going to vibrational excitation of N2 (approximately 48%), dissociation of O2 (approximately 20%, resulting in peak O2 dissociation fraction of up to 33%), and rapid heating (19%). No evidence of the number of vibrational quanta per N2 molecule was reported.

Since time-resolved and spatially-resolved N2 and O2 vibrational level populations, rotational temperature, and pressure data obtained in [21, 22] provide extensive character-ization of the afterglow over a wide range of time scales, they lend themselves to detailed kinetic modeling calculations. A 2D kinetic model of the nanosecond pulse discharge, cou-pled with state-specific vibrational kinetics, air chemistry and transient compressible flow equations would provide insight into coupling between kinetics of molecular energy and gas-dynamic expansion at these conditions. Also, the extensive set of experimental data of [21, 22] would be invaluable for vali-dation of such kinetic model.

4.6. Kinetic modeling

A detailed overview of the very extensive literature of state-specific kinetic modeling of molecular plasmas and flows at the conditions of strong vibrational disequilibrium, such as that studied by CARS and spontaneous Raman scattering experiments discussed above, is beyond the scope of the pres-ent work. One of the most widely used and recognized mono-graphs in this field, edited by Capitelli [102], includes chapters discussing modeling of nonequilibrium vibrational kinet-ics, dissociation and ionization of diatomic molecules [103] and their coupling with kinetics of plasma electrons [104]. Another monograph [105] addresses a wide range of issues relevant to modeling nonequilibrium high-enthalpy flows, such as state-specific vibrational relaxation and vibrationally stimulated chemical reactions at high gas temperatures [106] and their coupling with nonequilibrium hypersonic flow [107, 108]. A more recent book [109] discusses details of kinetic theory and modeling of electric discharges in N2, O2, and their mixtures, including coupled electron and vibrational kinetics, nonequilibrium plasma chemical reactions, and surface pro-cesses. An extensive body of work published recently includes the coupled master equation—Boltzmann equation modeling of vibrational energy transfer, kinetics of excited electronic

Figure 32. Raman spectra of the pumped region at 760 Torr and 300 K. Time delay between the pump and probe pulse is (a) 150 ns, and (b) 5 μs. Reproduced with permission from [90], Copyright 2004 Elsevier.

Figure 33. Spontaneous Raman scattering spectrum of N2 acquired 150 ns after the high voltage pulse on the centerline of the filament, close to the anode tip. Reproduced with permission from [99], Copyright 2012 Springer.

Figure 34. Temporal evolution of N2 vibrational and rotational temperatures on the discharge centerline [21].

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states and plasma chemical reactions in molecular gas dis-charge plasmas [110–114], optically pumped gas mixtures [87–89, 115, 116], and high-enthalpy nonequilibrium flows of nitrogen [117–120], to name just a few examples in addition to kinetic modeling calculations discussed in the present work. Kinetic modeling is critical for providing predictive quantita-tive insight into key energy transfer mechanisms involved, and its development, along with experimental techniques, is key to the fundamental understanding of these environments.

5. Future prospects

We conclude this review by briefly describing two recent advances in CARS diagnostics based on the use of ultrafast femtosecond laser sources, work that has been developed by the combustion diagnostics community. First, feasibility of performing 2D rotational/translational temperature imag-ing by pure rotational CARS has recently been demonstrated [121] using a femtosecond—picosecond hybrid approach. In the hybrid approach, the pump and Stokes beams are gener-ated from a femtosecond source, which, due to its high inten-sity and temporal coherence, is very efficient in generating

Raman coherence in the medium. Probing is performed using a picosecond laser, which results in spectral resolution of order a few tenths of a wavenumber, sufficient for processing the raw data in the spectral domain. Hyperspectral techniques are used to capture the CARS image with a traditional imag-ing grating and a CCD detector which has sufficient resolution to provide a 2D spatial image for each N2 rotational transition. The authors reported the ability to capture 15 000 spatially resolved measurements in N2 and air over a 2D field of dimen-sions 2 mm × 20 mm.

As a second example, CARS thermometry in reacting flows, using femtosecond lasers operated at high repetition rates, up to five kHz, has been reported recently [122]. The authors have demonstrated the ability to perform single laser shot femtosecond CARS thermometry in a gas turbine model combustor at 5 kHz repetition rate [123]. Femtosecond CARS is performed entirely in the time domain. Briefly, the Raman coherence produced by the pump and Stokes beams evolves rapidly in time due to the beating of the individual rotational resonances which evolve at different frequencies. A fre-quency chirped probe is used to encode the temporal evolu-tion as a function of probe wavelength. The chirped signal is

Figure 35. Comparison between experimental and predicted N2 vibrational level populations, with E–V energy transfer incorporated. Vibrational quantum numbers and time delay after the discharge pulse are indicated. Reproduced with permission from [100], Copyright 2013 AIAA.

Figure 36. Temporal evolution of N2 vibrational and rotational temperatures 0.72 mm off the discharge centerline [21]. Figure 37. Radial evolution of pressure measured at different delay

times after the pulse discharge near the plane electrode [22].

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detected with an ordinary grating spectrometer, in which the frequency axis is transformed to a time axis with order fem-tosecond temporal resolution. The Fourier transform of the time domain signal produces a CARS spectrum. Temperature measurement precision of 1.5–2% of the mean flame tem-perature has been obtained.

Finally, spontaneous Raman scattering using pulse-burst laser systems [98] for high-speed 1D line imaging of tem-perature, species number densities and vibrational level popu-lations in non-premixed turbulent flames, including flames enhanced by nonequilibrium short-pulsed plasmas, is rapidly becoming a possibility.

6. Summary

From the results discussed in section  4, it is apparent that remarkable progress has been made over the last 20–30 years in the use of CARS and spontaneous Raman spectroscopy for characterization of nonequilibrium plasmas and flows. Specifically, growing availability of picosecond pulse dura-tion, high peak power lasers, including modeless broadband dye lasers, has made possible the use of these diagnostics at relatively low pressures and potentially with a sub-nano-second time resolution, or obtaining single laser shot, high signal-to-noise spectra at higher pressures. This makes pos-sible electric field and temperature measurements in highly transient nonequilibrium plasmas, such as ionization waves. High spatial resolution provided by BoxCARS phase match-ing geometry and line-wise Raman spectra makes possible vibrational level population and temperature measurements in plasmas with high spatial gradients, such as pulse dis-charge filaments, near-surface ionization waves and nonequi-librium shock layers.

References

[1] Eckbreth A C 1988 Laser Diagnostics for Combustion Temperature and Species (Cambridge, MA: Abacus)

[2] Samukawa S 2012 The 2012 plasma roadmap J. Phys. D: Appl. Phys. 45 253001

[3] Harvey A B 1981 Chemical Applications of Nonlinear Raman Spectroscopy (New York: Academic)

[4] Nibler J W and Knighten G V 1979 Raman Spectroscopy of Gases and Liquids ed A Weber (Berlin: Springer) ch 7

[5] Yariv A 1989 Quantum Electronics 3rd edn (New York: Wiley) [6] Gavrilenko V P, Kupriyanova E B, Okolokulak D P, Ochkin V

N, Yu Savinov S, Tskhai S N and Yarashev A N 1992 Generation of coherent IR light on a dipole-forbidden molecular transition with biharmonic pumping in a static electric field JETP Lett. 56 1–5

[7] Evsin O A, Kupryanova E B, Ochkin V N, Savinov S Y and Tskhai S N 1995 Determination of the intensities of electric fields in gases and plasmas by the CARS method Quantum Electron. 25 278–82

[8] Ito T, Kobayashi K, Czarnetzki U and Hamaguchi S 2010 Rapid formation of electric field profiles in repetitively pulsed high-voltage high-pressure nanosecond discharges Phys. D: Appl. Phys. 43 062001

[9] Ito T, Kobayashi K, Mueller S, Czarnetzki U and Hamaguchi S 2010 Electric field measurements at near-atmospheric

pressure by coherent Raman scattering of laser beams J. Phys.: Conf. Ser. 227 012018

[10] Ito T, Kobayashi K, Mueller S, Luggenhölscher D, Czarnetzki U and Hamaguchi S 2009 Electric field measurement in an atmospheric of higher pressure gas by coherent Raman scattering of nitrogen J. Phys. D: Appl. Phys. 42 092003

[11] Lempert W R, Kearney S P and Barnat E V 2011 Diagnostic study of four wave mixing-based electric field measurements in high pressure nitrogen plasmas Appl. Opt. 50 5688

[12] Long D A 2002 The Raman Effect (London: Wiley)[13] Gallas J A 1980 Phys. Rev. A 21 1829[14] Asawaroengchai C and Rosenblatt G M 1980 J. Chem. Phys.

72 2664[15] Drake M 1982 Rotational Raman intensity-correction

factors due to vibrational anharmonicity: their effect on temperature measurements Opt. Lett. 7 440

[16] Ganguly B N, Lempert W R, Akhtar K, Scharer J E, Leipold F, Laux C O, Zare R N and Yalin A P 2005 Plasma diagnostics Non-Equilibrium Air Plasmas at Atmospheric Pressure ed K H Becker et al (Bristol: Institute of Physics) Ch 8 pp 446–536

[17] Roy S, Meyer T R and Gord J R 2005 Broadband coherent anti-Stokes Raman scattering spectroscopy of nitrogen using a picosecond modeless dye laser Opt. Lett. 30 3222

[18] Tedder S A, Wheeler J L and Danehy P M 2011 Characteristics of a broadband dye laser using pyrromethene and rhodamine dyes Appl. Opt. 50 901

[19] Montello A, Yin Z, Burnette D, Adamovich I V and Lempert W R 2013 Picosecond CARS measurements of nitrogen vibrational loading and rotational/translational temperature in nonequilibrium discharges J. Phys. D: Appl. Phys. 46 464002

[20] Yin Z, Montello A, Carter C D, Lempert W R and Adamovich I V 2013 Measurements of temperature and hydroxyl radical generation/decay in lean fuel-air mixtures excited by a repetitively pulsed nanosecond discharge Combust. Flame 160 1594

[21] Lo A, Cessou A, Boubert P and Vervisch P 2014 Space and time analysis of the nanosecond scale discharges in atmospheric pressure air: part 1. Gas temperature and vibrational distribution function of N2 and O2 J. Phys. D: Appl. Phys. 47 115201

[22] Lo A, Cessou A and Vervisch P 2014 Space and time analysis of the nanosecond scale discharges in atmospheric pressure air: part 2. Energy transfers during the post-discharge J. Phys. D: Appl. Phys. 47 115202

[23] Shaub W M, Nibler J W and Harvey A B 1977 J. Chem. Phys. 67 1883

[24] Smirnov V V and Fabelinskii V I 1978 JETP Lett. 28 427[25] Valyanskii S I, Vereschagin A, Vernke V, Yu Volkov A,

Pashinin P P, Smirnov V V, Fabelinskii V I and Chapovskii P L 1984 Sov. J. Quantum Electron. 14 1226

[26] Devyatov A A Dolenko S A, Rakhimov A T, Rakhimova T V, Roi N N and Suetin N V 1986 Investigation of kinetic processes in molecular nitrogen by the CARS method Sov. Phys. JETP 63 246–50

[27] Treanor C E, Rich J W and Rehm R G1968Vibrational relaxation of anharmonic oscillators with exchange-dominated collisions J. Chem. Phys. 48 1798–807

[28] Rich J W 1982 Relaxation of molecules exchanging vibrational energy Applied Atomic Collision Physics vol 3 eds E W McDaniel and W L Nighan (New York: Academic) pp 99–140

[29] Vereshchagin K A, Smirnov V V and Shakhatov V A 1997 CARS study of the vibrational kinetics of nitrogen molecules in the burning and afterglow stages of a pulsed discharge Tech. Phys. 42 487–94

J. Phys. D: Appl. Phys. 47 (2014) 433001

Topical Review

24

[30] Billing G D and Fisher E R 1979 VV and VT rate coefficients in N2 by a quantum–classical model Chem. Phys. 43 395–401

[31] Massabieaux B, Gousset G, Lefebvre M and Pealat M 1987 Determination of N2(X) vibrational level populations and rotational temperatures using CARS in a dc low pressure discharge J. Phys. 48 1939–49

[32] Dreier T, Wellhausen U, Wolfrum J and Marowsky G 1982 CARS studies of vibrationally excited nitrogen at low pressures Appl. Phys. B 29 31–6

[33] Kishimoto T, Wenzel N, Grosse-Wilde H, Lüpke G and Marowsky G 1992 Experimental study of a CO2 laser plasma by coherent anti-Stokes Raman scattering (CARS) Spectrochim. Acta 47B 51–60

[34] Doerk T, Ehlbeck J, Jauernik P, Stańco J, Uhlenbusch J and Wottka T 1992 Narrow-band BoxCARS applied to CO2 laser discharges Il Nuovo Cimento 14D 1051–63

[35] Ershov A, Augustyniak E and Borysow J 1994 Temporal evolution of the vibrational excitation within the X1Σg

+ state of N2 in the positive column of a pulsed electric discharge Phys. Rev. A 50 2341–6

[36] Baeva M, Dogan A, Ehlbeck J, Pott A and Uhlenbusch J 1999 CARS diagnostic and modeling of a dielectric barrier discharge Plasma Chem. Plasma Process. 19 445–66

[37] Baeva M, Luo X, Pfelzer B, Schafer J H, Uhlenbusch J and Zhang Z 1999 Experimental study of pulsed microwave discharges in nitrogen Plasma Sources Sci. Technol. 8 142–50

[38] Baeva M, Luo X, Pfelzer B and Uhlenbusch J 1999 Theoretical investigation of pulsed microwave discharge in nitrogen Plasma Sources Sci. Technol. 8 404–11

[39] Baeva M, Luo X, Pfelzer B, Repsilber T and Uhlenbusch J 2000 Experimental investigation and modelling of a low-pressure pulsed microwave discharge in oxygen Plasma Sources Sci. Technol. 9 128–45

[40] Bornemann T, Kornas V, Schulz-von der Gathen V and Dobele H F 1990 Temperature and concentration measurements of molecular hydrogen in a filamentary discharge by coherent anti-Stokes Raman spectroscopy (CARS) Appl. Phys. B 51 307–13

[41] Kornas V, Schulz-von der Gathen V, Bornemann T, Dobele H F and Prosz G 1991 Temperature measurements by H2-CARS in the reactive zone of a plasma test reactor for hydrocarbon synthesis Plasma Chem. Plasma Process. 11 171–84

[42] Kaminski C F and Ewart P 1997 Multiplex H2 CARS thermometry in a microwave assisted diamond CVD plasma Appl. Phys. B 64 103–9

[43] Tuesta A D, Bhuiyan A, Lucht R P and Fisher T S 2014 Laser diagnostics of plasma synthesis of graphene-based materials J. Micro Nano Manuf. 2 031002

[44] Shakhatov V A, De Pascale O and Capitelli M 2004 Theoretical and experimental CARS rotational distributions of H2(X1Σg

+) in a radio-frequency capacitive discharge plasma Eur. Phys. J. D 29 235–45

[45] Shakhatov V A, De Pascale O, Capitelli M, Hassouni K, Lombardi G and Gicquel A 2005 Measurement of vibrational, gas, and rotational temperatures of H2(X1Σg

+) in radio frequency inductive discharge plasma by multiplex coherent anti-Stokes Raman scattering spectroscopy technique Phys. Plasmas 12 023504

[46] Shakhatov V A and Gordeev O A 2005 Investigation of the glow and contracted discharge plasmas in nitrogen by coherent anti-Stokes Raman spectroscopy, optical interferometry, and numerical simulation Tech. Phys. 50 1592–604

[47] Péalat M, Taran J P E, Bacal M and Hillion F 1985 Rovibrational molecular populations, atoms, and negative ions in H2 and D2 magnetic multicusp discharges J. Chem. Phys. 82 4943–53

[48] Mosbach T, Katsch H-M and Döbele H F 2000 In situ diagnostics in plasmas of electronic-ground-state hydrogen molecules in high vibrational and rotational states by laser-induced fluorescence with vacuum-ultraviolet radiation Phys. Rev. Lett. 85 3420–3

[49] Filimonov S and Borysow J 2007 Vibrational and rotational excitation with the X1Σ state of N2 during the pulsed electric discharge and in the afterglow J. Phys. D: Appl. Phys. 40 2810–7

[50] Messina D, Attal-Tretout B and Grisch F 2007 Study of a non-equilibrium pulsed nanosecond discharge at atmospheric pressure using coherent anti-Stokes Raman scattering Proc. Combust. Inst. 31 825–32

[51] Montello A, Burnette D, Nishihara M, Lempert W R and Adamovich I V 2013 Dynamics of rapid localized heating in nanosecond pulse discharges for high speed flow control J. Fluid Sci. Technol. 8 147–59

[52] Little J, Takashima K, Nishihara M, Adamovich I and Samimy M 2012 Separation control with nanosecond pulse driven dielectric barrier discharge plasma actuators AIAA J. 50 350–65

[53] Taran J-P 2006 Optical diagnostics in rarefied flows Chin. J. Aeronaut. 19 151–9

[54] Roy S, Gord J R and Patnaik A K 2010 Recent advances in coherent anti-Stokes Raman scattering spectroscopy: fundamental developments and applications in reacting flows Prog. Energy Combust. Sci. 36 280–306

[55] Slenczka A, Marowsky G and Vodegel M 1988 H2 vibrational CARS thermometry Appl. Phys. B 47 41–6

[56] Grisch F, Bouchardy P, Pealat M, Chanetz B, Pot T and Coet M C 1993 Rotational temperature and density measurements in a hypersonic flow by dual-line CARS Appl. Phys. B 56 14–20

[57] Pulford D R N, Newman D S Houwing A F P and Sandeman R J 1994 The application of coherent anti-Stokes Raman scattering to temperature measurements in a pulsed high enthalpy supersonic flow Shock Waves 4 119–25

[58] Boyce R R Pulford D R N, Houwing A F P and Mundt Ch 1996 Rotational and vibrational temperature measurements using CARS in a hypervelocity shock layer flow and comparisons with CFD calculations Shock Waves 6 41–51

[59] Kozlov P V, Makarov V N, Pavlov V A and Shatalov O P 2000 Experimental investigation of vibrational deactivation of CO molecules in a supersonic gas flow Fluid Dyn. 35 926–32

[60] Grisch F et al 2000 Coherent anti-Stokes Raman scattering measurements and computational modeling of nonequilibrium flow AIAA J. 38 1669–75

[61] Osada T, Endo Y, Kanazawa C, Ota M and Maeno K 2009 Nonlinear CARS measurement of nitrogen vibrational and rotational temperatures behind hypervelocity strong shock wave J. Phys.: Conf. Ser. 147 012081

[62] Magre P and Bouchardy P 2000 Nitrogen and hydrogen coherent anti-Stokes Raman scattering thermometry in a supersonic reactive mixing layer Proc. Combust. Inst. 28 697–703

[63] Magre P, Collin G, Pin O, Badie J M, Olalde G and Clement M 2001 Temperature measurements by CARS and an intrusive probe in an air-hydrogen supersonic combustion Int. J. Heat Mass Transfer 44 4095–105

[64] Vereschagin K A, Smirnov V V, Stelmakh O M, Fabelinsky V I, Sabelnikov V A, Ivanov V, Clauss W and Oschwald M 2001 Temperature measurements by coherent anti-Stokes Raman spectroscopy in hydrogen-fuelled scramjet combustor Aerosp. Sci. Technol. 5 347–55

[65] Cutler A D, Danehy P M, Springer R R, O’Byrne S, Capriotti D P and DeLoach R 2003 Coherent anti-Stokes Raman spectroscopic thermometry in a supersonic combustor AIAA J. 41 2451–9

J. Phys. D: Appl. Phys. 47 (2014) 433001

Topical Review

25

[66] O’Byrne S, Danehy P M, Tedder S A and Cutler A D 2007 Dual-pump coherent anti-Stokes Raman scattering measurements in a supersonic combustor AIAA J. 45 922–33

[67] Cutler A D, Magnotti G, Cantu L, Gallo E, Danehy P M, Rockwell R, Goyne C and McDaniel J C 2012 Dual-pump CARS measurements in the University of Virginia’s dual-mode scramjet: configuration A 50th AIAA-2012-0114 Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition (Nashville, TN, 9–12 January)

[68] Cutler A D, Magnotti G, Cantu L M L, Gallo E C A, Danehy P M, Baurle R, Rockwell R D, Goyne C P and McDaniel J C 2012 Measurement of vibrational nonequilibrium in a supersonic freestream using dual-pump CARS 28th AIAA Aerodynamic Measurement Technology, Ground Testing, and Flight Testing Conf. (New Orleans, 25–28 June)

[69] Cutler A D, Magnotti G, Cantu L M L, Gallo E C A, Danehy P M, Rockwell R D, Goyne C P and McDaniel J C 2013 Dual-Pump CARS measurements in the University of Virginia’s dual-mode scramjet: configuration ‘C’ 51st Aerospace Sciences Meeting (Grapevine, TX, 7–10 January)

[70] Rich J W, Bergman R C and Lordi J A 1975 Electrically excited supersonic flow carbon monoxide laser AIAA J. 13 95–101

[71] Carroll D L 2005 Appl. Phys. Lett. 86 111104[72] Hicks A, Utkin Yu G, Lempert W R, Rich J W and

Adamovich I V 2006 Continuous wave operation of a non-self-sustained electric discharge pumped oxygen-iodine laser Appl. Phys. Lett. 89 241137

[73] Nishihara M, Takashima K, Jiang N, Lempert W R, Adamovich I V, Rich J W Doraiswamy S and Candler G V 2012 Development of a mach 5 nonequilibrium flow wind tunnel AIAA J. 50 2255–67

[74] Montello A, Nishihara M, Rich J W, Adamovich I V and Lempert W R 2012 Picosecond CARS measurements of vibrational distribution functions in a high pressure plenum of a nonequilibrium hypersonic wind tunnel AIAA J. 50 1367–76

[75] Montello A, Nishihara M, Rich J W, Adamovich I V and Lempert W R 2013 Picosecond CARS measurements of nitrogen rotational/ translational and vibrational temperature in a nonequilibrium mach 5 flow Exp. Fluids 54 1422

[76] Zuzeek Y, Choi I, Uddi M, Adamovich I V and Lempert W R 2010 Pure rotational CARS thermometry studies of low temperature oxidation kinetics in air and ethene–air nanosecond pulse discharge plasmas J. Phys. D: Appl. Phys. 43 124001

[77] Zuzeek Y, Bowman S, Choi I, Adamovich I V and Lempert W R 2011 Pure rotational CARS studies of thermal energy release and ignition in nanosecond repetitively pulsed hydrogen–air plasmas Proc. Combust. Inst. 33 3225–32

[78] Lanier S, Bowman S, Burnette D, Adamovich I V and Lempert W R 2014 Time-resolved temperature and O atom measurements in nanosecond pulse discharges in combustible mixtures submitted to J. Phys. D: Appl. Phys. in press

[79] Lanier S 2014 Heat release studies by pure rotational coherent anti-stokes Raman scattering spectroscopy in plasma assisted combustion systems excited by nanosecond discharges PhD dissertation Ohio State University

[80] Muller S, Luggenholscher D and Czarnetzki U 2011 Ignition of a nanosecond-pulsed near atmospheric pressure discharge in a narrow gap J. Phys. D: Appl. Phys. 44 165202

[81] Donko Z, Schulze J, Muller S and Czarnetzki U 2011 Kinetic simulation of a nansecond-pulsed hydrogen microdischarge Appl. Phys. Lett. 98 251502

[82] Boehm P, Luggenhoelscher D and Czarnetzki U 2013 Laser-spectroscopic electric field measurements in a ns-pulsed microplasma in nitrogen 66th Annual Gaseous Electronics Conf. (Princeton, NJ, 30 September–4 October) vol 58 p41

[83] Shkurenkov I, Burnette D, Lempert W R and Adamovich I V 2014 Kinetics of excited states and radicals in a nanosecond pulse discharge and afterglow in nitrogen and air Plasma Sources Sci. Technol. 23 065003

[84] Goldberg B, O’Byrne S and Lempert W R 2012 Picosecond E-field CARS; a diagnostic technique for measurement of electric field in pulsed plasmas AIAA Paper 2012-0240, 50th AIAA Aerospace Sciences Meeting (Nashville, TN, 9–12 January)

[85] Yu S, Akishev A V, Demyanov I V, Kochetov A P, Napartovich S V, Pashkin V, Ponomarenko V, Pevgov V G and Podobedov V B 1982 Determination of vibrational exchangeconstants in N2 from heating of gas High Temp. 20 658

[86] Supiot P, Blois D, De Benedictis S, Dilecce G, Barj M, Chapput A, Dessaux O and Goudmand P 1999 Excitation of N2(B3Πg) in the nitrogen short-lived afterglow J. Phys. D: Appl. Phys. 32 1887–93

[87] Ploenjes E, Palm P, Lee W, Chidley M D, Adamovich I V, Lempert W R and William Rich J 2000 Vibrational energy storage in high-pressure mixtures of diatomic molecules Chem. Phys. 260 353–66

[88] Lee W, Adamovich I V and Lempert W R 2001 Optical pumping studies of vibrational energy transfer in high-pressure diatomic gases J. Chem. Phys. 114 1178–86

[89] Plönjes E, Palm P, Lee W, Lempert W R and Adamovich I V 2001 RF energy coupling to high-pressure optically pumped nonequilibrium plasmas J. Appl. Phys. 89 5911–8

[90] Ahn T, Adamovich I V and Lempert W R 2004 Determination of nitrogen V–V transfer rates by stimulated Raman pumping Chem. Phys. 298 233–40

[91] Ahn T, Adamovich I and Lempert W R 2006 Stimulated Raman scattering measurements of V–V transfer in oxygen Chem. Phys. 323 532–44

[92] Ahn T, Adamovich I and Lempert W R 2007 Stimulated Raman scattering measurements of H2 vibration–vibration transfer Chem. Phys. 335 55–68

[93] Studer D and Vervisch P 2007 Raman scattering measurements within a flat plate boundary layer in an inductively coupled plasma wind tunnel J. Appl. Phys. 102 033303

[94] Studer D Boubert P and Vervisch P 2010 NO excitation and thermal non-equilibrium within a flat plate boundary layer in an air plasma Appl. Phys. B 101 689–700

[95] Studer D, Boubert P and Vervisch P 2010 Demonstration of NO production in air plasma–metallic surface interaction by broadband laser-induced fluorescence J. Phys. D: Appl. Phys. 43 315202

[96] Wehr L, Meier W, Kutne P and Hassa C 2007 Single-pulse 1D laser Raman scattering applied in a gas turbine model combustor at elevated pressure Proc. Combust. Inst. 31 3099–106

[97] Stopper U, Aigner M, Axa H, Meier W, Sadanandan R, Stöhr M and Bonaldo A 2010 PIV, 2D-LIF and 1D-Raman measurements of flow field, composition and temperature in premixed gas turbine flames Exp. Therm. Fluid Sci. 34 396–403

[98] Gabet K N, Jiang N, Lempert W R and Sutton J A 2010 Demonstration of high-speed 1D Raman scattering line imaging Appl. Phys. B: Lasers Opt. 101 1

[99] Lo A, Cléon G, Vervisch P and Cessou A 2012 Spontaneous Raman scattering: a useful tool for investigating the afterglow of nanosecond scale discharges in air Appl. Phys. B: Laser Opt. 107 229

J. Phys. D: Appl. Phys. 47 (2014) 433001

Topical Review

26

[100] Roettgen A, Adamovich I V and Lempert W R 2013 Measurements of N2 vibrational distribution function in pulsed nanosecond nonequilibrium discharge by spontaneous Raman scattering 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition (Grapevine, TX, 7–10 January)

[101] Xu D A, Lacoste D A, Rusterholtz D L, Elias P-Q, Stancu G D and Laux C O 2011 Experimental study of the hydrodynamic expansion following a nanosecond repetitively pulsed discharge in air Appl. Phys. Lett. 99 121502

[102] Capitelli M (ed) 1986 Nonequilibrium Vibrational Kinetics (Berlin: Springer)

[103] Cacciatore M, Capitelli M, DeBenedictis S, Dilonardo M and Gorse C 1986 Vibrational kinetics, dissociation and ionization of diatomic molecules under nonequilibrium conditions Nonequilibrium Vibrational Kinetics (Berlin: Springer) ch 2 pp 5–46

[104] Capitelli M, Gorse C and Ricard A 1986 Coupling of vibrational and electronic energy distributions in discharge and post-discharge conditions Nonequilibrium Vibrational Kinetics (Berlin: Springer) ch 11 pp 315–37

[105] Capitelli M (ed) 1996 Molecular Physics and Hypersonic Flows NATO Advanced Study Institute Series vol 482 (Dordrecht: Kluwer)

[106] Adamovich I V Macheret S O, Rich J W, Treanor C E and Fridman A A 1996 Vibrational relaxation, nonequilibrium chemical reactions, and kinetics of NO formation behind strong shock waves Molecular Physics and Hypersonic Flows NATO Advanced Study Institute Series vol 482 (Dordrecht: Kluwer) pp 85–104

[107] Candler G V, Bose D and Olejniczac J 1996 Interfacing Nonequilibrium Models with Computational Fluid Dynamics Methods NATO Advanced Study Institute Series vol 482 (Dordrecht: Kluwer) pp 625–44

[108] Ivanov M S, Antonov S G, Gimelshein S F, Kashkovsky A V and Markelov G N 1996 Statistical Simulation of Highly Nonequilibrium Hypersonic Rarefied Flows NATO Advanced Study Institute Series vol 482 (Dordrecht: Kluwer) pp 717–36

[109] Capitelli M, Ferreira C M, Gordiets B F and Osipov A I 2000 Plasma Kinetics in Atmospheric Gases Springer Series on Atomic Optical, and Plasma Physics vol 31 (Berlin: Springer)

[110] Guerra V and Loureiro J1997 Electron and heavy particle kinetics in a low-pressure nitrogen glow discharge Plasma Sources Sci. Technol. 6 361–72

[111] Guerra V and Loureiro J 1997 Self-consistent electron and heavy-particle kinetics in a low-pressure N2–O2 glow discharge Plasma Sources Sci. Technol. 6 373–85

[112] Mosbach T 2005 Population dynamics of molecular hydrogen and formation of negative hydrogen ions in a magnetically confined low temperature plasma Plasma Sources Sci. Technol. 14 610–22

[113] Pintassilgo C D, Guaitella O and Rousseau A 2009 Heavy species kinetics in low-pressure dc pulsed discharges in air Plasma Sources Sci. Technol. 18 025005

[114] Capitelli M, Colonna G, D’Ammando G, Laporta V and Laricchiuta A 2013 The role of electron scattering with vibrationally excited nitrogen molecules on nonequilibrium plasma kinetics Phys. Plasmas 20 101609

[115] Ploenjes E, Palm P, Chernukho A P, Adamovich I V and Rich J W 2000 Time-resolved Fourier transform infrared spectroscopy of optically pumped carbon monoxide Chem. Phys. 256 315–31

[116] Plönjes E, Palm P, Rich J W, Adamovich I V and Urban W 2002 Electron-mediated vibration-electronic (V-E) energy transfer in optically pumped plasmas Chem. Phys. 279 43–54

[117] Candler G V, Olejniczak J and Harrold B 1997 Detailed simulation of nitrogen dissociation in stagnation regions Phys. Fluids 9 2108–17

[118] Boyd I D and Josyula E 2011 State resolved vibrational relaxation modeling for strongly nonequilibrium flows Phys. Fluids 23 057101

[119] Kim J G and Boyd I D 2014 Monte Carlo simulation of nitrogen dissociation based on state-resolved cross sections Phys. Fluids 26 012006

[120] Panesi M, Jaffe R L, Schwenke D W and Magin T E 2013 Rovibrational internal energy transfer and dissociation of N2(1Σg

+)—N(4Su) system in hypersonic flows J. Chem. Phys. 138 044312

[121] Bohlin A and Kliewer C J 2013 2D gas-phase coherent anti-Stokes Raman spectroscopy (2D-CARS): simultaneous planar imaging and multiplex spectroscopy in a single laser shot J. Chem. Phys. 138 221101

[122] Richardson D R, Bangar D and Lucht R P 2012 Polarization suppression of the nonresonant background in femtosecond coherent anti-Stokes Raman scattering for flame thermometry at 5 kHz Opt. Express 20 21495

[123] Dennis C N, Slabaugh C D, Boxx I G, Meier W and Lssucht R P 2014 Chirped probe pulse femtosecond coherent anti-Stokes Raman scattering thermometry at 5 kHz in a gas turbine model combustor Proc. Combust. Inst. submitted

J. Phys. D: Appl. Phys. 47 (2014) 433001