The Ohio State University Nonequilibrium Thermodynamics Laboratory
Studies of Fast Ionization Wave Discharge PlasmasStudies of Fast Ionization Wave Discharge PlasmasUsing Optical Diagnostics
with Sub-Nanosecond Time Resolution
K. Takashima, A. Montello, W.R. Lempert, and I.V. AdamovichK. Takashima, A. Montello, W.R. Lempert, and I.V. Adamovich
Objectives
• Generating controlled, reproducible nsec pulse duration dischargesi l t l d i l (F t I i ti W ) t i iin plane-to-plane and axial (Fast Ionization Wave) geometries, in adischarge section with access for optical diagnostics
• Measurements of FIW speed in a wide range of pressures (P~1-100torr), and voltage waveforms (peak voltage, rise time, pulse repetitionrate)
• Development and testing of a new, portable psec CARS diagnosticDevelopment and testing of a new, portable psec CARS diagnosticsystem
• Time- and spatially resolved measurements of rapidly varyingelectric field in nsec pulse discharges (plane to plane and FIW) by IRelectric field in nsec pulse discharges (plane-to-plane and FIW) by IR(E-field) psec CARS
• Measurements of electron density in nsec pulse discharges byTh tt i *Thomson scattering*
*with luck
“Single pulse” nanosecond discharge in plane-to-plane geometry: spatially uniform?
The Ohio State University Nonequilibrium Thermodynamics Laboratory
20
Voltage, kV
p p g y p y
0
10
20Air, P=60 torr, ν=40 kHz
30
-20
-10
0 50 100 150 200-30
Time, nsec
Single pulse 100 pulse average
Broadband ICCD camera images, gate 2 μsecAir, P=60 torr, pulse repetition rate 10 Hz
Single pulse 100 pulse average
Repetitive nanosecond pulse discharge: effect of residual ionization on spatial uniformityp y
20Voltage, kV
10
20Camera gate: 1 µsec
-10
0
cathode
0 10 20 30 40 50 60 70Time, μsec
-20
anode
Single pulse ICCD camera images in air from 40 msec “burst” (P=60 torr, ν=40 kHz, 1000 pulses in a burst, 1 μsec camera gate)
Air plasma remains uniform during entire pulse burst at P=40-100 torr(after first 1-2 pulses): effect of residual ionization
Same result for short camera gates (down to 4 nsec): justifies the use of a quasi-1-D approach
Effect of residual ionization: uniform plasma on nanosecond time scale
The Ohio State University Nonequilibrium Thermodynamics Laboratory
Air, P=60 torr, ν=40 kHz, pulse #100 in the burst
Same result for shorter camera gates (down to 4 nsec): justifies the use of a quasi-1-D approach
Nanosecond pulse discharge plasma / sheath model(quasi-1-D drift-diffusion, time-dependent)
L
(q , p )
• Equations for electron and ion number density• Poisson equation for the electric field plasma
sheath
cathode anode
• Poisson equation for the electric field• Nitrogen, plane-to-plane discharge geometry• Both electrodes covered with quartz plates• Voltage pulse: Gaussian fit to experimental waveform
l ε
lsE
Voltage pulse: Gaussian fit to experimental waveform
T d i i ti ffi i t E/N fit t
sec15,20,exp2)(2
nkVVtt
lL
VtE peak
peakpeakapp ==
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛ −−
+= τ
τε
l,ε• Townsend ionization coefficient vs. E/N: fit to experimental data; local kinetics only• Dielectric plate charging / plasma shielding:
dd ⎞⎛ )()(
Numerical or analytic solution: time dependent
( ) ( )[ ]dxtxtxL
ledttdV
Ll
dttdV L
egapapp ∫ Γ−Γ+⎟
⎠⎞
⎜⎝⎛ += +0
0
,,12)(21)(
εεεCd CdCs(t) R(t)
Numerical or analytic solution: time-dependent electron density and electric field in the plasma and in the sheath, coupled pulse energy
Nanosecond pulse discharge plasma / sheath model:key processes and time scales
Eapp(t) - applied electric field (Gaussian fit to experimental pulse shape)2ttV ⎤⎡ ⎞⎛
ey p ocesses a d t e sca es
νi - electron impact ionization frequency
sec15,20,exp2)( nkVVtt
lL
VtE peak
peakpeakapp ==
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛ −−
+= τ
τε
22 00 nelnle ese μμ)( ⎥
⎤⎢⎡ BpAE
νc + νs - frequency of dielectric charging / sheath formationνRC - RC frequency of the load after breakdown (plasma / charged dielectrics / sheath)
a 11 0 −== νν,,
21 0
0
0
0
LLlL
ess
ec ε
μν
εεε
μν =⎟⎠⎞
⎜⎝⎛ +
=,exp)( ⎥⎦⎤
⎢⎣⎡−=EpApEiν
E0 =E(t0) - breakdown field
aaCR iloadplasma
RC ln== νν
( ) ( ) BpEtt
tEE ipeakapp
00
000 2/ln4
,γτν
τ=
−=
E*=E(t*) - field in the plasma at the moment when coupled power peaks
( )a
aEE
aaaa
EBpaE
EEEE
sc
iii 3
,ln
,23exp,,
0*
0* /
0
*
2
/
10
0
00 =
−=⎟⎟
⎠
⎞⎜⎜⎝
⎛=
+== ξξ
νννγνν
Nanosecond pulse discharge plasma / sheath model:key results
)( *⎧ app tEE(t): electric field in the plasma
ey esu ts
( )0,)(1
,1exp1
)(
)( 2*
*
0
=⎪
⎪⎪⎪⎪
⎨
⎧
⎟⎟⎠
⎞⎜⎜⎝
⎛+
≤′+′
= ∞p
app
i
app
p EtEEE
ttt
tEξξ
νγ
⎥⎥⎦
⎤
⎢⎢⎣
⎡=
RC
appp
tEtEtE
ν)(
),(max)(&
[ ],
)()(exp
*
1
2*021
10
⎪⎪⎪⎪
⎩
>′+−′+
⎟⎠
⎜⎝
i
pp
tttt
E
ξξ
νξξ
ξ ⎥⎦⎢⎣ RC
[ ] )(2
2
,2
)()()()( tEll
lLE
ll
lLtEtEtEtE app
s
s
s
spappapps
ε
+
+=
+
−⋅−+=
∞
∞
∞
∞
Es(t): electric field in the sheath
⎟⎟⎠
⎞⎜⎜⎝
⎛= ∞
∞
∞∞
0
ln)( n
nEElsis
ss ν
μ
ls∞: steady state sheath thickness
ss εε
ne(t): electron density in the plasma
aaan
aaann
aaan
aaaantn
EtEEtE pp
ln1
ln11,
1ln1)( 00
/)(/)(
0
00 −≈⎟
⎠⎞
⎜⎝⎛ −+=
−−
≈⎟⎟⎠
⎞⎜⎜⎝
⎛ −+= ∞∞ γγγ
Analytic and numerical solutions: Electric field in the plasma and in the sheathp
• Rapid field drop in the plasma after breakdown
• Dominant effect: plasma shielding by charging dielectric100
E, kV/cmplasma
• Dominant effect: plasma shielding by charging dielectric plates, sheath formation
• Steady-state electron density after shielding ne~1012 cm-3
•Steady-state sheath thickness / plasma thickness << 11
10
90 nsec
89 nsec
88 nsec87 nsec
Steady-state sheath thickness / plasma thickness << 1• Uniform field in the plasma• Analytic and numerical solutions: excellent agreement0.1
1
x cm
92 nsec
0.0 0.2 0.4 0.6 0.8 1.0
sheath
x, cm
Plasma electric field, kV/cmnumerical model
analytic solution
161820 applied voltage
1E+12
1E+13
ne, cm-3
89 nsec
92 nsec
plasma
1 5E 12
2.0E+12
Electron density, cm-3
shielded plasma
Vapp/(L+2l/ε)
468
101214
breakdown
1E+8
1E+9
1E+10
1E+11
86 nsec
88 nsec
88.5 nsec
h th5.0E+11
1.0E+12
1.5E+12
numerical model
analytic solution
70 75 80 85 90 95 100Time, nsec
024
shielded plasma1E+7
1E+8
x, cm
80 nsec
0.0 0.2 0.4 0.6 0.8 1.0
sheath
86 88 90 92 940.0E+0
Time, nsec
breakdown
Analytic and numerical solutions: Electron density in the plasma and coupled powery p p p
Power density, kW/cm3
numerical model50 1.2
Coupled pulse energy, mJ
analytic solution
30
40
V /(L+2l/ε)
breakdown
0.6
0.8
1.0
P*=60 torr V k=20 kV
0
10
20 Vapp/(L+2l/ε)
shielded plasma
0.0
0.2
0.4P 60 torr, Vpeak 20 kV
Numerical, w/o sheath
Numerical, with sheath
Analytic solution
80 90 100 110 120Time, nsec
⎥⎥
⎦
⎤
⎢⎢
⎣
⎡+⎟
⎟⎠
⎞⎜⎜⎝
⎛≈+= peakloadafterbreaktotal V
VVCQQQτνπ2
21
2
02
1E+7 1E+8 1E+9 1E+10 1E+11 1E+12 1E+13
Initial electron density, cm-3
• Most of the power coupled during breakdown pulse,
• Coupled pulse energy scales as the number density, can be increased by reducing τpulse
1.0~)(~/ 1−pulseRCbreakafter QQ τν
⎥⎦
⎢⎣
⎟⎠
⎜⎝ pulseRCpeakV τν2
• Pulse energies in N2 and air are almost the same: attachment insignificant at short pulse durations• Analytic and numerical solutions: excellent agreement• Good agreement with pulse energy inferred from O atom measurements by Two-Photon LIF
Fast Ionization Wave (FIW) discharge Test section schematic
The Ohio State University Nonequilibrium Thermodynamics Laboratory
Test section schematic
Air, P=10 torr, Upeak =16 kVν=10 kHz, L=20 cm
Wave propagation velocity ~ 4 cm/nsec (measured by capacitive probes)( y p p )
x=20 cmx=0
15
20
4cm
10
15
age
[kV]
4cm 10cm 18cm
0
5
Vol
ta
10 20 30 40 50 60-5
Time [ns]
Previous FIW discharge experimentsMoscow Institute of Physics and Technology (A. Starikovskii, S. Starikovskaya et al.)
Arrival time and amplitude of fast ionization wave in nitrogen P=24 torrArrival time and amplitude of fast ionization wave in nitrogen, P 24 torr
Kinetic modeling of FIW propagation(quasi-1-D, long wavelength approximation)
The Ohio State University Nonequilibrium Thermodynamics Laboratory
ne, cm-31
Space charge, nC
(q , g g pp )
1E+10
1E+11
1E+12
1E+13
31.6 nsec
10 nsec
1 nsec
3
4
5
10
1 nsec
1E+7
1E+8
1E+9
0 5 10 15 20 25 300
1
231.6 nsec
10 nsec
0 5 10 15 20 25 30x, cm
20
25E, kV/cm
x, cm
• Ey<<Ex
• Nitrogen, P=10 torr, Upeak=25 kV
5
10
15
31.6 nsec10 nsec
1 nsec • Channel height 1 cm, electrode gap 20 cm
• Both wave speed and peak electric field decrease along the length, u=1-4 cm/nsec
0
x, cm0 5 10 15 20 25 30
• Kinetic model needs to incorporate full Boltzmann equation, non-local kinetics effects. Collaboration with modeling experts welcome!
IR (E-Field) nsec CARS schematic and measurement region
The Ohio State University Nonequilibrium Thermodynamics Laboratory
InSb473nm Dichroic Mirrors
CaF2 Lens
IR LP Filter
PωPωSω ASω
vΔ
Spectrometer
476nm BP FilterFocusing Lens
500mm CaF2 Lens
IR Dichroic MirrorBeam Dump
CARS Generated Along ~11 mm Line Segment (Determined using scanning
CARS Energy Level Diagram
vΔ
Delay Path
SpectrometerCamera
500mm LensField Measurement
Volume
2
Non-Resonant CARS Signal vs Axial Location Relative to Nominal Waist
2.5
Segment (Determined using scanning microscope slide and NR background)
YAGDelay Path
Broadband Dye Laser
Volume532 nm
607 nm Volta
ge
0 5
1.0
1.5
2.0
Tunable Dye Laser
Position (mm)
-20 -10 0 10
0.0
0.5
Preliminary raw IR nsec CARS data(electric field measured between two plane electrodes
in atmospheric air, no breakdown)
The Ohio State University Nonequilibrium Thermodynamics Laboratory
in atmospheric air, no breakdown)
averaged over 32 pulses
averaged over 128 pulses128 pulses
Overview of new psec CARS system
The Ohio State University Nonequilibrium Thermodynamics Laboratory
Delay Path
Ekspla Nd:YAG laser10 Hz, ~150 psec pulses
125 mJ per pulse max @ 532 nm
Modeless Psec Dye LaserBroadband centered @ 607 nmBroadband centered @ 607 nm
~ 6% conversion efficiencyFromSpectrometer
Schematic of psec dye laser
The Ohio State University Nonequilibrium Thermodynamics Laboratory
Thin Film Polarizer ( fl t 90%)(reflect ~90%)
λ/2“Pump”
λ/2
Beam splitter ~80:20 HR 2
Reflecting prism
Beam splitter ~50:50
λ/2 beam outλ/2
Beam dumps
400 mm spherical lens (AR)
HR 1
Cylindrical lens ~100 mm (AR)
HR 3
Beam dumps
RA prism
“Stokes” beam out
Cylindrical lens ~50 mm (AR)
iris 600 mm lensoscillator cell
pre-amp cell
amplifier cell
Portable, broadband psec CARS diagnostic system
The Ohio State University Nonequilibrium Thermodynamics Laboratory
diagnostic system
First sensitivity test of psec CARS:Detecting N2 and CO in an optical absorption cell
The Ohio State University Nonequilibrium Thermodynamics Laboratory
g 2 p p
N2(v=0)
N2(v=0)
N2
CO(v=0)N2
(outside)
M t f CARS i l f i id th ll (20 30 h t i l l ti )
CO(v=0)
Most of CARS signal comes from inside the cell (20-30 shot signal accumulation)Blue: 8 torr CO, 74 torr N2 Red: 9 torr CO, 120 torr Ar
Capable of detecting O2(a1Δ) generated in electric discharges (partial pressure ~1 torr)p g 2( ) g g (p p )
Next sensitivity test: taking CARS spectra of N2-CO mixture vibrationally pumped by a c.w. CO laser
Here is what we expect to see (and more): Spontaneous Raman Spectra in CO/N2=4/96, P=400 torr (2001)
1.0E+0Relative population
N21.0E-1
1.0E 0
CO, experiment (Tv=3500 K)
N2, experiment (Tv=2200 K)
CO, calculation (Tv=5300 K)
N2, calculation (Tv=2700 K)
CO
v=39
1.0E-3
1.0E-2
570 575 580 585 590 595 600 605 610 615
Wavelength, nm
CO
0 10 20 30 401.0E-4
Vibrational quantum number
Laser power: 15 W, T≅500 K
5 vibrational levels of N2, 40 vibrational levels of CO
(signal averaging over a few hundred pulses)
Work in Progress / Technical Issues
The Ohio State University Nonequilibrium Thermodynamics Laboratory
N FIW di h ti till i l h• New FIW discharge section still in glass shop
• Need an IR detector / 1-D detector array with short response time(~10 nsec)
• Need to determine sensitivity limit at low pressures and electric field
• Need to synchronize high voltage nsec pulses and CARS laser pulsesd t l l “jitt ”and control pulse “jitter”
• Effect of EMI noise from the pulser on CARS system electronics yetto be determined