January, 2013

Plasma Science and Fusion Center Massachusetts Institute of Technology

Cambridge MA 02139 USA This work was supported by AFOSR, Grant No. FA9550-09-1-0363. Reproduction, translation, publication, use and disposal, in whole or in part, by or for the United States government is permitted.

PSFC/JA-11-51

Observation of Plasma Array Dynamics in 110 GHz Millimeter-Wave Air Breakdown

Cook, A.M., Hummelt, J.S., Shapiro, M.A., Temkin, R. J.

Observation of Plasma Array Dynamics in 110 GHz Millimeter-Wave AirBreakdown

Alan M. Cook,a) Jason S. Hummelt, Michael A. Shapiro, and Richard J. TemkinPlasma Science and Fusion Center, Massachusetts Institute of Technology, 167 Albany St., Cambridge,MA

(Dated: 22 July 2011)

We present dynamical measurements of self-organizing arrays of plasma structures in air induced by a 110GHz millimeter-wave beam with linear or circular polarization. The formation of the individual plasmas andthe growth of the array pattern are studied using a fast-gated (5 − 10 ns) intensified camera. We measurethe time-dependent speed at which the array pattern propagates in discrete steps toward the millimeter-wavesource, observing a peak speed greater than 100 km/s. We observe the expansion of an initially sphericalplasma into a disk or an elongated filament, depending on the polarization of the incident beam. The resultsshow good agreement with one-dimensional ionization-diffusion theory and two-dimensional simulations.

PACS numbers: 52.80.Pi, 52.40.Db, 84.40.Ik, 07.57.HmKeywords: electric breakdown,plasma electromagnetic wave propagation,millimeter wave

Experiments with high-intensity (MW/cm2)millimeter-wave beams focused in atmospheric-pressureair have observed discharge plasmas with complexdynamics that are unique to this frequency range (30GHz - 1 THz).1–3 The interaction of the radiation beamwith the near-critical-density breakdown plasma, in theabsence of the quantum and nonlinear optical effectsthat dominate laser-plasma interactions, leads to areflected-field interference pattern with periodicity onthe order of the characteristic length for electron diffu-sion. This allows subsequent breakdowns at the adjacentintensity maxima of the interference pattern to be seededby the preceding breakdown, causing a self-organizingarray-like pattern of plasma formations.4 Experimentalcharacterization of this phenomenon is important, as thecontinuing development of mm-wave/THz sources bringsnew capabilities5,6 and applications7,8 for high-powerquasi-optical beams that propagate in the atmosphere.

Early breakdown experiments observed a periodic pat-tern of plasma “filaments,” oriented parallel to the in-cident E-field polarization, that propagates in discretejumps toward the microwave source.1,2 Working at 110GHz (wavelength λ = 2.7 mm), Hidaka et al.9 observeda two-dimensional (2D) array of such filaments, usingsteady-state electromagnetic simulations to explain thedistinct triangular ∼ λ/4 array spacing. Fast-gated pho-tography showed the sequential pattern formation andestimated its speed at ∼ 10 km/s.

Self-consistent numerical models are able to reproducemany of the experimental results. 1D simulations of thereflection of millimeter waves by a plasma “slab” showthe appearance of a new breakdown at the nearest re-flected field maximum ∼ λ/4 upstream of the initialplasma, and the rapid subsequent reflection by the newplasma.4,10 2D simulations of a linearly-polarized plane

a)Electronic mail: alancook@mit.edu

wave incident on a plasma spheroid show the elonga-tion of the sphere into a filament due to enhancementof the external electric field at its poles, and the forma-tion of a pattern of filaments.11–14 Although these simu-lations closely match experiments, the predicted plasmastreamer dynamics have not been measured in this high-frequency, high-intensity regime.

In this letter, we present detailed measurements of theinstantaneous dynamics of plasma array patterns in at-mospheric air produced by linearly-polarized (LP) andcircularly-polarized (CP) 110 GHz millimeter waves. Themegawatt-level beam power allows discharge formation ina free volume of gas, with no surfaces or objects nearby.We simultaneously observe the formation of individualplasmas and the discrete axial propagation of the patternwith 20-50 ns temporal resolution over a 3 microsecondpulse. We measure a pattern propagation speed that de-creases by an order of magnitude during the life of thebreakdown, from > 100 km/s to 10 km/s. The transverseexpansion speed of an individual plasma is ∼ 5−10 km/sand shows good agreement with 1D ionization-diffusiontheory.15

The experimental setup is shown in Fig. 1. A linearly-polarized Gaussian millimeter-wave beam is produced by

gyrotron window

grating

lens

beam

optical diagnostics

E

x

y

k, z

FIG. 1. (color online) Experimental setup. The breakdownplasma initiates at the origin of the coordinate system, at thecenter of the focused beam waist.

2

FIG. 2. (color online) Open-shutter (blue) and fast-gated(orange overlay) photographs of breakdowns with linearly-polarized beam.

a 1.5 MW, 110 GHz gyrotron oscillator.16 The beam isreflected from a metal grating polarizer (10 grooves/cm)that can be rotated to select either linear or circular po-larization for the reflected beam. The beam is focusedby a high-density polyethylene lens to a peak intensityof 5 MW/cm2 (1/e spot radius w0 ≈ 4 mm, peak E field6 MV/m), causing breakdown in the air near the beamfocus. The gyrotron is pulsed at a rate of up to 4 Hz,and the plasma dynamics are observed over many shotsusing optical diagnostics.

On each shot, a digital camera with slow shutter speedtakes a time-integrated photograph capturing the entirebreakdown event. An avalanche photodiode detects theonset of optical emission from the breakdown plasma,marking t = 0. An intensified CCD camera (ICCD) witha fast shutter speed (5 − 10 ns) is triggered at a chosentime t during the breakdown. Because the behavior ofthe breakdown plasma is very repeatable from shot toshot, we can assemble the resulting sequence of fast im-ages into a time-resolved record of an entire breakdownevent. The visible emission detected by the ICCD cam-era is primarily from the C3Πu−B3Πg (second positive)system in neutral molecular nitrogen, which we verify byoptical spectroscopy. N2 excitation from the ground state

FIG. 3. (color online) Open-shutter (blue) and fast-gated(orange overlay) photographs of breakdowns with circularly-polarized beam.

to the C3Πu state is due to collisions with energetic elec-trons; since the collisional relaxation time τ <∼ 10−12 sat atmospheric pressure is much smaller than the timescale of the plasma dynamics, we take the excited N2

front to be an excellent approximation to the motion ofthe plasma electron density front.

Figure 2 shows a subset of the measured sequence forthe LP case, taken from hundreds of similar data points.Each frame is a separate breakdown event, with the fast-gated image (orange) overlaid on the corresponding slowimage (blue). The envelope of the focused incident beamis shown as a dashed line. The filaments stretch quasi-parallel to the E field polarization (x), which lies in theplane of the image. When viewed looking along x, weobserve the 2D array pattern described in detail in Ref.3. When the beam is circularly polarized, the preferreddirection is removed, and the plasma expands in both xand y to form disk-like structures that are azimuthallysymmetric (Fig. 3).17

It is apparent that each plasma begins as a spheroidon the axis of the Gaussian beam, and expands trans-versely under the influence of the incident field. Theaxial propagation of the pattern in the −z direction iscaused by reflection of the incident field and subsequentbreakdown at the standing-wave maximum field location∼ λ/4 upstream. We measure the axial propagationspeed vz by recording the position of the front plasmafilament as a function of t, shown in Fig. 4. We see thatvz changes dramatically during the breakdown event, de-creasing from > 100 km/s to 10 km/s, and is very similarfor both polarizations. This decrease in speed is due tothe decreasing intensity of the incident Gaussian beamas the plasma moves away from the focus. A logarithmicfunction is an excellent fit to the position data, indicatingan apparent front velocity that is inversely proportionalto time.

3

Plasma Front Distance vs. Time

01 10 100 1000 104

5

15

25

35di

stan

ce [m

m]

time [ns]

linear pol.circular pol.

FIG. 4. (color online) Position of the plasma pattern frontvs. camera trigger time t. The lines are logarithmic fits tothe data.

(b) 42 ns

(c) 66 ns (d) 100 ns

(a) 8 ns2 4 6 8

3040506070

gray

val

ue

vertical distance [mm]

(e) 158 ns (f) 204 ns

FIG. 5. (color online) Vertical profiles of pixel intensityat fixed z in fast-gated images of breakdown with linearly-polarized beam. Each frame is labeled with camera triggertime t. This sequence follows a filament born around 8 ns(a).

To measure the growth of an individual plasma forma-tion transverse to the z axis, we record the vertical (inx) pixel intensity profile at a fixed z position in sequen-tial fast-gated images. We choose a z position located ata newly-formed spherical plasma, and follow its growthin time. Fig. 5 shows a sequence of such profiles for afilament observed starting at 8 ns, in the LP case. Theobserved radial expansion speed of the plasma front fromthe axis is v⊥ ≈ 14 km/s early in the life of the fila-ment, and decreases to ∼3.5 km/s at later times. In theCP case, v⊥ ≈ 4 km/s at early times and decreases to∼1 km/s at later times.

The data shows that many new breakdowns occur inthe time it takes an individual filament to stretch outtransversely; for example, in Fig. 2c, about 10 new fila-ments have appeared in the time it has taken the earliest

filaments to reach full size. This indicates that the inci-dent field is reflected from the plasma early in the life ofthe filament, allowing a new breakdown to occur whilethe filament forms. Similar behavior is seen in the CPcase. Thus, the self-organization of the pattern is dom-inated by the part of the plasma near the axis of theincident beam. This is supported by the appearance ofa distinct dark channel on the beam axis in the time-integrated photos, which suggests that the incident mi-crowave power is most strongly reflected and absorbed bythe center part of the plasma, causing the downstream(earlier) on-axis plasma to extinguish quickly. As theplasma expands away from the beam axis, it does not cutoff power to earlier filaments as effectively. This is clearlyseen in the fast-gated photos (Fig. 2), which show thatthe center of each plasma formation disappears within< 50 ns while the off-axis part of the plasma persists for>∼ 500 ns. The 1D simulations of similar experimentalconditions in Ref. 4 show that the newly-formed plasmaheavily absorbs power and becomes highly reflecting in∼ 10 ns. The 2D simulation in Fig. 5 of Ref. 12 showsa similar dark channel in a time-averaged calculation ofthe electron density.

High-frequency streamer theory describes how aplasma spheroid in an external field distorts into an elon-gated shape by self-consistently calculating the effects ofthe changing plasma shape and density on the field.15

When the plasma approaches critical density, it has adielectric effect that enhances the field at the edges ofthe sphere. Depending on the beam polarization, theplasma grows into an elongated ellipsoid (filament) or aflattened ellipsoid (disk). This theory qualitatively ex-plains the observed difference in the plasma geometry inthe LP and CP cases. v⊥ is generally lower in the CPcase because the field-enhancing effect of the plasma isless pronounced for the flattened disk-like geometry.

We compare the transverse expansion data with simple1D ionization-diffusion theory, which describes the mo-tion of a plasma ionization front through a neutral gasin an external electric field. The advantage of using thissimple theory is that we do not need to assume any un-known parameters, such as the initial electron density orplasma aspect ratio. The speed ve of the front is foundby solving an electron continuity equation, including asource term for ionization due to the millimeter-wavepulse,

∂ne∂t

= De∇2ne + νine, (1)

where ne is the electron density and De is the free elec-tron diffusion coefficient at 760 Torr.18 We assume thatDe is uniform in the region because it depends weakly onthe electric field. The net ionization rate νi is given by

νi = νa

(EincEc

)β− νa, (2)

where νa = 5 × 104 p Hz is the electron-neutral attach-ment rate in air at pressure p (Torr), Einc/Ec is the ra-

4

0 500 1000 1500 2000 2500

0 500 1000 150001

23

45

6

0

12

3

45

6

1D theorydata

Filament Width vs. Time

Disk Width vs. Time

time [ns]

time [ns]

radi

al si

ze [m

m]

radi

al si

ze [m

m]

(a)

(b)

FIG. 6. (color online) Radial size of (a) filaments (linear po-larization) and (b) disks (circular polarization) vs. cameratrigger time t, for plasmas born at different times.

tio of the incident field amplitude to the high-pressurebreakdown threshold field Ec = 3200p (V/m),18 and β isan empirically determined constant (β = 5.33 for air).19

Eqs. 1 and 2 yield a 1D solution for an ionization fronttraveling at speed13

ve = 2√Deνi. (3)

ve is independent of the direction of the applied field, anddoes not account for the observed differences in LP andCP plasma expansion speeds.

Fig. 6 shows the measured transverse expansion ofplasma streamers born at different times, plotted as theradial size of the plasma versus camera trigger time t,for the LP (filaments, Fig. 6a) and CP (disks, Fig. 6b)cases. The data is compared with the 1D theory of Eq. 1,using the unperturbed incident beam field. To calculatethe radial size, Eq. 3 is integrated numerically in time,accounting for the radial field variation Einc(r). The the-ory agrees qualitatively with the data, showing that v⊥ ishigher closer to the axis of the beam where the incidentfield intensity is the highest. The calculated expansionstops at larger radii, where Einc is low enough that at-

tachment balances ionization; the observed plasma con-tinues to grow beyond this point due to the field enhance-ment by the plasma. For the plasma born earliest, before∼ 200 ns, the data for both polarizations lies well belowthe theory curve because the growth is slowed by thehigh reflection/absorption near the beam axis. It is no-table that the 1D theory shows reasonable quantitativeagreement without any assumed or variable parameters.

These measurements show the dynamics of a self-organized millimeter-wave discharge plasma array and itsconstituent streamers simultaneously. By observing therelative time scales of individual plasma formation (fil-ament or disk) and pattern propagation, we show thatthe pattern is formed by the early breakdown plasmasnear the axis of the beam. Subsequently, the individualplasma streamer growth is effectively decoupled from thepattern formation, driven instead by the incident beam.

The authors thank Y. Hidaka for fabrication of thegrating, and J. Verboncoeur, A. Vikharev and M. Gitlinfor useful discussions. This work was supported byAFOSR grant FA9550-09-1-0363 on the Basic Physics ofDistributed Plasma Discharges.

1A. Vikharev et al., Sov. Phys. JETP 67, 724 (1988).2A. L. Vikharev, A. M. Gorbachev, A. V. Kim, and A. L. Kolysko,Sov. J. Plasma Phys. 18, 554 (1992).

3Y. Hidaka, E. M. Choi, I. Mastovsky, M. A. Shapiro, J. R. Sirigiri,and R. J. Temkin, Phys. Rev. Lett. 100, 035003 (2008).

4S. K. Nam and J. P. Verboncoeur, Phys. Rev. Lett. 103, 055004(2009).

5K. Felch, B. Danly, and H. Jory, Proc. IEEE 87, 752 (1999).6K. Sakamoto, A. Kasugai, and K. Takahashi, Nature Phys. 3,411 (2007).

7Y. Oda, K. Komurasaki, and K. Takahashi, J. Appl. Phys. 100,113307 (2006).

8V. L. Granatstein and G. S. Nusinovich, J. Appl. Phys. 108,063304 (2010).

9Y. Hidaka, E. Choi, I. Mastovsky, M. Shapiro, J. Sirigiri,R. Temkin, G. Edmiston, A. Neuber, and Y. Oda, Phys. Plasmas16, 055702 (2009).

10W. M. Bollen, C. L. Yee, A. W. Ali, M. J. Nagurney, and M. E.Read, J. Appl. Phys. 54, 101 (1983).

11J.-P. Boeuf, B. Chaudhury, and G. Q. Zhu, Phys. Rev. Lett. 104,015002 (2010).

12B. Chaudhury, J.-P. Boeuf, and G. Q. Zhu, Phys. Plasmas 17,123505 (2010).

13G. Q. Zhu, J.-P. Boeuf, and B. Chaudhury, Plasma Sources Sci.Technol. 20, 035007 (2011).

14Q. Zhou and Z. Dong, Appl. Phys. Lett. 98, 161504 (2011).15V. B. Gil’denburg, I. S. Gushchin, S. A. Dvinin, and A. V. Kim,Sov. Phys. JETP 70, 645 (1990).

16E. Choi, A. Cerfon, I. Mastovsky, M. Shapiro, J. Sirigiri, andR. Temkin, Fusion Sci. Technol. 52, 334 (2007).

17S. I. Gritsinin, I. A. Kossyi, and N. M. Tarasova, Sov. Tech. Phys.Lett. 11, 382 (1985).

18A. D. MacDonald, Microwave Breakdown in Gases (Wiley,1966).

19W. C. Taylor, W. E. Scharfman, and T. Morita, Advances inMicrowaves, Vol. 7 (Academic Press, 1971).