Choi, E.M.

Hidaka, Yoshiteru

Mastovsky, I.

Shapiro, M.

Sirigiri, J.

Temkin, R.

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                         Plasma Science and Fusion Center Massachusetts Institute of Technology Cambridge  MA  02139  USA    (Submitted to Physical Review Letters, October, 2007)           This work was supported by US AFOSR MURI04 program on the Nano-Physics of High Current Density Cathodes and Breakdown.  Reproduction, translation, publication, use and disposal, in whole or in part, by or for the United States government is permitted.  PSFC/JA-07-15                  Observation of Large Arrays of  Plasma Filaments  in Air Breakdown  by 1.5 MW, 110 GHz Gyrotron Pulses   Hidaka, Yoshiteru; Choi, E.M.;  Mastovsky, I.;  Shapiro, M. A.; Sirigiri, J. R.;  and Temkin, R. J.   Observation of Large Arrays of Plasma Filaments in Air Breakdownby 1.5 MW, 110 GHz Gyrotron PulsesYoshiteru Hidaka, E. M. Choi, I. Mastovsky, M. A. Shapiro, J. R. Sirigiri, and R. J. TemkinPlasma Science and Fusion Center, Massachusetts Institute of Technology,167 Albany Street, Cambridge, Massachusetts 02139, USA(Dated: October 5, 2007)We report the observation of two-dimensional plasma filamentary arrays with more than onehundred elements generated during breakdown of air at atmospheric pressure by a focusedGaussian beam from a 1.5 MW, 110 GHz gyrotron operating in 3 microsecond pulses. Eachelement is a plasma filament elongated in the electric field direction and regularly spaced aboutone quarter wavelength apart in the plane perpendicular to the electric field. The developmentof the array is explained as a result of diffraction of the beam around the filaments, leadingto the sequential generation of high intensity spots, at which new filaments are created, abouta quarter wavelength upstream from each existing filament. Electromagnetic wave simulationscorroborate this explanation and show very good correlation to the observed pattern of filaments.PACS numbers: 52.80.Pi, 52.40.Db, 52.77.Fv, 52.38.HbWe report the observation of large, two-dimensionalregular arrays of plasma filaments generated duringbreakdown of air at atmospheric pressure by a focusedGaussian beam from a 1.5 MW, 110 GHz gyrotron with3 µs pulse length. These filamentary arrays consist ofa large number of regularly spaced elements, more thanone hundred in some cases. They are observed both involume breakdown and in breakdown at surfaces. Thefilamentary arrays are notably different from the wellknown filamentation observed in laser-induced plasmas.Laser generated filaments are aligned along the directionof propagation, while the filaments observed here are per-pendicular to the direction of propagation. Each filamentis aligned parallel to the direction of the electric field.There is an extensive literature on gas breakdown atmicrowave frequencies [1–3] and at optical frequencies[4, 5]. Recent research has also addressed a number of im-portant issues in breakdown at surfaces [6]. However, dueto the scarcity of powerful sources in the millimeter wave-length range, there have been relatively few studies onz, k y, Bx, E CollectorGyrotron WindowGaussian   Beam  FlatMirrorLensDielectric  Sample    rfDiodePhoto-diodes   MIGElectron   GunSuperconducting Magnet4-Mirror Internal Mode ConverterMicrowave ResonatorFIG. 1: Schematic of air breakdown experiments. Ex-periments were conducted with volume and (as shown)dielectric surface breakdown.gas breakdown at these wavelengths. Studies have beencarried out with gyrotrons at frequencies of 35 to 86 GHz[7–10] at power levels up to 250 kW and pulse lengths of0.05 to 20 ms. The available power in these studies wasinsufficient to achieve breakdown in air at atmosphericpressure, but careful studies were conducted either byusing lower pressure (where the breakdown threshold isreduced), using alternate gases such as helium, or usinginitiators such as a collection of fine wires placed nearthe beam focus. These studies yielded some interestingevidence of filamentary structures in the breakdown vol-ume. However, none of these studies produced the large,two-dimensional, filamentary regular arrays seen in thepresent experiments. Also, the present study differs sub-stantially from these studies in terms of time scales (3µs vs. 0.05-20 ms) as well as intensities (on the order of106 vs. 104 W/cm2) used for initiating and sustainingthe breakdown plasma. A number of theoretical studieshave also been reported to explain the structures such as“snakes” and “chains” that have been observed in high-pressure microwave breakdown research [11–13]. Theseexplanations emphasize the role of plasma kinetics andinstabilities. In this study, we explain the array as devel-oping from a sequential process of electromagnetic wavediffraction. Incident microwave power is diffracted fromplasma filaments formed early in the breakdown process.As the technology of high power millimeter wavesources matures and their applications broaden, break-down will inevitably be an issue in transporting througha gas, or on the surface of a window through which suchradiation is transmitted. This was our motivation forconducting volume and surface breakdown experimentsin this relatively unexplored frequency band.Figure 1 shows the experimental setup for the break-down studies. The 110 GHz gyrotron, operating at 962rf diodew/o BDrf diodew/ BDPhoto-diodesDiode Signals [a.u.] Time [µs]  0 1 2 3 4 5 6 7 -1 0 1 2 3 4 5 6  FIG. 2: Traces of rf diode and two photodiodes for avolume breakdown shot, and an rf diode trace when nobreakdown occurs.2 mm (c)y, Bz, kBeam(d)(b)Beam(a)z, kx, E2 mm FIG. 3: Typical time-integrated volume breakdownplasma images in (a) E-plane and (b)-(d) H-plane. (cam-era exposure time >> pulse width)kV beam voltage and 40 A beam current, can produce1.5 MW of output power in 3 µs pulses [14]. The TE22,6mode generated in the resonator is then converted to aquasi-Gaussian output beam by a mode converter insidethe gyrotron. The beam is linearly polarized in the x -axis as defined in Fig. 1, and has a waist at the outputgyrotron window with a beam radius of 1.5 cm. Thisbeam is further focused by a high density polyethylene(HDPE) lens with 14 cm focal length to a waist size ofabout 4 mm. For surface breakdown studies, a dielec-tric sample is placed at the beam waist, as shown in Fig.1; it is absent for volume breakdown experiments. Thetested dielectric materials included Lexan (polycarbon-ate), HDPE, and Teflon. No clear dependence on mate-rials was found. An rf diode measures the transmittedbeam power. Two fast photodiodes are positioned forstudies of the breakdown delay time as well as the prop-agation direction and speed of the ionization front. Anrf diode trace for a breakdown shot is shown in Fig. 2,along with the corresponding two photodiode signals anda transmitted power pulse without breakdown.Figure 3 shows a typical volume breakdown for an in-cident 3 µs pulse with a field strength above 4.4 MV/m(2.5 MW/cm2 in power density). Figure 3(a) shows the1 mm(b) (c) (d) (e) (a) BeamMetalPostFIG. 4: (color online) (a) Volume breakdown image in H-plane with a crescent region enclosing a curved plasmastructure of interest. E-field magnitude with (b) 1, (c) 2,and (d) 3 filaments modeled as metal posts (white circles)in simulations. (e) Superposition of (d) on top of (a).time-integrated plasma image in the E-plane. The sen-sor of the digital camera was exposed during the entirepulse width. The observed plasma appears to consist ofmultiple filamentary plasma columns, instead of a singlediffuse plasma. These filaments are parallel to the elec-tric field. The filamentary array structure is more clearlyconfirmed in the H-plane (a plane perpendicular to theE-plane). Figures 3(b)-(d) show H-plane breakdown im-ages from three different shots.The remarkable feature of Figs. 3(b) - (d) is the obser-vation of a regular, two-dimensional array of filaments.The filaments are found to have a typical radius of 0.1to 0.2 mm, much smaller than the free space wavelengthλ (= 2.73 mm) of the 110 GHz radiation. The averageaxial distance between adjacent filament centers on thebeam axis is 0.76 mm with 10% standard deviation overmany shots.The same phenomenon as reported in this Letter wasobserved consistently in the experiments separated overmany months with widely different experimental condi-tions such as air humidity as well as using a focusing lensmade of Teflon with 18 cm focal length. Raising the fieldstrength effectively up to 6 MV/m by using reflectionfrom dielectric slabs also produced arrays of the samecharacteristics with slightly reduced regularity.Figure 4(a) shows one of the typical filamentary arraypatterns seen in volume breakdown. The curved fila-mentary structure enclosed in the crescent region of Fig.4(a) resembles the pattern of a wave diffracting aroundan obstacle. The obstacle would be the three rightmostfilaments in this case. We believe that these patterns canbe analyzed to show that diffraction plays an important3role in the development of the filamentary array.From a series of measurements using the two axiallydisplaced photodiodes, we have determined that break-down is typically initiated in the focal region and propa-gates backwards towards the gyrotron power source. InFig. 4(a), this would mean that breakdown first occursat the point farthest to the right in the figure, and thendevelops backwards (to the left) with increasing time.Note that every experimental photograph presented inthis Letter shows the entire emission history of an evolv-ing array, and hence does not tell how large an emissivepart of the array is at any one moment. For instance,in Fig. 2, the signal from the downstream photodiode(the earlier of the two photodiode signals) starts to de-cay even before the incident power starts to decay. Thisimplies that the filaments generated downstream at anearly stage extinguish before the end of the pulse. Thisis probably due to the microwaves being cut off or ab-sorbed by new upstream filaments, and unable to sustainthe old downstream filaments.We observe experimentally that the initial breakdownproduces a single filament that appears as a single break-down spot in an H-plane view. We then use a theoreticalmodel, based on the HFSS code [15] and, as shown inFigs. 4(b)-(d), to predict the subsequent development ofthe filamentary array. In the model, a Gaussian beam of∼4 mm waist radius is excited in a box with radiationboundaries and a symmetry boundary. We assume thatthe initial filament develops a highly conductive plasma.The filament is thus modeled as a metal post, which isshown as a white circle in Fig. 4(b). This simulationshows that diffraction around the post results in a maxi-mum field occurring approximately a quarter wavelength(= 0.68 mm) upstream of the metal post. Then, the nextbreakdown should occur near this maximum position.Assuming that breakdown does occur at that location,a second metal post will develop, as shown in Fig. 4(c).Diffraction will again result in a maximum field positionroughly λ/4 upstream of the second metal post. Simi-larly, at the next stage, a third metal post is included inthe simulation as shown in Fig. 4(d). From Fig. 4(d), wealso see that diffraction will result in arcs of high inten-sity upstream from the three metal posts. The presenceof filaments along such arcs is observed experimentallyand can be clearly seen in Fig. 3(d) and Fig. 4(a). Fig-ure 4(e) shows Fig. 4(a) with Fig. 4(d) overlaid on top.The curved structure falls well within the enhanced fieldregion. Hence, we believe the enhanced field effect due toscattering plays a major role in determining where newfilaments are created. In addition, the measured averageaxial filament distance of a quarter wavelength stronglycorroborates this hypothesis. This distance also makessense, considering that a field maximum is generated ata distance λ/4 upstream from a flat metal surface whena plane wave is reflected from that surface.Filamentary arrays are also found to occur in surfacebreakdown. Surface breakdown has been studied by plac-ing dielectric slabs at the beam waist formed by the fo-y, Bz, k2 mm BeamLexanslabFIG. 5: Typical time-integrated surface breakdownplasma image in H-plane with a beam impinging on a di-electric surface. (camera exposure time >> pulse width)2 mm (a) (b) (c) (d) (e) Beamy, Bz, kFIG. 6: (color online) Simulations of a filament propa-gation scenario in a surface breakdown, showing E-fieldmagnitude when (a) 1, (b) 2, (c) 4, and (d) 16 filamentsexist. (e) Expansion of Fig. 5 with (d) overlaid on top.Scale of (a) also applies to (b)-(e).cusing lens. Figure 5 shows a typical H-plane breakdownimage with the beam incident on a tilted Lexan slab.The purpose of tilting is to minimize the reflected powerpropagating back to the gyrotron. Similar results wereobtained for a range of different tilt angles. The photo-graph of Fig. 5 clearly demonstrates a highly periodicarray of plasma filaments. There are usually two distinctbreakdown regions with any tilt angle. In the region veryclose to the surface, the filaments (white circles in the H-plane) are arranged in layers parallel to the surface. Inthe region far from the surface, the filaments are alignedwith the beam axis, as clearly seen in Fig. 5. In betweenthese regions, the filaments show a transition from onealignment to the other and there may be dark spots, thatis, filaments missing from the array.In the far region, the average axial distance (along thebeam axis) between adjacent filament centers is deter-mined to be 0.74±0.06 mm, which is slightly larger thanλ/4, as we have also observed in volume breakdown. Fur-thermore, this distance has no dependence on the tilt an-4gle of the slab. Thus, it appears that the presence of adielectric surface has little effect on the mechanisms lead-ing to the filamentary array aligned along the beam axisin the region far from the surface.To explain the pattern near the surface in Fig. 5, wehave carried out a series of simulations of the surfacebreakdown as shown in Fig. 6. In this model, a Lexanslab of 1.1 mm thickness is placed at the beam waist andtilted from the plane perpendicular to the beam by 30 de-grees. Figure 6(a) assumes that one filament has alreadydeveloped at the maximum field position created by re-flection from the slab. As in the case of volume break-down, the adjacent filament lies within the strongest fieldcontour. Then, in Fig. 6(b), this new filament is modeledas another post. The resultant field distribution againfits with the locations of other nearby filaments. Figure6(c) shows a possible next stage, after the appearance oftwo new posts (or filaments). Note that, as well as themost strongly enhanced region right near the existing fil-aments, there are always other enhanced field regions farfrom the dielectric surface, each of which is roughly a halfwavelength apart. Since these regions are not as strong asthe near-surface region, development of filaments in thefar region requires more time. Eventually, however, a fil-ament appears in the far region and often leaves a darkgap between the near-surface breakdown region and thefar breakdown region as evident in Fig. 5. From thispoint on, the presence of the surface has little effect onthe total field distribution, which is supported by the ex-perimental fact that any tilt angle resulted in the sametype of filamentary array with roughly identical spacing.A hypothetical later stage of the breakdown propagationwith 16 existing filaments is simulated and shown in Fig.6(d), and with the overlaid plasma image in Fig. 6(e).The contours show excellent agreement with the subse-quent filament positions.The model in Figs. 4 and 6 was based on an arrayof perfectly conducting metal posts, but a plasma fila-ment will have a finite conductivity. The simulationshave been repeated for posts with a range of conductiv-ity values. We find that if the conductivity is less than∼100 S/m, the reflected power is too weak to cause thelarge field enhancement seen in Figs. 4 and 6. A con-ductivity of 100 S/m or higher is expected if the plasmahas an electron density ne of 1016 cm−3 with an electrontemperature Te of 0.1 to 1 eV. These values for ne andTe have not been verified in the present experiments butare thought to be reasonable. The reflectivity of the fil-aments was also directly verified in the experiments. Anrf diode detector was placed so as to measure power re-flected from the breakdown region. A substantial amountof reflected power was detected whenever a breakdownoccurred. Therefore, the filaments must have sufficientconductivity to be reflecting.In summary, we have observed highly periodic, large,two-dimensional arrays of filamentary plasmas in atmo-spheric air breakdown with a MW-class, 110 GHz, lin-early polarized Gaussian beam. The structured plasmasappear both in volume breakdown and surface break-down. The most likely cause of the development of sucha structure is sequential development of filaments by fieldenhancement approximately a quarter wavelength up-stream of each existing filament. We have shown thatthe total field distribution due to scattering from fila-ments modeled as metal posts in the HFSS simulationscorroborates well with the hypothesis above. The ob-served filamentary arrays look like photonic crystal struc-tures. They may prove useful in guiding or manipulatingbeams of millimeter wave radiation.This research was supported by the US AFOSRMURI04 program on the Nano-Physics of High CurrentDensity Cathodes and Breakdown. The authors thankC. D. Joye for his help in imaging, and A. Neuber, G.Nusinovich and P. Woskov for helpful discussions.REFERENCES[1] A. D. MacDonald, Microwave Breakdown in Gases(Wiley, New York, 1966).[2] Y. P. Raizer, Gas Discharge Physics (Springer,Berlin, 1991).[3] A. V. Gurevich, N. D. Borisov, and G. M. Mi-likh, Physics of Microwave Discharges (Gordon andBreach, Amsterdam, 1997).[4] N. Kroll and K. M. Watson, Phys. Rev. A 5, 1883(1972).[5] Y. P. Raizer, Laser-induced Discharge Phenomena(Consultants Bureau, New York, 1977).[6] A. Neuber, L. Laurent, Y. Y. Lau, and H.Krompholz, Windows and RF Breakdown, editedby R. J. Barker and E. Schamiloglu, High-PowerMicrowave Sources and Technologies, pp. 325-375(IEEE Press, Piscataway, NJ, 2001).[7] Yu. Ya. Brodskii et al., Sov. Phys. JETP 57, 989(1983).[8] A. L. Vikharev et al., Sov. Phys. JETP 67, 724(1988).[9] A. L. Vikharev et al., Sov. J. Plasma Phys. 18, 554(1992).[10] V. G. Brovkin and Yu. F. Kolesnichenko, J. MoscowPhys. Soc. 5, 23 (1995).[11] V. B. Gil’denburg and A. V. Kim, Sov. J. PlasmaPhys. 6, 496 (1980).[12] O. A. Sinkevich and V. E. Sosnin, High Temperature39, 180 (2001).[13] P. V. Vedenin and N. A. Popov, JETP 96, 40 (2003).[14] E. M. Choi et al., Fusion Sci. 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Observation of Large Arrays of Plasma Filaments in Air Breakdown by 1.5 MW, 110 GHz Gyrotron Pulses

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Observation of Large Arrays of Plasma Filaments in Air Breakdown by 1.5 MW, 110 GHz Gyrotron Pulses

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