We report the observation of two-dimensional plasma filamentary arrays with more than 100 elements generated during breakdown of air at atmospheric pressure by a focused Gaussian beam from a 1.5-MW, 110-GHz gyrotron operating in 3-mu s pulses. Each element is a plasma filament elongated in the electric field direction and regularly spaced about one-quarter wavelength apart in the plane perpendicular to the electric field. The development of the array is explained as a result of diffraction of the beam around the filaments, leading to the sequential generation of high intensity spots, at which new filaments are created, about a quarter wavelength upstream from each existing filament. Electromagnetic wave simulations corroborate this explanation and show very good correlation to the observed pattern of filaments.open424

A. Neuber

A. D. MacDonald

A. L. Vikharev

A. V. Gurevich

E. M. Choi

E. M. Choi

I. Mastovsky

J. R. Sirigiri

M. A. Shapiro

R. J. Temkin

V. B. Gil’denburg

V. G. Brovkin

Y. P. Raizer

Yoshiteru Hidaka

Yu. Ya. Brodskii

Physical Review Letters

Crossref

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

Hidaka, Yoshiteru

Choi, EunMi

Mastovsky, I.

Shapiro, M. A.

Sirigiri, J. R.

Temkin, R. J.

ScholarWorks@UNIST

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(Received 5 July 2007; published 24 January 2008)We report the observation of two-dimensional plasma filamentary arrays with more than 100 elementsgenerated during breakdown of air at atmospheric pressure by a focused Gaussian beam from a 1.5-MW,110-GHz gyrotron operating in 3-s pulses. Each element is a plasma filament elongated in the electricfield direction and regularly spaced about one-quarter wavelength apart in the plane perpendicular to theelectric field. The development of the array is explained as a result of diffraction of the beam around thefilaments, leading to the sequential generation of high intensity spots, at which new filaments are created,about a quarter wavelength upstream from each existing filament. Electromagnetic wave simulationscorroborate this explanation and show very good correlation to the observed pattern of filaments.DOI: 10.1103/PhysRevLett.100.035003 PACS numbers: 52.80.Pi, 52.38.Hb, 52.40.Db, 52.77.FvWe report the observation of large, two-dimensionalregular arrays of plasma filaments generated during break-down of air at atmospheric pressure by a focused Gaussianbeam from a 1.5-MW 110-GHz gyrotron with 3-s pulselength. These filamentary arrays consist of a large numberof regularly spaced elements, more than 100 in some cases.They are observed both in volume breakdown and in break-down at surfaces. The filamentary arrays are notably differ-ent from the well-known filamentation observed in laser-induced plasmas. Laser generated filaments are alignedalong the direction of propagation, while the filamentsobserved here are perpendicular to the direction of propa-gation. Each filament is aligned parallel to the direction ofthe 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 ofimportant issues in breakdown at surfaces [6]. However,due to the scarcity of powerful sources in the millimeterwavelength range, there have been relatively few studieson 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 near thebeam focus. These studies yielded some interesting evi-dence of filamentary structures in the breakdown volume.However, none of these studies produced the large, two-dimensional, filamentary regular arrays seen in the presentexperiments. Also, the present study differs substantiallyfrom these studies in terms of time scales (3 s vs 0.05–20 ms) as well as intensities (on the order of 106 vs104 W=cm2) used for initiating and sustaining the break-down plasma. A number of theoretical studies have alsobeen reported to explain the structures such as ‘‘snakes’’and ‘‘chains’’ that have been observed in high-pressuremicrowave breakdown research [11–13]. These explana-tions emphasize the role of plasma kinetics and instabil-ities. In this study, we explain the array as developing froma sequential process of electromagnetic wave diffraction.Incident microwave power is diffracted from plasma fila-ments formed early in the breakdown process.As the technology of high power millimeter wavesources matures and their applications broaden, breakdownwill inevitably be an issue in transporting through a gas, oron the surface of a window through which such radiation istransmitted. This was our motivation for conducting vol-ume and surface breakdown experiments in this relativelyunexplored frequency band.Figure 1 shows the experimental setup for the break-down studies. The 110 GHz gyrotron, operating at 96-kVbeam voltage and 40-A beam current, can produce 1.5 MWof output power in 3-s pulses [14]. The TE22;6 modeFIG. 1. Schematic of air breakdown experiments. Experimentswere conducted with volume and (as shown) dielectric surfacebreakdown.PRL 100, 035003 (2008) P H Y S I C A L R E V I E W L E T T E R S week ending25 JANUARY 20080031-9007=08=100(3)=035003(4) 035003-1 © 2008 The American Physical Societygenerated in the resonator is then converted to a quasi-Gaussian output beam by a mode converter inside thegyrotron. The beam is linearly polarized in the x-axis asdefined in Fig. 1 and has a waist at the output gyrotronwindow with a beam radius of 1.5 cm. This beam is furtherfocused by a high density polyethylene (HDPE) lens with14-cm focal length to a waist size of about 4 mm. Forsurface breakdown studies, a dielectric sample is placed atthe beam waist, as shown in Fig. 1; it is absent for volumebreakdown experiments. The tested dielectric materialsincluded Lexan (polycarbonate), HDPE, and Teflon. Noclear dependence on materials was found. An rf diodemeasures the transmitted beam power. Two fast photodi-odes are positioned for studies of the breakdown delay timeas well as the propagation direction and speed of theionization front. An rf diode trace for a breakdown shotis shown in Fig. 2, along with the corresponding twophotodiode signals and a transmitted power pulse withoutbreakdown.Figure 3 shows a typical volume breakdown for anincident 3-s pulse with a field strength above4:4 MV=m (2:5 MW=cm2 in power density). Figure 3(a)shows the time-integrated plasma image in the E plane.The sensor of the digital camera was exposed during theentire pulse width. The observed plasma appears to consistof multiple filamentary plasma columns, instead of a singlediffuse plasma. These filaments are parallel to the electricfield. The filamentary array structure is more clearly con-firmed in the H plane (a plane perpendicular to the Eplane). Figures 3(b)–3(d) show H plane breakdown im-ages from three different shots.The remarkable feature of Figs. 3(b)–3(d) is the obser-vation of a regular, two-dimensional array of filaments.The filaments are found to have a typical radius of 0.1 to0.2 mm, much smaller than the free space wavelength ( 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 phenomenon of an array of filaments as reported inthis Letter was found to be reproducible in experimentalruns with different conditions, such as humidity and tem-perature, conducted over a period of many months. Thearrays were reproduced when lenses of different focallength were used. The arrays were also observed whenthe field strength was raised up to 6 MV=m by usingreflection from dielectric slabs. These results lead us tobelieve that the phenomenon of an array of filaments is acharacteristic effect of gas breakdown with high-frequencymicrowave radiation.Figure 4(a) shows one of the typical filamentary arraypatterns seen in volume breakdown. The curved filamen-tary structure enclosed in the crescent region of Fig. 4(a)resembles the pattern of a wave diffracting around anobstacle. The obstacle would be the three rightmost fila-ments in this case. We believe that these patterns can beanalyzed to show that diffraction plays an important role inthe 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 toward the gyrotron power source. InFig. 4(a), this would mean that breakdown first occurs atthe point farthest to the right in the figure and then developsbackwards (to the left) with increasing time.Note that every experimental photograph presented inthis Letter shows the entire emission history of an evolvingarray and hence does not tell how large an emissive part ofthe array is at any one moment. For instance, in Fig. 2, thesignal from the downstream photodiode (the earlier of thetwo photodiode signals) starts to decay even before theincident power starts to decay. This implies that the fila-ments generated downstream at an early stage extinguishbefore the end of the pulse. This is probably due to themicrowaves being cut off or absorbed by new upstreamfilaments, and unable to sustain the old downstreamfilaments.µ FIG. 2 (color online). Traces of rf diode and two photodiodesfor a volume breakdown shot, and an rf diode trace when nobreakdown occurs.FIG. 3. Typical time-integrated volume breakdown plasmaimages in (a) E plane and (b)–(d) H plane (camera exposuretime  pulse width).PRL 100, 035003 (2008) P H Y S I C A L R E V I E W L E T T E R S week ending25 JANUARY 2008035003-2We 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)–4(d), to predict the subsequent developmentof the filamentary array. In the model, a Gaussian beamof 4-mm waist radius is excited in a box with radiationboundaries and a symmetry boundary. We assume that theinitial filament develops a highly conductive plasma. Thefilament is thus modeled as a perfectly conducting metalpost, which is shown as a white circle in Fig. 4(b). Thissimulation shows that diffraction around the post results ina maximum field occurring approximately a quarter wave-length (  0:68 mm) upstream of the metal post. Then, thenext breakdown should occur near this maximum position.Assuming that breakdown does occur at that location, asecond metal post will develop, as shown in Fig. 4(c).Diffraction will again result in a maximum field positionroughly =4 upstream of the second metal post. Similarly,at the next stage, a third metal post is included in thesimulation as shown in Fig. 4(d). From Fig. 4(d), we alsosee that diffraction will result in arcs of high intensityupstream from the three metal posts. The presence offilaments along such arcs is observed experimentally andcan be clearly seen in Figs. 3(d) and 4(a). Figure 4(e) showsFig. 4(a) with Fig. 4(d) overlaid on top. The curved struc-ture falls well within the enhanced field region. Hence, webelieve the enhanced field effect due to scattering plays amajor role in determining where new filaments are created.In addition, the measured average axial filament distanceof a quarter wavelength strongly corroborates this hypothe-sis. This distance also makes sense, considering that a fieldmaximum is generated at a distance =4 upstream from aflat metal surface when a plane wave is reflected from thatsurface.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 focus-ing lens. Figure 5 shows a typical H plane breakdownimage with the beam incident on a tilted Lexan slab. Thepurpose of tilting is to minimize the reflected power prop-agating back to the gyrotron. Similar results were obtainedfor a range of different tilt angles. The photograph of Fig. 5clearly demonstrates a highly periodic array of plasmafilaments. There are usually two distinct breakdown re-gions with any tilt angle. In the region very close to thesurface, the filaments (white circles in the H plane) arearranged in layers parallel to the surface. In the region farfrom the surface, the filaments are aligned with the beamaxis, as clearly seen in Fig. 5. In between these regions, thefilaments show a transition from one alignment to the otherand there may be dark spots, that is, filaments missing fromthe 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 largerthan =4, as we have also observed in volume breakdown.Furthermore, this distance has no dependence on the tiltangle 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 axis inthe region far from the surface.To explain the pattern near the surface in Fig. 5, we havecarried out a series of simulations of the surface breakdownas shown in Fig. 6. In this model, a Lexan slab of 1.1-mmthickness is placed at the beam waist and tilted from theplane perpendicular to the beam by 30 degrees. Figure 6(a)assumes that one filament has already developed at themaximum field position created by reflection from the slab.As in the case of volume breakdown, the adjacent filamentlies within the strongest field contour. Then, in Fig. 6(b),FIG. 5. Typical time-integrated surface breakdown plasma im-age in the H plane with a beam impinging on a dielectric surface(camera exposure time  pulse width).FIG. 4 (color online). (a) Volume breakdown image in the Hplane with a crescent region enclosing a curved plasma structureof interest. E-field magnitude with (b) 1, (c) 2, and (d) 3filaments modeled as metal posts (white circles) in the simula-tions. (e) Superposition of (d) on top of (a).PRL 100, 035003 (2008) P H Y S I C A L R E V I E W L E T T E R S week ending25 JANUARY 2008035003-3this new filament is modeled as another post. The resultantfield distribution again fits with the locations of othernearby filaments. Figure 6(c) shows a possible next stage,after the appearance of two new posts (or filaments). Notethat, as well as the most strongly enhanced region rightnear the existing filaments, there are always other en-hanced field regions far from the dielectric surface, eachof which is roughly a half wavelength apart. Since theseregions are not as strong as the near-surface region, devel-opment of filaments in the far region requires more time.Eventually, however, a filament appears in the far regionand often leaves a dark gap between the near-surfacebreakdown region and the far breakdown region as evidentin Fig. 5. From this point on, the presence of the surface haslittle effect on the total field distribution, which is sup-ported by the experimental fact that any tilt angle resultedin the same type of filamentary array with roughly identicalspacing. A hypothetical later stage of the breakdownpropagation with 16 existing filaments is simulated andshown in Fig. 6(d), and with the overlaid plasma image inFig. 6(e). The contours show excellent agreement with thesubsequent filament positions.The model in Figs. 4 and 6 was based on an array ofperfectly conducting metal posts, but a plasma filamentwill have a finite conductivity. The simulations have beenrepeated for posts with a range of conductivity values. Wefind that a conductivity of the plasma filaments of about100 S=m is needed to produce total field profiles similar tothose shown in Figs. 4 and 6. The existence of reflectedpower from the filaments was directly verified using an rfdiode, but the magnitude of the reflected power was diffi-cult to estimate because the power is reflected over a widerange of angles.In summary, we have observed highly periodic, large,two-dimensional arrays of filamentary plasmas in atmos-pheric air breakdown with a MW-class, 110-GHz, linearlypolarized Gaussian beam. The structured plasmas appearboth in volume breakdown and surface breakdown. Themost likely cause of the development of such a structure issequential development of filaments by field enhancementapproximately a quarter wavelength upstream of each ex-isting filament. We have shown that the total field distri-bution due to scattering from filaments modeled as metalposts in the HFSS simulations corroborates well with thehypothesis above. The observed filamentary arrays looklike photonic crystal structures. They may prove useful inguiding or manipulating beams of millimeter waveradiation.This research was supported by the U.S. AFOSRMURI04 program on the Nano-Physics of High CurrentDensity Cathodes and Breakdown. The authors thank C. D.Joye and W. J. Mulligan for their help in the experiments,and A. Neuber, G. Nusinovich, and P. Woskov for helpfuldiscussions.[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. Milikh, Physicsof Microwave Discharges (Gordon and Breach,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, edited by R. J. Barker andE. Schamiloglu, High-Power Microwave Sources andTechnologies (IEEE Press, Piscataway, NJ, 2001),pp. 325–375.[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. Mosc. Phys.Soc. 5, 23 (1995).[11] V. B. Gil’denburg and A. V. Kim, Sov. J. Plasma Phys. 6,496 (1980).[12] O. A. Sinkevich and V. E. Sosnin, High Temp. 39, 180(2001).[13] P. V. Vedenin and N. A. Popov, JETP 96, 40 (2003).[14] E. M. Choi et al., Fusion Sci. Technol. 52, 334 (2007).[15] High Frequency Structure Simulator, www.hfss.com,Ansoft Corporation, Pittsburgh, PA, USA.FIG. 6 (color online). Simulations of a filament propagationscenario in a surface breakdown, showing E-field magnitudewhen (a) 1, (b) 2, (c) 4, and (d) 16 filaments exist. (e) Expansionof Fig. 5 with (d) overlaid on top. Scale of (a) also applies to (b)–(e).PRL 100, 035003 (2008) P H Y S I C A L R E V I E W L E T T E R S week ending25 JANUARY 2008035003-4

Observation of large arrays of plasma filaments in air breakdown by 1.5-MW 110-GHz gyrotron pulses

Observation of large arrays of plasma filaments in air breakdown by 1.5-MW 110-GHz gyrotron pulses

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