Millimeter wave scattering and diffraction in 110 GHz air breakdown plasma

Transcription

1 PSFC/JA Millimeter wave scattering and diffraction in 11 GHz air breakdown lasma Cook, A.M., Hummelt, J.S., Shairo, M.A, Temkin, R.J. February, 213 Plasma Science and Fusion Center Massachusetts Institute of Technology Cambridge MA 2139 USA This work was suorted by AFOSR, Grant No. FA Reroduction, translation, ublication, use and disosal, in whole or in art, by or for the United States government is ermitted.

2 Millimeter Wave Scattering and Diffraction in 11 GHz Air Breakdown Plasma Alan M. Cook *, Jason S. Hummelt, Michael A. Shairo, and Richard J. Temkin Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA 2139 Abstract: We resent measurements of the scattering, reflection, absortion, and transmission of a 1.5 MW, 11 GHz quasiotical gyrotron beam by a self-induced air breakdown lasma. The breakdown forms a eriodic array of lasma filaments roagating toward the gyrotron source and oriented arallel to the incident electric field olarization. For an incident intensity of 3 MW/cm 2, calorimetric measurements show that about 45% of the microwave beam ower is absorbed by the lasma, 1% is reflected directly backward, and the remainder is diffracted into a wide angular distribution. The far-field diffraction atterns, which show distinctive sidelobes, have been measured as a function of time during the discharge. The measured atterns show good agreement with a simle model of absortion by the lasma as the lasma varies in size during the breakdown ulse. We also observe that aroximately 1 times more ower is scattered in the direction erendicular to the filaments than arallel. Key words: gyrotron, millimeter wave, air breakdown, quasiotical * Present address: Naval Research Laboratory, Code 684, 4555 Overlook Ave SW, Washington, D.C., 2375 Corresonding author, hummelt@mit.edu 1

3 I. Introduction Megawatt-level millimeter wave beams, roduced by gyrotrons, have alications in key areas of lasma science. For examle, tokamak devices rely on absortion of millimeter waves via electron cyclotron resonance to heat lasma for fusion [1, 2]. In that case, a quasiotical beam is formed to coule the radiation into a low-loss overmoded transmission line [3, 4]. Other alications, such as lasma roulsion [5] or stand-off detection, [6] use a beam focused into atmosheric air at high intensity to create an electric discharge lasma. When a quasiotical beam is intense enough to induce an electrical discharge in a gas, the resulting lasma distorts the beam [7, 8]. Reflection of the incident beam from the lasma can cause the ionization front to move back toward the microwave source, as the combined intensity of the incident and reflected waves initiates a new discharge [9]. Because the incident beam is near the intensity threshold for breakdown, this small amount of reflected ower raises the field in front of the filament above threshold and is resonsible for the unique formation of filaments at λ/4 wavelengths [1, 11].Scattering and diffraction of the beam occur when the beam is strongly focused, such that the discharge lasma is smaller than or comarable in size to the focused beam. Recent exeriments have studied air breakdown lasmas roduced by a focused Gaussian beam of 11 GHz millimeter waves. [12, 13] The megawatt-level beam roduces a eriodic array of lasma filaments that roagates in discrete stes toward the microwave source, due to reflection of the incident beam by the lasma. In this aer, we resent measurements of the scattering, reflection, transmission, and absortion of the beam by the breakdown lasma. We observe that significant fractions of the incident 2

4 beam ower are transmitted and absorbed, and most of the remaining ower is scattered at large angles to the beam direction. The aer is organized as follows. Section II describes the exerimental setu and the raw data collected. Section III resents a simle lasma absortion model to describe the far-field diffraction attern and the ower balance observed at different times in the lasma lifetime. Section IV discusses the conclusions of this study. II. Exeriment The exerimental setu is illustrated in Fig. 1(a). A linearly-olarized Gaussian millimeter wave beam is generated by a 1.5 MW, 11 GHz gyrotron oscillator, oerated at eak ower levels in the range 8-9 kw [14]. The beam is focused to a small sot (1/e sot radius w ~ 4 mm) by a high-density olyethylene lens, reaching a high enough intensity to cause breakdown at atmosheric ressure (eak intensity ~ 3 MW/cm 2 ). A radiofrequency (rf) diode detector mounted on a rotating arm is ointed at the breakdown and moved through a large range of angles, observing microwave ower that is transmitted and scattered by the lasma. The diode is fed by an oen-ended WR8 rectangular waveguide. A variable attenuator is used in conjunction with the diode to rovide -3 db of dynamic range relative to the eak incident beam intensity. A calorimeter is used for absolute-scale measurements of the average transmitted and scattered ower, allowing the absorbed ower to be estimated. From the diode measurements it is determined that aroximately 1% of the incident eak ower is reflected into a backward cone of ±7º 3

5 Figure 1. (color online) (a) Exerimental setu. (b) Time-integrated grayscale hoto of lasma in yz lane. (c) Time-integrated hoto of lasma in xz lane. Fig. 1(b) is a time-integrated hotograh of the breakdown in the yz lane, showing the tos of the lasma filaments oriented along the electric field olarization. Fig 1(c) is a hotograh in the xz lane, showing a side view of the filaments. Angular intensity distributions of scattered and transmitted ower are measured in yz (erendicular to filaments) and xz (arallel to filaments). The oening of the rectangular waveguide connected to the diode detector is oriented with the broad wall dimension always erendicular to the E field olarization. To enable the xz-lane measurements, an extra mirror is added to the setu to rotate the incident olarization by 9 degrees. 4

6 Fig. 2(a) shows examles of the ower waveforms measured by the diode before the beam focal lane (incident ower) and downstream of the breakdown lasma (transmitted ower) on the beam axis. The start of the breakdown is measured as a distinct erturbation in the diode waveform, e.g. estimated at 2.5 μs for the waveform in Fig. 2(a) [15]. Fig. 2(b) shows tyical diode waveforms measured at various angles in the yz lane. The temoral structure of the eaks and dis in the waveform deends on the observation angle. At smaller angles, 1 deg., the transmitted ower decreases monotonically in time similar to the on-axis case. At larger angles, 1-45 deg., a high or low ower level is measured deending on the time during the ulse, and is very reeatable at a fixed angle. At angles 45 deg., the eak signals are weaker by ~2 db and the temoral structure varied significantly shot-to-shot. The reeatability of the waveforms at angles 45 deg. allows us to comile the ower levels measured at a given time value into an angular intensity distribution. We thus measure the far-field diffraction attern of the beam transmitted through the lasma by recording the diode signal levels measured between 4 deg. at a fixed time after the start of the breakdown. Fig. 3 comares the measured angular distributions in the yz and xz lanes, 1 µs into the breakdown. The angular distribution measured without the lasma is shown for reference. The symmetric side lobes of a diffraction attern are clearly seen at aroximately ±2 degrees in the yz lane measurement with lasma resent (Fig. 3(a)). Near zero degrees, the transmitted intensity is reduced by db relative to the incident beam. Figure 3(b) shows the same measurement in the xz lane; the side lobe structure is much less distinct than in the yz lane 5

7 Figure 2. (color online) (a) Measured incident ower (dashed black line) waveform comared with transmitted ower measured at y = deg (solid blue line). Breakdown starts at 2.5 μs. (b) Power waveforms measured by diode laced at y = 1 17 deg. 6

8 Figure 3. (color online) Angular intensity distribution (black circles) measured in (a) yz lane and (b) xz lane, relative to eak incident beam intensity, 1 s after breakdown. Solid blue line shows Gaussian beam intensity distribution measured with no breakdown lasma. 7

9 The scattered ower is measured by scanning the diode at large angles, -4 to -17 degrees. The detected waveform exhibits multile eaks in time, as shown in Fig. 2b. Because the temoral structure of the scattered ower varies shot-to-shot, the shot-to-shot average of the eak signal value during the entire breakdown event was recorded at each angle. Fig. 4 shows the result of this measurement in the yz and xz lanes. The detected ower level in the yz lane is ~5-1 db above that in the xz lane. The eak scattered ower in the yz lane occurs near -1 degrees, and is -15 db below eak beam intensity. In the xz lane, a minimum scattered ower level of -3 db occurs near -7 degrees. The reflected ower level, measured nearly straight backward at -17 degrees, is aroximately -22 db below eak intensity. From the measurement of the reflected ower, we estimate that a total of about 1% of the incident ower is reflected directly back towards the source. A calorimeter is laced in different ositions next to the breakdown lasma, to measure the absolute ower levels averaged over the entire ulse. The full beam average ower incident to the breakdown region, measured before the focal lane, is 2.6±.1 W for a 3 μs gyrotron ulse (.87 MW eak ower) at a reetition rate of one ulse er second. Placing the calorimeter directly downstream of the breakdown, subtending an angle of 9 degrees, we measure an average transmitted ower of 1.2±.1 W, which is 46% of the incident ower. Placed at 9 degrees to the beam direction and facing the lasma (Fig. 1a),.1 W is observed scattered in the yz lane and.1 W scattered in the xz lane; this 1 db difference is consistent with the diode measurements of instantaneous scattered ower in Fig. 4. The calorimeter measurements rovide order-ofmagnitude confirmation of the ~2 db relative intensity difference between the eak 8

10 transmitted beam (Fig. 3) and the scattered ower (Fig. 4). From all of these measurements, we then estimate that about 46% of the ower is transmitted into the forward direction; about 9% of the ower is scattered in the transverse direction and about 1% is reflected directly back towards the source. The missing ower, amounting to about 45% of the incident ower, is absorbed. Figure 4. (color online) Peak scattered ower measured in yz (red circles) and xz (black diamonds), relative to eak incident beam intensity, as a function of angle. III. Absortion-Diffraction Model We use a simlified lasma model to calculate the main features of the instantaneous far-field diffraction attern of the gyrotron beam assing through the breakdown lasma. The lasma region is modeled as a cylinder oriented along the z axis, with length L and radius r determined exerimentally by fast-gated hotograhy, as shown in Fig. 5. Within the cylinder, the lasma density distribution is modeled as uniform in z and 2 2 Gaussian in r as given by the exression n( r, z) n ex( r / r ). n is taken to be 9

11 .1 c n, where n c m e = 4 x 1 21 m -3 is the critical density including collisions at f = 11 GHz, where 5.31 e 9 [Torr] is the collision frequency in Hz at a ressure. This value of n is consistent with values derived in more detailed theories [16, 17] and will be found to give reasonable agreement for our simlified model. This simlification effectively relaces the density distribution of a closely-saced grou of lasma filament structures with an assumed average density distribution, in order to estimate the total wave absortion near the beam center. Because the lasma radius is less than the beam radius, attenuation of the microwave beam by absortion distorts the beam field distribution in a non-uniform way. The distorted field distribution is calculated at the downstream end of the lasma by considering the lasma comlex ermittivity, and a Fraunhofer integral is used to find the far-field angular intensity attern at the measurement osition. For simlicity, we assume for this calculation that the lasma is cylindrically symmetric. We comare the results of this 1D calculation with measurements of the diffraction attern in the yz lane, which was more readily measured than that in the xz-lane (Section II). 1

12 Figure 5. (a) Diagram of lasma absortion model, showing Gaussian beam enveloe (dashed line) and lasma cylinder. The beam roagates in the z direction. The small axes show the radial lasma density distribution inside the cylinder. (b) Fast-gated images taken in the yz lane using 1 ns shutter, at 15 ns, 3 ns, 1 s, and 2 s after the beginning of breakdown. The measured values of r and L are shown to the right. The amlitude of the incident microwave beam before assing through the aroximately cylindrical lasma is given by 2 2 A ( r, z) E ex( r / ) (1) w where w z w ( 1 2) (2) z z 2 / (3) w 11

13 Since the waist size w 4 mm, z =18 mm and z L, and we may use w w (1). Assuming a cold, collisional lasma, the dielectric constant in the lasma is in Eq n 1 (1 i ) (4) n c where n n( r) ex r 2 / r 2 r r r r (5) is the cylindrical lasma density rofile. Using the above exression, the amlitude of the microwave beam after assing through the lasma is given by the exression B( r, L ) A ( r)ex A ( r)ex ikl ikl 1 n n c (1 i ) r r r r (6) where k 2 / is the free-sace wavenumber of the millimeter waves. Figure 6 shows the radial microwave amlitude B r, L ) for the various values of r and L which ( corresonds to the hysical dimensions of the lasma at 15 ns, 3 ns, 1 μs, and 2 μs. 12

14 Figure 6. Radial microwave amlitude B r, L ) for a) r =1.4 mm and L =1 mm, b) ( r =1.9 mm and L =5 mm, c) r =4.3 mm and L =4 mm, and d) r =5.7 mm and L =3 mm corresonding to the hysical dimensions of the lasma at 15 ns, 3 ns, 1 μs, and 2 μs, resectively. In the case where both n/ 1 and ( n / nc) 2 1, Eq. (4) takes on the simlified form n c c 13

15 A ( r)ex B( r, L ) A ( r)ex ikl ikl 1 ex - kl 2 n c nc r r r r which is in general true for all of the values of n, r, and L considered in this aer. The far-field diffraction attern of the beam exiting the lasma is calculated by the Fourier transform of the radial microwave amlitude B r, L ), ( 1 F( r, z) B r L J krr z krdr z (, ) ( / ) (7) At a distance z >> r from the lasma, the angle is given by q = r/z. The final form of the angular intensity attern at distance z, relative to the eak beam intensity at r =, is given by B( r) J k r rdr ( ) F( ). (8) B( r) rdr Figure 7 shows the measured and calculated angular intensity atterns (~ F 2 (θ)) of the beam transmitted through the lasma, at different times during the breakdown. At each time, the values of the lasma dimensions r and L were taken from Fig. 5; At earlier times (15 ns and 3 ns) the effective radius of the lasma is small, and the far field diffraction attern exhibits a wide central eak and a single side lobe in the range of the measurement. At later times, when the size of the lasma is large, the central eak narrows and more side lobes are observed. The data show good overall agreement with the calculated diffraction atterns. There is excellent quantitative agreement in the shae and relative amlitude of the central eak of the diffraction atterns and the ositions of 14

16 the first minima at each time. There is good agreement in the ositions of the subsequent minima. Figure 7. (color online) Measured far-field diffraction atterns (circles) of beam assing through lasma at (a) 15 ns, (b) 3 ns, (c) 1 s, and (d) 2 s after the beginning of breakdown. The calculated unerturbed diffracted Gaussian beam (dashed blue line) is shown for reference against the calculated diffraction attern from the absortiondiffraction model (solid red line). 15

17 IV. Discussion and Conclusions We resent the results of the measured scattered, reflected, absorbed and transmitted ower in air breakdown induced by an intense 11 GHz beam from a gyrotron. Measurements of the scattered ower show good agreement with a simlified model of a cylindrical collisional lasma with uniform lasma density along the axis and a Gaussian rofile transverse to the axis. While the far-field diffraction measurements do not resolve the sub-wavelength eriodic structure of the breakdown lasma, the filamentary geometry is manifested in the measured scattered ower. The scattered ower observed in the yz lane was aroximately 1 times that observed in the xz lane, indicating that the linearly olarized millimeter waves referentially scatter erendicular to the filament orientation and olarization direction xˆ. This may be due to the sub-wavelength lasma filaments acting as diole scattering sources, which has been studied reviously as a microwave diagnostic technique [18]. The ercentage of ower observed reflected backward is small. This is likely because the breakdown lasma subtends a limited ortion of the beam, < 5% by area. The amount of ower reflected (at ~ 17 deg) is seen to grow significantly at later times in the breakdown (1 2 s, Fig. 2(b)), when the transverse size of the lasma is larger. In addition, some of the reflected ower may be reabsorbed in filaments and filaments in the rocess of forming. Only a small ercentage reflection is needed to raise the electric field above the breakdown threshold, since the ionization frequency i in air deends on the incident field E as i E [19]. 16

18 These findings have imortant imlications for alications in which millimeter wave radiation scattered from air breakdown lasma is measured as a means of stand-off detection or characterization [2]. The beam olarization and lasma size may need to be considered when choosing detector lacement and designing the rf diagnostics. 17

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