Antenna Impedance Measurements in a Magnetized Plasma. Part I: Spherical Antenna

Transcription

1 Naval Research Laboratory Washington, DC NRL/MR/ Antenna Imdan Measurements in a Magnetized Plasma. Part I: Spherical Antenna David D. Blackwell David N. Walker Sarah J. Messer William E. Amatucci Charged Particle Physics Branch Plasma Physics Division October 6, 2006 Approved or public release; distribution is unlimited.

2 Form Approved REPORT DOCUMENTATION PAGE OMB No Public reporting burden or this collection o inormation is estimated to average hour r response, including the time or reviewing instructions, searching existing data sours, gathering and maintaining the data needed, and completing and reviewing this collection o inormation. Send comments regarding this burden estimate or any other asct o this collection o inormation, including suggestions or reducing this burden to Department o Deense, Washington Headquarters Servis, Directorate or Inormation Orations and Reports ( ), 25 Jeerson Davis Highway, Suite 204, Arlington, VA Respondents should be aware that notwithstanding any other provision o law, no rson shall be subject to any nalty or ailing to comply with a collection o inormation i it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS.. REPORT DATE (DD-MM-YYYY) 2. REPORT TYPE 3. DATES COVERED (From - To) Memorandum Report 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Antenna Imdan Measurements in a Magnetized Plasma. Part I: Spherical Antenna 6. AUTHOR(S) David D. Blackwell, David N. Walker, Sarah J. Messer, and William E. Amatucci 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 5d. PROJECT NUMBER e. TASK NUMBER 5. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Naval Research Laboratory 4555 Overlook Avenue, SW Washington, DC PERFORMING ORGANIZATION REPORT NUMBER NRL/MR/ SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES) Oi o Naval Research 875 North Randolph Street Arlington, VA DISTRIBUTION / AVAILABILITY STATEMENT 0. SPONSOR / MONITOR S ACRONYM(S). SPONSOR / MONITOR S REPORT NUMBER(S) ONR Approved or public release; distribution is unlimited. 3. SUPPLEMENTARY NOTES 4. ABSTRACT The input imdan o a metal sphere immersed in a magnetized plasma is measured with a network analyzer at requencies up to GHz. The exriments were done in the Spa Physics Simulation Chamber at the Naval Research Laboratory. The hot-ilament argon plasma was varied between weakly (w < w ) and strongly (w > w ) magnetized plasma with electron densities in the range cm -3. It is observed that the lower-requency resonan o the imdan characteristic previously associated with series sheath resonan w sh in the unmagnetized plasma occurs at a hybrid sheath requency o w r = w sh + kw, with k a constant 0.5 < k <. As seen in previous exriments, the higher requency resonan associated with the electron plasma requency w in the unmagnetized plasma is relocated to the upr hybrid requency w 2 uh = w w. As with the unmagnetized plasma, the maximum power deposition occurs at the lower requency resonan w r. 5. SUBJECT TERMS Plasma diagnostics Plasmas Antennas 6. SECURITY CLASSIFICATION OF: a. REPORT b. ABSTRACT c. THIS PAGE Unclassiied Unclassiied Unclassiied 7. LIMITATION OF ABSTRACT i 8. NUMBER OF PAGES UL 6 9a. NAME OF RESPONSIBLE PERSON David Blackwell 9b. TELEPHONE NUMBER (include area code) (202) Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std. Z39.8

3 I. INTRODUCTION Antenna imdan in a plasma has been an active area o research or many years, with the largest amount o work, both theoretical and exrimental, conducted beore 980 []-[8]. Most o this research was or spacrat and rocket mounted plasma diagnostics or electron density measurements in the ionosphere. Rently, there has been renewed interest in this subject as advans in measurement and computer technology have allowed scientists to collect more accurate readings and model antennas more realistically than was previously possible [9]-[8]. The use o imdan measurements or spa physics research is still a airly active ield, but there have also been new applications; or example, plasma electron density measurements under exrimental conditions that make it diicult to get Langmuir probe readings, such as plasma thrusters [] and prossing plasmas [4]. There is also a desire to understand antenna-plasma coupling better with the application o developing improved methods or plasma wave launching and detection in ionospheric and spa environments [5]. Finally, there are basic plasma physics issues that can be uncovered with antenna imdan measurements [7]. It is such applications that motivate our current work with antenna imdan measurements. As most previous exrimental results have been rom sounding rocket applications, the data is limited to plasma conditions ound in the ionosphere. There are ar ewer controlled laboratory exriments where changes in the imdan curve can be tracked over a large range o requencies. There are also only limited exrimental results in strongly magnetized plasmas where the cyclotron requency is greater than the plasma requency (ω > ω ). And we could ind no exrimental or theoretical results where the antenna size transitions rom short, meaning signiicantly smaller than wavelengths excted in the plasma, to long, meaning the antenna is on the order o the plasma wavelength. In the irst part o this two part par, we will examine antenna imdan under such variations in exrimental parameters or an antenna with spherical geometry, which is a natural extension o previous exriments done in unmagnetized plasmas [3] [6]. In part II, we will present results rom a simple dipole antenna. Manuscript approved August 28, 2006.

4 II. THEORY A sphere o radius R susnded in a cold, uniorm, collisionless, unmagnetized plasma has an imdan given by [] with Z(ω) = + jωc sh jω4πǫ 0 ǫ p R () ǫ p = ω2 ω 2 (2) where ω is the electron plasma requency, and C sh the sheath capacitan which or an ion sheath o thickness s can be approximated by ( ) R + s C sh = 4πǫ 0 R s ( ) R + s = C 0, (3) s deining C 0 = 4πǫ 0 R as the vacuum capacitan o the sphere. Expression has two resonant requencies, known as the parallel resonan at ω = ω, and the series resonan at s ω = ω sh = ω R + 2s With no magnetic ield present, a good approximation or the ion sheath thickness s is s 5λ d, with λ d the Debye length. When a magnetic ield is introdud, two things hapn: the sheath around the sphere may become deormed such that the expression or C sh changes, and the expression or ǫ p will be expression 2 in the direction parallel to the magnetic ield, while rndicular to the ield we have ω2 (4) ǫ =, (5) ω 2 ω 2 with ω the electron cyclotron requency. In an early par by Craword [2], the argument was made that or smaller magnetic ields, such that the electron gyroradius ρ e is large compared to the sheath thickness, no correction is nessary or the expression or the sheath capacitan C sh. This condition is met or ρ e = ω >>. In our exriment we λ d ω sometimes orate with ω ω, but as a starting point will use the unmagnetized sheath resonan or comparison as well. Substituting 5 into changes the parallel resonan to the upr hybrid requency ω 2 uh = ω 2 + ω 2, while the series resonan becomes ω 2 r = ω 2 sh + ω 2 (6) 2

5 where ω sh is the unmagnetized series resonan. This result is only valid or a probe with only rndicular electric ields with resct to to the magnetic ield, i.e., a planar probe. A spherical probe involves scaling the coordinate system such that the point charge potential is written as V = q 4πǫ 0 ǫp ǫ x 2 + ǫ p ǫ y 2 + ǫ z 2 (7) Equation 7 can then be integrated over the sura o a sphere to get a value or the imdan. This was done by Balmain[5], and the expression or imdan, including the sheath, is with Z = jωc sh + m = jωc 0 ǫ m ln ǫ p ǫ ( ) + m m (8) III. EXPERIMENTAL ARRANGEMENT The imdan probe used is a 2-cm diameter aluminum sphere mounted on a length o 0.25 in. 50-Ω semi rigid coax. Measurement o the sphere imdan has been described in detail in previous pars [3][6], and in this exriment little has been changed. The complex relection coeicient Γ is measured with a network analyzer and the imdan calculated according to Z = Z 0 + Γ Γ where Z 0 is the anayler internal imdan o 50 Ω. The diiculty in this measurement lies in eliminating the eects o the cabling and body o the probe rom equation 9. This is done by building a matched load, an electrical short, and on termination and calibrating out the unwanted stray capacitan and cabling such that we get Γ values o 0, -, and, resctively. The probe is positioned near the nter o the Spa Physics Simulation Chamber plasma. The chamber is a 2-m diameter, 5-m long vacuum vessel surrounded by ive 3-m diameter magnet coils. Improvements have been made to the plasma sour in that the -m square ilament array now consists o 72 shorter ilaments connected in parallel to a power supply capable o supplying up to 300 A. Extra ilaments were subsequently added around the (9) 3

6 rimeter o this array to create as uniorm a density proile as possible. Additional diagnostics are a heated Langmuir probe, an emissive probe, and magnetic probes, although the latter were not used in these measurements. The chamber is illed to a pressure o p 0 4 Torr Argon. A weakly ionized (n ) plasma is created by the heated ilaments biased at -45 V with resct to a grounded grid. The magnetic ield can be raised to a maximum value o 44 Gauss. Typical electron and ion temratures are typically T e 0.5 ev and T i 0.05 ev. A drawing o the exrimental setup is shown in igure. IV. RESULTS Figure 2 shows the magnitude and phase o the sphere imdan versus requency as the ratio o ω /ω decreases rom a actor o three to approximateley /4. For comparison purposes, we have normalized the magnitudes to unity and normalized the requency axes versus the resctive values o ω. Also shown are theoretical plots corresponding to equation 8. The conditions chosen here are or ω comparable to ω, with plasma density cm 3. The eect o the magnetic ield can be observed as a lattening o the magnitude and increase in phase at requencies below the lower resonan. As the magnetic ield is urther increased, both the upr and lower resonans move to the right on the requency axis due to the integration o ω into both resonan requencies. Figure 3 shows exrimental and theoretical imdan characteristics at higher plasma density (n cm 3 ). The smaller ratio o ω to ω results in a wider distan between the two resonans; however, the eects o the magnetic ield are still apparent below the lower resonan. Again, there is very good agreement between measurements and calculations as the magnetic ield is changed. The sheath resonan requency ω sh can be calculated rom the plasma density according to equation 4. The lower resonan ound exrimentally, normalized by this requency, is plotted against ω in igure 4. The exllent linear it shows that the resonan requency can be expressed as ωr 2 = ωsh 2 + κω2, with κ This agrees with previous results [res] in which the lower resona was bounded by ω sh < ω r < ωsh 2 + ω2. Thus, a simple substitution o ǫ or ǫ p in equation 8 which gives the result κ = is actually a airly good approximation o the probe behavior. The relection coeicient Γ is plotted vs requency or the various plasma conditions in 4

7 the exriment in igure 5. A sharp dip can be seen at the lower series resonan under all conditions including ω r > ω. V. CONCLUSIONS Exrimental measurements o imdan or a spherical antenna in a magnetized plasma have been made over a large range o plasma conditions. Previous exriments have been limited to plasmas with ω sh < ω < ω ; this exriment extends that work by considering larger magnetic ields (ω > ω ). By doing this we were able to make observations regarding the nature o the probe imdan which heretoore have not been published. It is observed that the low-requency series resonan, reerred to as the sheath resonan or the unmagnetized plasma, becomes a hybrid sheath resonan with requency ωr 2 = ωsh 2 + κω2. The parallel resonan which or the unmagnetized plasma ocurred at ω is shited to the upr hybrid requency ω uh. With a suiciently strong magnetic ield, both resonans can actually be higher than the plasma requency. The power deposition into the plasma is still maximum at this lower resonan regardless o where it occurs. Thus, while the probe in the unmagnetized plasma always had maximum power into the plasma below the plasma requency, the magnetized plasma allows or this to occur at any requency between the unmagnetized series sheath resonan and the upr hybrid requency, including ω > ω. Also, we can see that using the unmagnetized sheath capacitan in the expression or imdan is a good approximation even when ω ω. These results are directly applicable to plasma conditions ound at higher altitudes in the ionosphere, and also in high density, high magnetic ield prossing discharges such as helicons. [] Harp RS, Craword FW, Journal O Applied Physics 35 (2): 3436 (964) [2] Craword FW, J. Appl. Phys 36 (0) 342, (965) [3] Dote T, Ichimiya T, Journal o Applied Physics 36 (6): 866 (965) [4] Oya H, Obayashi T, Report o Ionosphere and Spa Research in Japan 20 (2): 99 (966) [5] Balmain, K. IEEE Transactions on Antennas and Propagation vol.ap-4, no.3 : 402 (966) [6] Uramoto J Physics O Fluids 3 (3): 657 (970) 5

8 [7] T. H. Y. Yeung and J. Sayers, Proc. Phys. Soc. London, Sect. B 70, 663 (957) [8] K. Takayama, H. Ikegami, and S. Miyazaki. Phys. Rev. Lett., 5, 238 (960) [9] Jensen MD, Baker KD, Journal o Spacrat and Rockets 29 (): 9 (992) [0] Steigies CT, Block D, Hirt M, Hipp B, Piel A, Grygoczuk J, Journal o Physics D 33 (4): 405 (2000) [] Bilen, S.G., Haas, J.M., Gulczinski, F.S. Gallimore, A.D., Letoutchaia, J.N., AIAA , 35th Joint Propulsion Coneren, Los Angeles, CA, June 999. [2] Kim J, Seong D, Lim J, Chung K, Applied Physics Letters 83 (23): 4725 (2003) [3] Blackwell,D.D., Walker, D.N., Amatucci, W.E., Review o Scientiic Instruments vol.76, no.2 : , (2005) [4] Kokura H, Nakamura K, Ghanashev IP, Sugai H, Japanese Journal o Applied Physics 38 (9A): 5262 (999) [5] Ward J., Swenson C., Furse C., IEEE Transactions on Antennas and Propagation vol.53, no.8, pt.2 : 27-8, Aug [6] Blackwell, D.D., Walker, D.N., Messer, S.J., Amatucci, W.E. Physics o Plasmas vol.2, no.9 : , (2005) [7] Walker, D.N.; Fernsler, R.F.; Blackwell, D.D.; et al. Physics o Plasmas vol.3, no.3 : , March 2006 [8] Ku VPT, Annaratone BM, Allen JE, Journal o Applied Physics 84 (2): 6536 (998) [9] Amatucci et. al., Journal o Geophysical Research 03 (A6): 7 (998) 6

9 LIST OF FIGURES Figure : Sketch o the Spa Plasma Simulation Chamber used or the antenna imdan measurements. Figure 2: Exrimental (solid lines) and theoretical (dashed lines) plots o (a) magnitude and (b) phase o the imdan o a 2 cm sphere in a plasma vs requency with electron density density n cm 3 as the magnetic ield is increased. Figure 3: Exrimental (solid lines) and theoretical (dashed lines) plots o (a) magnitude and (b) phase in a plasma vs requency with electron density n cm 3 as the magnetic ield is increased. Figure 4: The lower resonan ω r taken rom the data in igures 2 and 3. The quantity ω2 r ω 2 sh is plotted vs ω2 ω 2 sh to demonstrate the linear relationship according to ω 2 r = ω 2 sh + κω2. The quantity ω sh is the sheath resonan requency calculated according to equation 4 which does not include magnetic ield eects. Figure 5: Relection coeicient o the spherical antenna vs requency under the lower density (n cm 3 ) condition with increasing magnetic ield showing a minimum at the lower resonan requency ω r. This minimum corresponds to a maximum energy depostion into the plasma. 7

10 igure 8

11 0. 0. Z ( ) 0.0 E E E E / igure 2 (a)

12 Z (rad) / igure 2 (b)

13 0. 0. Z ( ) 0.0 E-3 E-4 E E-3. E E-3 E E-3 / 2 9 igure 3 (a)

14 .5.5 Z (rad) / igure 3 (b)

15 00 r 2 / sh / sh 2 igure 4

16 / igure 5