dipole antenna: experiment/theory status timothy w. chevalier umran s. inan timothy f. bell february...
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Dipole antenna: Experiment/theory status
Timothy W. ChevalierUmran S. InanTimothy F. Bell
February 18, 2009
2
Stanford MURI Tasks
Scientific Issues: The sheath surrounding an electric dipole antenna operating in a plasma has
a significant effect on the tuning properties.
Terminal impedance characteristics vary with applied voltage.
Active tuning may be needed.
Stanford has developed a general AIP code to determine sheath effects Stanford has developed a general AIP code to determine sheath effects on radiation process. on radiation process.
MURI Tasks: Validation of our AIP code by laboratory experiments using LAPD.
UCLA will provide time measurements of voltage, current and field patterns for dipole antennas to compare with Stanford model.
Locate sources of error in current model and identify means for improvement.
Perform LAPD experiments on magnetic loop antennas.
3
Cold Plasma Fluid Approximation
Fluid Description:
Generalized Ohms Law
Closure Assumption:
d~J ®dt
+º®~J ®=q®m®
³q®n®~E + ~J ®£ ~Bo
´
P =nkT = 0
@t(nm)+r ¢(nmu) = 0
@t(nmu) +r ¢(nmuu+P ) ¡ nq(E +u £ B) = 0
@t(P ) +r ¢(uP +Q) +fP ¢r (u) + c £ Pgsym =0
@t(Q) +r ¢(vQ +R)+fQ ¢r (u) + c £ Q ¡ P r ¢(P )1nm
gsym =0
Valid for transmitting antenna under small applied potentials (q<kT)
4
Finite Difference Time and Frequency Domain Techniques (FDTD/FDFD)
Time Domain (FDTD)
Computational Mesh:
FDTD Method: Time domain solution of Maxwell’s
equations. Wide spread use in EM community
Frequency Domain (FDFD)r £ ~H =
X
N
¾®~E +²oj ! ~E
r £ ~E = ¡ ¹ oj ! ~H
¾® = ²o! 2p (j ! I ¡ )¡ 1
=
0
@¡ º ¡ ! bz ! by! bz ¡ º ¡ ! bx¡ ! by ! bx ¡ º
1
A
Solves: Ax=B
r £ ~H =X
N
~J ®+²od~Edt
r £ ~E = ¡ ¹ od~Hdt
d~J ®dt
+º®~J ®=q®m®
³q®n®~E + ~J ®£ ~Bo
´
5
Simulation Setup – Perpendicular Antenna (Chevalier et. al. 2008)
Computational Domain: Antenna Properties Length: 100 m Diameter: 20 cm Orientation: Perpendicular to Bo
Position: Equatorial Plane
Plasma Properties Hydrogen Plasma Te ~ 0.2 eV
L=2 L=3N = 2x103 cm-3 N = 1x103 cm-3
fpe = 401 kHz fpe = 284 kHz
fce = 110 kHz fce = 33 kHz
6
Current Distributions for 100 m Antenna at L=2
Excitation frequency: f < fLHR Excitation frequency: f > fLHR
7
L=2 L=3
Simulation vs. Theory
[Wang and Bell., 1969,1970][Wang., 1970][Bell et. al., 2006]
Input Impedance FormulaPrevious Analytical Work
Zin =V(f )I (f ) =
(R ~E ¢dl)
f eed
(H ~H ¢dl)
f eed
8
Non-triangular Current Distributions
Plasma Frequency = 10 MHz
Plasma Frequency = 20 MHz
Antenna Length = 2 km
Antenna Length = 4 km
Dependence of current distribution on increase in plasma frequency and antenna length w.r.t L=2 operating conditions.
f=5kHz (f > fLHR)
9
Previous Laboratory Work
Laboratory experiments involving radiation patterns Stenzel [1976] and Amatucci et al. [2005] - Studies of whistler mode
radiation patterns of electric dipole and loop antennas in a laboratory setting.
Laboratory experiments performed in the area of sheath formation and impedance calculations Stenzel [1988] - Examined the plasma sheath resonance in a collisionless
laboratory plasma. Blackwell et al. [2005] and Walker et al. [2006] determined the sheath
thickness and terminal impedance of small spherical probes immersed in a laboratory plasma.
Blackwell et. al. [2007] and Blackwell et. al. [2007a] – Antenna input impedance measurements for spherical and dipole antennas.
Dipole antenna results for f>fce.
Large Plasma Device (LAPD) at UCLA
10
LAPD Operating Environments
11
LAPD Experiment Outline
12
LAPD Experiment Outline
13
Simulation Setup – Parallel Antenna
Computational Domain: Antenna Properties Length: 8 cm Diameter: 2.5 mm Gap separation: 2 mm Orientation: Parallel to Bo
Plasma Properties Helium Plasma Te ~ 0.5 eV Number density: 1012 cm-3
Magnetic Field: 200 GSimulation Properties Computational Space: 0.5 m x 0.5 m x 0.5 m Cell Size: 2 mm – 4 mm Truncated with Perfectly Matched Layer (PML) – Berenger, [1994].
Code validation for antenna – Chevalier et. al. [2008]?
14
Current Distributions for Frequencies in Vicinity of fLHR
Excitation frequency: f < fLHR Excitation frequency: f > fLHR
f/fce = 0.003 f/fce = 0.018
fLHR = f/fce = 0.012
15
Simulation vs. Theory
[Wang and Bell., 1969,1970][Wang., 1970][Bell et. al., 2006]
Analytical Work
Input Impedance Formula
Zin =V(f )I (f ) =
(¡R ~E ¢dl)
f eed
(H ~H ¢dl)
f eed
f/fce = 0.003
f/fce = 0.3
16
Simulation vs. Experiment
f/fce = 0.003
f/fce = 0.3
17
Next Steps
Determine source of disagreement between simulation and experiment Theory and simulation agree fairly well. Change simulation parameters to more accurately reflect
experiment design. Radiation pattern
Extract far field pattern from current distribution using Wang & Bell [1972].
Compare with UCLA LAPD. Finish LAPD experiment outline
Higher voltages – warm plasma effects important. Compare measurement of densities within sheath region with
electrostatic simulation results. Loop antennas.
18
References
Amatucci, W., D. Blackwell, D. Walker, G. Gatling, and G. Ganguli, Whistler wave propagation and whistler wave antenna radiation resistance measurements, IEEE Transactions on Plasma Science, 33 (2), 637–646, doi:10.1109/TPS.2005.844607, 2005.
Bell, T. F., U. S. Inan, and T. Chevalier (2006), Current distribution of a VLF electric dipole antenna in the plasmasphere, Radio Sci., 41, RS2009, doi:10.1029/2005RS003260. 1972.
J.-P. Berenger (1994) A Perfectly Matched Layer for the Absorption of Electromagnetic Waves, Journal of Computational Physics, vol. 114, no. 2, pp. 185–200.
Blackwell, D., D.Walker, and W. Amatucci, Measurement of absolute electron density with a plasma impedance probe, Review of Scientific Instruments, 76 (2), 023,503–023,506, 2005.
Chevalier, T.W. Inan, U.S. Bell, T.F., "Terminal Impedance and Antenna Current Distribution of a VLF Electric Dipole in the Inner Magnetosphere," Antennas and Propagation, IEEE Transactions on , vol.56, no.8, pp.2454-2468, Aug. 2008
David D. Blackwell, David N. Walker, Sarah J. Messer, and William E. Amatucci, Antenna impedance measurements in a magnetized plasma. I. Spherical antenna, Phys. Plasmas 14, 092105 (2007), DOI:10.1063/1.2779284
David D. Blackwell, David N. Walker, Sarah J. Messer, and William E. Amatucci, Antenna impedance measurements in a magnetized plasma. II. Dipole antenna, Phys. Plasmas 14, 092106 (2007), DOI:10.1063/1.2779285
Stenzel, R., Antenna radiation patterns in the whistler wave regime measured in a large laboratory plasma, Radio Science, 11, 1045–1056, 1976.
19
References (cont’d)
Stenzel, R. L., Instability of the sheath-plasma resonance, Phys. Rev. Lett., 60 (8), 704–707, 1988.
Walker, D., R. Fernsler, D. Blackwell, W. Amatucci, and S. Messer, On collisionless energy absorption in plasmas: theory and experiment in spherical geometry, Physics of Plasmas, 13 (3), 032108 1-9, 2006.
Wang, T., and T. Bell (1969), Radiation resistance of a short dipole immersed in a cold magnetoionic medium, Radio Science, 4, 167.
Wang, T., and T. Bell (1970), On VLF radiation resistance of an electric dipole in a cold magnetoplasma, Radio science, 5 (3), 605–10.
T. N.-C. Wang, (1970), Vlf input impedance characteristics of an electric antenna in a magnetoplasma, Ph.D. dissertation, Stanford University.
T. Wang and T. Bell, “VLF/ELF radiation patterns of arbitrarily oriented electric and magnetic dipoles in a cold lossless multicomponent magnetoplasma,” Journal of geophysical research, vol. 77, pp. 1174–89.
K. Yee, (1966) Numerical solution of initial boundary value problems involving Maxwells equations in isotropic media, IEEE transactions on antennas and propagation, vol. AP-14, no. 3, pp. 302–307.