Dipole antenna: Experiment/theory status

Timothy W. ChevalierUmran S. InanTimothy F. Bell

February 18, 2009

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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.

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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)

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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

´

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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

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Current Distributions for 100 m Antenna at L=2

Excitation frequency: f < fLHR Excitation frequency: f > fLHR

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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

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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)

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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

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LAPD Operating Environments

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LAPD Experiment Outline

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LAPD Experiment Outline

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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]?

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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

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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

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Simulation vs. Experiment

f/fce = 0.003

f/fce = 0.3

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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.

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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.

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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.