Copyright© 1998, American Institute of Aeronautics and Astronautics, Inc.

AIAA-98-2567

PLASMA ANTENNAS: THEORETICAL AND EXPERIMENTAL CONSIDERATIONS

Larry L. Altgilbers, Ira Merritt*Phillip Tracyf

Yuri Tkach, Slava Tkach*

Abstract

One way to increase the directivity of anantenna is to increase its effective area. However, inmany applications this is not practical due torestrictions on size and mass. One possible antennathat may allow one to enhance the performance of theradiating device, without significantly changing itssize or mass, is a plasma antenna. The objectives ofthis paper are to examine the physics underlying thedevelopment of a pulsed plasma antenna and todemonstrate its feasibility through experimentation.This is accomplished by examining an explosivedriven plasma jet in an external magnetic field.

Introduction

There are three types of plasma antennas: 1)plasma dielectric antennas, 2) plasma hornantennas and 3) plasma mirror antennas1. Theplasma dielectric antenna consists of a plasma jet orcloud that has been generated within an externalmagnetic field that is used to constrain the plasma.The plasma horn antenna consists of a metal hornfilled with plasma. Both of these antennas are activeradiators. As the name suggests, the mirror plasmaantenna is a passive reflector.

Interest in plasma antennas can be traced backto the 1960s2. In order to verify experimentally thatplasma columns could be used to radiateelectromagnetic energy, Askar'yan and Raevskii2 usedhigh power lasers to generate optical breakdown inaerosol clouds comprised of powdered B4C ormicroscopic water droplets. The geometry of theplasma cloud and the properties of the plasmadepended on the technique used to focus the laserbeam and the properties of the laser. They studied thereflection of radio waves having a wavelength of

approximately 0.8 cm from a slab of aerosol and foundit to be a good reflector. They also found that plasmaantennas are complex entities and, as a result, that thedependence of its properties on the parameters of theradiated signal must be taken into account.

Askar'yan and Raevskii3 also investigated theproperties of a plasma filled horn antenna. Aschematic diagram of the plasma horn antenna ispresented in Fig. 1. The antenna was a circularwaveguide with a tapered horn. A prism was installedinside the waveguide at an angle to ensure totalinternal reflection of a laser beam. A pulsedneodymium laser with pulse duration of 30 ns andenergy per pulse of 6 J was used to initiateatmospheric breakdown and to form a plasma jet alongthe length of the axis of the antenna. In theexperiments, a hom with detector was used as thereceiver. A second horn antenna with detector wasdeployed at an angle of 15-deg relative to the axis ofthe transmitting horn antenna and the antennas wereconnected to a high-speed oscilloscope. By comparingthe amplitudes of the two receiving antennas, theefficiency of the plasma horn antenna could beestimated. Microwave radiation that drives the plasmahorn antenna propagates along the axis of the plasmajet. They observed a significant increase (byapproximately a factor of 3) in the intensity of 8-mmwavelength electromagnetic radiation detected by thereceiving waveguide antenna when the plasma wasformed from an aerosol. The duration of theamplification period exceeded the laser pulse lengthand lasted 50 usec.

Using an arrangement similar to that in Fig. 1,Kalpakov et al4 used a neodymium laser to create aplasma channel between two horn antennas with a 30-deg beam width. They observed an increase in theamplitude of the signal detected by the receive antenna

* AIAA Sr. Member, Advanced Technology Directorate, Missile Defense and Space Technology Center, U.S.Army Space and Missile Defense Command, P.O. Box 1500, Huntsville, AL, 35807.* Teledyne Brown Engineering, Huntsville, AL* Institute of Electromagnetic Research, Kharkov, Ukraine.

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for wavelengths of 3, 7.5, and 10 cm. The authorsthought that this phenomenon was due to thepropagation of E-type surface waves along thedistributed plasma.

The concept of using plasmas produced bylaser-guided electric discharges in the atmosphere wasfirst investigated in the US in 1973. Dwyer, Greig,and Perm5 conducted experiments with a plasmaantenna in the shape of a folded monopole antennathat consisted of a laser-guided electric dischargegenerated by a Marx bank. The authors investigatedthe efficiency of transmitting and receiving signals at112 MHz. The useful lifetime of the antenna variedfrom approximately 200 usec to 2000 usec and theexperiments demonstrated that these antennas haveefficiencies nearly as good as those of a referencefolded copper monopole antenna with the samedimensions. They also demonstrated that the plasmaantenna is not a significant noise source at 112 MHz.

These early experiments established thatplasma antennas are a viable option, and their massand size may meet requirements of particular specialapplications since they are simple, reliable, andcompact. At present, it appears that a plasma jetproduced by an explosive cartridge, if properlydesigned, is a suitable form of this antenna. Thechemical composition of the explosive must becarefully chosen to ensure that the antenna operates ina nonlinear mode so as to enrich its high-frequencyspectral output. Experiments have shown thatexplosive cartridges provide a jet of weakly ionizedhigh density plasma with a diameter that depends onthe diameter of the cartridge. In order to shape the jet,it is enclosed within a cylindrical insulating shield.The insulating shield determines the dimensions andthe electrodynamics of the jet and the wave modes thatare established hi the plasma, which in turn determinesthe properties of the radiated energy.

Theoretical Considerations

As far as it is known, no consistent andcomprehensive theory has been developed to describeactive plasma radiators. In Ref. 1, a semi-empiricalapproach used to analyze the radiated output of theplasma dielectric antenna. It was assumed that a tramof dipoles form along the axis of the plasma jet andthat these dipoles radiate like a linear phased array.The major findings of this study are that the radiatedenergy depends on the properties of the explosivesused and the external magnetic field.

To up-shift the frequency of the radiatedenergy and enhance the directivity of the antenna, it is

necessary to exploit the nonlinear properties of theplasma. If the plasma is operating in a non-linearmode, then high-frequency harmonics of the wavespropagating in the plasma can be excited. The higherthe number of harmomics that are initially excited hithe plasma by the antenna feed unit (the solenoid), themore efficient the antenna is.

An alternate approach would be to treat theantenna as a partially-filled plasma waveguide. Kralland Trivelpiece6 showed that surface waves wouldform on unmagnetized plasma columns hi a partiallyfilled cylindrical waveguide with perfectly conductingwalls (Fig. 2). Following Krall and Trivelpiece'sanalysis, the differential equations that describe thepropagating modes hi the waveguide are:

IV 2I vr

for 0 < r < a and

= o

for a < r < b, where(2)

^ 2 \d d \ #Vr =--—r — + -=•—=-.r dr dr r2 dO2

(3)

The waves associated with the solution of theseequations for Elz are called E modes and for Blz theyare called B modes. Even though both fields satisfythe same equations, they will have differenteigenmodes, since the boundary conditions at theplasma-vacuum interface and the wall-vacuuminterface will affect the two solutions in differentways. If the waves are azimuthally symmetric, the Eand B modes are not coupled at the plasma-vacuuminterface, but they are if the waves are not azimuthallysymmetric. The solution of these equations for the Emodes propagating at speeds less than the speed oflight is:

I0(r0a)K0(T0b) -(4)

Where

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CO

t =k —c (5)

The functions I0 and KO are the modified Bessel'sfunction of the first and second kind, respectively. IfEu is selected so that it is finite at r = 0, continuous atr = a, and zero at r = b and if B16 is continuous at r = a,then the dispersion relation for these waves is:

where the prime denotes differention with respect tothe argument of the function. When the frequency ofthe waves is much less than the plasma frequency, thewaves are nondispersive and propagate with a phasevelocity much less than the speed of light. But as thefrequency increases, the fields tend to concentrate atthe surface of the plasma column and propagate athigher velocities. These surface waves are travelingwaves on the plasma column that carries most of theenergy. Since then- fields do not penetrate appreciablyinto the plasma, the plasma, hi this case, behaves likean ordinary metal conductor. The ratio of Elz/EIroutside the plasma is small, and the propagating modeis similar to that of transverse electromagnetic wavespropagating along a coaxial line.

If the plasma is immersed hi an externalmagnetic field, the motion of the electrons becomesmuch more complicated, hi that they now undergoboth space-charge and cyclotron oscillations.Depending on the orientation of the electric fieldassociated with the space-charge oscillations, bothordinary and extraordinary waves may be excited. If itis assumed that the magnetic field has a finite valueand that the phase velocity of the space-charge wavesis much less than the velocity of light, then it issometimes possible to neglect the magnetic fieldassociated with the wave. Following the analysis ofKrall and Trivelpiece, the dispersion relation for theseconditions is:

(7)For waves to propagate, it is necessary that k2 > 0. Inaddition to the wave modes identified above, upper-hybrid wave modes and, like the unmagnetized plasma

in a partially filled waveguide, surface waves arepossible. The latter is true if the waveguide is partiallyfilled and has either a conducting or dielectricboundary. For surface waves to exist, there must be avacuum region between the plasma column and thewalls of the waveguide.

An alternate analysis is presented byAnishchenko7 in which he treats the plasma columngenerated by excimer lasers as an inductive slow-wavestructure (surface waves) with an impedance thatvaries along the length of the column. Theelectromagnetic wave propagating along the column ispartly radiated and partly reflected. Superposition ofthe radiation generated by step-like changes hi theimpedance along the column in the far-fielddetermines the directivity of the antenna.Anishchenko notes that a specific feature of thedirectivity diagram is the absence of side lobes, whichis typical of antennas with smoothly changing surfaceimpedance. There is a 15 dB decrease hi powerdensity at an angle of 10 deg off bore sight.

Plasma Dielectric Antennas

The plasma dielectric antenna consists of aplasma source and a current carrying solenoid (Fig. 2).The plasma can be generated hi many ways, but wewill focus on using a high explosive to create a plasmajet. When the high explosive is detonated, it createsan ionized shock front that propagates along the axisof the solenoid. The plasma is immersed in amagnetic field created by a pulse of electric currentflowing through the solenoid. As shown hi an earlierpaper1, the velocity of the shock wave and the degreeof ionization depend on the type and mass of explosiveused and the properties of the ambient gaseousmedium. One explanation of how these antennasradiate is that oscillations are set up hi the plasma,where each oscillation can be treated as a dipole.Treating the antenna as a series of dipoles, it wasshown that the plasma antenna, when compared to thesolenoidal coil, if it were assumed to be the antenna,would have greater directivity and could radiate higherfrequencies than the solenoidal coil.

Another possible mechanism is that surfacewaves on the plasma jet radiate. The radiatingefficiency of the surface waves depends on the abilityof the plasma to couple energy into the free space,which can be expressed hi terms of the "wavereflection factor", which depends on the phase velocityof the wave at the end of the antenna. Analysis of thedispersion equation shows that the phase velocityincreases as the radius of the plasma waveguide

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decreases. For example, the phase velocity of thewave will gradually increase from 0.6c to 0.9c, wherec is the speed of light in vacuum, as the radius of thewaveguide decreases from 150 mm to 120 mm. Thelength of the plasma antenna must be optimized so thatthe wave reflection factor is reduced to a minimumvalue and the antenna has the desired directivity. Theoptimized length probably needs to lie in the range of1.5-2.0 times the wavelength of the radiated energy.

Energy is coupled into the plasma from thesolenoid, when its magnetic field penetrates into theplasma and excites electric fields that accelerate theelectrons and nonlinear oscillations. There are twoways for exciting nonlinear oscillations: 1) by excitinghigh amplitude waves in the plasma and 2) bymodifying the composition of the plasma. The formercan be achieved by using a non-symmetric winding inthe solenoid, and the second by adding a ferromagneticmaterial such as iron. In order to excite the electricfield, the symmetry of the magnetic field may bedisrupted by inserting metal rods into the plasmastream.

EXPERIMENTAL RESULTS

Simple experiments have been conducted. Aplasma jet was generated in a cone-shaped hornantenna, which was coupled to a 10 cm wavelengthmicrowave source as shown in Fig. 1. Instead of theplasma jet being formed along the axis of the horn bya laser, it was generated by an explosive cartridge.The radiation pattern of the horn was studied, and itwas observed that the beam width of the radiatedsignal decreased when the plasma jet was introducedinto the horn, thus increasing its directivity. Theamount of decrease in the beam width of the radiatedsignal depended on the input power and the parametersof the plasma. In addition, the plasma gun proposed tobe used in the design presented in this paper was builtand successfully tested.

A schematic drawing of the plasma source forthe antenna is presented in Fig. 2. A 1-3 gram seededexplosive charge, which contained the followingconstituents - Fe, Pb, C, N, K, Cl, and O - was used tocreate the plasma. The plasma jet propagated adistance of 4000 mm in 1 msec and had a diameter of8 mm, a temperature of 3650 K, and estimated plasmadensity of 5 x 1019/cm3. The plasma temperature wasmeasured with an optical pyrometer that establishedthe surface temperature of the plasma by measuringthe optical radiation emitted. The measurement errorwas ±10-15%.

Assuming equilibrium conditions for theplasma jet, it is estimated that the free electron densitymay be about lO'Vcm3. This relatively low electrondensity is the result of the rapid attachment ofelectrons to Cl to form the negative ion, Cl".

To estimate the order of magnitude of theinitial oscillations excited in the plasma jet, assumethat the antenna feed unit, which drives theoscillations, is a solenoid with N turns that surroundsthe plasma jet. Variations in the magnetic flux withinthe solenoid induce fields in the plasma along withperturbations of the electron density. Using Maxwell'sequations and letting I = 30 kA, ro = 1 GHz, coil radiusa = 1 cm, and the number of turns N = 5, then theelectron density perturbations are estimated to be:

(8)Comparing the magnitude of the perturbed andunperturbed electron densities, it can be inferred thatnonlinear processes do occur.

The above estimates deal with the magnitudeof the driving fields. Density oscillations, however,also depend on the wave mode. In the event of asymmetric mode, which contains the field componentsEe, H,, and Hz, it can be shown that the followingequality holds:

.*-!S.r ae = 0

(9)This equality is due to the electric field beingindependent of the angle in the symmetric case. Forperturbations to take place, the symmetry must bedistorted. The driving coil should lack symmetry withrespect to the radius, and this can be achieved byinserting ferrite rods between the spiral coil and theplasma jet.

CONCLUSIONS

Estimates show that low-temperature plasmajets can be used as plasma antennas. The density ofthe jet can reach values of 1 to 5 x 10" cm"3 and thetemperature 4000 deg K for plasmas with especiallyselected chemical compositions. If the oscillations inthe plasma are driven by magnetic fields, it is feasibleto achieve density fluctuations of 10" to 1012 cm"3.The magnitudes of these perturbations are sufficient todrive broad spectral oscillations in the plasma and theradiated frequency can range from 0.1 to 6.0 GHz.

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REFERENCES1. Tracy, P., L. Altgilbers, I. Merritt, and M. Brown."Plasma Dielectric Antennas", to be published.2. Askar'yan, G.A. Letters of Journal ofExperimental and Theoretical Physics (JETF), Vol. 1,No. 18, 1965.3. Askar'yan, G.A. Letters to Journal of TechnicalPhysics (JTF), Vol. 8, No. 18. 1982, p. 1131.4. Kolpakov, V.I. Letters to Journal of TechnicalPhysics (JTF), Vol. 17, No. 10, 1991, p. 67.5. Dwyer, T.J., J.R. Greig, D.P. Murphy, J.M. Perm,R.E. Pechacek, and M. Raleigh. "On the Feasibility ofUsing an Atmospheric Discharge Plasma as an RFAntenna", IEEE Transactions on Antennas andPropagation, Vol. AP-32, No. 2, 1984, pp. 141-146.6. Krall, N.A. and A.W. Trivelpiece. Principles ofPlasma Physics. San Francisco Press, Inc., SanFrancisco, 1986.7. Anishchenko, Yu.V. "Radiation Initiated by aSurface Wave Propagating along a Long PlasmaColumn with a Varying Impedance", Plasma PhysicsReports, Vol. 23, No. 12, 1997, pp.1001 - 1006.

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FIGURES

Figure 1. Experimental test setup for investigating plasma antenna. 1 - pulsed neodynium laser, 2 -microwave input, 3 - prism, 4 - laser beam, 5 - plasma jet, 6 - radiating horn, 7 - receiving horn, 8 - detector,9 - oscilloscope, and 10 - coupling window.

2 \3 \4 \5 \6 \7 \8

Figure 2. Diagram of a plasma antenna with an explosive cartridge as the plasma source. 1 - input wiresfrom power source, 2 - connectors, 3 - bridge wire, 4 - explosives, 5 - cartridge housing, 6 - low frequencysolenoid, 7. high frequency solenoid, 8 - ferrite inserts, 9 - plasma jet, and 10 - cylindrical metal casing.

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