Plasma and a New Antenna

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May 18, 2009

Contents

1 Introduction to Plasma Physics 2

1.1 Definition of a plasma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Plasma Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Waves in a plasma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Plasma Antennae 5

2.1 Passive elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Active elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3 Why use Plasma antennae? . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

A Appendix 10

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1 Introduction to Plasma Physics

1.1 Definition of a plasma

A simple definition of a plasma is a gas that consists of charged and neutral particles[5].However if we consider the Saha equation:

ni

nn 2.4 1015

T 3/2

nieUi/kBT (1)

This equation gives a ratio of the density of ionized particles (ni) to that of neutral particles(nn) as a function of temperature (T ) and the ionization energy of the atom (Ui), where kBis the Boltzmann constant. This equation shows that as the temperature is increased neutralparticles will separate into ions, and the higher the temperature the larger the number ofions. Using the simple definition of a plasma this means that any gas at a finite temperatureshould be considered a plasma. According to this many gases that are not considered plasmasshould be. Since most gases will contain ions, there needs to be a definition of plasmas thattakes into account the relative number of ions and neutral particles and how they interact.To do this we can introduce parameters for the definition of plasmas.

1.2 Plasma Parameters

Figure 1: Example of how Debye shielding works[5].

To come up with a more descriptive definition of a plasma we can consider what happensif we place a charged sphere into an ionic mixture. Particles of opposite charge will build uparound the sphere to neutralize it, this is called Debye shielding, figure 1, and is a propertythat needs to be found in a gas for it to be classified as a plasma[5]. Now if we considerparticles at a finite temperature, hence they have thermal motion, there will be an exchange

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of particles to and from this shield where the electric field is too weak to overcome thekinetic energy of the ions. The approximate thickness of this cloud where exchange ofparticles occurs is called the Debye length, D. The Debye length can be expressed in termsof the kinetic energy of the electrons (the electron temperature, Te)[5].

D

(kBTe

4pinie2

)1/2(2)

We can now define a requirement that for a plasma the Debye length is much less than thesmallest dimension, L, of the total system[5].

For the Debye shield to be valid statistically there is a requirement that the cloudconsists of a large number of particles. This gives the second criterion for a plasma: Thetotal number of particles in the Debye shield has to be much larger than 1[5].

A third and final requirement for a gas of ionized atoms to be classified as a plasma isthat the number of collisions between electrons and neutral particles are rare compared toelectron-electron collisions[5]. With these three parameters we can now determine if a gassesproperties will be dominated by collisions of particles, as in a normal gas, or long rangeelectromagnetic interactions, as in a plasma.

1.3 Waves in a plasma

Waves in plasma can be separated into two distinct types: electron modes and ion modes[9].In the case that the velocity of the electrons is comparable or larger than the ions and thewave propagates as electron density variations (electron modes). To calculate these modesthe ion mass can be considered infinite compared to the electrons and therefore acts as astationary background charge. The second type of modes can be found by assuming the elec-trons mass is infinitely small when compared to the ions, hence the electrons can redistributeinstantaneously. In this case the wave propagates as variations in ion density. More complexmode types exist but will not be considered through this report. The electron modes are themodes that will be consider when looking at electromagnetic-wave/plasma interactions.

The most fundamental oscillatory behaviour to look at is called the plasma frequency(p). When a disturbance displaces the electrons and ions relative to each other the coulombforce pulls the electrons back towards the ions. The rapid oscillations of the electrons to cor-

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rect these disturbances give rise to waves in a plasma at a specific frequency. The equation[9]:

p =

nee2

0me(3)

can be used to calculate the plasma frequency for a plasma where electron modes dominate.Where e is the charge of an electron, me is the mass of an electron and 0 is the permeabilityof free space. Since the plasma frequency depends on the electron density, it can be manip-ulated by varying the amount of ionized gas.

An antenna is a device used to control the propagation of electromagnetic (EM) waves.This means that what happens as an EM wave crosses a free-space/plasma boundary isimportant when considering using a plasma as a component in antennas. The simplest caseis when no external magnetic field is applied. The complex dielectric constant for a plasmacan be written as[9]

r = 12p

( i)(4)

where is the frequency of a time dependant (eit) EM wave and is the frequency ofelectron collisions in the plasma. With freedom to select any arbitrary axis we can set anincident EM plane wave to propagate along the x-axis

E = Eeikx (5)

Looking at the case when the electron temperature is low then the electron collisions are low( 0) and the propagation constant k is then given by[9]

k = k0

1

2p

2(6)

where k0 is the propagation constant in free space. There are three cases to consider for EMwaves with this propagation constant: If the frequency of the incident wave is greater thanthe plasma frequency the propagation constant is real leading to a propagating EM wave. Inthe second case the incident wave has a lower frequency than the plasma frequency resultingin a decaying wave, known as an evanescent wave, in the plasma. The final case is when thefrequency of the incident wave is equal to the plasma frequency, this is called the criticalfrequency and is the boundary between a propagating wave and an evanescent wave. Theposition & motion of the electrons in the plasma can couple to these EM fields and vice versa.

Another thing to consider with an incident EM wave is whether it will transmit through orbe reflected by the plasma. To predict which behaviour will occur the reflection coefficientis of use. The absolute value of the reflection coefficient can be written in terms of theimpedance of the plasma, , an the impedance of free space, 0[9].

|| =

0 + 0 (7)

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(a) active element[6] (b) passive element[6]

Figure 2: Example of a active and passive element using plasma.

the impedance of a plasma can be calculated using the formula[9]:

=

0

0r(8)

2 Plasma Antennae

Conventional antennae utilize metal to guide the movement of charges to generate an oscil-lating electromagnetic field of a specific pattern. These antennae can also be used to convertan oscillating electromagnetic field to an electrical current. Plasma antennas are antennaethat work around microwave and radio wave frequencies, and use a plasma in place of ametal to facilitate the movement of charges.

To use a plasma as an antenna there are many technical considerations that must firstbe considered. To control the pattern of the radiation emitted by a plasma, the containmentshape and plasma density can be used. To act as an antenna the plasma needs to take ona specific spatial shape. The easiest way to create a plasma in a specific shape is to confinea noble gas in a glass tube, the gas can then be be ionized by various methods to create aplasma. The methods used include electrical discharge, lasers and heating.

When constructing an antenna there are passive elements that are used to redirect theEM waves and there are active elements that are used to convert the EM wave into anelectrical signal. Plasma can be used to replace the metal components in both types ofelements, figure 2.

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2.1 Passive elements

In an antenna the passive elements are the components, such as reflectors, used to redirectthe electromagnetic waves towards the active elements (the section used to convert the elec-tromagnetic waves into an electrical signal signal and vice versa). In the previous section thereflection coefficient was derived for an incident EM wave at a free-space/plasma boundary.By tuning the properties of the plasma, such as density of electrons and velocity, it can bemade to have high reflectivity below the plasma frequency.

To create a reflecting element it is as simple as using sheets of plasma in the same manneras a sheet of metal in a conventional antenna, figure 3. Approaching the reflector as a mirror,with ray tracing there will be a defined surface where the incident ray is reflected, in thecase of a plasma this surface is called the critical surface. For plasma reflectors to be aviable option the critical surface needs to be reproducible and consistent over the timesinvolved in transmission and reception.

Figure 3: Example of a reflector sheet constructed from multiple discharge tubes[6].

The Naval research laboratory in Washington D.C. has performed experiments to char-acterize the capabilities of plasma reflectors in the microwave spectrum [7]. To generatethe plasma they used a low pressure gas excited using an anode and cathode. Their resultsshowed that when the gas sheet was ionized a detector behind it no longer received a signalwhile a detector placed to detect reflected beams would then receive a signal. They foundthat their method of ionizing the gas had a reproducible critical surface that was notsensitive to fluctuations in the current and voltage of the power supply. The final resultsshowed a plasma reflector that could reflect waves with frequencies up to 10GHz, that could

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be switched on/off in under 10s was achievable, figure [7].

2.2 Active elements

A plasma cannot transmit EM waves below the plasma frequency, this means that it canonly transmit EM waves above the plasma frequency. The dispersion relation for thesetransmitted waves are 2 = 2p + k

2c2. By controlling the electron density and the collisionrate of electrons the plasma frequency can be tuned and the operating frequency of a plasmaantenna can be adjusted. There are three main methods for implementing plasma antennae:electrode excitation, surface wave excitation and laser excitation.

Figure 4: A loop plasma antenna that uses two electrodes to excite the gas[6].

Electrode excitation is one of the more cumbersome methods for creating the plasmain an antenna. A tube containing a noble gas requires two or more electrodes to ionizethe gas and create the plasma, figure 4. This type of antenna commonly employs a loopconfiguration. By using multiple electrodes, this type of antenna can be made to work ondifferent bands by changing which electrodes the voltage is applied across, figure 5.

The previous method has two main disadvantages. It requires the two electrodes to beplaced across the region of gas that needs to be ionized. The second disadvantage is thenoise that is present compared to a metallic antenna, figure 6. To overcome these problemsthe gas can be excited using surface waves. At the plasma frequency a wave mode exists that

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Figure 5: A configurable antenna design using multiple electrodes to excite different plasmapaths [8].

propagates along the boundary of a plasma-dielectric interface. It has been demonstratedthat these modes can be excited using RF signals. These waves cause heating that can beused to establish a plasma column that will act like a metal cylinder that can be used as adipole antenna. This method has a similar noise spectrum to a metallic antenna and muchless than the multiple electrode method.

The final method for exciting a plasma antenna is using a laser. A laser beam travellingthrough a gas creates a linear plasma column. For this type of antenna the gas can becontained [1], or this method can also utilize atmospheric gas [2], figure 7. By ionizing apath through the atmosphere a short lived plasma path can be established that can be usedto transmit and receive EM radiation.

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(a) Surface wave antenna [4] (b) Noise spectra [4]

Figure 6: (a) Example of a plasma antenna excited by surface waves from one end. (b)The different noise spectra for a (a) multiple electrode plasma antenna, (b) a surface waveplasma antenna and (c) a metal antenna.

(a) Standing wave laser excitation [1] (b) Atmospheric plasma laser [2]

Figure 7: (a) patent designs for laser excited plasma antennas.

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2.3 Why use Plasma antennae?

One of the most obvious reasons to use plasma antennae is the ability to control the shapeand conductivity of the plasma. Controlling these parameters allows dynamic variation ofthe radiation pattern and the bandwidth rapidly. Control over these parameters can also beused to turn a reflecting element into an absorber or transmitter very quickly.

Once the driving frequency of a metal antenna is turned off it can continue to radiateas the oscillations die down, this is known as ringing [3]. This can be reduced in Plasmaantennae, once the source of ionization is turned off a plasma quickly returns to a neutralgas suppressing the EM waves. The ability to turn the plasma off also reduces the radarcross section (RCS) lowering the probability of interception of communications. This isfavourable for military applications where reducing RCS can help reduce the chance of de-tection by an enemy. By ionizing the gas only when each packet of data is sent the visibilitytime is greatly reduced decreasing the chance of an enemy determining the radar position [3].

If multiple antennae are used in close proximity, such as on a ship, careful placement isneeded to prevent different antennas from interfering with one another. In the case of plasmaantennas they can be made to only interact with EM radiation when they are transmittingor receiving, reducing the interference with other antennae [4].

A Appendix

I have written this report to be directed at people who know some physics, however theydo not need to know a comprehensive amount of electromagnetism theory. I hope that byreading this report a person can appreciate what plasmas are, some basic physics behindthem, how they interact with electromagnetic waves and the future applications of plasmaantennae and the advantages over conventional antennae. In writing this assignment I havelearnt learnt a significant amount about both plasmas and antennae, extending from the inclass lectures. I have not covered all the material I learnt about in this written part of theassignment since I have aimed this report at a more general audience and have decided notto get bogged down in the detail. For these reasons I feel I have satisfied the requirementsfor this assignment and that it meets a standard of > 80%.

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References

[1] T. R. Anderson. Standing wave plasma antenna with reflector. Pat. No. 6046705.,August 2000.

[2] T. R. Anderson. Laser driven plasma antenna. Pat. No. 6650297, November 2003.

[3] G. G. Borg, V. Kamenski, H. J. Harris, G. Miljak, and N. M. Martin. Plasma antenas.Defence Science and Technology Organistion release, 2006.

[4] G. G. Borg, V. Kamenski, H. J. Harris, G. Miljak, and N. M. Martin. Plasmas asantennas: Theory, experiment and applications. PHYSICS OF PLASMAS, 7:21982202,2006.

[5] F. F. Chen. Introduction to Plasma Physics. Plenum Press, New York, 1st, edition, 1974.

[6] D. C. Jenn. Plasma antennas: Survey of techniques and the current state of the art.Naval Postgraduate School release, September 2003.

[7] R. A. Meger, J. Mathew, J. A. Gregor, R. E. Pechacek, R. F. Fernsler, W. Manheimer,and A. E. Robson. Experimental investigations of the formation of a plasma mirror forhigh-frequency microwave beam steering. PHYSICS OF PLASMAS, 2:25322538, 1995.

[8] E. G. Norris, T. R. Anderson, and I. Alexeff. Reconfigurable plasma antenna. Pat. No.6369763, April 2002.

[9] L. Spitzer Jr. Physics of Fully Ionized Gases. Interscience Publishers, New York, 2ndedition, 1962.

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