Research of numerical simulation on the spatial distribution of plasma antenna radiation field based on MATLAB

Lei BIAN，Run-xuan QIN，Chen CHEN（School of Energy and Power Engineering，Wuhan University of Technology，Wuhan 430063，China）

Research of numerical simulation on the spatial distribution of plasma antenna radiation field based on MATLAB

Lei BIAN*，Run-xuan QIN，Chen CHEN
（School of Energy and Power Engineering，Wuhan University of Technology，Wuhan 430063，China）

Plasma has excellent electric conductivity.Compared to ordinary metal antenna，plasma antenna which uses Plasma as an electromagneticenergy conductive medium，has greater stealth，smaller volume，lighter weight，and dynamically refactoring features.Therefore，study of plasma antenna is of great significance.This paper uses the numerical simulation based on MATLAB to study the antenna radiation field problem.As is shownin the results：thecurrent distribution map and radiationpattern will changeaccordingly with the changes of antenna length，density and other parameters.That is to say，the radiation direction is controllable.

Numerical simulation based on MATLAB，Plasma antenna，Radiation field，Spatial distribution，Controllability

Hydromechatronics Engineering

http：//jdy.qks.cqut.edu.cn

E-mail：jdygcyw@126.com

1 Introduction

The plasma antenna refers to an antenna，which can replace the metalconductor and act as communication media.Compared with the traditional metal antenna，the plasma antenna has lighter weight，shorter open time，greater stealth，controllable antenna parameters and many other advantages.Due to this，it has great application value in military and commercialcommunication.Internationally，the concept of plasma antenna was put forward for the first time in the navy communication field.In the 1990s，the Naval Research Laboratory set about studying the plasma antenna in America and achieved good results［1］.In the University of Canberra in Australia，electrical engineering and applied physicslaboratory was set up in 2000，and the study of incentive method ofplasma column antenna RF was started，where the network analyzer tests，instruments and other equipments were used to achieve the expected effect.Plasma laboratory at the Australian National University made a research about the basic theory and parameters of the plasma antenna，and obtained a patent.During the process，A.D.Cheetham made a research about the plasma focus measurement，spiral wave excitation radiofrequency energy coupling control system and the plasma parameters choice；J.P.Rayner concentrated on the waves in plasma coupling，antenna and RF energy related theory and the measurement of antenna parameters.In the domestic，Liu Liangtao and Zhu Dajun in the University of Electronic Science and Technology haddiscussed a basic principle of several types of plasma antenna，surface wave driven plasma impedance，power etc.；Professor Zhao Guowei and other researchers in Chinese Academy of Sciences，according to the impedance of antenna radiation pattern，made several numerical methods in the study.In this paper，the method of numerical simulation is employed through the computer simulation of radiation power to get spatial distribution mapunder different plasma parame-ters.What’s more，the distribution maps of radiationdirection of the corresponding graph and the current are obtained with the changes of the plasma parameters，which is aimed to illustrate the controllabilityof its radiation direction.

2 Plasma system

Plasma is different from the general gas，which is composed of molecules，of which the intermolecular force with each other is short-range force.Only when molecules crash into others，forces have an obvious effect.It is described in kinetic theory theoretically. However，the coulombic force of plasma between particles is long-range force，which has a more obvious effect than particles due to the collision.When charged particles move in the plasma，it will make positive and negative charges gather each other，and generate anelectricfield.Meanwhiledirectional movement of charges can form the current，and also a magnetic fieldwill be accompanied.The existence of the electromagnetic field will cause a movement of the charged particles around，accompanied by strong heat conduction and thermal radiation.At the same time，the magnetic field will constrain plasma to conduct the cyclotron motion，etc.Because of these characteristics of plasma that are different from other gases，it is called a fourth state matter.Plasma has ion effect，that is to say，when the density of electrons in the plasma is high enough，it can make the plasma frequencyvery high（usually 8 MHz）.At this time，signal communication will be blocked.The performance of plasma system is mainly affected by the movement of charged particles.Each of the charged particles can interact with a lot of charged particles，and the large amounts of charged particles in the plasma can produce obvious collective oscillation.Plasma is a kind of oscillations phenomenon of high frequency static electricity，which is a collective movement caused by plasma groups interacting with each other，and usually radiateelectromagnetic wave outward.If a plasma area had an instant positive or negative electric charge，the charge will generate oscillation.As is shown in Fig.1，if the plasma is distributed equably and its density is N，the electrons in regional ABCD are moved a short distance to the right x，reaching A′B′C′D′.If ion holds still，positive charge will appear in AB B′A′because of the leaving electrons，at the same time，equal amounts of negative chargewill emerge in the other side because of the entering electrons［2］.

Fig.1 Map of charge distribution of pIasma

3 Theoretical analysis

The composed of dielectric constant material of plasma antenna for equivalence：

In the formula：

Er—Plasma equivalent dielectric constant；

E0—Vacuum dielectric constant；The plasma frequency；

VC—The electron collision frequency；

X—The working frequency；

N—The electron density；

e—The electric charge；

m—Electronic quality；

XPand VC—Determined by the physicalparameters of the plasma density，pressureand temperature etc.

The uniform distribution of the plasma column is assumed，it is propagating along the surface ofthe electromagnetic wave to the wave vector represented by the formula：

In the formula：

Er—Plasma equivalent dielectric constant；

In（#）—The first class of the N modified GaiBeisel function；

Kn（#）—The second class of the N modified Gai-Beisel function；

r—The radius of the plasma column；

k—The wave vector of the plasma；

k0=X/c—The wave vector space of freedom.

The conductive of plasma antenna and the emission of electromagnetic waves are to obtainhigher plasma density，and the plasma frequency is greater than thefrequency of antenna.If satisfied，then the wave vector k of the imaginary part of Im（k）is very small，namely the electromagnetic wave attenuation in the transmission process is very small，while the real part of the wave vector Re（k）K0and the free space in the similar，at this time the plasma，metallic two antenna can replace each other.The composition of the plasma antenna structure as shown in Fig.2.

Fig.2 The composition of the pIasma antenna structure

3.1 Radiation power of short antenna

When the length of the antenna is much smaller than the wavelength，the radiation produced is called electric dipole radiation.For example，a antenna of which center feed length is 1，in half segment of the antenna，the current direction is the same.A feed point current has maximum value，and the antenna currentsare zero at both ends.If the antenna length 1，the current distribution on the antenna is approximately linear form：

Electric dipole moment change

Substituting type（5），the radiation power of short antenna：

This type is suitable for l，easy to see，in the antenna current under the same condition，the radiation power is proportional to the short antenna（）2.By the power of radiation formula（7），that is proportional to the radiation power，the power loss of the radiation power can be put to be equivalent to the radiation power，this is called the equivalent resistance to radiation resistance，makeCompared with the

The greater the power antenna radiation，in a certain input current，the greater the radiation power，so the radiation resistance can be seen as a radiation ability of characterizing antenna.From the type（6），it can be seen that theradiation resistance of short antenna is proportional to，which is very small，and so short antenna radiation ability is very weak.In order to improve the ability of radiation，the antenna length and the wavelength tare at the same order，but now antenna radiation cannot represent the electric dipole radiation.

3.2 The radiation power of a half wave antenna

Take the same linear center fed antenna，the above current is similar with the wave forms，the length of the antenna is 1，both ends are Wave Festival，current distribution is：

In the vector potential formula（8），make J（x′）dV′change toIdland put the type（10）to it，then：

when compute the far field，let r=R-zcosθ，R is distance from origin to the far field.When take 1/R to the minimum time item，r in the denominator can change to R，the type（11）become：

After conversion by the Euler formula，the imaginary part is an odd function，the integral is zero.Take it to the type（12）

It can be calculated of the electromagnetic radiation zone

The radiation energy flux density is：

The radiation angular distribution can get by factors.It is similar to the dipole radiation angular distribution，but more concentrates on the plane.The total radiation power：

Use variable substitution，finishing simplification to

4 Numerical simulation based on MATLAB

The initial conditions of plasma antenna are input into the MATLAB for the simulation，the current distribution of plasma antenna radiation is as below.The direction of MATLAB numerical simulation radiation varies with the length of the antenna.An analysisof the influence of radiation wavelength and the antennalength is based on this result.Antenna input impedance will change，reactance and the occurrencechanges with frequency，and the influence of the relationship between them will be observed.

4.1 Antenna vibrator

1）When the 0.5 unit length of wavelength，the length of the antenna are respectively 5 per unitlength，a length of 1.4，0.25 units of length.The current distribution is shown in Fig.3（a），（b）and（c），where the abscissa represents the coordinate antenna on the Z axis，and the ordinate is the current distribution.

Fig.3 Current distribution map of different antenna Iength

From Fig.3 itcan be concluded that the current on the antenna will decay in thecommunication process；the length of antenna becomes smaller；the current decay is more obvious.Compared with the long antenna，current of short antenna has obvious attenuation.In Fig.3（a）spreading outward from the center in the process of current attenuation is small，and the approximate sine form，Fig.3（c）current attenuation of half wave antenna is very obvious.Therefore，to get more stable and stronger signal strength，a longer an-tenna is required.

2）Radiation pattern of the plasma antenna（E surface）as shown in Fig.4（a），（b）and（c）

Fig.4 PIasma E pIane radiation pattern of the antenna

Fig.4 is adirection diagram for the observation of radiation direction perpendicular to the electric field. The number of antenna lobe antenna is all equal to themultiples of a half wavelength.The longer the antenna is，the more radiation lobes are.The smaller the width of the main lobe is，the strongerthe antenna direction is，and the antenna radiation energy is more concentrated.From the process of graph 4（c）-4（a），the width of lobe is smaller and smaller during the lengthincreasing of the antenna，and the direction ofradiation is changed，which is getting better and better.Therefore，the transmitting antenna are generally very long.And the effective lengthofthe plasma antenna is controllable，so the plasmaantenna is also controllable.

3）Radiation pattern of the antenna（H plane）

Due to the radiation is independent on，H plane patterns are always round，the patterns perpendicular to the magnetic field direction radiation are the same，and has nothing to do with the antenna length parameters.

Fig.5 PIasma H pIane radiation pattern of the antenna

4）Radiation field distribution of three dimensional

Three dimensional radiation pattern of the plasma antenna is shown in Fig.6，which consists of a threedimensional graph can be seen from the center to the surrounding radiation antenna.In the figure，the length of antenna decreases，and the radiation field are also changed obviously.Directivity diagram of 6（a）is the best，of which radiation energy is the most concentrated，which is also the most wanted one in the practical application.At the same time，for the receiving end，the accuracy，quality and strength of signal receiving will increase with the increase of direction［3-5］.

4.2 The frequency of plasma antenna

At the same time on the plasma antenna frequency is analyzed by simulation in MATLAB environment. From Fig.7 and Fig.8，it can be seenthat the input resistanceincreasesand then decreases with plasma antenna frequency.There will be apeak in the region，and gradually decreases along with the the plasma frequency，then the peak will decrease.The input reactance decreases rapidly when the frequency is zero and decrease to zero，and tends to be stable.At the maximum frequency point of input resistance，the input reactance also can be the largest，which can be negative at the right of the input resistance maximum frequency point.If the antenna frequency itself is higher，the input resistance will be bigger［5-6］.

Fig.6 Three-dimensionaI map of PIasma antenna

Fig.7 Input resistance change with the frequency

Fig.8 Input reactance with frequency variation

4.3 The result of simulation

Through the above analysis of the antenna oscillator and frequency of antenna，we can draw that the signal wavelength and antenna length have obvious influence on the antenna radiation.

The current distribution，radiation pattern，and radiation power will change accordingly with changes of plasma antenna length，radius and other parameters. Thesmaller the width of antenna main lobe is，the stronger the directional antenna radiation energy is，the more concentrated it is.So，the transmitting antennas are generally long，but the antenna is not the longer the better.With the antenna is extended，there will be the amplification of other problems.In the diagram，the length is half wave antenna，which is widely used in short wave and ultrashort wave.

5 Conclusions

In the MATLAB environment，we conclude that the radiation diagram of plasma antenna and the current distribution diagram will change with the change of the radius of antenna，signal wavelength and other parameters.One of the characteristics of plasma antenna is that these parameters can realize the dynamic reconstruction.Therefore，the plasma antenna has the characteristic such ascontrollable radiationdirection.

Acknowledgements

This paper is supported by National Training Programs of Innovation and Entrepreneurship for Undergraduate（No.20141049712003）and Independent innovation research fund of Wuhan University of Technology（No.2014-HY-B1-06）.

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基于MATLAB数值仿真的等离子天线辐射场空间分布研究

卞 磊*，秦润轩，陈 晨
武汉理工大学能源与动力工程学院，武汉 430063

等离子体具有优异的导电性能，利用等离子体作为电磁能量传导介质的等离子天线相比于普通的金属天线，具有隐身性好、体积更小、重量更轻、可动态重构等特性。采用MATLAB数值仿真模拟研究了天线的辐射场问题。结果表明：随着天线长度、密度等参数的不同，其电流分布图、辐射方向图都会发生相应的变化，也就是说其辐射方向具有可控性。

MATLAB数值仿真；等离子天线；辐射场；空间分布；可控性

10.3969/j.issn.1001-3881.2015.12.014Document code：A

TN827+.9

10 August 2014；revised 25 December 2014；accepted 2 March 2015

*Corresponding author：Lei BIAN.

E-mail：1132199231@qq.com