Compton散射對(duì)激光等離子體通道天線特性的影響

禹定臣， 郝東山

(1.黃淮學(xué)院信息工程學(xué)院， 駐馬店 463000； 2.鄭州工業(yè)應(yīng)用技術(shù)學(xué)院信息工程學(xué)院， 新鄭 451150)

Compton散射對(duì)激光等離子體通道天線特性的影響

禹定臣1， 郝東山2

(1.黃淮學(xué)院信息工程學(xué)院， 駐馬店 463000； 2.鄭州工業(yè)應(yīng)用技術(shù)學(xué)院信息工程學(xué)院， 新鄭 451150)

應(yīng)用多光子非線性Compton散射模型和數(shù)值計(jì)算方法，研究了激光等離子體通道天線傳播和輻射特性，結(jié)果表明：隨通道周圍介質(zhì)損耗和傳輸模式階數(shù)的增大，傳輸模式THnm衰減常數(shù)明顯增大.這是因散射使通道內(nèi)外電場(chǎng)和磁場(chǎng)增強(qiáng)，粒子間碰撞頻率增大，電場(chǎng)使更多分子電離而吸收更多能量的緣故.隨模式階數(shù)增大，電性有耗介質(zhì)使相移常數(shù)明顯減小.這是因散射使高階模式可能存在被耦合電場(chǎng)俘獲的緣故.等離子體耦合頻率為0.7附近，衰減常數(shù)隨頻率增大而劇烈增大.這是因散射使介質(zhì)分子發(fā)生二、三階電離，更多電子被耦合電場(chǎng)急劇加速的緣故.隨天線長(zhǎng)度增加，天線輻射方向圖主瓣和副瓣數(shù)量、寬度和最大輻射方向發(fā)生明顯變化.這是因散射使天線頻率增大，輻射波長(zhǎng)變短，粒子電離幾率增大，輻射波能量和頻率成分增大的緣故.

激光等離子體通道天線； 傳輸模式； 輻射特性； 耦合； 多光子非線性Compton散射

1 引 言

因大功率等離子體天線有重要應(yīng)用，如大功率微波武器[1]、隱身技術(shù)[2]、核聚變快點(diǎn)火[3]等，故引起了人們的關(guān)注[4-7].Caillault等[8]設(shè)計(jì)出平面等離子體反射天線結(jié)構(gòu).Donald等[9]給出了該天線反射電磁波噪聲產(chǎn)生機(jī)制.鑒福升等[10]指出，等離子體碰撞頻率是影響反射波的主要因素.胡強(qiáng)林等[11]指出，圓和線極化行波輻射阻尼效應(yīng)隨等離子體密度增大而增大，高激光脈沖重復(fù)率頻率可提高輻射阻尼效應(yīng)[12].Petrova等[13]指出，注入不同條件激光可使通道壽命延長(zhǎng)，不同線型脈沖對(duì)壽命影響較大[14].楊利霞等[15]提出新的電流密度拉普拉斯變換時(shí)域有限差分法計(jì)算等離子體球輻射.大多研究基于玻璃管封裝惰性氣體產(chǎn)生等離子體，使大功率等離子體天線增益受限[16,17].如何尋求大功率等離子體天線已成為亟待解決的重要課題.近期，夏新仁等[18]提出新概念激光等離子體通道天線構(gòu)想.應(yīng)指出的是，以上對(duì)等離子體通道天線研究均未考慮非線性Compton散射.文樺等[19]指出，等離子體內(nèi)波強(qiáng)達(dá)1016W/cm2量級(jí)，非線性Compton散射開(kāi)始顯現(xiàn).可見(jiàn)，Compton散射對(duì)等離子體天線輻射影響不可忽略.本文正是對(duì)該問(wèn)題進(jìn)行了研究.

2 天線設(shè)計(jì)及工作原理

等離子體通道天線的設(shè)計(jì)原理圖如圖1所示，其工作原理是：激光器發(fā)出的超強(qiáng)激光使空氣電離且發(fā)生多光子非線性Compton散射，入射光和Compton散射光形成耦合等離子體通道，同步信號(hào)脈沖器的脈沖通過(guò)天線耦合到等離子體通道內(nèi)，脈沖和通道以接近光速的速度同步向前傳輸，通過(guò)通道的側(cè)面向外輻射電磁波.

圖1 等離子體通道天線示意圖Fig.1 Sketch map of plasma channel antenna

3 天線傳播特性

因由通道導(dǎo)行傳輸?shù)碾姶挪ㄊ冀K滯后激光脈沖極短時(shí)間，且通道可近似為半徑恒定、密度均勻的等離子體圓柱，故可將天線等效為周圍充滿有耗氣體的無(wú)限長(zhǎng)圓柱體，其模型如圖2所示.

圖2 等離子體通道天線電磁模型Fig.2 Electromagnetic model of plasma channel antenna

若等離子體中發(fā)生非線性Compton散射(簡(jiǎn)稱散射)，入射與散射光形成的耦合光頻為[6]

(1)

(2)

(4)

(5)

(6)

通道內(nèi)外耦合矢量位可分別表示為

exp(-jkz)+(Δωμ0εp+ωμ0Δεp+ωμ0εp)

exp(-jkz)，r≤a

(7)

exp(-jkz)+j(ΔωμLεL+ωΔμL+ωμLΔεL)

exp(-jkz)+j(ΔωμLεL+ωΔμL+ωμLΔεL)

(8)

ΔxpJnBn+

(9)

(10)

(11)

(12)

其中xp=ppa，Δxp=Δppa；xL=pLa，ΔxL=ΔpLa.由式(9)～(12)非零解條件，可得

(ΔμrH+μrΔH)](J-εLpH)-(J-μtH)[ΔJ-

(13)

取通道周圍有耗介質(zhì)的電和磁性參數(shù)分別為Reεcr=5.5和μcr=1及Reμcr=5.5和εcr=1、ωcpe/ω=0.5、a/λ=6時(shí)，通道內(nèi)THnm衰減和相移常數(shù)隨介質(zhì)損耗變化如圖3～5所示.由圖3～5知，衰減隨通道周圍介質(zhì)損耗和傳輸模式階數(shù)增大明顯增大，同階模式下，前者遠(yuǎn)大于后者.這是因散射使電和磁場(chǎng)增強(qiáng)，碰撞頻率增大使更多電離分子吸收更多能量的緣故.同階模式下，前者對(duì)相移影響大于后者，隨模式階數(shù)增大，相移常數(shù)明顯減小.這是因散射使高階模式被電場(chǎng)俘獲的緣故.

圖3 電性有耗介質(zhì)下傳輸模式衰減常數(shù)隨介質(zhì)損耗的變化Fig.3 Changes on attenuation constant of propagation model along dielectric loss under electric dielectric

圖4 磁性有耗介質(zhì)下傳輸模式衰減常數(shù)隨介質(zhì)損耗的變化Fig.4 Changes on attenuation constant of propagation model along dielectric loss under magnetism dielectric

圖5 傳輸模式相移常數(shù)隨周圍介質(zhì)介質(zhì)損耗的變化Fig.5 Changes on phase moving constant of propagation model along near dielectric loss

取等離子體通道周圍的電性和磁性介質(zhì)的參數(shù)分別為εcr=5.66(1-j)和μcr=1及μcr=5.66-5.66j和εcr=1、a/λ=6，THnm的衰減常數(shù)和相移常數(shù)隨著ωcp/ω的變化分別如圖6～8所示.由圖6知，同階模式的電性和磁性介質(zhì)對(duì)相移常數(shù)的影響幾乎是相等的，隨著模式階數(shù)的增大，該常數(shù)發(fā)生了微小的減小.這是因?yàn)樯⑸涫闺娮拥妮椛渥枘嵩鰪?qiáng)效應(yīng)導(dǎo)致高階模式吸收的能量減小，其被電場(chǎng)俘獲效應(yīng)消失的緣故.由圖7和8知，ωcp/ω=0.7附近，衰減常數(shù)隨著ωcp/ω的增大而劇烈地增大.這是因?yàn)樯⑸涫狗肿影l(fā)生了二階和三階電離，有更多的電子被電場(chǎng)急劇加速的緣故.

圖6 傳輸模式相移常數(shù)隨等離子體頻率的變化Fig.6 Changes on phase moving constant of propagation model along plasma frequency

圖7 通道周圍為電性有耗氣體介質(zhì)時(shí)，傳輸模式衰減常數(shù)隨等離子體頻率的變化Fig.7 Changes on attenuation constant of propagation model along plasma frequency dielectric loss under electric dielectric near channel

圖8 通道周圍磁性為有耗氣體介質(zhì)，模式衰減常數(shù)隨等離子體頻率的變化Fig.8 Changes on model attenuation constant along plasma frequency under magnetism dielectric near channel

4 天線輻射特性

將激光等離子體通道天線等效為周圍充滿空氣、密度均勻、半徑和長(zhǎng)度為a和L的如圖9和10所示等離子體圓柱體，分別為從天線初始端耦合電磁波的單極式天線和從通道中間耦合電磁波的駐波對(duì)稱振子式天線.

圖9 單極式等離子體通道天線示意圖Fig.9 Sketch map of channel antenna of single polar laser plasma

圖10 駐波對(duì)稱振子式等離子體通道天線示意圖Fig.10 Sketch map of channel antenna of laser plasma of standing wave symmetry oscillation

圖9天線，信號(hào)在通道表面以行波傳輸且與等離子體發(fā)生散射時(shí)，其表面耦合電流為

′)+ΔJx(Δz′)≈

J0exp[j(ωt-kz′)]+ΔJ0exp[j(ωt-kz′)]

(14)

式中，ω為信號(hào)頻率；J0和ΔJ0分別為散射前的電流振幅及其擾動(dòng).對(duì)于較短的天線，輻射電場(chǎng)方向函數(shù)為

(15)

對(duì)圖10天線，其表面耦合電流為

(16)

由式(15)和(16)，可得

(17)

取εcr=μcr=1，結(jié)合輻射場(chǎng)對(duì)稱性及其主模式為n=0的TM表面波，得TM波在天線周圍空氣中的縱和橫向電磁場(chǎng)在圓柱坐標(biāo)系中的關(guān)系為

(18)

由式(18)，可得橫向電磁場(chǎng)切向分量及橫向電磁場(chǎng)分別為

(19)

Ecφ=0

(20)

Ecpz=Ac1J0(ppr)exp(-jkz)+

Ac1ΔJ0(Δppr)exp(-jkz)

(21)

Hcpz=0

(22)

(23)

橫向電磁場(chǎng)的切向分量為

(24)

Ecpφ=0

(25)

對(duì)單極天線取ωcp=31.4 GHz,νcp=4 GHz,a=2 mm,ω=500 MHz，L=λ/4、λ/2、λ時(shí)，E面輻射方向和f(φc)隨φc=φ+Δφ變化如圖10和11所示.由圖10知，0

圖11 單極式天線的fcΦ隨Φ的變化Fig.11 Changes on f cΦ of single polar antenna

對(duì)于稱振子式天線取圖10和11中的參數(shù)，E面輻射方向隨著天線長(zhǎng)度的變化關(guān)系如圖12所示.由圖12知，當(dāng)0

圖12 對(duì)稱振子式天線方向圖隨天線長(zhǎng)度的變化Fig.12 Changes on direction map of symmetry oscillation along antenna length

圖13 對(duì)稱振子式天線方向圖隨等離子體密度的變化Fig.13 Changes on direction map of symmetry oscillation along plasma density

圖14 對(duì)稱振子式天線方向圖隨通道半徑的變化Fig.14 Changes on direction map of symmetry oscillation along channel radius

5 結(jié) 論

本文基于多光子非線性Compton散射模型，分析了散射對(duì)天線特性的影響，得出如下結(jié)論：

1)與散射前相比，隨通道周圍介質(zhì)損耗和模式階數(shù)增大，模式衰減常數(shù)明顯增大.電性有耗介質(zhì)使較高階模式相移常數(shù)明顯減小.隨同階模式階數(shù)增大，兩介質(zhì)對(duì)相移常數(shù)影響幾乎相等.

2)等離子體耦合頻率ωcp/ω=0.7附近, 衰減常數(shù)隨耦合頻率增大而急劇增大.

3)隨單極式天線長(zhǎng)度增加, 其輻射方向圖主瓣寬明顯減小, 最大輻射方向由180°向90°方向明顯移動(dòng)，主瓣和第一副瓣方向系數(shù)均明顯增大.對(duì)稱振子式天線長(zhǎng)度0

4)隨電子密度增大, 輻射方向主瓣由2瓣變?yōu)?瓣, 最大輻射方向由0°和180°方向轉(zhuǎn)向90°方向, 主瓣明顯變寬.

5)隨等離子體通道半徑增大, 輻射方向主瓣由2瓣變?yōu)?瓣, 最大輻射方向由0°和180°方向轉(zhuǎn)向90°方向, 主瓣更寬.

對(duì)以上結(jié)論給出了初步物理解釋.這些結(jié)論對(duì)于人們?cè)O(shè)計(jì)和控制等離子體通道天線傳輸特性應(yīng)具有一定的參考價(jià)值.

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Influences of Compton scattering on the properties of laser plasma channel antenna

YU Ding-Chen， HAO Dong-Shan

( 1. College of Information Engineering， Huanghuai University， Zhumadian 463000, China； 2. College of Information Engineering， Zhengzhou University of Industrial Technology， Xinzheng 451150, China )

By using the model of multi-photon nonlinear Compton scattering and the numerical computing means， the properties of the propagation and radiation of laser plasma channel antenna are studied. The results show that the attenuation constant of the propagation model THnmis clearly increased along the increases of the dielectric loss near the channel and the propagation model step number. The causes are that the electric field and magnetic field in and outside the channel are increased by Compton scattering， the collision frequency between the particle and particle is increased， and even more energies are absorbed by the even molecules ionized by Compton scattering. The phase moving constant is clearly decreased by the electric loss dielectric along the increasing model step number. This is dus to the possibility on the capture of the high step model by the coupling electric field. Near 0.7 coupling plasma frequency， the attenuation constant is acutely increased along the increasing frequency. The cause are that the 2nd and 3rd step ionizations of the medium molecule are taken by Compton scattering， and the even more electrons are sharply accelerated by the coupling electric field. The numbers of the main and vice piece， the widths and the maximum radiation directions in the map of the antenna radiation direction are clearly changed along the increasing antenna length. The cause are that because of the scattering，the antenna frequency is creased， the radiation wave length is decreased， the probability particle ionization is increased， and the energy and radiation wave frequency composition are increased.

Laser plasma channel antenna； Propagation model； Radiation characteristic； Coupling； Multi-photon nonlinear Compton scattering

2014-09-04

河南省基礎(chǔ)與前沿技術(shù)資助項(xiàng)目(092300410227)

禹定臣(1970—), 男，副教授，碩士，主要從事信號(hào)傳輸技術(shù)研究.

郝東山.E-mail: haodongshan@126.com

103969/j.issn.1000-0364.2015.10.016

TN011

A

1000-0364(2015)05-0815-08