魏浩 孫鳳舉 呼義翔 邱愛慈

1)(西安交通大學(xué),電力設(shè)備電氣絕緣國家重點實驗室,西安 710049)

2)(西北核技術(shù)研究所,強脈沖輻射環(huán)境模擬與效應(yīng)國家重點實驗室,西安 710024)

欠匹配型磁絕緣感應(yīng)電壓疊加器次級阻抗優(yōu)化方法?

魏浩1)2)?孫鳳舉2)呼義翔2)邱愛慈1)2)

1)(西安交通大學(xué),電力設(shè)備電氣絕緣國家重點實驗室,西安 710049)

2)(西北核技術(shù)研究所,強脈沖輻射環(huán)境模擬與效應(yīng)國家重點實驗室,西安 710024)

磁絕緣感應(yīng)電壓疊加器,次級阻抗,磁絕緣最小電流,鞘層電子流再俘獲

磁絕緣感應(yīng)電壓疊加器(MIVA)次級阻抗對脈沖功率驅(qū)動源和負(fù)載之間的功率耦合具有重要影響.基于穩(wěn)態(tài)磁絕緣Creedon層流理論和鞘層電子流再俘獲(re-trapping)理論,建立了負(fù)載欠匹配型MIVA電路分析方法,數(shù)值分析獲得了MIVA輸出參數(shù)(輸出電壓、陰/陽極電流和電功率)隨負(fù)載欠匹配程度的變化規(guī)律.考慮陰極傳導(dǎo)電流作為閃光X射線照相二極管的有效電流,建立了以MIVA末端X射線劑量率最大為目標(biāo)的次級阻抗優(yōu)化方法.獲得了欠匹配型MIVA次級優(yōu)化阻抗Z?op的變化規(guī)律:隨著X射線劑量率對電壓依賴程度提高,欠匹配型MIVA次級優(yōu)化阻抗Z?op呈指數(shù)降低;負(fù)載阻抗越大,Z?op越大.

1 引 言

磁絕緣感應(yīng)電壓疊加器(magneticallyinsulated induction voltage adder,MIVA)可產(chǎn)生電壓數(shù)十兆伏、電流數(shù)百千安的高功率電脈沖[1?5].MIVA作為強流脈沖功率加速器的驅(qū)動源,在閃光X射線照相、強脈沖輻射環(huán)境模擬等領(lǐng)域具有重要應(yīng)用[3?9].MIVA通常由多級兆伏級感應(yīng)腔串聯(lián)組成,次級采用磁絕緣傳輸線(magneticallyinsulated transmission line,MITL)[10,11]實現(xiàn)電功率疊加和傳輸.MIVA次級MITL阻抗(包括阻抗大小和變換形式)對MIVA輸出參數(shù)以及驅(qū)動源和負(fù)載之間的功率耦合具有重要影響[12,13].

對于十?dāng)?shù)級感應(yīng)腔串聯(lián)MIVA裝置,在次級電脈沖到達負(fù)載前,脈沖前沿?fù)p失部分電子在陽極上,為后續(xù)脈沖建立磁絕緣提供所需磁場,次級MITL運行在磁絕緣最小電流或自限制流工作點[14?16].當(dāng)電脈沖傳輸至負(fù)載時,若負(fù)載阻抗大于或等于MITL運行阻抗,磁絕緣特性完全由傳輸線本身確定,與負(fù)載無關(guān),該類型MIVA為負(fù)載匹配型.若負(fù)載阻抗小于MITL運行阻抗,反射波由負(fù)載向MIVA傳輸,MIVA末端電壓降低,陰、陽極電流增大,該類型MIVA為負(fù)載欠匹配型[16?18].

MIVA次級電流由陰極傳導(dǎo)電流和鞘層電子流兩部分組成.對于一些高功率負(fù)載(例如用于產(chǎn)生高能脈沖X射線的閃光照相二極管),只有陰極傳導(dǎo)電流才能作為負(fù)載有效電流,鞘層電子流對負(fù)載X射線劑量率無貢獻[1,3,19].對于負(fù)載匹配型MIVA,隨著MIVA輸出電壓提高,陰極電流占總電流比例Ic/Ia降低.當(dāng)MIVA輸出電壓大于10 MV時,Ic/Ia小于40%[1,12],大部分電流以鞘層電子流形式存在,這極大地降低了MIVA裝置的電流和功率利用效率.近年來國際上提出MIVA末端采用低阻抗照相二極管(相對于150—350 ?的傍軸和浸磁等高阻抗二極管,自磁箍縮或負(fù)極性桿箍縮二極管的阻抗較低,一般約30—50 ?),使MIVA工作在負(fù)載欠匹配模式,通過鞘層電子流再俘獲,來減小鞘層電子流,增大陰極傳導(dǎo)電流[20?24].

文獻[25]給出了負(fù)載匹配型MIVA次級阻抗優(yōu)化方法.由于欠匹配型MIVA輸出參數(shù)同時受次級阻抗和負(fù)載阻抗影響,其電路分析方法和次級阻抗優(yōu)化方法與負(fù)載匹配型MIVA不同.本文基于磁絕緣Creedon層流理論和鞘層電子流再俘獲理論,建立了欠匹配型MIVA電路分析方法;以閃光照相二極管X射線劑量率最大為優(yōu)化目標(biāo),考慮陰極傳導(dǎo)電流作為負(fù)載有效電流,建立了欠匹配型MIVA次級阻抗優(yōu)化方法.需要指出的是,本文中次級阻抗優(yōu)化主要針對MIVA輸出端(最末級感應(yīng)腔對應(yīng)次級MITL)次級阻抗數(shù)值,假定MIVA各級感應(yīng)腔對應(yīng)次級MITL運行阻抗線性增大.

2 負(fù)載欠匹配型MIVA電路分析方法

2.1 磁絕緣鞘層電子流再俘獲理論

圖1給出了磁絕緣鞘層電子流再俘獲示意圖.在磁絕緣前行波到達負(fù)載前,前行波經(jīng)過區(qū)域運行在磁絕緣最小電流工作點(U0,I0),前行波傳輸特征阻抗為MITL運行阻抗Zop.當(dāng)前行波抵達負(fù)載時,由于負(fù)載欠匹配,反射波由負(fù)載向MIVA反向傳輸,反射波經(jīng)過區(qū)域MITL線電壓由U0降低至Ud,陽極電流由最小電流I0增大為Id,鞘層電子流中部分空間電子被重新俘獲至陰極,陰極傳導(dǎo)電流Ic增加,鞘層電子流If減小,鞘層變薄(圖1中反射波經(jīng)過區(qū)域電子鞘層緊貼陰極表面),反射波傳輸特征阻抗接近MITL真空阻抗Zv[13,21].反射波傳輸速度vref取決于負(fù)載Zd和次級運行阻抗Zop之間阻抗失配程度,兩者不匹配程度越高,vref越大,vref通常約為0.3—0.6倍光速[13].

圖1 (網(wǎng)刊彩色)磁絕緣鞘層電子流再俘獲示意圖[4]Fig.1. (color online)Sketch of re-trapping the magnetically-insulated sheath electron fl ow[].

2.2 負(fù)載欠匹配型MIVA電路分析方法

圖2給出了負(fù)載欠匹配型MIVA工作曲線.圖中實線為前行波工作曲線,負(fù)載匹配型MIVA(Zd≥Zop)磁絕緣運行在該曲線上.虛線是由負(fù)載Zd確定的工作曲線,與負(fù)載大小密切相關(guān)(如圖2中A,B,C).當(dāng)MIVA由前行波工作點O(U0,I0)調(diào)整至負(fù)載限定工作點A(Ud,Id)時,需經(jīng)過反射波工作曲線(圖2中虛線),曲線斜率為MITL真空阻抗Zv.反射波和負(fù)載限定工作曲線的電路方程分別為

其中,磁絕緣前行波的線電壓U0和陽極電流I0為

其中,Vs,Zs分別為MIVA前級脈沖源的等效饋入電壓和等效驅(qū)動阻抗,可由負(fù)載匹配型MIVA電路分析獲得[25,26].

圖2 磁絕緣鞘層電子流再俘獲時MIVA運行曲線Fig.2.Operating cures of MIVA when the sheath electron fl ow is re-trapped.

聯(lián)合(1)和(2)式推導(dǎo)得到鞘層電子流俘獲后MITL電壓Ud和陽極電流Id分別為

(3)式表明欠匹配型MIVA輸出電壓Ud取決于次級阻抗Zop和負(fù)載阻抗Zd.

由穩(wěn)態(tài)磁絕緣Creedon層流理論[18,27],MIVA輸出端陰極傳導(dǎo)電流Ic為

其中,γm為磁絕緣電子鞘層邊界的相對論因子,γm為磁絕緣線電壓Ud、陽極電流Id和MITL幾何阻抗因子g的隱性函數(shù)[18,27],

其中,Iav為阿爾芬電流常數(shù),Iav≈8500 A[18,27].陽極相對論因子γ00和幾何因子g分別為[18,27]

由(3)—(6)式推導(dǎo)得到,陰極電流Ic可表征為次級阻抗Zop和負(fù)載阻抗Zd的隱性函數(shù),

雖然無法給出(7)式的解析表達式,但可以通過數(shù)值方法求解.

2.3 MIVA輸出參數(shù)隨負(fù)載欠匹配程度的變化規(guī)律

假定10級感應(yīng)腔串聯(lián)MIVA輸出端磁絕緣最小電流工作點為:U0=14 MV,I0=133 kA,Zop=105 ?.MIVA輸出參數(shù)(輸出電壓、陰/陽極電流和電功率)隨負(fù)載阻抗的變化規(guī)律如圖3所示.隨著負(fù)載阻抗Zd減小,MIVA輸出電壓逐漸降低,陰/陽極電流均逐漸增大,陰極電流占陽極電流比例Ic/Ia增大.與磁絕緣最小電流工作點相比,當(dāng)負(fù)載阻抗Zd為80 ?時,負(fù)載電壓Ud降低至12 MV,陰、陽電流分別為150和113 kA;當(dāng)Zd減小至40 ?時,Ud=7.5 MV,Ia=186 kA,Ic=176 kA,鞘層電子流僅10 kA.隨著負(fù)載阻抗Zd減小,MIVA向負(fù)載耦合的總電功率降低,但有效電功率先增大、后減小.當(dāng)Zd=61 ?時,MIVA向負(fù)載耦合的有效電功率最大.

圖3 10級MIVA裝置輸出參數(shù)隨負(fù)載欠匹配程度的變化規(guī)律 (a)負(fù)載電壓和陰、陽極電流隨負(fù)載阻抗的變化;(b)總電功率、有效電功率隨負(fù)載阻抗的變化Fig.3.Change law of the output parameters depending on the under-matching degree of loads:(a)Load voltage,anode current,and cathode current varies with the load impedances;(b)total and e ff ective electrical power functions as the load impedances.

3 負(fù)載欠匹配型MIVA次級阻抗優(yōu)化

3.1 以負(fù)載輻射X射線劑量率最大為目標(biāo)的次級阻抗優(yōu)化方法

以驅(qū)動閃光照相二極管的MIVA裝置為例,通過優(yōu)化MIVA次級MITL運行阻抗Zop,使MIVA末端二極管輻射X射線劑量率最大.已有研究表明,高能脈沖閃光照相二極管X射線劑量率與二極管電壓Ud、陰極傳導(dǎo)電流Ic的定標(biāo)關(guān)系為[3,25]

其中,α,β均為常數(shù),其取值與二極管特性(二極管類型、工作狀態(tài)等)密切有關(guān)[3].現(xiàn)有研究表明,常數(shù)α取值范圍為1＜α＜3[3].當(dāng)α=β=1時,(8)式為MIVA耦合到二極管負(fù)載上的有效電功率.由于β僅影響劑量率絕對值,本文假定β≡1.

將(3)和(7)式的二極管電壓、電流公式代入(8)式,得到二極管劑量率為

雖然無法給出(9)式的顯性表達式,(9)式表明X射線劑量率取決于MITL運行阻抗Zop、負(fù)載阻抗Zd和定標(biāo)系數(shù)α.以X射線劑量率最大為目標(biāo)函數(shù)的MIVA次級阻抗優(yōu)化問題可表示為:

(11)式中優(yōu)化變量Zop下限值是為了滿足負(fù)載欠匹配條件,上限值Zop_upper通常出于MIVA工程實際考慮.由(2)式可知,當(dāng)給定前級脈沖源饋入?yún)?shù)Zs和Vs時,線電壓U0隨Zop增大而線性增加,但受感應(yīng)腔最高耐受電壓的限制,U0存在最大值,即次級阻抗存在最大值Zop_upper.

3.2 運行阻抗對MIVA輸出參數(shù)的影響規(guī)律

給定MIVA前級饋入脈沖源參數(shù)Vs=22 MV,Zs=60 ?(MIVA感應(yīng)腔串聯(lián)級數(shù)n=10,每級并聯(lián)饋入脈沖路數(shù)m=1,每路電脈沖幅值電壓1.1 MV,驅(qū)動阻抗6 ?).假定每級感應(yīng)腔最高耐受電壓為1.5 MV,由(2)式計算運行阻抗上限值Zop_upper=129 ?.

由于二極管的實際工作阻抗隨時間動態(tài)變化,只能近似給出穩(wěn)態(tài)階段阻抗變化范圍.現(xiàn)有研究表明,對于低阻抗閃光照相二極管(自磁箍縮或負(fù)極性桿箍縮二極管),其阻抗變化范圍為30—50 ?[22],本文選取三個典型負(fù)載阻抗值(30,40,50 ?)作為優(yōu)化對象.

圖4—圖6分別給出了不同負(fù)載Zd時,MIVA輸出電壓Ud、陰陽極電流比例Ic/Ia和電功率隨運行阻抗Zop的變化規(guī)律.對于給定負(fù)載阻抗Zd,隨著運行阻抗Zop降低(但仍滿足欠匹配條件Zop＞Zd),由于MIVA次級MITL與負(fù)載之間的阻抗失配程度減弱,MIVA輸出電壓Ud逐漸增大.當(dāng)Zop=Zd(MIVA與負(fù)載阻抗匹配)時,負(fù)載電壓Ud取最大值,Zd為30,40,50 ?時,Ud最大值分別為7.3,8.8和10 MV.若Zop繼續(xù)降低,當(dāng)Zop＜Zd時,MITL運行在磁絕緣最小電流工作點,MIVA輸出特性與負(fù)載大小無關(guān),負(fù)載電壓Ud隨Zop減小逐漸降低.

圖4 運行阻抗對MIVA負(fù)載電壓的影響Fig.4.The load voltage functions as the operating impedances.

由圖5可知,對于給定負(fù)載Zd,隨著Zop降低(阻抗失配程度減弱),鞘層電子流再俘獲作用減弱,陰、陽極電流比例Ic/Ia減小;當(dāng)Zop≤Zd時,無鞘層電子流再俘獲,隨著Zop降低,MITL線電壓減小,Ia,Ic和Ic/Ia均增大.

圖5 運行阻抗對陰、陽極電流比例Ic/Ia的影響Fig.5.The ratio of the cathode current and anode current varies with the operating impedances.

由圖6可知,隨著運行阻抗Zop降低,MIVA輸出總電功率P和有效電功率Peff均先增大后減小,但峰值P和峰值Peff對應(yīng)的運行阻抗不同.當(dāng)Zop=Zd(MIVA次級MITL與負(fù)載匹配)時,總電功率P最大,但此時有效電功率Peff極低,Peff在Zop＞Zd(負(fù)載欠匹配)時獲得.

圖6 (網(wǎng)刊彩色)運行阻抗對MIVA輸出電功率的影響Fig.6.(color online)Electrical power of MIVA varies with the operating impedances.

3.3 使二極管輻射X射線劑量率最大的次級優(yōu)化阻抗

圖7 給出了MIVA末端X射線二極管選取三個典型阻抗值(Zd分別為30,40,50 ?)時,最大X射線劑量率隨次級優(yōu)化阻抗p和定標(biāo)系數(shù)α的變化規(guī)律.需要指出的是,圖7所示為劑量率的相對值(假定(8)式中β=1).圖8給出了使劑量率最大的優(yōu)化阻抗p(最佳阻抗)與定標(biāo)系數(shù)α的關(guān)系.對于給定負(fù)載阻抗Zd,最佳阻抗p隨α增大(劑量率對電壓依賴程度提高)近似指數(shù)衰減,這與負(fù)載匹配型MIVA存在顯著區(qū)別,后者最佳阻抗p隨定標(biāo)系數(shù)α增大而線性增加[26].兩種類型MIVA次級優(yōu)化阻抗變化規(guī)律不同的本質(zhì)原因在于,MIVA輸出電壓隨次級阻抗Zop的變化趨勢不同,負(fù)載匹配型MIVA輸出電壓隨Zop增加而增大,但欠匹配型MIVA輸出電壓隨Zop增加反而逐漸減小(見圖4).由(8)式可知,MIVA輸出電壓對X射線劑量率的影響程度很大(特別是定標(biāo)系數(shù)α較大時).正是由于次級阻抗對兩種類型MIVA輸出電壓影響規(guī)律的差異,導(dǎo)致最大劑量率對應(yīng)的次級阻抗(最佳阻抗)隨定標(biāo)系數(shù)α的變化趨勢不同.

圖7 三種典型負(fù)載阻抗下,二極管輻射X射線劑量率隨定標(biāo)系數(shù)α和優(yōu)化阻抗Zo?p的變化規(guī)律Fig.7. The radiated X-ray dose rate varies with the scaling factor α,and the optimized operating impedance Zo?punder three typical load impedances.

圖8 三種典型負(fù)載阻抗時最佳阻抗Z?op隨定標(biāo)系數(shù)α的變化規(guī)律Fig.8.Optimized operating impedance Z?opvaries with the scaling factor α under three typical load impedances.

對于欠匹配MIVA,經(jīng)數(shù)值擬合得到,使X射線劑量率最大的次級阻抗p與定標(biāo)系數(shù)α的關(guān)系可表示為[26]

式中C1,C2和k1,k2為常數(shù),取值與負(fù)載Zd、前級脈沖源等效驅(qū)動阻抗Zs相關(guān)[26].

4 結(jié) 論

基于穩(wěn)態(tài)磁絕緣Creedon層流理論和鞘層電子流再俘獲(re-tapping)理論,建立了負(fù)載欠匹配型MIVA電路分析方法和次級MITL運行阻抗優(yōu)化方法.當(dāng)給定次級運行阻抗時,獲得了MIVA輸出參數(shù)(輸出電壓、陰/陽極電流和電功率)隨負(fù)載欠匹配程度的變化規(guī)律.當(dāng)給定負(fù)載阻抗時,數(shù)值分析獲得了次級運行阻抗對MIVA輸出參數(shù)的影響規(guī)律.獲得了使MIVA末端輻射X射線劑量率最大的次級優(yōu)化阻抗值的變化規(guī)律:隨著二極管X射線劑量率對電壓依賴程度提高(定標(biāo)系數(shù)α增大),最佳阻抗近似指數(shù)下降.本文建立的欠匹配MIVA電路分析方法和次級阻抗優(yōu)化方法已應(yīng)用于MIVA裝置電路分析和物理設(shè)計.

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Method of optimizing secondary impedances for magnetically-insulated induction voltage adders with impedance under-matched loads?

Wei Hao1)2)?Sun Feng-Ju2)Hu Yi-Xiang2)Qiu Ai-Ci1)2)
1)(State Key Laboratory of Electrical Insulation and Power Equipment,Xi’an Jiaotong University,Xi’an 710049,China)
2)(State Key Laboratory of Intense Pulsed Radiation Simulation and E ff ect,Northwest Institute of Nuclear Technology,Xi’an 710024,China)

10 March 2017;revised manuscript

3 July 2017)

The magnetically-insulated induction voltage adder(MIVA)is a pulsed-power accelerator widely used in the X-ray fl ash radiography andγ-ray radiation simulation.The operating impedance of magnetically-insulated transmission line(MITL)on the secondary side of MIVA will produce signi fi cant in fl uence on the power coupling between the pulsedpower driving source and the terminal load.Therefore,optimizing the secondary impedance of MIVA to maximize the electrical-power or radiated output of load is critical for the design of MIVA facility.According to whether the MITL operating impedance is smaller than the load impedance,MIVAs can be divided into two different types,i.e.,the impedance-matched case and impedance undermatched case.For the impedance-matched MIVA,because the MITL of MIVA operates at the minimal current point or self-limited fl ow,the output of MIVA just depends on the MITL operating impedance and is independent of load.Correspondingly,the circuit analysis is relatively easy.However,for MIVA with impedance undermatched load,the analysis method is more complicated.Based on the classical Creedon theory of the magnetic insulation equilibrium and the sheath electron re-trapping theory,a circuit method is established for MIVA with impedance under-matched load.The analysis process consists of two steps.Firstly,the working point of the forward magnetic insulation wave is solved by the minimal current theory on the assumption that the MIVA is terminated by impedance-matched load.Then,the actual operating point after the re-trapping wave has passed is solved,in which the characteristic impedance of the re-trapping wave is treated as a vacuum impedance.And the relationship between the output parameters of MIVA,e.g.,the output voltage,the cathode and anode current,and the electrical power,and the undermatched extent of load is obtained numerically.Based on the analysis method,a method to optimize the secondary impedance of MIVA with ten-stage cavities stacked in series to drive X-ray radiographic diodes is developed.This optimization method aims at maximizing the radiated X-ray dose rate of the diode loads on the assumption that only the cathode current is available for the X-ray radiographic diode.The optimization secondary impedance,p,varying with the scaling factor,α,is achieved,whereαis the power exponent between the dose rate and the diode voltage().αis usually determined by the diode type,geometrical structure,and operating characteristics.It is found that the optimization secondary impedancepdecays exponentially with the increase of valueα,i.e.,the increase of the diode-voltage-dependent degree of the radiated X-ray dose rate.And the larger the load impedance,the larger the value ofpis.The circuit analysis method and the impedance optimization method developed in this paper are specially useful for the applications of MIVA in the fl ash radiographic fi elds.

magnetically-insulated induction voltage adders,secondary impedance,minimal current of magnetic insulation,re-trapping of sheath electron fl ow

(2017年3月10日收到;2017年7月3日收到修改稿)

10.7498/aps.66.208401

?國家自然科學(xué)基金(批準(zhǔn)號:11505138,51577156)資助的課題.

?通信作者.E-mail:weihao@nint.ac.cn

?2017中國物理學(xué)會Chinese Physical Society

http://wulixb.iphy.ac.cn

PACS:84.70.+p,52.59.—f,02.60.Pn,84.30.NgDOI:10.7498/aps.66.208401

*Project supported by the National Natural Science Foundation of China(Grant Nos.11505138,51577156).

?Corresponding author.E-mail:weihao@nint.ac.cn