磁绝缘无损形成过程的理论研究
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摘要
暂停核试验后,加强地面实验能力成为各国核武器研究的一个重点。美国圣地亚国家实验室在上世纪末发现,快Z箍缩装置驱动金属丝阵负载可以产生核爆模拟研究所需要的高能量密度物理学实验条件,并且可能相对经济地实现聚变点火。因此,大型快Z箍缩装置的研制成为当今脉冲功率技术领域的热点。磁绝缘传输线(MagneticallyInsulated Transmission Line,简称MITL)是大型快Z箍缩装置的关键部件,起着脉冲功率的传输和汇聚作用。
MITL在阴极表面发生电子爆炸发射后,仍能够利用传导电流产生的自磁场箍缩在极间运动的电子,使其无法到达阳极,从而确保脉冲功率继续向负载方向传输,功率流密度可达TW/cm~2量级。这一传输过程的物理模型与真空线传输有很大区别,被称为磁绝缘传输。
磁绝缘传输理论早在1921年就开始出现,上世纪70至90年代得到很大发展。磁绝缘传输理论包括磁绝缘稳态理论和磁绝缘形成理论两大类,主要根据极间电子的运动轨迹特征来研究磁绝缘传输现象。磁绝缘传输理论不仅用于解释和分析磁绝缘传输现象,还可以帮助建立MITL的电路模型,实现对MITL传输过程的电路模拟。但在MITL电路模型的建模过程中有两个问题没有解决:(1)如何利用现有磁绝缘稳态理论,计算电路模型中的分布参数;(2)如何计算无损磁绝缘形成过程(在磁绝缘形成过程中,没有电子到达阳极表面)导致的MITL传导电流和传导电压变化。本文主要围绕上述两个问题展开研究。
首先,作为研究基础,本文从Creedon的磁绝缘稳态层流模型出发,构筑了一个新的变量空间(h_2,C_1,γ),并在此变量空间中用简单的解析公式描述了磁绝缘稳态下的极间电磁场、电荷密度和电流密度分布。Creedon模型描述了磁绝缘稳态下的传导电流(又称线电流)、传导电压(又称线电压)和阴极表面电流等的关系,并未给出极间电磁场、电荷密度和电流密度的分布规律,因此这一结果完善Creedon的层流模型。利用相关结果,本文模拟计算了Z加速器MITL的极间电磁场等参量的分布,所得结果与真空传输状态有很大区别。此外,还利用这些分布公式证明了Creedon层流模型和Mendel层流近似模型这两个磁绝缘稳态模型在物理上具有一致性。Mendel层流近似模型在工程中应用广泛,是从Mendel关于磁绝缘稳态的任意动量模型近似而来,但Mendel的任意动量模型的建模思想与Creedon层流模型完全不同,因此Mendel层流近似模型与Creedon层流模型是否具有物理一致性,这是已有磁绝缘稳态理论中的一个疑问。
第二,利用磁绝缘稳态下极间电磁场在(h_2,C_1,γ)变量空间中的解析表达式,本文研究了MITL电路模型在磁绝缘稳态下的分布电感和分布电容表征问题。研究发现,磁绝缘稳态下的传导电流回路和线电荷分布区随脉冲功率传输状态变化,这与真空传输状态(电流回路和电荷分布区的几何边界固定)完全不同。因此,本文将磁绝缘稳态下的分布电感和分布电容用张量描述,由此从物理上清晰地看到分布电感和分布电容既与磁绝缘稳态的状态参数(线电压和线电流等)有关,又与电流回路和电荷分布区域的几何特征变化有关。不过,用张量去表征分布电感和分布电容不能简化磁绝缘稳态的电路模型,因此本文又在描述电路模型的方程中引入了等效分布电感和等效分布电容两个概念,它们是磁绝缘稳态的状态参数的函数。已有文献未见类似研究。
本文最后一个研究内容是量化无损磁绝缘形成过程前后的线电压和线电流变化。磁绝缘形成是真空传输状态和磁绝缘稳态之间的过渡阶段,分有损磁绝缘形成过程(过程中电子可以到达阳极)和无损磁绝缘形成过程(过程中由于线电流在极间产生了很强磁场,电子无法到达阳极)两类。无损磁绝缘形成过程在传输强流的负载限制型MITL(其线长度相对于脉冲波长很短,或称短线。Z加速器的MITL就属此类型)中经常出现,因此研究该过程在工程上有重要意义。本文首先研究了在磁绝缘形成过程中,极间点电荷与所处位置的电磁场之间的能量交换关系;然后利用这一关系进一步推导得到经历无损磁绝缘形成全过程的极间电子(大量极间电子是在过程中才进入极间的,并非经历了全过程)所获得的动能。此外,本文又研究得到了MITL横截面在无损磁绝缘形成过程中的总电磁场储能的变化。利用描述这些关系的方程组,本文给出了一个新的无损磁绝缘形成过程模型,它关联了无损磁绝缘形成过程始末时刻的线电压和线电流,且其中的参量都能根据真空线理论和前述极间电磁场分布的解析公式计算。本文利用Z加速器MITL在实验中观察到的三个现象验证了该模型,所得结果模拟结果与实验现象符合很好。该模型的建模思想与已有的磁绝缘形成模型完全不同,且已有磁绝缘形成模型不能计算无损磁绝缘形成过程导致的线电流和线电压变化。
Since CTBT was signed in 1996,Above Ground Experiments have become a focus in nuclear weapon states.At the end of last century,the Sandia National Laboratory of the United States found that using the fast Z-pinch driving wire array,the condition of high energy density physics required by the nuclear explosion simulation could be obtained and the fusion ignition could be achieved in a relatively economical manner.So the design of large fast Z-pinch facility has become a focus in the area of pulse power technology. Magnetically Insulated Transmission Line(MITL),functioning as conflux and transmission of pulse power,is a key component in fast Z-pinch facility.
Because electrons emitting from cathode are prevented to reach at anode by magnetic-field produced by linear-current of MITL,the power flow in MITL can still transmit ahead with flow density up to TW/cm~2 level.The model of the MITL is different from that of vacuum transmission line.
The theories of MITL,which include magnetic-insulation steady state model and magnetic-insulation formation process model,occurred early in 1921 and developed between 1970s and 1990s.These theories mainly study the tracks of electron in gap of MITL during magnetically insulated transmission.
These theories have been used not only to explain the phenomena of magnetic-insulation transmission but also to construct MITL circuit model.However,these theories can not resolve the following problems in MITL circuit modeling:(1) how to compute the distribution parameters of magnetically-insulated steady state circuit model;and(2) how to compute the change of linear-current and -voltage caused by magnetically-insulated formation process without space electron loss.This paper focuses on these two problems.
Firstly,this paper constructs a variable space(h_2,C_1,γ) basing on the laminar flow model of Creedon which is a theory of magnetically-insulated steady state,and then the analytic equations of distributions of electromagnetic field,charge density and current density under magnetically-insulated steady state in the gap of MITL are described in the variable space.However,the model of Creedon does not construct such a variable space,nor give the distribution equations of these parameters.Using these distribution equations,this paper obtained these curves of distributions of electromagnetic field and so on in the gap of Z-accelerator MITL.Moreover,by using these distribution equations,this paper proves that the laminar flow model of Creedon is consistent physically with that of Mendel which was deduced from the arbitrary momentum model of Mendel and widely used in engineering. Mendel's thought of arbitrary momentum model of magnetically-insulated steady state is completely different from that of Creedon's laminar flow,so whether there was different between the laminar flow model of Mendel and that of Creedon is still a problem for a long time.
Secondly,with these analytic equations of electromagnetic field and so on,this paper computes distributed-inductance and -capacitance in MITL circuit model of magnetically-insulated steady state.It finds that,contrary to vacuum transmission state which geometry boundaries of current loop and charge distribution zones are fixed,the geometry boundaries of linear-current loop and linear-charge distribution zones under magnetically-insulated steady state are varied.Therefore,this paper defines the distributed-inductance and -capacitance of magnetic-insulation steady state with tensor,and explains the relationship of distributed-inductance and -capacitance between the state parameters of magnetically-insulated steady state and the geometry of the distribution zones of current loop and charges.However,since the tensors of distributed-inductance and -capacitance can not simplify the circuit model,this paper defines also equivalent-distributed-inductance and -capacitance to simplify the circuit model.The similar investigations are not found in the existing lectures.
The final problem addressed in this paper is to determine the quantitative relationship between the linear-voltage and -current at start and terminal time during magnetic-insulation formation process of without electron loss.Formation of magnetic-insulation is a transition between vacuum transmission state and magnetic-insulation steady state,including formation processes with electron loss and that without electron loss.The formation process without electron loss occurs often in the load-limited MITL which length is extremely shorter than the pulse length and the linear-current are very large.Investigation the magnetic-insulation formation process without electron loss could be of great importance for design of MITL. This paper studied the relationship of exchange between the space-electron kinetic energy and electromagnetic-field energy during the magnetic-insulation formation process,and then derives an equation on the total kinetic energy of space-electrons which exit in the whole process and an equation on the changes of total energy of electromagnetic field on MITL cross-section during the process.By these equations,this paper presented a new model of magnetic insulation formation process without electron loss,and then the change of linear-voltage and -current at the start and end time of the formation process was determined. This paper validates the model by three phenomena observed in Z accelerator's MITL,and the simulation results are well consistent with those phenomena.The existing magnetic insulation formation model can not determine the change of linear-current and -voltage caused by magnetic insulation formation process without electron loss.
MITL在阴极表面发生电子爆炸发射后,仍能够利用传导电流产生的自磁场箍缩在极间运动的电子,使其无法到达阳极,从而确保脉冲功率继续向负载方向传输,功率流密度可达TW/cm~2量级。这一传输过程的物理模型与真空线传输有很大区别,被称为磁绝缘传输。
磁绝缘传输理论早在1921年就开始出现,上世纪70至90年代得到很大发展。磁绝缘传输理论包括磁绝缘稳态理论和磁绝缘形成理论两大类,主要根据极间电子的运动轨迹特征来研究磁绝缘传输现象。磁绝缘传输理论不仅用于解释和分析磁绝缘传输现象,还可以帮助建立MITL的电路模型,实现对MITL传输过程的电路模拟。但在MITL电路模型的建模过程中有两个问题没有解决:(1)如何利用现有磁绝缘稳态理论,计算电路模型中的分布参数;(2)如何计算无损磁绝缘形成过程(在磁绝缘形成过程中,没有电子到达阳极表面)导致的MITL传导电流和传导电压变化。本文主要围绕上述两个问题展开研究。
首先,作为研究基础,本文从Creedon的磁绝缘稳态层流模型出发,构筑了一个新的变量空间(h_2,C_1,γ),并在此变量空间中用简单的解析公式描述了磁绝缘稳态下的极间电磁场、电荷密度和电流密度分布。Creedon模型描述了磁绝缘稳态下的传导电流(又称线电流)、传导电压(又称线电压)和阴极表面电流等的关系,并未给出极间电磁场、电荷密度和电流密度的分布规律,因此这一结果完善Creedon的层流模型。利用相关结果,本文模拟计算了Z加速器MITL的极间电磁场等参量的分布,所得结果与真空传输状态有很大区别。此外,还利用这些分布公式证明了Creedon层流模型和Mendel层流近似模型这两个磁绝缘稳态模型在物理上具有一致性。Mendel层流近似模型在工程中应用广泛,是从Mendel关于磁绝缘稳态的任意动量模型近似而来,但Mendel的任意动量模型的建模思想与Creedon层流模型完全不同,因此Mendel层流近似模型与Creedon层流模型是否具有物理一致性,这是已有磁绝缘稳态理论中的一个疑问。
第二,利用磁绝缘稳态下极间电磁场在(h_2,C_1,γ)变量空间中的解析表达式,本文研究了MITL电路模型在磁绝缘稳态下的分布电感和分布电容表征问题。研究发现,磁绝缘稳态下的传导电流回路和线电荷分布区随脉冲功率传输状态变化,这与真空传输状态(电流回路和电荷分布区的几何边界固定)完全不同。因此,本文将磁绝缘稳态下的分布电感和分布电容用张量描述,由此从物理上清晰地看到分布电感和分布电容既与磁绝缘稳态的状态参数(线电压和线电流等)有关,又与电流回路和电荷分布区域的几何特征变化有关。不过,用张量去表征分布电感和分布电容不能简化磁绝缘稳态的电路模型,因此本文又在描述电路模型的方程中引入了等效分布电感和等效分布电容两个概念,它们是磁绝缘稳态的状态参数的函数。已有文献未见类似研究。
本文最后一个研究内容是量化无损磁绝缘形成过程前后的线电压和线电流变化。磁绝缘形成是真空传输状态和磁绝缘稳态之间的过渡阶段,分有损磁绝缘形成过程(过程中电子可以到达阳极)和无损磁绝缘形成过程(过程中由于线电流在极间产生了很强磁场,电子无法到达阳极)两类。无损磁绝缘形成过程在传输强流的负载限制型MITL(其线长度相对于脉冲波长很短,或称短线。Z加速器的MITL就属此类型)中经常出现,因此研究该过程在工程上有重要意义。本文首先研究了在磁绝缘形成过程中,极间点电荷与所处位置的电磁场之间的能量交换关系;然后利用这一关系进一步推导得到经历无损磁绝缘形成全过程的极间电子(大量极间电子是在过程中才进入极间的,并非经历了全过程)所获得的动能。此外,本文又研究得到了MITL横截面在无损磁绝缘形成过程中的总电磁场储能的变化。利用描述这些关系的方程组,本文给出了一个新的无损磁绝缘形成过程模型,它关联了无损磁绝缘形成过程始末时刻的线电压和线电流,且其中的参量都能根据真空线理论和前述极间电磁场分布的解析公式计算。本文利用Z加速器MITL在实验中观察到的三个现象验证了该模型,所得结果模拟结果与实验现象符合很好。该模型的建模思想与已有的磁绝缘形成模型完全不同,且已有磁绝缘形成模型不能计算无损磁绝缘形成过程导致的线电流和线电压变化。
Since CTBT was signed in 1996,Above Ground Experiments have become a focus in nuclear weapon states.At the end of last century,the Sandia National Laboratory of the United States found that using the fast Z-pinch driving wire array,the condition of high energy density physics required by the nuclear explosion simulation could be obtained and the fusion ignition could be achieved in a relatively economical manner.So the design of large fast Z-pinch facility has become a focus in the area of pulse power technology. Magnetically Insulated Transmission Line(MITL),functioning as conflux and transmission of pulse power,is a key component in fast Z-pinch facility.
Because electrons emitting from cathode are prevented to reach at anode by magnetic-field produced by linear-current of MITL,the power flow in MITL can still transmit ahead with flow density up to TW/cm~2 level.The model of the MITL is different from that of vacuum transmission line.
The theories of MITL,which include magnetic-insulation steady state model and magnetic-insulation formation process model,occurred early in 1921 and developed between 1970s and 1990s.These theories mainly study the tracks of electron in gap of MITL during magnetically insulated transmission.
These theories have been used not only to explain the phenomena of magnetic-insulation transmission but also to construct MITL circuit model.However,these theories can not resolve the following problems in MITL circuit modeling:(1) how to compute the distribution parameters of magnetically-insulated steady state circuit model;and(2) how to compute the change of linear-current and -voltage caused by magnetically-insulated formation process without space electron loss.This paper focuses on these two problems.
Firstly,this paper constructs a variable space(h_2,C_1,γ) basing on the laminar flow model of Creedon which is a theory of magnetically-insulated steady state,and then the analytic equations of distributions of electromagnetic field,charge density and current density under magnetically-insulated steady state in the gap of MITL are described in the variable space.However,the model of Creedon does not construct such a variable space,nor give the distribution equations of these parameters.Using these distribution equations,this paper obtained these curves of distributions of electromagnetic field and so on in the gap of Z-accelerator MITL.Moreover,by using these distribution equations,this paper proves that the laminar flow model of Creedon is consistent physically with that of Mendel which was deduced from the arbitrary momentum model of Mendel and widely used in engineering. Mendel's thought of arbitrary momentum model of magnetically-insulated steady state is completely different from that of Creedon's laminar flow,so whether there was different between the laminar flow model of Mendel and that of Creedon is still a problem for a long time.
Secondly,with these analytic equations of electromagnetic field and so on,this paper computes distributed-inductance and -capacitance in MITL circuit model of magnetically-insulated steady state.It finds that,contrary to vacuum transmission state which geometry boundaries of current loop and charge distribution zones are fixed,the geometry boundaries of linear-current loop and linear-charge distribution zones under magnetically-insulated steady state are varied.Therefore,this paper defines the distributed-inductance and -capacitance of magnetic-insulation steady state with tensor,and explains the relationship of distributed-inductance and -capacitance between the state parameters of magnetically-insulated steady state and the geometry of the distribution zones of current loop and charges.However,since the tensors of distributed-inductance and -capacitance can not simplify the circuit model,this paper defines also equivalent-distributed-inductance and -capacitance to simplify the circuit model.The similar investigations are not found in the existing lectures.
The final problem addressed in this paper is to determine the quantitative relationship between the linear-voltage and -current at start and terminal time during magnetic-insulation formation process of without electron loss.Formation of magnetic-insulation is a transition between vacuum transmission state and magnetic-insulation steady state,including formation processes with electron loss and that without electron loss.The formation process without electron loss occurs often in the load-limited MITL which length is extremely shorter than the pulse length and the linear-current are very large.Investigation the magnetic-insulation formation process without electron loss could be of great importance for design of MITL. This paper studied the relationship of exchange between the space-electron kinetic energy and electromagnetic-field energy during the magnetic-insulation formation process,and then derives an equation on the total kinetic energy of space-electrons which exit in the whole process and an equation on the changes of total energy of electromagnetic field on MITL cross-section during the process.By these equations,this paper presented a new model of magnetic insulation formation process without electron loss,and then the change of linear-voltage and -current at the start and end time of the formation process was determined. This paper validates the model by three phenomena observed in Z accelerator's MITL,and the simulation results are well consistent with those phenomena.The existing magnetic insulation formation model can not determine the change of linear-current and -voltage caused by magnetic insulation formation process without electron loss.
引文
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44 王文斗,谢卫平,宋盛义,等.四种磁绝缘传输线的横向空间电荷流,强激光与离子束,Vol..18,No.3,p525-528.
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46 KARAT软件说明书,私人交流资料。
47 W.E.Weseloh.TLCODE:a Transmission Line Code for Pulsed Power Design,IEEE.Pro.of the 7~(th)International Pulse Power Conference,1989,p989-992.
48 M.L.Kiefer,and M.M.Winder.SCREAMER:a Single Line Pulsed Power Design Tool,IEEE.Pro.of the 5~(th) International Pulse Power Conference,1985,p685-688.
49 谢卫平,王文斗,邓建军,等.快Z箍缩物理过程的PISPICE电路模拟方法分析,《强激光与粒子束》,2003,Vol 15,No01,p61-63。
50 P.A.Corcoran,et.Al.PBFA-Z Vacuum Section Design Using TLCODE Simulation,Pro.of the 11~(th)International Pulse Power Conference,1997,p466-473.
51 K.W.Struve,T.H.Martin,R.B.Spielman,W.A.Stygar,et.al.Circuit-code Modeling of the PBFA-Z for Z-pinch Experiments,Pro.of the 11~(th) International Pulse Power Conference,1997,p 162-167.
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55 宋盛义,冯晓辉,周之奎,等.共顶点同轴圆锥形及园盘形传输线的电参数计算公式,强激光与粒子荣,Vol.16,No.2,2004,p256-260.
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58 陈振国,“微波技术基础与应用”,北京邮电大学出版社.
59 王莹,《高功率脉冲电源》,原子能出版社,1989.
60 G.A.Mesyats,D.I.Proskurovsky.Pulsed Electrical Discharge in Vacuum,Springer Series on Atoms and Plasma.,Springer-Verlag Berlin,1989.
61 R.V.Latham.High Voltage Vacuum Insulation:the Physical Basis,A Subsidiary of Harcourt Brace Jovanovich.Academic Press Limited,London,1995.
62 Burkhard JUTTNER.Vacuum Breakdown,Nuclear Instruments and Methods in Physics Research,1988,p390-396.
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