Numerical investigation of the physical model of a high-power electromagnetic wave in a magnetically insulated transmiss
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MA DYNAMICS
Numerical Investigation of the Physical Model of a HighPower Electromagnetic Wave in a Magnetically Insulated Transmission Line A. A. Samokhin Troitsk Institute for Innovation and Fusion Research, Troitsk, Moscow oblast, 142092 Russia Received April 28, 2009
Abstract—An efficient numerical code for simulating the propagation of a highpower electromagnetic pulse in a vacuum transmission line is required to study the physical phenomena occurring in such a line, to analyze the operation of presentday megavolt generators at an ~10TW power level, and to design such new devices. The main physical theoretical principles are presented, and the stability of flows in the nearthreshold region at the boundary of the regime of magnetic selfinsulation is investigated based on onedimensional telegraph equations with electron losses. Numerical (difference) methods—specifically, a method of characteristics and a finitedifference scheme—are described and their properties and effectiveness are compared by ana lyzing the highfrequency modes. DOI: 10.1134/S1063780X10020066
INTRODUCTION A vacuum transmission line (VTL) is an important component of presentday highpower pulsed current generators with a pulse duration of ~100 ns and a cur rent amplitude of ~10 MA that are used to produce soft X radiation from selfcompressed emitting discharges ignited by exploding wire liners [1]. The density of the power transmitted to the load increases with the energy density to reach values at which the field strength in a VTL exceeds the autoelectronic explosive emission threshold at the cathode surface, ~100 kV/cm [2]. An unlimited emission from the electrode plasma pro duces electrons in the interelectrode gap and initiates the shunting current there, the maximum amplitude of which, at a given voltage and a zero magnetic field, is restricted by the space charge. The magnetic field dis torts straight electron trajectories: it turns the elec trons toward the cathode, thereby giving rise to the magnetic selfinsulation effect at a sufficiently high current in the line [3]. In the singleparticle approxi mation, the limitation on the current is obtained by comparing the electron gyroradius and the length of the interelectrode gap:
I > I Ae γ − 1/ Z , 2
where IAe = 17 kA is the electron Alfvén current, Z is the impedance of the line, γ = 1 + eV/mec2, V is the anode potential, and –e and me are the charge and mass of an electron. In the presence of the vacuum electron current, the magnetic selfinsulation current is higher (by an amount of RC, the dimen sionless impedance is Z = 2ln(RA/RC). For the VTL portion over which the interelectrode distance dAC is much less than the line radius R = 1/2(RA + RС), we can use the approximate relationship Z = 2dAC/R Ⰶ 1, regardless of the line geometry. In a uniform VTL (C, L = const) without losses (je = 0), the solution to Eqs. (1.1a) depends on the wave impedance ρ and is represented as a superposi tion of two waves—an incident wave with the ampli tude A and a reflected wave with
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