On the mechanism of the runaway of electrons in a gas: The upper branch of the paschen curve

Abstract

Basing on the simulation results, it is shown that the Townsend mechanism of electron multiplication in a gas at su¯ciently large interelectrode distances is valid at least up to such large values of E/p at which relativistic electrons are generated. Correspondingly, the runaway electron producing in a gas is determined not by the local criteria accepted presently, but by the ratio of interelectrode distance and the characteristic electron multiplication length. It is shown that the critical discharge voltage U, at which the runaway electrons appear in a given gas, is a function of the product of the interelectrode distance by the gas pressure. This function (U -pd dependence) de nes not only well-known Paschen curve but also an additional branch, which describes the absence of a self-sustained discharge at a high voltages su¯ciently rapidly supplied across the electrodes. Critical discharge voltage dependence for helium and xenon are presented.

Runaway of electrons in dense gases and mechanism of generation of high-power subnanosecond beams

“…2 Dependence of cross-sections of electron -He atom collision on energy: curve 1 is the cross-section of elastic collisions σ el (ε); curve 2 is the ionization cross-section σ i (ε); curve 3 is the excitation cross-section 2 1 P; curve 4 is the excitation cross-section 2 1 S; curve 5 is the excitation cross-section 2 3 P; curve 6 is the excitation cross-section 2 3 S (according to [17-19, 22, 24] [18,19,22]. Dependence of cross-sections of electron -N 2 molecule collision on energy (a) and energy loss due to excitation of vibrations (b) and electronic states (c): curve 1 is the total cross-section; curve 2 is the ionization cross-section; curve 3 is the cross-section of dissociative ionization; curve 4 is the cross-section of excitation of electrons; curve 5 is the cross-section of excitation of vibrations (according to [21,22] Fig. 6 Dependence of cross-sections of electron -SF 6 molecule collision (in cm 2 ) on energy (ŕ) and energy loss (in eV) due to excitation of electrons (b) and vibrations (c): σ el is the crosssection of elastic collisions; σ att is the cross-section of attachment; σ vib is the cross-section of excitation of vibrations; σ ex is the cross-section of excitation of electrons; σ ion1 , σ ion2 , σ ion3 are the ionization cross-sections (according to [34,35] Fig.…”

“…We will discuss below the results of simulations of multiplication process for He [17-19, 22, 24], Ne [25], Xe [18,19,22], N 2 [21,22] and SF 6 [19], which were performed within the framework of a model described in [34,35]. In these simulations an electron motion in a flat gap (between two planes spaced by a distance dand driven by the applied voltage U ) was considered.…”

“…The Paschen curves usually have a right-hand and left branches, which are directed from the minimum U br (pd ) in the area of the large and small values of pd. However, according to [17][18][19][20][21][22][23][24][25], the curve of ignition of the self-sustained discharge should contain also the upper branch. This branch stipulated by the falling of α i with the encrease of E/p demarcates the area of discharge and the area of e-beam.…”

“…Our interpretation of the experiments [26][27][28][29][30][31][32][33] described in [26,27] is based on a non-local criterion (9) for the occurrence of a large amount of electrons leaving the volume without multiplication [17][18][19][20][21][22][23][24][25] and on a mechanism suggested in [26,27]. Two phases can be distinguished in the mechanism of an electron beam formation under atmospheric pressure.…”

“…Contrary to this viewpoint we will show that the mechanisms of the electron runaway in gas-discharge plasma and in fully ionized plasma differ radically. Namely, both the numerical simulations and analytic consideration show that in the case of a gas-discharge plasma with sufficiently large distances between anode and cathode there is no acceleration of quite all electrons [17][18][19][20][21][22][23][24][25]. If the interelectrode distance is sufficiently large, the predominant number of electrons ionizes the gas in the Townsend mode at arbitrarily high field strength.…”