Electron energy distribution function and dense-gas ionization in the presence of a strong field

The mechanism for dense-gas ionization is analyzed in the case when the deceleration of electrons by gas can be neglected in the equation of motion of a single electron. An expression for the electron energy distribution function in the presence of a strong field is derived. The characteristic width of the distribution corresponds to the energy acquired by the electron at a length determined by the inverse Townsend coefficient. The electron energy distributions are calculated for various distances form the cathode. It is demonstrated that the distribution becomes independent of the coordinate at a distance from the cathode that is significantly greater than the inverse Townsend coefficient. In this case, the distribution coincides with the distribution obtained with analytical calculations. The absence of the coordinate dependence is realized even in the presence of an extremely strong field when, in accordance with the commonly accepted point of view, the majority of electrons are runaway electrons.     

纳秒脉冲下高能量快电子逃逸过程的计算

基于快电子的逃逸击穿机理将是一种能解释纳秒脉冲高过电压倍数下气体放电现象的理论，对高能量快电子的逃逸运动、碰撞电离引导电子崩的发展等进行了分析，并根据电子能量与阻力关系式，对电子的俘获或逃逸过程进行了计算.结果表明外加场强越高，更多的电子能逃逸，逃逸的能量阈值越低，气压对电子的逃逸过程影响也较大.同时也定性描述了纳秒脉冲下逃逸击穿放电过程. 关键词： 气体放电 快电子 逃逸击穿 纳秒脉冲     

Numerical Analysis of Electron Runaway in the Presence of Enhanced Field in the Vicinity of a Microtip

Technical Physics - Transition of field-emission electrons to the runaway regime in the region of enhanced electric field determined by the configuration of a microtip on a cathode is studied at...     

On the influence of the voltage pulse rise time and cathode geometry on the generation of a supershort avalanche electron beam

The influence of the voltage pulse rise time on the amplitude of a runaway electron beam and X-ray generation in air and nitrogen under atmospheric pressure is studied experimentally and theoretically. Generalization of the whistle criterion for the case of a nonuniform field is suggested. It is shown that the maximal energy of beam electrons and the beam current amplitude grow when the voltage pulse rise time decreases. It is found that the amplitude of the runaway electron current reaches a maximum at a certain curvature of the cathode. The maximal energy of electrons increases when the radius of curvature of the cathode exceeds the value at which the beam current amplitude is the highest. If the field is nonuniform, its critical value at which many electrons run away is more than an order of magnitude lower than in the uniform field.     

Simulations of plasma formation in the cathode sheath of an efficient excimer lamp

Based on the available experimental data and computer simulations, analytical approximations of the quantities characterizing electron multiplication in the cathode sheath are proposed. The critical electric field is found above which runaway electrons are observed. Using the approximations proposed, the dependences of the plasma parameters (the electron and ion densities and currents and the electric field strength) on the distance from the cathode are analyzed. Simple formulas for the total current, the cathode sheath thickness, and the cathode potential drop as functions of the electric field on the cathode surface are derived.     

Investigating the separatrices for the runaway threshold of cosmic ray electrons in a thunderstorm atmosphere

Using a modified GEANT4 code, we calculated the probabilities for cosmic ray electrons to become runaway particles in an electric field with a strength ranging from 0 to 5 kV/cm. About 10 million trajectories were calculated for particles with initial energies of 0.1 to 100 MeV. Instead of a single separatrix determining the region of runaway electrons, a set of curves connecting points with equal probabilities of a runaway regime (from 0 to 100%) was obtained. It was shown that not only is the threshold for a runaway regime probabilistic in character, but the critical field as well. This must be considered when calculating variations in the intensity of cosmic rays during thunderstorms.     

On the mechanism of the runaway of electrons in a gas: The upper branch of the self-sustained discharge ignition curve

Based on the results of simulation by the method of particles, it is shown that the Townsend mechanism of electron multiplication in a gas at a sufficiently large electrode spacing is valid at least up to such large values of E/p at which relativistic electrons are generated. On the other hand, the phenomenon of electron runaway in a gas is determined by the electrode spacing, which must be either comparable with or smaller than the characteristic electron multiplication length, rather than the local criteria accepted presently. It is shown that, for a particular gas, the critical voltage across the electrodes at which the runaway electrons comprise a significant fraction is a universal function of the product of the electrode spacing by the gas pressure. This function also determines the condition of self-sustained discharge ignition. It not only incorporates the known Paschen curve but also additionally contains the upper branch, which describes the absence of a self-sustained discharge at a high voltage sufficiently rapidly supplied across the electrodes.     

近地雷暴电场与羊八井地面宇宙线关联的模拟研究

雷暴期间地面宇宙线强度变化的研究对理解大气电场加速宇宙线次级带电粒子的物理机理具有重要意义. 分析西藏羊八井ARGO实验中2012年大气电场的数据后发现, 近地雷暴电场的强度可达1000 V/cm甚至更高. 用Monte Carlo方法模拟研究了近地雷暴电场与羊八井地面宇宙线强度的关联. 当雷暴电场强度(取1500 V/cm)大于逃逸电场时, 宇宙线次级粒子中正、负电子的数目呈指数增长, 在大气深度约520 g/cm²处达到极大值, 与Gurevich等提出的相对论电子逃逸雪崩机理和Dwyer理论相符. 当雷暴电场强度小于逃逸电场时, 在所有负电场范围和大于600 V/cm的正电场范围, 总电子数目随电场强度的增大而增加; 当正电场小于400 V/cm时, 总电子数目均出现一定幅度的下降; 在电场为400–600 V/cm范围内, 总电子数目的变化与原初粒子的能量有关, 原初能量小于80 GeV时, 其次级粒子中总电子数目增加, 原初能量在80–120 GeV 范围内时, 总电子数目变化不明显, 原初能量大于120 GeV时, 总电子数目出现下降, 下降幅度约4%. 模拟结果可对羊八井ARGO实验的观测结果给予合理的解释.     

Spectra of electrons and X-ray photons in a diffusive nanosecond discharge in air under atmospheric pressure

The spectra of electrons and X-ray photons generated in nanosecond discharges in air under atmospheric pressure are investigated theoretically and experimentally. Data for the discharge formation dynamics in a nonuniform electric field are gathered. It is confirmed that voltage pulses with an amplitude of more than 100 kV and a rise time of 1 ns or less causing breakdown of an electrode gap with a small-radius cathode generate runaway electrons, which can be divided into three groups in energy (their energy varies from several kiloelectronvolts to several hundreds of kiloelectronvolts). It is also borne out that the formation of the space charge is due to electrons appearing in the gap at the cathode and a major contribution to the electron beam behind the foil comes from electrons of the second group, the maximal energy of which roughly corresponds to the voltage across the gap during electron beam generation. X-ray radiation from the gas-filled diode results from beam electron slowdown both in the anode and in the gap. It is shown that the amount of group-3 electrons with an energy above the energy gained by runaway electrons (in the absence of losses) at a maximal voltage across the gap is much smaller than the amount of group-2 electrons.     

Spectrum of fast electrons in a dense gas in the presence of a nonuniform pulsed field

The problems of gas preionization in discharges related to laser physics are considered. The propagation of fast electrons injected from the cathode in the presence of a nonuniform nonstationary field and the motion of multiplying electrons at the edge of the avalanche in the presence of a nonuniform nonstationary field are simulated. The effect of the voltage pulse steepness and the field nonuniformity on the mean propagation velocity of fast electrons and their energy distribution is demonstrated. At certain combinations of the voltage pulse rise time and amplitude and at a certain time interval, the center of gravity of the electron cloud can move in the opposite direction relative to the direction of force acting upon electrons. It is also demonstrated that the number of hard particles (and, hence, the hard component of the x-ray bremsstrahlung) increases with both an increase in the voltage amplitude and a decrease in the pulse rise time. For nonoptimal conditions of the picosecond voltage pulse, an assumption is formulated: an electron beam in gas is formed due to the electrons at the edge of the avalanche rather than the background multiplication wave approaching the anode.     

Current dynamics during disruptions in large tokamaks

Self-consistent modeling of the evolution of the plasma current during disruptions in large tokamaks is presented, taking into account both the generation of runaway electrons and their backreaction on the electric field. It is found that the current profile changes dramatically, so that the postdisruption current carried by runaway electrons is much more peaked than the thermal predisruption current. Although only a fraction of the thermal current is converted into runaway electrons, the central current density increases significantly for typical parameters in JET and ITER. It is also shown that the radial runaway profile can easily become filamented in the radial direction.     

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

New understanding of mechanism of the runaway electrons beam generation in gases is presented. It is shown that the Townsend mechanism of the avalanche electron multiplication is valid even for the strong electric fields when the electron ionization friction on gas may be neglected. A non-local criterion for a runaway electron generation is proposed. This criterion results in the universal two-valued dependence of critical voltage U _cr on pd for a certain gas (p is a pressure, d is an interelectrode distance). This dependence subdivides a plane (U _cr , pd) onto the area of the efficient electron multiplication and the area where the electrons leave the gas gap without multiplication. On the basis of this dependence analogs of Paschen’s curves are constructed, which contain an additional new upper branch. This brunch demarcates the area of discharge and the area of e-beam. The mechanism of the formation of the recently created atomospheric pressure subnanosecond e-beams is discussed. It is shown that the beam of the runaway electrons is formed at an instant when the plasma of the discharge gap approaches to the runaway electrons is formed at an instant when the plasma of the discharge gap approaches to the anode. In this case a basic pulse of the electron beam is formed according to the non-local criterion of the runaway electrons generation. The role of the discharge gap preionization by the fast electrons, emitted from the plasma non-uniformities on the cathode, as well as a propagation of an electron multiplication wave from cathode to anode in a dense gas are considered.     

Experimental observation of increased threshold electric field for runaway generation due to synchrotron radiation losses in the FTU Tokamak

The threshold electric field for runaway generation has been investigated during runaway suppression experiments by means of electron-cyclotron-resonance heating in the flattop phase of FTU discharges. Runaway suppression has been experimentally found to occur at electric fields substantially larger than those predicted by the relativistic collisional theory of runaway generation, ER=nee3lnΛ/4πε0(2)mec2. These experimental results are consistent with an increase of the critical electric field due to the electron synchrotron radiation losses. No runaway electrons are found in FTU experiments below the radiation threshold. These results support evidence for a new threshold electric field for runaway generation that accounts for the effect of the synchrotron losses, and which should be considered when making predictions on runaway generation and mitigation in devices such as ITER.     

Deceleration and acceleration of fast electrons in a dense gas in an electric field

The propagation of electrons in a gas at energies higher than the excitation energy of the K shell of the gas atoms is simulated numerically. Calculations show that, without a field, the penetration depth of the electrons into a gas heavier than nitrogen is limited primarily by their elastic collisions with atomic nuclei. For electrons moving in an electric field, the effect of elastic collisions is that there is no definite electric field strength above which an electron with a given energy will be continuously accelerated. Even in an electric field much stronger than the critical one, only a fraction of electrons are accelerated. The remaining electrons turn back due to elastic collisions and lose their energy in deceleration by the field. In this case, the propagation velocity of the centroid of the electrons tends to a constant value.     

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

Basing on the simulation results, it is shown that the Townsend mechanism of electron multiplication in a gas at sufficiently 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) defines not only well-known Paschen curve but also an additional branch, which describes the absence of a self-sustained discharge at a high voltages sufficiently rapidly supplied across the electrodes. Critical discharge voltage dependence for helium and xenon are presented.     

Numerical investigation of the methods for reducing the runaway electron beam divergence

We have performed a comparative numerical analysis of two methods for reducing the runaway electron beam divergence using an external magnetic field or a dielectric tube. The generation of runaway electrons takes place in an inhomogeneous medium that consists of a hot channel (spark channel, laser torch, etc.) surrounded by air under normal conditions. The model makes it possible to consistently calculate the formation of a subnanosecond gas discharge and the generation of accelerated electrons under these conditions. The possibility of effectively decreasing the runaway electron beam divergence using an external magnetic field, as well as a dielectric tube, has been demonstrated. However, the number of runaway electrons in the case with the tube is considerably smaller than in the case with the magnetic field due to the fact that some runaway electrons settle on the tube walls. The energy spectra of the runaway electrons significantly differ in these cases, which can be explained by the differences in the dynamics of the discharge formation.     

Leading Edge Erosion of a Low-Energy Beam Injected into a Gas in a Magnetic Field

The leading edge erosion of a low-energy high-current electron beam injected into a low-energy neutral gas in a magnetic field has been investigated. The system’s parameters at which a virtual cathode arises, the erosion duration of the beam leading edge, and the time of complete charge neutralization have been determined.     

Runaway-Ströme hoher Intensität in einer toroidalen Entladung

Intensive currents of runaway electrons with energies of 50 keV or more have been observed at high pressures in a plasma betatron in addition to betatron accelerated electrons at lower pressures. The measurements agree with the assumption that these electrons are accelerated in the external field while they are guided by the self magnetic field of the plasma current. Macroscopic instabilities and plasma waves can be excluded as accelerating mechanisms. The strong dependence of the runaway flux upon the gas pressure and the electric field can be explained by collisions between electrons and the other plasma particles. Furthermore the influence of the external magnetic field on the movement of the plasma current to the torus wall was investigated. A maximum circulating runaway current of more than 2000 A (Xenon) appeared when the plasma current was kept approximately in balance by the external magnetic field.     

Townsend coefficient,escape curve,and fraction of runaway electrons in copper vapor

Ionization and drift characteristics of electrons in copper vapor in the presence of an external electric field are analyzed. In contrast to normal gases, in copper vapor, the excitation energy of lower states is significantly lower than the ionization potential and the excitation cross section is several times greater than the ionization cross section at the incident-electron energy on the order of the ionization energy. This can affect the characteristics of electron bunching in gas. It is demonstrated that, as in previously studied gases, the notion of the Townsend coefficient remains meaningful even in the presence of strong fields at which the electric force exceeds the electron drag force acting in gas. The dependences of the main ionization and drift characteristics on the reduced field strength, the escape curve (which separates the region of effective electron multiplication and the region where electrons leave the discharge gap without multiplication), and the curves of equal efficiency for the formation of runaway electrons are obtained. It is demonstrated that a relatively high excitation cross section of copper levels leads to a sharper peak on the dependence of the Townsend coefficient on the field strength and a narrower region of the effective electron multiplication in comparison with previously studied gases.