Townsend coefficient and runaway of electrons at relativistic velocities

An electron-multiplication regime at large field strengths, in which case an electron can acquire a relativistic kinetic energy over the multiplication length, is considered. It is shown that, even in such superstrong fields, the Townsend electron-multiplication mechanism is valid if the distance between the electrodes is rather large. The Townsend coefficient and the drift velocity in helium are obtained in such fields. The electron-escape curve, which separates the region of efficient electron multiplication from the region where electrons escape from the gap without undergoing multiplication, is obtained.     

Boundary between the regions of drift and runaway of electrons outside the townsend discharge domain boundary

An explicit form of the boundary between the regimes of drift motion and runaway of electrons outside the boundaries between the drift regime and the Townsend discharge and between the Townsend discharge and the electron runaway regime is obtained.     

Townsend coefficient and efficiency of the formation of runaway electrons in neon

Basic ionization and drift properties are simulated for neon by the method of multiparticle dynamics. This calculation revealed that, in neon—in just the same way as in other gases that were studied previously—the Townsend ionization regime is realized even in strong fields if the distance between electrodes is rather large. The dependences of basic ionization and drift properties on the reduced electric-field strength are obtained. The results agree with available experimental data. The escape curve separating the region of efficient electron multiplication from the region in which electrons leave the discharge gap without undergoing multiplication is found for neon. The efficiency of the formation of a runaway-electron beam in helium and neon is simulated.     

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.     

等离子体中充入工作气体抑制电子逃逸行为分析

利用NaI闪烁体探测器组成的伽马射线探测系统和BF₃正比计数管、³He正比计数管和ZnS闪烁体探测器组成的中子探测系统,研究了欧姆放电平稳阶段充入工作气体后对逃逸电子产生过程的影响.实验结果表明:在欧姆放电平稳阶段充入工作气体严重影响了逃逸电子行为,充入的工作气体能有效抑制逃逸电子的产生.     

等离子体中充入工作气体抑制电子逃逸行为分析

利用NaI闪烁体探测器组成的伽马射线探测系统和BF3 正比计数管、3He正比计数管和ZnS闪烁体探测器组成的中子探测系统,研究了欧姆放电平稳阶段充入工作气体后对逃逸电子产生过程的影响。实验结果表明：在欧姆放电平稳阶段充入工作气体严重影响了逃逸电子行为,充入的工作气体能有效抑制逃逸电子的产生。     

Stimulation of high-frequency breakdown of gas in Uragan-3M torsatron by runaway electrons

In experiments on confinement and heating of plasma in the Uragan-3M torsatron, the method of high-frequency breakdown of the working gas is used. In these experiments, in conditions of a relatively stable magnetic field, the rf power supplied to the setup chamber has a frequency close to the ion-cyclotron frequency. Such a method of gas breakdown is not always sufficiently reliable. In our experiments, preliminary ionization of the working gas by the run-away electron beam is used for stabilizing the breakdown. This work contains the results of experiments on enhancement of the runaway electron beam and on the interaction of the runaway electron beam in the Uragan-3M torsatron with the HF electromagnetic pump field. This enables us to formulate a number of recommendations for using spontaneously formed beams of accelerated particles for stimulating the rf breakdown. Our results confirm the possibility of gas breakdown by runaway electrons.     

Conditions for runaway electrons in a gas diode with a strongly nonuniform electric field

The dynamics of runaway electrons in a gas diode in a sharply nonuniform electric field determined by the geometry of electrodes is considered. The analytical solution of the equation of motion of electrons for an edge cathode shows that their runaway at the periphery in the region of weak field is possible only if the applied potential difference exceeds a certain threshold determined by the interelectrode distance and the parameters of the gas. This condition supplements a classical runaway condition that the field strength at the emission edge of the cathode should be higher than a threshold value depending only on the parameters of the gas. According to our estimates, this new condition imposes higher requirements than the classical condition on the field strength in the limit of the strongly sharp edge of the cathode.     

Commensurability oscillations by runaway and pinned electrons

We report on an investigation of commensurability oscillations in antidot square-lattices, and show that the commensurate peaks in resistivity ρ_xxderive from two kinds of electron: runaway and quasipinned electrons. The runaway electrons, which skip away along the antidot arrays, increase the value of conductivity σ_xx; and the quasipinned electrons, which orbit some antidots for a long time, decrease the value of σ_xx. Therefore, by competition between the two different types of electron, the conductivity σ_xxis determined. The conductivity σ_yxin the antidot lattice always has dips at the peaks in ρ_xx. As a result, by combining the of values of σ_xxand σ_yx, the resistivity is determined through the orthodox relation of ρ_xx =  σ_xx/ (σ_xx²  +   σ_yx²).     

Formation of the distribution function for runaway electrons in strong fields of pulsed gas discharges

A simplified Boltzmann equation describing the escape of electrons in a weakly ionized gas is constructed. The electric fields are assumed to be so strong that all electrons are runaway electrons and the electron distribution function is strongly anisotropic. The equation is solved analytically, and it is shown that the electron density in relatively weak fields exponentially increases with time, while the momentum dependence of the distribution function exponentially decreases. In strong fields, the electron density increases with time logarithmically and the momentum dependence of the electron distribution function is nonmonotonic. The characteristic scales of time and energy, which determine different scenarios, are obtained.     

The runaway effect in a Lorentz gas

The Lorentz gas of charged particles in a constant and uniform electric field is studied. The gas flows through the medium of immobile, randomly distributed scatterers. Particles with velocity v suffer collisions with frequency proportional to ¦v¦ ⁿ . Forn < 0 runaway of the gas is forced by the field: the mean velocity of the flow increases without bounds. By a simple physical argument an integral relation is established between the probability of collisionless motion and the velocity distribution. It is then shown that whenn < –1 a fraction of particles moves as if the scattering centers were absent. The detailed discussion of this uncollided runaway is presented. Some qualitative features of the velocity distribution are illustrated on rigorous solutions in one dimension.     

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.     

Transverse runaway of hot electrons and the electron-temperature approximation

This paper discusses the transverse runaway effect in the electron-temperature approximation. The combinations of scattering mechanisms and the corresponding threshold electric fields for which transverse runaway develops are determined. It is shown that the transverse-runaway effect is not associated with any approximation. Zh. éksp. Teor. Fiz. 113, 688–692 (February 1998)     

Positron creation and annihilation in tokamak plasmas with runaway electrons

It is shown that electron-positron pair production is expected to occur in post-disruption plasmas in large tokamaks, including JET and JT-60U, where up to about 10(14) positrons may be created in collisions between multi-MeV runaway electrons and thermal particles. If the loop voltage is large enough, they are accelerated and form a beam of long-lived runaway positrons in the direction opposite to that of the electrons; if the loop voltage is smaller, the positrons have a lifetime of a few hundred ms, in which they are slowed down to energies comparable to that of the cool ( less, similar 10 eV) background plasma before being annihilated.     

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.     

Synchrotron radiation intensity and energy of runaway electrons in EAST tokamak

A detailed analysis of the synchrotron radiation intensity and energy of runaway electrons is presented for the Experimental Advanced Superconducting Tokamak(EAST). In order to make the energy of the calculated runaway electrons more accurate, we take the Shafranov shift into account. The results of the analysis show that the synchrotron radiation intensity and energy of runaway electrons did not reach the maximum at the same time. The energy of the runaway electrons reached the maximum first, and then the synchrotron radiation intensity of the runaway electrons reached the maximum.We also analyze the runaway electrons density, and find that the density of runaway electrons continuously increased. For this reason, although the energy of the runaway electrons dropped but the synchrotron radiation intensity of the runaway electrons would continue rising for a while.     

Mechanism of generation of runaway electrons in a lightning leader

A mechanism is analyzed of the electric field enhancement in a lightning leader up to the level permitting runaway of low-energy electrons. The ionization wave propagation in the preionized domain in front of the leader makes it possible to overcome the limitation imposed on the field intensity by transversal expansion of the leader front. By means of numerical simulations, it is demonstrated that, at the final stage of formation of a new leader step, generation of an electric field is possible in the channels of the streamer zone ahead of the new step with intensity sufficient for electron runaway and, consequently, for producing the X-ray and γ-ray pulses observed in correlation with the lightning leader steps.     

Energy limit of runaway electrons in the HT-7 tokamak

The energy limit of runaway electrons in the HT-7 tokamak is investigated by measuring the synchrotron radiation originated from the runaway electrons and the hard X-ray radiation (HXR) when they hit the first wall. An upper boundary on the runaway energy can appear due to the resonance between the electron gyromotion and the magnetic field ripple in the low field side. The experimental derived maximum energy in the core is about 26 MeV, and maximum energy in the edge region is blocked to no more than 5 MeV. This resonance interaction of runaways with the nth harmonic of the magnetic field ripple can account for the observed energy gap of the runaways.