A. A. Grishkov

On the dynamics of a subnanosecond breakdown in nitrogen below atmospheric pressures

The dynamics of a breakdown in a gas-filled diode with a highly inhomogeneous electric field was studied in experiments at a time resolution of ∼100 ps and in numerical simulation by the 2D axisymmetric particle-in-cell (PIC) code XOOPIC. The diode was filled with nitrogen at pressures of up to 100 Torr. The dynamics of the electric field distribution in the diode during the breakdown was analyzed, and the factors that limit the pulse duration of the runaway electron beam current at different pressures were determined.

Experimental investigation of electron beam in the squeezed state

The electron beam transported in a two-section drift tube of a SINUS-7 setup has been studied. A high-density electron beam in the “squeezed” state has been obtained with a relativistic factor γb below that corresponding to the limiting current (γ > Γ1/3).

Measuring the virtual cathode velocity

An electron beam with a virtual cathode (VC) transported in a two-section drift tube of a SINUS-7 high-current electron accelerator has been studied. The dependence of the VC velocity on the injected current has been experimentally determined for the first time. It is established that the VC motion in the drift tube is accompanied by microwave oscillations, which are caused by transient processes involved in the formation of a compressed electron beam.

The virtual cathode velocity during electron beam transport in a drift tube

A solution corresponding to a thin annular electron beam in a homogeneous drift tube featuring a uniformly moving virtual cathode (VC) has been obtained. The dependence of the VC velocity on the injected and transmitted currents is determined and it is established that this velocity has a limiting value. Theoretical results agree with the results of numerical calculations performed by means of the electromagnetic PIC code KARAT.

Stability of runaway electron beam currents in nitrogen at 100 Torr. Experiments and numerical simulation

This paper reports on a series of identical experiments and on a respective particle-in-cell and Monte Carlo simulation to investigate the stability of runaway electron beam currents produced in nitrogen at a highly inhomogeneous electric field. The experiments demonstrate a strong effect of cathode emissivity on the beam current. The numerical simulation shows that the cathode emissivity influences not only the current of the beam but also the mechanisms of its formation.

The current of an annular electron beam with virtual cathode in a drift tube

An analysis based on the laws of conservation of energy and the z components of the field and particle momentum shows that a thin magnetized annular electron beam in a homogeneous drift tube behind a virtual cathode under stationary conditions occurs in a “squeezed” state corresponding to a slow left-hand branch of the current characteristic with a relativistic factor in the interval 1≤γ≤Γ1/3. The beam current I1 behind the virtual cathode in a homogeneous drift tube can vary from zero up to a limiting value Ilim, while the injection currents (I2) and the current of electrons reflected from the virtual cathode (I3) for every stationary state are single-valued functions of I1 and fall within the intervals IF/2≤I2≤Ilim and 0≤I3≤IF/2, respectively, where IF is the Fedosov current.

Current in a pulsed gas breakdown at a highly inhomogeneous electric field

This paper reports on a particle-in-cell and Monte Carlo simulation of the evolution of a pulsed breakdown in a gas-filled diode at a highly inhomogeneous electric field. The simulation shows that even during the formation of a conducting plasma channel, the diode can experience a current flow capable of greatly decreasing the diode voltage compared to its value in idle mode. This current is almost independent of the gap width and is due to fast plasma motion from the cathode to the anode.

Motion of a virtual cathode in a cylindrical channel with electron beam transport in the “compressed” state

This paper studies the motion of a virtual cathode in a two-section drift tube with the formation and breakup of the “compressed” state of an electron beam. Experimental arrangements to intercept part of the injected current during the voltage pulse and to provide virtual cathode motion toward the collector are proposed. The arrangements were implemented on the SINUS-7 high-current electron accelerator. Theoretical and experimental dependences of the virtual cathode velocity on the injected current and cathode voltage are presented. The experimental data on virtual cathode motion agree with its theoretical model based on analytical solutions of equations assisted by computer simulation with the PIC code KARAT. The results of the work demonstrate the feasibility of controlling the virtual cathode motion which can be used in collective ion acceleration and microwave generation.

The electron beam with virtual cathode in a two-section drift tube

An analysis based on the law of conservation of the z component of field and particle momentum in a thin annular magnetized monoenergetic electron beam in a two-section drift tube composed of tube segments with different radii (R1<R2) allowed the critical injected beam current to be determined for which a virtual cathode, formed in the wider tube at the joint section, starts traveling through the narrower tube toward the beam injection region. A region behind the traveling virtual cathode features a “squeezed” single-flux state of the beam (corresponding to the “slow” left branch of the current characteristic, high charge density, but low relativistic factor). When the injected current decreases below a critical transition level (Iin<ITr), the virtual cathode returns to the initial position and restores the double-flux electron beam. This current is smaller than (Ilim1+Ilim2)/2, and, depending on R2, varies from the limiting transport current for the narrower section (Ilim1) up to IF/2, where IF is the Fedosov current for this tube section.

Effect of the ionization wave velocity on the current and voltage of a gas-filled diode

Here, continuing our research in the breakdown of a gas diode with a highly inhomogeneous electric field, we present an analytical model which relates the diode current and voltage to the ionization wave velocity from cathode to anode in an axisymmetric statement. The model shows that the voltages cross- and lengthwise the diode can differ greatly and that the difference increases as the wave moves faster. This effect should be taken into account when analyzing subnanosecond pulsed breakdowns in a highly inhomogeneous electric field, otherwise a large discrepancy is possible between measured and actual diode voltages. The analytical model is based on charge conservation laws and Lorentz transforms for electric field strengths and coordinates, and it has been verified using the KARAT particle-in-cell (PIC) and X-Object Oriented Particle-in-cell PIC/Monte Carlo codes. The simulation results agree well with the analytical model developed.