A. Ya. Ender

Switching of nonneutral plasma diodes. I. Analytic theory

The transient nature of the electron beam dynamics in plasma diodes caused by a weak instantaneous switching of the collector voltage is studied analytically. The solution for a pure electron vacuum diode, found recently [P. V. Akimov et al., J. Appl. Phys. 93, 1246 (2003)], is extended to treat the electron dynamics under the influence of an immobile ion background. In this case new branches of equilibria are obtained from which new perspectives for switching between different states can arise. Moreover, the space-charge limit (SCL) of the electrical current, well known for pure electron diodes, can be overcome by an appropriate choice of the branch and of the ion density. It is emphasized that the line of critical SCL points, obtained by a sweep of the collector voltage, coincides with the line of marginal stability of linear perturbations with respect to equilibria without reflection. For the switching analysis use is made of the Laplace transform technique, and a remarkably simple expression for the L...

Time-dependent regimes of a Bursian diode I: Stability of steady solutions

A study is made of physical phenomena characteristic of the Bursian diode—a plane vacuum diode with a monoenergetic electron beam. The paper consists of two parts. The first part is devoted to analyzing the stability of steady solutions against small perturbations. It is shown that there exists a critical current density below which all steady solutions with a virtual cathode that lie on branch B are stable. The second part is aimed at investigating the features of oscillatory solutions.

On the self-consistent states of a planar vacuum diode with an electron beam

The self-consistent stationary solutions for a planar vacuum diode with a monoenergetic electron beam are fully classified. Formulas are presented to calculate potential distributions of all types and the maximum electric current that can pass through the diode under steady-state conditions at an arbitrary applied voltage. The stability of the solutions is studied.

Some general properties of the nonlinear collision integral in the Boltzmann equation

A new method for computing matrix elements of the collision integral in the Boltzmann equation makes it possible to consider many problems of the kinetic theory of gases in a new way. Nonlinear kernels of the collision integral are studied and similarity relations, which simplify significantly the problem of constructing of such kernels, are proved.

The Pierce-diode approximation to the single-emitter plasma diode

The possibility of modeling fast processes in the collisionless single-emitter plasma diode (Knudsen diode with surface ionization, KDSI) by means of the Pierce-diode is studied. The KDSI is of practical importance in that it is an almost exact model of thermionic energy converters (TICs) in the collisionless regime and can also be used to model low-density Q-machines. At high temperatures, the Knudsen TIC comes close to the efficiency of the Carnot cycle and hence is the most promising converter of thermal to electric energy. TICs can be applied as component parts in high-temperature electronics. It is shown that normalizations must be chosen appropriately in order to compare the plasma characteristics of the two models: the KDSI and the Pierce-diode. A linear eigenmode theory of the KDSI is developed. For both nonlinear time-independent states and linear eigenmodes without electron reflection, excellent agreement is found between the analytical potential distributions for the Pierce-diode and the corres...

The transverse magnetic field effect on steady-state solutions of the Bursian diode

A study of steady-states of a planar vacuum diode driven by a cold electron beam (the Bursian diode) under an external transverse magnetic field is presented. The regime of no electrons turned around by a magnetic field only is under the consideration. The emitter electric field is evaluated as a characteristic function for the existence of solutions depending on the diode length, the applied voltage, and the magnetic field strength. At certain conditions, it is shown that a region of non-unique solutions exists in the Bursian diode when the magnetic field is absent. An expression for the maximum current transmitted through the diode is derived. The external magnetic field is put forth to control fast electronic switches based on the Bursian diode.

Matrix elements and kernels of the collision integral in the Boltzmann equation

This article elaborates upon our previous work in which some general properties of the matrix elements and kernels of the gain and loss terms of the collision integral were found. The object of study is the loss term of the collision integral, since related analytical expressions are simple. Formulas to calculate the matrix elements are derived. The kernels of power-law interaction potentials are completely investigated and constructed using analytical and numerical approaches.

Relations between nonlinear kernels of the collision integral

Previously, to solve the Boltzmann equation by the moments method with expansion of the distribution function by spherical Hermit polynomials, a new computational method was suggested which allowed to construct nonlinear matrix elements of the collision integral with very large indices. This made it possible to substantially advance in construction of the distribution function. Limitations to convergence of the distribution function that appear in moment method are eliminated if we come to expansion by spherical harmonics from expansion by spherical Hermit polynomials. In this case, a complex five-fold collision integral is replaced by a set of comparatively simple integral operators, and kernels Gl1,l2l(c, c1, c2) of these operators become the analog of matrix elements. We found the relations between expansions of the distribution function in the reference frames with various velocities of motion along marked axis. Starting from the invariance condition of the collision integral with respect to selection of such reference frames, we derived recurrent relations between the kernels with various indices. These relations allow us to construct any nonlinear kernel Gl1, l2l(c, c1, c2), if the kernel G0,00(c, c1, c2) is known.

Kinetics of ions in a neutral gas upon abrupt application of an electric field. II: Various models of interaction

A new method for calculating the matrix elements of the collision integral in the Boltzmann equation is used for studying the behavior of an ion impurity upon an abrupt application of an electric field. For five models of interaction, the behavior of mobility is analyzed and the evolution of the distribution function for various values of the electric field is illustrated. The initial stage of runaway of ions is studied in the case of the Coulomb interaction. Two methods for improving the convergence of the polynomial expansions of the distribution function are considered.

Time-dependent regimes of a Bursian diode II: Characteristic features of nonlinear oscillations

A study is made of the physical phenomena characteristic of nonlinear oscillations in a Bursian diode in the regime with a virtual cathode. The question of how the shape of the oscillations varies as the beam current density increases is investigated for the first time. Sharp jumps in the time evolution of the convective current are revealed, and their causes are explained. The reason is found for the onset of long-lived electrons, and their properties are analyzed.