"Kinetic phenomena in rarefied gases and plasma"
RESEARCH AREA:
Head: leading researcher, prof A.Ya.Ender
The Group consists of 7 researchers (including 1 prof. and 4 PhD) and 3 technicians.
The main lines of work
I. Physical processes in TIC under a Knudsen mode
In the Laboratory, studies on thermionic energy converters (TIC) have been carried out since 1957. In 1962, in-pile tests of TIC fuel element were successfully accomplished, being a background to manufacture a national in-pile converter with TIC, TOPAZ-2. These studies were conducted under prof. Yu.A.Dunaev and prof. M.B.Barabash.
For more insight into physics of the processes essential in TIC operating, the studies of the kinetic processes in plasma and the plasma-electrode interaction were initiated.
Historically, the Laboratory proceeds the studies on physics (both theoretical and experimental) TIC in the collisionless (Knudsen) mode. The experiment are accomplished with the devices of Ba-Cs filling. Complex investigations give an opportunity to reveal the main physical points of the Knudsen regime and optimize the output characteristics of TIC. For the first time, TIC parameters were obtained at the high (2300-2500K) and the ultrahigh (over 2500K) emitter temperatures. It was proved the undisputed gain of the Knudsen TIC mode over the traditional ones at such temperatures.
It was advanced a project of TIC with solar heating of the emitter in a domain of high and ultrahigh emitter's temperatures. The heating was carried out with two-stage concentrator including the parabolic mirror and a focon. The calculation to the optimization of such concentrators were carried out. It was developed a space bimodal power and propulsion system with solar heated TIC.
Equipment
3 vacuum setups with microprocessing system for emitter's heating and temperature stabilization up to 3000K with 1% accuracy, the experimental data auto-processing system.
Main publications
II. Nonlinear time-dependent and oscillation processes in a collisionless plasma
To study the dynamic processes of collisionless plasma, it was developed 1D numerical code which asserts the calculation of a velocity distribution function of the charged particles with needed accuracy, being of the largest capabilities as compared with all known codes in plasma physics.
The investigations of the time-dependent and oscillation processes in TIC Knudsen regime were accomplished. A theory of stability of equilibrium solutions and theory of nonlinear oscillations in TIC was developed. TIC as high-effective generator of alternating current was advanced.
The nonlinear electron processes in beam-plasma diodes were studied in details. All the equilibrium solutions of the diode with uniform ion background were revealed with arbitrary compensation rate of electrons' charges by ions and their stability was investigated. The effects of a lot of parameters on the oscillation and transient processes in such diodes were studied.
Main publications
III. Structure of the shock wave and kinetics of physical-chemical permutations
Distribution function of the particles' velocities turns out to be the strongly nonequilibrium one through a shock. The shock's width is of order of a free path length and the changes in the main gasdynamic parameters can be of orders higher than their initial values. Under such large gradients, a common transport theory can not be applied, and only a solution of a full Boltzmann equation can give an answer about the processes inside the shock wave. The extreamely strong deviations from equilibrium should be expected concerning the interactions between the shock waves.
A disturbance of the distribution function over velocities through the shock or in an interaction region of the shock waves can involve an essential acceleration in the chemistry processes and physical permutations (excitation, ionization, etc.) in a gas. These processes can be of importance being an original exciter of one or other reaction in a gas. To describe the processes under question and to be able to predict the intensities of these processes, not only a mere solution of the Boltzmann equiation is needed but a possibility to build-up the distribution function in a domain of the highest velocities.
At present, when solving the problems of kinetics, the most widely used are the different variants of the Monte Carlo method. This method is successful enough in obtaining the main characteristics of a gas under large deviations from equilibrium. Commonly, it works fairly well in solving the engineer problems. However, the serious troubles occur when building-up a distribution function in a domain of large velocities. This is due to a small amount of the particles in the domain under question as well as a drastic growth in errors at the statistical modeling. Recently, the principally new results in gas kinetics theory were obtained through the efforts of two research teams of the Ioffe Institute and the St.-Petersburg State University. These results were published in a monograph (A. Ya. Ender and I. A. Ender. Collision Integral of the Boltzmann Equation and the Method of Moments. SPb: University Press Ed., 2003). It was shown that principal complexity of the moment method is computation of the non-linear matrix elements of the collision integral. With the present-day literature formulas, they could be calculated at the smaller values of the indices. A series of theorems was proved from which follows that all the matrix elements are not the independent ones but they are interrelated via a selection of relatively simple relationships. These relationships can be used as the recurrent ones. A set of the codes was developed for calculations of the matrix elements with large indices. Treating a problem concerning isotropic relaxation, it was showed that the distribution function could be built up in a domain of very high velocities (up to 10 times the thermal velocities) when applying a great number of the coefficients in the distribution function expansion over the Sonine polynomials (up to 128).
The moment method application is good with small Mach numbers. Here, there are the promising perspectives in solving the problems concerning the structure of shock wave and shock waves interaction, the distribution function being built-up. With the large Mach numbers (M more than 2), this method meets the principal obstacles because of violation of a Grad criterion. To overtake this difficulty, we advance a new approach. We propose to expand the distribution function over spherical harmonics with the coefficients depending only on the velocity module. The Boltzmann equation is reduced to a system of integro-differential equations for these isotropic functions. The kernels of the relevant terms are found to be expressed via the matrix elements of the collision integral. Now, when the calculations of the matrix elements with the large indices are available, the kernels of the most complicated integral part of the Boltzmann equation can be obtained for any law of particles' interaction. Note, these kernels being known in the case under question, an essential progress in solving a selection of the problems of kinetics is well obtained. Thus, the promising perspectives are revealed in solving a problem about the structure of a shock wave in a simple gas as well as in a mixture of gases involving the different laws of particles' interaction, and in solving a non-stationary problem of two shock wave interaction.
Earlier, it was said that the strong deviations from equilibrium should be forthcoming within a shock wave as well as in a region of shock waves interaction. As this takes place an essential increase in the number of the particles is bound to be in a domain of the large velocities. Of course, a measure of deviation does to be a function of the Mach number as well as a sort of interaction between the gas particles. The distribution function having been built-up, the rates of a number of various physical-chemical permutations can be easily calculated in such an nonequilibrium domain. As this takes place, one can easily find the Mach numbers which are to be applied for these or other reactions. As a rule, the complicated reactions are of a stepwise form. The distribution functions being known, the most important bottleneck in this stepwise process could be found, e.g., an excitation of a certain level. Now, it would be clear to say what a reagent should be involved and which extra force should be bound to a system for an additional acceleration of this reaction. As such external agents, the electron beams of specified energy or laser radiation of specified frequency could be applied. Such selective excitation would result in essential reducing in energy consumption. A progress in these works in parallel with the expensive experiments makes possible reducing in time and expenditures.
Main publications