A.S. Bankovsky – Ph. D. (Phys.-Math.), Associate Professor, Department «Electronic devises and equipment», Yuri Gagarin State Technical University (Saratov)
A.A. Zakharov – Dr. Sc. (Eng.), Professor, Department «Electronic devises and equipment», Yuri Gagarin State Technical University (Saratov). E-mail: firstname.lastname@example.org
A.A. Ivanova – Student, Department «Electronic devises and equipment», Yuri Gagarin State Technical University (Saratov). E-mail: email@example.com
In the paper, the energy parameters are calculated for the Maxwell plasma of the positive column of a gas discharge subject to the basic condition that follows from the energy balance equation of electrons and concludes in the fact that a space charge should be the fairly small.
For the calculation, a model of planar plasma is choosen, in which the ambipolar diffusion of particles on the dielectric wall is implemented, at a frequency of elastic collisions of electrons with gas atoms independent of the colliding particles velocity.
The condition imposed on the plasma parameters, under which the plasma has a constant temperature, is found. The analysis of this condition leads to the fact that the limited Maxwell plasma can exist only at a relatively high pressure gas and a large cross section of the positive column.
Usually, in papers, ionization coefficient and the electron temperature is determined on the basis of the solution of the equations for the eigenvalues of the electron balance equation for certain boundary conditions for the electrons concentration – zero boundary conditions or boundary conditions of Granovsky for plasma, in which the space charge is not zero.
For the calculation of the electron temperature, which does not depend on the size of the space charge, we note that the effect of the magnetic field on the charged particles does not change their kinetic energy because of the magnetic Lorentz force is perpendicular to the velocity. The change of the kinetic energy of a charged particle in a magnetic field can be written in a form independent of the magnetic field. This suggests that the energy parameters of the plasma such as the rate of volume ionization and electron temperature are invariant with respect to the magnetic field. The plasma in a magnetic field with a null space charge becomes homogeneous in the transverse direction, and it properties is determined by the electron balance equation, which is a differential equation of the first order.
In a transverse magnetic field the space charge of plasma is decreased and the longitudinal electric field that provides the discharge current is increased.
Using the condition of homogeneity in the cross section of the plasma, the directional velocity and ambipolar electric field were determined. Volume ratio of ionization in plasma has been determined based on the properties of such homogeneous plasma, i.e. without the use of boundary conditions for the concentration. Accordingly, if limited planar plasma without magnetic field has an electron temperature, then its temperature coincides with the temperature specified above for plasma in a magnetic field.
The influence of electron temperature on the transverse distribution of charged particles in the Maxwell plasma was studied. It is shown that depending on the value of the electron temperature, which determines the value of the boundary conditions, the plasma can be homogeneous or non-homogeneous one over the cross section.
The minimum value of the electron temperature at which there may be the Maxwell plasma homogeneous over the cross section of the discharge was calculated. Homogeneous plasma over the cross section of the discharge is not formed at a temperature lower than the minimum temperature.
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