Effect of electron temperature on the distribution of plasma parameters on the phase planes for thermionic diode with low temperature emitter

Influence of temperature distribution of thermal and fast electrons on the distribution of the ion current density in the electrode gap diode has been studied. Studies on the phase planes, especially in the plane of the plasma density – ion current density have been carried out. It is shown that the generation of ions in the electrode gap is specified by the fast electron temperature.


Introduction
To effectively control the surface plasma processing technology products it is necessary to know the distributions of plasma parameters and mechanisms of their formation. One critical parameter of the plasma is the distribution ion current density in the interelectrode gap which occurs due to the mechanism of generation of ions. For plasma processing of the surfaces of products, as a rule, glow discharge is used, rather complex structure on the phenomenon. Probe characteristics this discharge have two extended linear section [1, p. 316]. This is interpreted as the temperature distribution of the two group electrons. The impact of these distribution on ionization processes remains unclear. On the other hand, cesium low-temperature plasma of thermionic diode has similar probe characteristics [2]. But cesium discharge thermionic diode is simpler in structure as compared with the glow discharge and therefore it is easier to study the mechanism of generation of ions.
At a certain combination of parameters thermionic diode, in particular at low temperatures emitter probe semilog cesium plasma arc characteristics have two linear areas. Processing of these characteristics gives two electrons temperature distribution in the interelectrode gap (IEG) [2,3]: in the low (thermal) energy of the electrons and the electrons in the high energy range. The latter group is associated [2] with the electrons which have major influence on the processes of generation of excited atoms and cesium ions.
With a low temperature plasma model [2] we can obtain the distribution of plasma parameters which are not measured in the experiment: the ion current density, electron energy density, function generating ions in the plasma volume; for spectroscopic measurementsthe potential of the space occupied by the plasma. It is interesting to study the influence of two electron temperature distribution in the distribution of unmeasured plasma parameters, especially the function of the ion generation electrode in the diode gap.
As a method of research we used the analysis of experimental distributions and unmeasured plasma parameters on the phase planes [4][5][6][7][8] things, designing qualitative and quantitative criteria for the comparison of distributions of plasma parameters.
In this paper we investigate the effect of the distributions of two electron temperature distribution in the experimental and unmeasured (calculated) cesium plasma parameters for a thermionic diode with a low temperature emitter. On the experimental material checked the results of theoretical research model distributions of plasma parameters on the phase planes [8].

The model of calculating the distribution of the ion current density
The equation for the ion current density in the IEG thermionic diode (taking into account the friction forces on the ions, electrons ie e ei RJ   ) can be written as [2]: continuity equation for the ion current density can be written as:

Results and discussion
Experimental distribution of the plasma density and two temperatures of the electrons were obtained [2,3] for two current density To construct the distribution of plasma parameters on the phase planes we must calculate their spatial derivatives, so the experimental distribution approximated. We used the following  T T x  the best approach to fitness criteria (exponential dependence) was SSE and RSMSE and a linear relationship was for the remaining two criteria of fitness. Perhaps this is a reflection of the fact that on the one hand the fundamental solution of the heat equation is the exponential function and on the other hand because of the smallness of the IEG solution is actually linearized. In further calculations we used the exponential approximation (see, figure 1 (b)).    (figure 1 (b)) in the range 0.15≤ x ≤0.75 cm then the range is considerably reduced for 2 J : 0.15≤ x ≤0.35 cm. Approximation based on both temperatures vary throughout the measuring range (see, figure 1 (b)). By increasing the current density, the plasma density is increased by 3-4 times, respectively, the thermal conductivity of low-energy electron gas increases and the temperature decreases. The size of the electrode sheaths with non-equilibrium plasma is ~ 10 -3 cm, which it is much less IEG. Relaxation length of the electron energy distribution function for the Maxwell distribution for the electrode of the plasma parameters