# Suppression of Instabilities in a Plasma Voltage Stabilizer
## 4 Discussion  
Table 1 presents the axial distribution of the plasma parameters before the onset of oscillations. The generation function \(G\) (shows the number of ions generated per unit volume in 1 s) was found using (10) and the measured Legendre component of the EVDF \(f_{0}\). The quantity \(D=n_{i}/\tau\) determines the departure of ions from the plasma channel in the radial direction, where \(\tau\sim r/\overline{v}_{dr}\) is the radial ion diffusion time, and the ion velocity \(\overline{v}_{dr}\) in a radial field with a strength \(E_{\rm r}\) of \(\sim\)5 V/cm is about 2 \(\times\) 10\({}^{5}\) cm/s [28]. It can be seen from the table that \(D\) increased slightly with the distance from the cathode in the axial region of the plasma due to an increase in the radial concentration and E-field gradient. At the same time, due to the influence of radial diffusion and inelastic processes, the fast part of the EVDF was depleted. This led to a decrease in the function of the generation of ions \(G\). Near the anode, the values of \(G\) and \(D\) were comparable (Figure 8), which made it possible to write the stationarity condition of the ion concentration in the form \(G\approx D\). If this condition is violated (at \(G\geq D\)), an excess amount of ions forms in the anode region, followed by an increase in the current of thermal electrons to the anode and the onset of relaxation oscillations, the nature of which also depends on the anode load. At \(G\leq D\), a deficiency of ions can lead to current interruption. \begin{table}
\begin{tabular}{c c c c c c c} \hline \(Z\), mm & \(\varphi\), V & \(n_{0}\), 10\({}^{9}\) cm\({}^{-3}\) & \(n_{t}\), 10\({}^{11}\) cm\({}^{-3}\) & \(\tau\), s & \(D=n_{t}/\tau\), 10\({}^{17}\) cm\({}^{-3}\) s\({}^{-1}\) & \(G\), 10\({}^{17}\) cm\({}^{-3}\) s\({}^{-1}\) & \(G\)/\(D\) \\ \hline
1 & 20.1 & 15 & 0.5 & 4.0 & 0.1 & 6.0 & 60.0 \\ \hline
2 & 20.7 & 12 & 0.75 & 5.5 & 0.13 & 4.8 & 37.0 \\ \hline
3 & 21.2 & 7 & 1.23 & 7.0 & 0.17 & 2.8 & 16.4 \\ \hline
4 & 21.4 & 4 & 1.6 & 8.5 & 0.2 & 1.6 & 8.0 \\ \hline
5 & 22 & 2.74 & 2.5 & 10 & 0.24 & 1.1 & 4.58 \\ \hline
6 & 22.4 & 1.75 & 3.73 & 11.5 & 0.27 & 0.7 & 2.59 \\ \hline
7 & 22.8 & 1.11 & 5.57 & 13 & 0.3 & 0.44 & 1.47 \\ \hline
8 & 23.3 & 0.71 & 8.29 & 14.5 & 0.34 & 0.28 & 0.82 \\ \hline \end{tabular}
\end{table} 
Table 1: Axial distribution of plasma parameters at \(P_{He}\) = 2 Torr and a discharge current of 0.5 A.  
Figure 7: Oscillation frequency vs. helium pressure. Thus, the nature of the onset of oscillations can be understood by considering the relationship between the processes of ion generation in the plasma and the escape of ions from the interelectrode gap. It can be seen from (10) that the generation function increased with an increase in helium pressure, and that the ion diffusion flux to the anode increased (the travel time of ions in the MA-to-cathode gap was in the range of milliseconds, which was in good agreement with the oscillation frequencies). This compensated for the near-anode space charge of thermal electrons previously trapped in the potential well between the cathode and the main anode. As a result, their chaotic current to the MA \(i_{t}\) will increase. Assuming a zero near-anode potential barrier, the quantity \(i_{t}\) can be written as  
\[i_{t}=\frac{1}{4}en_{e}v_{t}S\]  
where \(e\) is the electron charge, \(n_{e}\) is the concentration of electrons near the main anode, \(v_{t}\) is the thermal velocity of electrons, and \(S\) is the MA surface area. Estimates at \(P_{He}\) = 5 Torr, \(n_{e}\) \(\sim\)10\({}^{11}\) cm\({}^{-3}\), and \(T_{e}\) \(\sim\)1 eV gave \(i_{t}\) \(\sim\)1.8 A, which was close to the recorded values (Figure 6). Based on the conducted research, a method to suppress current and voltage oscillations was proposed [29]. If we consider the gap between the main anode and the control electrode, the hole in the anode acts as a plasma cathode and the current transfer here is carried out mainly by thermal electrons from the plasma in the cathode-MA gap.