# Suppression of Instabilities in a Plasma Voltage Stabilizer
## 3 Results  
In the experiment, the role of the plasma-forming component was played by helium, since it had the highest ionization and excitation potentials among other inert gases. This helps the nonlocal effects in plasma to manifest themselves most clearly. The experiments were carried out at currents of 0.1 to 2 A and helium pressures of 0.1 to 10 Torr. Such conditions were chosen because a plasma can transfer to both local and nonlocal modes. In the latter case, the relaxation lengths for electron-electron \(L_{ee}\) and electron-atom \(L_{eu}\) collisions exceeded the length of the interelectrode gap \(d\)[25]. It is well known that the EVDF in a beam-discharge plasma is formed by two separate groups of electrons, thermal \(f_{t}\) and fast beam \(f_{0}\) electrons, with concentrations and average energies of \(n_{t}\), \(\overline{e}_{t}\) and \(n_{0}\), \(\overline{e}_{0}\), respectively [5,7,20]. The velocity distribution of thermal electrons is close to an isotropic Maxwellian one, while the group of fast electrons is characterized by significant anisotropy of the distribution. Comparison of the energies of thermal and beam electrons revealed a strong nonequilibrium of the EVDF; the energy of thermal electrons was about 2 eV, and the energy of fast electrons was about 25 eV. Such an EVDF shape is a result of the potential distribution over the interelectrode gap. If the current at the main anode is zero, the potential distribution is typical for LVBD (Figure 4, curve 1). There was a potential drop at the anode \(\varphi_{a}\approx 1.5\overline{e}_{t}\), which is an almost insurmountable barrier for thermal plasma electrons. The electrons emitted by the cathode were accelerated by the near-cathode sheath and formed a beam with a small energy scatter that went through the interelectrode gap. The creation of thermal electrons occurred as a result of the ionization of helium atoms by the beam electrons. The excitation and ionization potentials for He were \(U_{m}\approx 19.8\) V and \(U_{ion}\approx 24.6\) V, respectively; they determine the dominant role of the beam in inelastic processes and current transfer [6,7,20]. In order to study the processes occurring in the plasma conditions under consideration, the Legendre components of the EVDF decomposition \(f_{0}\)-\(f_{6}\) were reconstructed based on the recorded values of \(I_{U}^{{}^{\prime\prime}}(qU,\alpha)\), which determine the set of the most important plasma parameters: concentration, electron current density, electron pressure anisotropy, etc. [21]. In particular, the function of atomic excitation and ion generation using the component \(f_{0}\) can be calculated as  
\[G=4\pi N_{a}\int_{v_{tr}}^{\infty}v\sigma_{\alpha a}^{i}(v)f_{0}(v)v^{2}dv, \tag{10}\]  
where \(\sigma_{\alpha a}^{i}\) is the energy dependence of the cross-section of the corresponding process, and \(v\) is the velocity of the incident electron. As already mentioned, an LVBD can be unstable with the excitation of various types of oscillations [13, 14, 15, 25, 26] that negatively affect the operating modes of plasma electronic devices. Figure 5 shows the current-voltage curves of the helium LVBD recorded for a three-electrode voltage stabilizer. Curve 1 demonstrates the negative differential conductivity that causes oscillations of the discharge current and voltage [14,16,27]. Figure 6 shows the typical form of such oscillations at different values of helium pressure. They occurred at a full modulation of the current in the discharge at frequencies of 50 to 150 kHz and at peak voltage values reaching 30 V. Under constant pressure conditions, the oscillation frequency changed little with changes in the discharge current. If the current increased, the modulation depth dropped to 10%. With an increase in the vapor pressure, the frequency of oscillations increased almost linearly (Figures 6 and 7). Figure 4: Potential distribution over the gap of the experimental device at helium pressure \(P_{He}\) = 2.5 Torr; currents at the CE \(i_{ce}\), A: 1–0; 2–0.04.