Most plasma sources have to undergo a breakdown process, during which, energy is injected, and particles are ionized. However, we still know little about this fast evolution process. In this work, a one-dimensional direct implicit particle-in-cell/Monte-Carlo collision (PIC/MCC) program is used to study the breakdown process of a capacitively coupled plasma (CCP) driven by dual radio frequencies. The results show that the breakdown process can be divided into three phases: the pre-breakdown, transition, and post-breakdown phases. In the pre-breakdown phase, the plasma density and heating power grow exponentially. The electric field can penetrate the whole discharge region without any shielding, resulting in a higher-than-average electron energy. Secondary electron emission is critical to grow the electron numbers under these discharge conditions. During the transition phase, the formation of sheaths maximizes the electron generation rate and heating power. The formation of sheaths also causes a drastic change in the electrical characteristics of CCP devices. In the post-breakdown phase, the plasma parameters gradually evolve until a steady state is reached. The decreasing rate of generation and the increasing rate of particle loss gradually equalize. The trends of the power gain and plasma loss are similar to the curves for the particle generation and loss rates, and a dynamic equilibrium is finally reached in the last steady state.

We have simulated tokamak breakdown phase driven by pure Ohmic heating with implicit particle in cell/Monte Carlo collision (PIC/MCC) method. We have found two modes can be differentiated. When performing breakdown at low initial gas pressure, we find that it works at lower density and current, but higher temperature, and requires lower heating power, compared to when having a high initial pressure. Further, two stages can be distinguished during the avalanche process. One is the fast avalanche stage, in which the plasma is heated by induced toroidal electric field. The other is the slow avalanche stage, which begins when the plasma density reaches 1015 m−3. It has been shown that ions are mainly heated by ambipolar field and become stochastic in the velocity distribution. However, when the induced electric field is low, there exists a transition phase between the two stages. Our model simulates the breakdown and early hydrogen burn-through under ideal conditions during tokamak start-up. It adopted fewer assumptions, and can give an idealized range of operative parameters for Ohmic start-up. Qualitatively, the results agree well with certain experimental observations.

Tokamak start-up is strongly dependent on the state of the initial plasma formed during plasma breakdown. We have investigated through numerical simulations the effects that the pre-filling pressure and induced electric field have on pure ohmic heating during the breakdown process. Three breakdown modes during the discharge are found, as a function of different initial parameters: no breakdown mode, successful breakdown mode and runaway mode. No breakdown mode often occurs with low electric field or high pre-filling pressure, while runaway electrons are usually easy to generate at high electric field or low pre-filling pressure (${<}1.33\times 10^{-4}$  Pa). The plasma behaviours and the physical mechanisms under the three breakdown modes are discussed. We have identified the electric field and pressure values at which the different modes occur. In particular, when the electric field is $0.3~\text{V}~\text{m}^{-1}$ (the value at which ITER operates), the pressure range for possible breakdown becomes narrow, which is consistent with Lloyd’s theoretical prediction. In addition, for $0.3~\text{V}~\text{m}^{-1}$, the optimal pre-filling pressure range obtained from our simulations is $1.33\times 10^{-3}\sim 2.66\times 10^{-3}$  Pa, in good agreement with ITER’s design. Besides, we also find that the Townsend discharge model does not appropriately describe the plasma behaviour during tokamak breakdown due to the presence of a toroidal field. Furthermore, we suggest three possible operation mechanisms for general start-up scenarios which could better control the breakdown phase.

In the reversed field pinch, there is considerable interest in investigating the plasma breakdown. Indeed, the plasma formed during the breakdown may have an influence on the confinement and maintenance in the latter process. However, up to now there has been no related work, experimentally or in simulation, regarding plasma breakdown in reversed field pinch (RFP). In order to figure out the physical mechanism behind plasma breakdown, the effects of the toroidal and error magnetic field, as well as the loop voltage have been studied. We find that the error magnetic field cannot be neglected even though it is quite small in the short plasma breakdown phase. As the toroidal magnetic field increases, the averaged electron energy is reduced after plasma breakdown is complete, which is disadvantageous for the latter process. In addition, unlike the voltage limits in the tokamak, loop voltages can be quite high because there are no requirements for superconductivity. Volt-second consumption has a small difference under different loop voltages. The breakdown delay still exists in various loop voltage cases, but it is much shorter compared to that in the tokamak case. In all, successful breakdowns are possible in the RFP under a fairly broad range of parameters.

The controlling effect of an electron injection on the electron energy distribution function (EEDF) and on the energetic electron flux, in a capacitive radio-frequency argon plasma, is studied using a one-dimensional particle-in-cell/Monte Carlo collisions model. The input power of the electron beam is as small as several tens of Watts with laboratory achievable emission currents and energies. With the electron injection, the electron temperature decreases but with a significant high energy tail. The electron density, electron temperature in the sheath, and electron heating rate increase with the increasing emission energy. This is attributed to the extra heating of the energetic electrons in the EEDF tail. The non-equilibrium EEDF is obtained for strong non-local distributions of the electric field, electron heating rate, excitation, and ionization rate, indicating the discharge has transited from a volume heating (a-mode dominated) into a sheath heating (c-mode dominated) type. In addition, the electron injection not only modifies the self-bias voltage, but also enhances the electron flux that can reach the electrodes. Moreover, the relative population of energetic electrons significantly increases with the electron injection compared to that without the electron injection, relevant for modifying the gas and surface chemistry reactions.