The review article has evaluated three different particle and fluid simulations for low-temperature plasma discharges. The investigated methods are fluid, particle-in-cell and hybrid simulations. The plasma discharge includes complexities in itself but the disciplined models can offer research guidelines, better design alternatives and better operation conditions. The selected model is adapted to the specific plasma conditions. The weakness of the simulations results from the uncertainties of the input parameters and the assumptions. For plasma simulations, cross sections, secondary electron emission coefficients and rate constants cannot be identified strictly.
In fluid models, Maxwell equations are solved with fluid equations. The values for density, mean velocity and mean energy are found by the continuity, the flux and the energy equations. The approximation used here is that collisional frequency is higher than RF frequency. The drift-diffusion (DD) approximation neglects the inertia of the charged particles and evaluates the mean velocity with respect to electric field promptly. DD can be used for electrons in plasmas whose pressure is higher than 100 mTorr. The ions are considered in total flux equation and their temperature is assumed constant as neutral gas. However, the particle energy distribution is not known so the velocity distribution should be assumed. Local field approximation (LFA) is an implicit assumption which equalizes the gained energy from the electric field with the lost energy in particle collisions. However, it is not valid for large gradients. Another way to solve the particle velocities is to adapt the Maxwellian distribution but it also fails in high energy levels. The fluid simulations require less time but also it is less accurate. They are applicable for high pressure plasmas with dominant collisions instead of having non-local effects.
PIC models evaluate higher number of particles (super particle-10^5-7) in a cell. It is computationally more demanding but also it includes less assumptions and predicts the values in higher confidence level at boundaries where the reflection, absorption and emission of the particles are important. The Maxwell equations are solved with Newton-Lorentz equation. The position and velocity of the particles are updated at every step by weighting the known values to the grid. Comparing fluid model, following super particles are not time-efficient. There are some ways to reduce the computation time such as adding an imaginary collision probability. The simulations can be noisy due to the high number of particles simulated. Numerical heating which describes the numerical fluctuations in a value – electric field in plasma modelling – can be observed in low-energy electrons.
Hybrid models combine the first and second methods. The computation time is between fluid and PIC simulations. They are more accurate than fluid models. Ions can be evaluated in fluid model while electrons can be tracked in PIC model. Time steps are determined to be smallest one to satisfy both models. For the steady state solutions, time is reduced without considering transient behavior. All three models can be preferred for different plasma and boundary conditions.
Reference: Kim, H.C.; Iza, F.; Yang, S.S.; Radmilovic-Radjenoiv, M.; Lee, J.K. “Particle and fluid simulations of low-temperature plasma discharges: benchmarks and kinetic effects,” Journal of Physics D: Applied Physics, 2005, 38, R283-R301.
Course: AME 60637