Implicit particle-in-cell algorithm for simulations of low temperature plasmas

Implicit particle-in-cell algorithms represent a powerful tool for simulations of high density plasmas, where the commonly used momentum-conserved explicit particle-in-cell algorithm becomes impractical due to the well-known limitations demanding resolution of the Debye length with the grid cell and the plasma period with the time step. Whereas the former is related to the finite-grid-instability and can be mitigated by using the energy-conserving algorithm even in its explicit variant (in which case, however, energy is conserved for a vanishingly small time step only), the latter requires an iterative technique to solve for the new particle coordinates in phase space and new field components discretized on the field grid. Despite such an iteration scheme incurs additional computational cost, there is a number of benefits, such as the energy conservation for a finite step, easily implementable adaptive time step algorithms, and the possibility of using a time step well exceeding the plasma period. This talk discusses utilization of the energy-conserving implicit method for simulations of technological plasmas. In particular, the effects of reactor boundaries, collisions, and external circuit are addressed and examples of such simulations are given.