SLPIC: a PIC algorithm for accelerating low-velocity plasma kinetics modeling*

Speed-limited particle-in-cell simulation (SLPIC) is a PIC-based simulation method that allows increased time-steps by slowing down the fastest particles in such a way that slow dynamics of interest are preserved, while significantly reducing the number of time-steps required to complete such a simulation.

In a 1D plasma sheath simulation to steady-state, SLPIC demonstrated a speed-up advantage over comparable PIC simulation by a factor of 27 for a hydrogen plasma and over 200 for an argon plasma, each time correctly determining the end state of the plasma.

SLPIC introduces a speed-limiting factor β(v) ≤ 1, modifying the equations of motion such that dx/dt = β(v)v and dv/dt = β(v)a, and weights particles to the grid as β(v)w where w is the macroparticle weight. SLPIC is accurate as long as β(v_s) ≈ 1, where v_s (the “speed-limit”) is the maximum velocity of any dynamics of interest, and β(v)|v| ≤ v_s. For the aforementioned sheath simulation, v_s is the ion drift velocity, and the speed-up is correlated to the relation ∆t_SLPIC = ∆x/v_s ≫ ∆t_PIC = ∆x/v_e where v_e is the maximum electron velocity. The SLPIC speed-up relative to PIC arises as we effectively reduce the vast speed differences between electrons and ions.