  First-principles particle-in-cell (PIC) simulation is a powerful tool for
understanding plasma behavior, but this power often comes at great
computational expense. Artificially reducing the ion/electron mass ratio is a
time-honored practice to reduce simulation costs. Usually, this is a severe
approximation. However, for steady-state collisionless, electrostatic
(Vlasov-Poisson) systems, the solution with reduced mass ratio can be scaled to
the solution for the real mass ratio, with no approximation. This 'scaled mass'
method, which works with already-existing PIC codes, can reduce the computation
time for a large class of electrostatic PIC simulations by the square root of
the mass ratio. The particle distributions of the resulting steady state must
be trivially rescaled to yield the true distributions, but the self-consistent
electrostatic field is independent of the mass ratio. This method is equivalent
to 'numerical timestepping,' an approach that evolves electron and ion
populations with different timesteps. Numerical timestepping can be viewed as a
special case of the speed-limited PIC (SLPIC) method, which is not restricted
to steady-state phenomena. Although the scaled-mass approach is simplest,
numerical timestepping and SLPIC more easily generalize to include other
effects, such as collisions. The equivalence of these new approaches is
demonstrated by applying them to simulate a cylindrical Langmuir probe in
electron-argon plasma, speeding up simulation by two orders of magnitude.
Methods such as SLPIC can therefore play an invaluable role in interpreting
probe measurements by including geometric effects, collisions, secondary
emission, and non-Maxwellian distributions.
