  Upon inclusion of collisions, the speed-limited particle-in-cell (SLPIC)
simulation method successfully computed the Paschen curve for argon. The
simulations modelled an electron cascade across an argon-filled capacitor,
including electron-neutral ionization, electron-neutral elastic collisions,
electron-neutral excitation, and ion-induced secondary-electron emission. In
electrical breakdown, the timescale difference between ion and electron motion
makes traditional particle-in-cell (PIC) methods computationally slow. To
decrease this timescale difference and speed up computation, we used SLPIC, a
time-domain algorithm that limits the speed of the fastest electrons in the
simulation. The SLPIC algorithm facilitates a straightforward, fully-kinetic
treatment of dynamics, secondary emission, and collisions. SLPIC was as
accurate as PIC, but ran up to 200 times faster. SLPIC accurately computed the
Paschen curve for argon over three orders of magnitude in pressure.
