Simulation of pulsed high-frequency breakdown in hydrogen

We present a simulation of the breakdown stage of high-power, short-pulse h igh-frequency discharges in hydrogen, produced when an electric field of th e form E(t)=E-max(IW)(1-e(-t/tau))sin(omega t) is applied to a cylindrical resonant cavity. Typical discharge operating conditions considered are appl ied powers 1-15 kW, gas pressures 0.1-20 Torr, cavity diameter of 25.71 cm, tube radius of 0.8 cm, field frequency omega/2 pi=1.12 GHz, pulse width t( P)=10 mu s, and rising times tau of a few microseconds. Under these conditi ons, discharge breakdown occurs before the electric field reaches its maxim um amplitude E-max(IW), this situation corresponding to the so-called incre asing wave (IW) regime. The simulation is based on a Monte Carlo model to c alculate the breakdown times, t(b), and fields, E-b, for different field ri sing slopes E-max(IW)/tau similar or equal to 10(-1)-10(3) V cm(-1) ns(-1). The results obtained show that a breakdown criterion based on the electron energy balance (epsilon(gain)=epsilon(loss), where epsilon(gain) and epsil on(loss) are, respectively, the mean electron energy gain and loss) yields excellent agreement between calculated and measured values of t(b) and E-b, while the classical particle rate balance criterion (nu(gain)=nu(loss), wh ere nu(ion) and nu(loss) are, respectively, the mean electron production an d loss frequencies) is satisfied only at pressures below 0.5 Torr. It is fu rther shown that: (i) the IW limit for long breakdown times (t(b)similar or equal to tau -->infinity) corresponds to the continuous wave regime; and ( ii) there is an equivalence between pulsed excitation, with pulse width t(P ), and IW regimes, for short breakdown times such that t(b)=t(P)<<tau. (C) 2000 American Institute of Physics. [S0021-8979(00)05918-1].