Simulation of pulsed high-frequency breakdown in hydrogen

We present a simulation of the breakdown stage of high-power, short-pulse high-frequency discharges in hydrogen, produced when an electric field of the form E(t) = EIWmax(1 - e-t/τ)sin(ωt) is applied to a cylindrical resonant cavity. Typical discharge operating conditions considered are applied powers 1-15 kW, gas pressures 0.1-20 Torr, cavity diameter of 25.71 cm, tube radius of 0.8 cm, field frequency ωl2π = 1.12 GHz, pulse width tp = 10 μs, and rising times τ of a few microseconds. Under these conditions, discharge breakdown occurs before the electric field reaches its maximum amplitude EIWmax, this situation corresponding to the so-called increasing wave (IW) regime. The simulation is based on a Monte Carlo model to calculate the breakdown times, tb, and fields, Eb, for different field rising slopes EIWmax/τ [asymptotically equal to] 10-1 - 103 V cm-1 ns-1. The results obtained show that a breakdown criterion based on the electron energy balance (εgain = εloss, where εgain and εloss are, respectively, the mean electron energy gain and loss) yields excellent agreement between calculated and measured values of tb and Eb, while the classical particle rate balance criterion (νgain = νloss, where νion and νloss are, respectively, the mean electron production and loss frequencies) is satisfied only at pressures below 0.5 Torr. It is further shown that: (i) the IW limit for long breakdown times (tb [asymptotically equal to] τ -> infinity ) corresponds to the continuous wave regime; and (ii) there is an equivalence between pulsed excitation, with pulse width tp, and IW regimes, for short breakdown times such that tb = tp very much less than τ. © 2000 American Institute of Physics.