Temporal Evolution of Multipactor Discharge

Multipactor is an important resonant discharge phenomenon on which there have been surprisingly few publications in the open literature. Here, we extend the theoretical analysis of an idealized model. Emphases have been placed on the mutual interactions between the multipactor discharge and the rf. We show that the multipactor current may reach a very high level, transiently, before it settles to a steady state. The multipactor current saturates primarily by its loading of the cavity; the image space charge force associated with the multipactor electrons plays a relatively minor role. When saturation occurs, the secondary emission coefficient is unity, corresponding to the "first cross-over point" in the secondary electron yield curve. The parameters attained in the steady state agree with the predicted values from an analytic theory. The analysis is extended to include the effects of an external magnetic field. Multipactor is a well known phenomenon of rf breakdown in microwave cavities, windows, satellite rf payloads, and accelerator structures [1-3]. When an AC electric field exists across a gap, an electron from one surface is accelerated toward the other surface, the impact upon which may release more than one electron by secondary emission. It is easy to see that if the electron transit time across the gap equals to half of the rf period, a resonant discharge could result. There exist few theoretical analyses of multipactor, most of which are concentrated on the response of a single electron to an imposed rf electric field. Analytic expressions have been derived for the phase of the emitted electron, and the range of the rf electric field in which a stable, steady state multipactor may exist [1,4]. While some calculations have included the space charge effects associated with the multipactor electrons [4,5], most of these calculations omit the important processes of loading and detuning of the rf cavities as the multipactor current grows [2]. In this paper, we use a simple model to address these issues, the analysis of which yields interesting information on the multipactor saturation level, the saturation mechanism, the time scale over which multipactor evolves, and possibly the drastic transient growth of multipactor current before the steady state solution is reached. For simplicity, we shall use a one dimensional model where the multipactor occurs inside a planar gap [Fig. 1]. The gap separation is D and the gap voltage is Vg(t). The multipactor discharge is modeled by a single electron sheet of surface density σ that moves across this gap. Upon impact on a gap surface, a new electron sheet is generated by secondary emission. We assume that the voltage Vg that drives the multipactor is provided by an rf cavity, of characteristic frequency ωo and quality factor Q [Fig. 1] . As the multipactor electron sheet moves inside the gap, it induces a wall current, Im (t), which loads the cavity. Thus, the present model allows for the progressive loading and detuning of the cavity as the multipactor current builds up. This loading, in turn, modifies the electron’s energy and phase at impact. Hereafter, we shall use dimensionless quantities with the following normalization scales: D for distance, ωo for frequency, 1/ωo for time, v = ωoD for velocity, U = mv2 for energy, U/e for voltage, E = U/eD for electric field, Σ = εoE for surface charge density, AΣv/D for current. Here, m is the electron mass, e = 1.602 x 10 Coulomb, A is the surface area of the gap, and εo is the free space permittivity. The cavity is driven by the normalized ideal current source Id, and by the multipactor current Im, according to the circuit equation [Fig. 1]: