**Geometrical Aspects of a Hollow-cathode Magnetron (HCM)**

Authors: Zhehui Wang and Samuel A. Cohen

A hollow-cathode magnetron (HCM), built by surrounding a planar sputtering-magnetron cathode with a hollow-cathode structure (HCS), is operable at substantially lower pressures than its planar-magnetron counterpart. We have studied the dependence of magnetron operational parameters on the inner diameter D and length L of a cylindrical HCS. Only when L is greater than L_{0}, a critical length, is the HCM operable in the new low-pressure regime. The critical length varies with HCS inner diameter D. Explanations of the lower operational pressure regime, critical length, and plasma shape are proposed and compared with a one-dimension diffusion model for energetic or primary electron transport. At pressures above 1 mTorr, an electron-impact ionization model with Bohm diffusion at a temperature equivalent to one-half the primary electron energy and with an ambipolar constraint can explain the ion-electron pair creation required to sustain the discharge. The critical length L_{0} is determined by the magnetization length of the primary electrons.