Modeling the gas breakdown for helium in the planar magnetron discharge

Abstract A physics-based model to describe the helium breakdown in the planar magnetron, where Paschen’s law is invalid, is developed and validated by means of one-dimensional particle-in-cell/Monte Carlo kinetic simulations. In the theoretical model, the ionization coefficient and the ion-induced secondary electron emission (SEE) coefficient are derived by accounting for the effect of the complex magnetic field topology: electrons <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mtext mathvariant="bold">E</mml:mtext> <mml:mo>×</mml:mo> <mml:mtext mathvariant="bold">B</mml:mtext> </mml:mrow> </mml:math> drift and recapture of SEE electrons at the target. The characteristic curve of the breakdown voltage as a function of the helium pressure predicted by kinetic simulations shows good agreement with the theoretical model at the low pressure range 0.1 Pa–100 Pa of practical interest. Kinetic simulations detect that electrons are in the nonlocal regime over the pressure range 0.1 Pa–1000 Pa, where spatially periodical peaks of the ionization coefficient are observed. The phenomena of ionization peaks is found to be associated with the competing process between the energy gain of ballistic electrons in the electric field and their energy loss in inelastic collisions.