Reduced-order non-self-consistent Monte Carlo simulation of a planar magnetron discharge: electron heating, recapture and racetrack formation

Abstract

A reduced-order non-self-consistent Monte Carlo model is presented for a circular planar magnetron discharge in argon. The model combines two magnetic-field representations, namely a superposition of magnetic dipoles and a numerically integrated field of the finite permanent magnets, with a prescribed one-dimensional sheath-bulk potential, adaptive fourth-order Runge-Kutta orbit integration, and a null-collision treatment of electron-argon collisions. The collision module reproduces the dependence of the electron drift velocity on the reduced electric field, but overestimates its absolute value by approximately a factor of 1.5. The resulting transport predictions are therefore interpreted semi-quantitatively. Applied to a magnetron geometry based on published Langmuir-probe measurements, the simulations reproduce the qualitative emergence of a cold electron population away from the cathode while retaining a hotter near-cathode component. Electrons returning to the cathode are reflected with a prescribed probability RC, which controls their availability for further ionising collisions. For racetrack calculations initiated with at least 2 x 10^4 cathode-emitted electrons and RC = 0.5, the finite-magnet field produces a more sharply localised erosion profile whose full width at half maximum is close to a geometric racetrack-width estimate. The dipole approximation yields a broader profile. The model is not a replacement for self-consistent PIC-MCC simulations, but is a computationally light tool for comparing magnetic-field representations and analysing electron heating, ionisation localisation, and racetrack formation.