On the optimal chamber length and electron heating mechanism in low pressure inductive discharges

Plasma resistance with the chamber length was measured at different plasma densities in low pressure inductively coupled plasmas. It was found that the plasma resistance has a maximum at specific chamber length, $L_{\mathrm{opt}}$, and the $L_{\mathrm{opt}}$ is changed with the plasma density. It is related to the maximum collisionless electron heating, which simultaneously satisfies the conditions of both the bounce resonance and the transit time resonance. Therefore, $L_{\mathrm{opt}}$ is an optimal chamber size for the power transfer to the plasma.