Induced magnetic-field effects in inductively coupled plasmas

In inductive plasma sources, the rapid spatial decay of the electric field arising from the skin effect produces a large radio frequency (RF) magnetic field via Faraday's law. We previously determined that this magnetic field leads to a reduction of the electron density in the skin region, as well as a reduction in the collisionless heating rate. The electron deficit leads to the formation of an electrostatic potential which pulls electrons in to restore quasineutrality. Here we calculate the electron density including both the induced and electrostatic fields. If the wave frequency is not too low, the ions respond only to the averaged fields, and hence the electrostatic field is oscillatory, predominantly at the second harmonic of the applied field. We calculate the potential required to establish a constant electron density, and compare with numerical orbit-code calculations. For times short compared to ion transit times, the quasineutral density is just the initial ion density. For timescales long enough that the ions can relax, the density profile can be found from the solution of fluid equations with an effective (ponderomotive-like) potential added. Although the time-varying electrostatic potential is an extra source of heating, the net effect of the induced magnetic and electrostatic fields through trapping, early turning, and direct heating is a significant reduction in collisionless heating for parameters of interest