{'fraction_non_alphanumeric': 0.01757944557133198, 'fraction_numerical': 0.002704530087897228, 'mean_word_length': 5.090534979423868, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Two-dimensional modeling of nonlocal electron heating in inductively coupled plasma sources

Summary form only given, as follows. Nonlocal (collisionless) electron heating can be important in low-pressure inductively coupled rf discharges. We have developed a two-dimensional, electromagnetic, PIC-MCC code to study power deposition in an inductively coupled plasma source. Simulation results for the collisionless healing power are found to be significantly higher than that predicted by the analytic model of Vahedi et al. (1995). This discrepancy can be attributed to the fact that they consider only the axial motion of the electrons to determine the collisionless heating. In this work we present an analytic model to consider the nonlocal heating of the electrons during their radial motion as well as their axial motion. We consider electrons moving both axially and radially. The azimuthal electric field decays exponentially into the plasma along the axial direction and has a nonuniform radial profile typical of ICPs. In addition to being reflected by the sheath potential while moving axially toward the dielectric window, an electron can be reflected by the sheath potential at the cylindrical chamber wall during its radial motion as well. In our model we also allow the height of the system to be finite. We obtain an expression for the collisionless heating power. This two-dimensional analytic model gives good agreement with the results of particle simulations.