Interaction between electric field and plasma in inductively coupled discharges

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In regard to collisionless heating in inductively coupled discharges, two approaches have been widely adopted to describe the energy transfer between electrons and the radio frequency field. One approach is based on consistent kinetic theory, by which the resulting field can be expressed as the superposition of a series of plane waves and resonant interactions can happen between electrons and each wave, which might dominate the heating. Another approach is based on the single-particle approach, which assumes that the electric field can be approximated as a spatially exponential function. The energy gained by electrons can then be obtained analytically, and effective energy transfer occurs between the electrons and the field due to nonresonant transit time damping. Although the two approaches demonstrated equivalence in some parameter regimes, it is still unclear how to unite the physical picture in the two models. In this work, test particle simulations have been conducted to show how electrons interact with the electric field expressed as a spatially exponential function and as a sum of a series of plane waves. It is found that as an electric field can be approximated by an exponential function, the resonant interaction between electrons and the field is weak and the nonresonant interaction is dominant, so Vahedi’s model is good enough to describe this interaction. When the imaginary part of the surface impedance becomes important, the electric field cannot be well approximated by an exponential function. It is shown that the resonant interaction dominates the power dissipation of the coupled field.