Revisiting the Anomalous rf Field Penetration into a Warm Plasma

Abstract

Radio frequency waves do not penetrate into a plasma and are damped within it. The electric field of the wave and plasma current are concentrated near the plasma boundary in a skin layer.Electrons can transport the plasma current away from the skin layer due to their thermal motion.As a result, the width of the skin layer increases when electron temperature effects are taken into account. This phenomenon is called anomalous skin effect. The anomalous penetration of the rf electric field occurs not only for transversely propagating to the plasma boundary wave (inductively coupled plasmas) but also for the wave propagating along the plasma boundary (capacitively coupled plasmas). Such anomalous penetration of the rf field modifies the structure of the capacitive sheath. Recent advances in the nonlinear, nonlocal theory of the capacitive sheath are reported. It is shown that separating the electric field profile into exponential and non-exponential parts yields an efficient qualitative and quantitative description of the anomalous skin effect in both inductively and capacitively coupled plasma.

Intense boundary emission destroys normal radio-frequency plasma sheath

“…Yet the structure of plasma, i.e. bulk plasma connected by Bohm presheath and Child-law sheath, is supposed to be untouched and mean wall potential remains negative relative to plasma [17][18][19][20][21] .In this letter, we show that boundary emission can bring very strong disturbance and restructure entire RF plasma, which happens when 𝛤 𝑒𝑚 is greater than averaged plasma electron flux 〈𝛤 𝑒𝑝 〉 𝑇 . It is well known that a space-charge limited (SCL) sheath is formed if 𝛤 𝑒𝑚 > 𝛤 𝑒𝑝 near floating boundary, such as thermionic emitter, emissive probe, Hall thruster, etc [22][23][24] .…”

“…Yet the structure of plasma, i.e. bulk plasma connected by Bohm presheath and Child-law sheath, is supposed to be untouched and mean wall potential remains negative relative to plasma [17][18][19][20][21] .…”

Penetration depth of an electric field in a semi-infinite plasma

“…These difficulties have been analyzed recently in a clear formulation in Ref. [26]. In various approximations (see, for instance, Refs.…”

“…A non-linear x-dependence (∼ x 2/3 ) is related to model assumptions made upon the surface and an asymptotic treatment of the Landau damping for the Boltzmann kinetic equation (see, for instance, Ref. [26]). We show here that, when the surface condition (surface term) is included explicitly, the attenuated field obeys the standard exponential attenuation law e −x/λe (apart from factors oscillating in space), where λ e is an extinction length (penetration depth, attenuation length) which is computed here explicitly; up to immaterial numerical factors, it is of the order…”

Analytical solution of the skin effect problem with the displacement current in Maxwell plasma by the source method

“…There has been substantial interest to this problem. [6][7][8] In Ref. 5, the behavior of plasma near the resonance is not considered.…”