Slow-wave propagation and sheath interaction in the ion-cyclotron frequency range

Abstract

In previous work [Myra J R and D'Ippolito D A 2008 Phys. Rev. Lett. 101 195004] we studied the propagation of slow-wave resonance cones launched parasitically by a fast-wave antenna into a tenuous magnetized plasma. Here we extend the treatment of slow wave propagation and sheath interaction to "dense" scrape-off-layer plasmas where the usual coldplasma slow wave is evanescent. Using the sheath boundary condition, it is shown that for sufficiently close limiters, the slow wave couples to a sheath plasma wave and is no longer evanescent, but radially propagating. A self-consistent calculation of the rf-sheath width yields the resulting sheath voltage in terms of the amplitude of the launched slow wave, plasma parameters and connection length. The conditions for avoiding potentially deleterious rf-wall interactions in tokamak rf heating experiments are summarized.

Self consistent radio-frequency wave propagation and peripheral direct current plasma biasing: Simplified three dimensional non-linear treatment in the “wide sheath” asymptotic regime

“…This conclusion is qualitatively similar to Ref. 38. But the details of the radial distributions differ in the two papers, due to the different assumptions made.…”

“…We believe that if radiation conditions are applied in the present model while sheath widths get large in Ref. 38, the radial profiles of V rf (x) in the two papers converge to a common solution. Since V rf (x) / E // (x)d(x) and d(x) is different in the two models, then the field maps E // (x) will differ at the lateral boundaries.…”

“…17,[36][37][38] In presence of RF-SBCs, these eigenmodes are only well defined if parameter K Àde == =(L == e sh ) can be treated as a constant. 17 However in realistic situations, the dielectric tensor has a radial profile, the self-consistent sheaths can adopt different widths at the two lateral boundaries, and the 2D map d(x, y) is generally inhomogeneous over similar spatial scale-lengths as the RF field.…”

“…From Child-Langmuir law (2.15), the sheath widths d then grow very large. In this "wide sheath regime," it was early noticed that the RF SBCs (2.4) or (2.6) get simplified, some physical quantities becoming nearly independent of d. 17,38 The principle is then to split the fields in the problem (e.g., V rf ) into successive approximations V rf ðx; y; zÞ ¼ V rf ð0Þ ðx; y; zÞ þ V rf ð1Þ ðx; y; zÞ þ …: (3.1)…”

“…For this purpose, we follow Ref. 38: in this subsection d is assumed known and homogeneous over the lateral boundaries. We then seek the SPW under the form of two plasma modes with symmetric and antisymmetric toroidal parity.…”