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We investigate theoretically how sheath radio-frequency (RF) oscillationsrelate to the spatial structure of the near RF parallel electric field E//emitted by Ion Cyclotron (IC) wave launchers. We use a simple model of SlowWave (SW) evanescence coupled with Direct Current (DC) plasma biasing viasheath boundary conditions in a 3D parallelepiped filled with homogeneous coldmagnetized plasma. Within a "wide sheaths" asymptotic regime, valid forlarge-amplitude near RF fields, the RF part of this simple RF+DC model becomeslinear: the sheath oscillating voltage VRF at open field line boundaries can bere-expressed as a linear combination of individual contributions by everyemitting point in the input field map. SW evanescence makes individualcontributions all the larger as the wave emission point is located closer tothe sheath walls. The decay of |VRF| with the emission point/sheath poloidaldistance involves the transverse SW evanescence length and the radialprotrusion depth of lateral boundaries. The decay of |VRF| with theemitter/sheath parallel distance is quantified as a function of the parallel SWevanescence length and the parallel connection length of open magnetic fieldlines. For realistic geometries and target SOL plasmas, poloidal decay occursover a few centimeters. Typical parallel decay lengths for |VRF| are foundsmaller than IC antenna parallel extension. Oscillating sheath voltages at ICantenna side limiters are therefore mainly sensitive to E// emission by activeor passive conducting elements near these limiters, as suggested by recentexperimental observations. Parallel proximity effects could also explain whysheath oscillations persist with antisymmetric strap toroidal phasing, despitethe parallel anti-symmetry of the radiated field map. They could finallyjustify current attempts at reducing the RF fields induced near antenna boxesto attenuate sheath oscillations in their vicinity.

Spatial proximity effects on the excitation of Sheath RF Voltages by evanescent Slow Waves in the Ion Cyclotron Range of Frequencies