Broadening of rectified potential structures induced by rf currents in a magnetized plasma: Application to ITER scrape-off-layer

Abstract

International audienceMeasurements show that the vicinity of powered ion cyclotron range of frequency (ICRF) antennae is biased positively with respect to its environment [ J. Gunn et al., Proc. 22nd IAEA Fusion Energy Conference, Geneva 2008, EX/P6-32 ]. This is attributed to radio-frequency (rf) sheath rectification. The radial penetration of these direct current (dc) potentials from ICRF launchers into the tokamak scrape-off layer (SOL) determines the power deposition on the walls and especially on the antenna structure, which is a key point for long time clean discharges. Within independent flux tube models of rf sheath rectification the radial penetration of dc potentials is determined by the skin depth x0 = c/ωpe for the slow wave. When self-consistent exchange of transverse rf current is allowed between neighboring flux tubes, such a structure can be broadened radially up to a characteristic transverse length L. Broadening arises as soon as L>x0. A linear modeling of the process gives a first evaluation of the theoretical length L = (L∥ρci/2)1/2. Within the “flute assumption,” it scales with the length L∥ of open flux tubes and the ion Larmor radius Ωci. This trend has been confirmed by nonlinear fluid simulations using the SEM code taking into account nonlinearities of the sheath dynamics. Parametric regimes are outlined where broadening or nonlinearity arise. Langmuir probe measurements on Tore Supra suggest that the observed broadening is lower than predicted by the code. This suggests that actual rf current exchanges probably do not occur over the whole length of magnetic field lines but only on a fraction of it. This “effective parallel magnetic connection length” L∥eff is estimated from the measurements. The model is finally applied to several potential maps generated by an ITER antenna, with different plasma parameters depending on possible SOL scenarios in ITER, and “reasonable assumptions” about L∥eff. It comes out that L ranges between 1 and 10 cm depending on local L∥eff and on typical ITER plasma parameters

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

“…No other frequency is considered, contrary to Ref. 19. At the left sheath V l ðx; y; z ¼ ÀL == =2; tÞ ¼ V DCl ðx; yÞ þ V rf l ðx; yÞcosðx 0 t þ uÞ:…”

“…6,8,10,11,16 Yet its quantitative validity is questionable. 17 Moreover, contradictions appeared with recent measurements, e.g., the scaling of rectified DC plasma potential with RF power, 18 the radial penetration of the plasma bias, 19 or the non-linear generation of edge DC currents by RF waves. 10,20,21 Although no consensus presently exists over an alternative approach, RF-sheath physics needs improvement towards the first principles.…”

“…No other frequency than 0 and x 0 is considered and some transport coefficients remain phenomenological, contrary to Ref. 19. The RF model incorporates only one wave polarization (the slow wave) and the simulation geometry is restricted to parallelepipedic shape.…”

Simulation as a tool to improve wave heating in fusion plasmas

“…This simulation, when done on a tiny domain, gives the feeling of this phenomenon and provides accurate Physics, but without the possibility of being relevant for ITER cases in the near future due to the computation requirements knowing that a 10 x10 cm area needs 10 7 particles per species to have a significant result above the noise level. Recent experiments introduce new facts in contradiction with the existing models, e.g., the scaling of rectified DC plasma potential with RF power (Wukitch et al 2009), the radial penetration of the plasma bias (Faudot et al 2010) or the non-linear generation of edge DC currents by RF waves (Bobkov et al 2010), for which a fluid model has been built (Faudot et al 2013). Although no consensus presently exists over an alternative approach, RF-sheath physics needs improvements using the first principles.…”

“…The non-linear coupling between flux tubes can be found in (Faudot et al 2006). Its effects for ICRH ITER antenna are available in (Faudot et al 2010). The main ingredient to determine the RF potential along a magnetic field line E is generally computed from conventional antenna codes in the absence of sheaths, i.e., perfect electric conductors are assumed in direct contact with the plasma.…”