Numerical results for the three mono-energetic transport coefficients required for a complete neoclassical description of stellarator plasmas have been benchmarked within an international collaboration. These transport coefficients are flux-surface-averaged moments of solutions to the linearised drift kinetic equation which have been determined using field-line-integration techniques, Monte Carlo simulations, a variational method employing Fourier-Legendre test functions and a finite difference scheme. The benchmarking has been successfully carried out for past, present and future devices which represent different optimisation strategies within the extensive configuration space available to stellarators.A qualitative comparison of the results with theoretical expectations for simple model fields is provided. The behaviour of the results for the mono-energetic radial and parallel transport coefficients can be largely understood from such theoretical considerations but the mono-energetic bootstrap current coefficient exhibits characteristics which have not been predicted.

The neoclassical prediction of the “electron root,” i.e., a strongly positive radial electric field, Er (being the solution of the ambipolarity condition of the particle fluxes), is analyzed for low-density discharges in Wendelstein-7-AS [G. Grieger, W. Lotz, P. Merkel, et al., Phys. Fluids B 4, 2081 (1992)]. In these electron cyclotron resonance heated (ECRH) discharges with highly localized central power deposition, peaked Te profiles [with Te(0) up to 6 keV and with Ti≪Te] and strongly positive Er in the central region are measured. It is shown that this “electron root” feature at W7-AS is driven by ripple-trapped suprathermal electrons generated by the ECRH. The fraction of ripple-trapped particles in the ECRH launching plane, which can be varied at W7-AS, is found to be the most important. After switching off the heating the “electron root” feature disappears nearly immediately, i.e., two different time scales for the electron temperature decay in the central region are observed. Monte Carlo simulations in five-dimensional phase space are presented, clearly indicating that the additional “convective” electron fluxes driven by the ECRH are of the same order as the ambipolar neoclassical prediction for the “ion root” at much lower Er. For the predicted “electron root,” the ion fluxes calculated based on the traditional neoclassical ordering are much too small; shortcomings of the usual approach are indentified and a new ordering scheme is proposed.

The impurity dynamics in stellarators has become an issue of moderate concern due to the inherent tendency of the impurities to accumulate in the core when the neoclassical ambipolar radial electric field points radially inwards (ion root regime). This accumulation can lead to collapse of the plasma due to radiative losses, and thus limit high performance plasma discharges in non-axisymmetric devices. A quantitative description of the neoclassical impurity transport is complicated by the breakdown of the assumption of small E × B drift and trapping due to the electrostatic potential variation on a flux surfaceΦ compared to those due to the magnetic field gradient. The present work examines the impact of this potential variation on neoclassical impurity transport in the Large Helical Device (LHD) stellarator. It shows that the neoclassical impurity transport can be strongly affected byΦ. The central numerical tool used is the δf particle in cell (PIC) Monte Carlo code EUTERPE. TheΦ used in the calculations is provided by the neoclassical code GSRAKE. The possibility of obtaining a more generalΦ self-consistently with EUTERPE is also addressed and a preliminary calculation is presented.

ECRH-driven transport of suprathermal electrons is studied in non-axisymmetric plasmas using a new Monte Carlo simulation technique in 5D phase space. Two different phases of the ECRH-driven transport of suprathermal electrons can be seen; one is a rapid convective phase due to the direct radial motion of trapped electrons and the other is a slower phase due to the collisional transport. The important role of the radial transport of suprathermal electrons in the broadening of the ECRH deposition profile is clarified in W7-AS. The ECRH driven flux is also evaluated and put in relation with the "electron root" feature recently observed in W7-AS. It is found that, at low collisionalities, the ECRH driven flux due to the suprathermal electrons can play a dominant role in the condition of ambipolarity and, thus, the observed "electron root" feature in W7-AS is thought to be driven by the radial (convective) flux of ECRH generated suprathermal electrons. The possible scenario of this "ECRH-driven electron root" is considered in the LHD plasma.

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