V. Fuchs

Enhanced heat flux in the scrape-off layer due to electrons accelerated in the near field of lower hybrid grills

As a result of experimental observations of localized heat flux on components magnetically connected to radiating waveguides in Tore Supra and in TdeV, the acceleration of electrons near lower hybrid (LH) antennas has been investigated. A simple analytical model has been developed to compute the dynamics of the particles in the near field approximation. Landau damping of the very high N|| (20 < N|| < 100) component of the launched spectrum on the thermal electrons of the scrape-off layer (SOL) is found to occur. Simulation of a typical LH pulse in Tore Supra indicates that the electrons can be accelerated up to 2-3 keV. Modelling of the interaction of this fast electron population with the edge plasma allows a calculation of the heat flux on plasma facing components that are magnetically connected to the antenna. Model results and the results of experiments in Tore Supra and TdeV are compared. The calculated heat fluxes are found to be fairly consistent when the variation of convective heat flux at the grill aperture is taken into account. From this analysis, it is concluded that, for an LH power density of 25 MW/m2, the resulting heat flux along the field lines (3.5 MW/m2) is manageable for the components connected to the antenna, provided that good coupling can be maintained at a low density in front of the grill.

Acceleration of electrons in the vicinity of a lower hybrid waveguide array

The interaction of tokamak plasma edge electrons with the electric near field generated by a lower hybrid slow wave antenna is studied. Antenna field spectra of interest for current drive and/or plasma heating have lobes at high‐n∥ values (n∥≳30) intense enough for resonant acceleration of the relatively cold (∼25 eV) edge electrons. For waveguide electric fields, typically around 3 kV/cm, the higher‐order modes overlap in the phase‐space [B. V. Chirikov, Phys. Rep. 52, 263 (1979)], so that electron global stochasticity is induced. For Tokamak de Varennes (TdeV) [Decoste et al., Phys. Plasmas 1, 1497 (1994)] conditions and for 90° waveguide phasing, the stochastic limit in the current drive direction is about 2 keV, determined by the last overlapping mode. The progress of electrons through accessible phase space is very efficient: the TdeV 32 waveguide array can accelerate the electrons to the possible limit. An area‐preserving map is derived to study the electron dynamics. Surface‐of‐section plots fully ...

On self‐consistent ray‐tracing and Fokker–Planck modeling of the hard x‐ray emission during lower‐hybrid current drive in tokamaks

A detailed investigation is presented on the ability of combined ray‐tracing and Fokker–Planck calculations to predict the hard x‐ray (HXR) emission during lower‐hybrid (LH) current drive in tokamaks when toroidally induced ray stochasticity is important. A large number of rays is used and the electron distribution function is obtained by self‐consistently iterating the appropriate power deposition and Fokker–Planck calculations. It is shown that effects due to radial diffusion of suprathermal electrons and to radiation scattering by the inner wall can be significant. The experimentally observed features of the HXR emission are fairly well predicted, thus confirming that combined ray‐tracing and Fokker–Planck codes are capable of correctly modeling the physics of LH current drive in tokamaks.

Mach probe interpretation in the presence of suprathermal electrons

The collisionless theory of Mach probes assuming isothermal, Maxwellian electrons is extended to include an isotropic, two-temperature electron distribution function. The kinetic equations for ion and electron motion in the probe wake are solved using a quasineutral particle-in-cell method, which compares qualitatively well with the results of a simple fluid model. The measured Mach number decreases slightly with increasing hot electron concentration, but the main effect is on the measured electron temperature. Due to the fact that the probe is sensitive to even a tiny population of hot electrons, the resulting ion sound speed can be overestimated by up to a factor of 2, leading to measurements of absolute flow speed that are too large.

Bright spots generated by lower hybrid waves on JET

Observations of bright spots on the JET divertor aprons during lower hybrid current drive experiments are described. These bright spots are important because they can potentially cause damage to large tokamaks. The bright spots arise due to the impact of a fast particle beam. This beam originates from the front of the lower hybrid launcher, where thermal particles are accelerated according to theory by interaction with the high spatial harmonics of the lower hybrid wave. The bright spots are clearly related to the lower hybrid power as they disappear when the lower hybrid power is switched off. According to the analysis versus various parameters, the brightness of the spots clearly decreases with increasing plasma–wall distance, i.e. the distance between the last closed flux surface and the poloidal limiter. This is clearly beneficial for ITER, as it is designed to operate at a large plasma–wall distance.

Simulations of lower hybrid current drive and Ohmic transformer recharge

It is planned to use lower hybrid current drive (LHCD) in the Tokamak de Varennes to support continuous operation for the entire duration (30 s) of the toroidal field. In the nominal Ohmic equilibrium, lower hybrid slow wave accessibility is poor (n1 access 3), which severely limits the number of resonant electrons and LHCD efficiency. Careful modelling is therefore needed to estimate the minimum RF power requirements and the recharge possibilities while maintaining a constant total plasma current. The Bonoli-Englade code has been modified with respect to evolution of narrow Brambilla spectra, RF current diffusion and proportional-integral-derivative feedback control of the plasma current. It appears that 200 kA of current could be maintained in a steady state with about 1 MW of LH power at 3.7 GHz and with n0 = 4 × 1019 m−3. With the same power, in an alternating Ohmic/RF scenario, the Ohmic transformer could be recharged to 2 Vs in about four seconds at a slightly reduced density.

Calculation of a wave field from ray tracing

Radio frequency heating and current drive are important features of many tokamaks. In order to predict the efficiency of the current drive and where it takes place in the tokamak profile, computational techniques which couple calculations of the wave field to Fokker–Planck solutions of the electron distribution function have been developed. In the electron cyclotron and lower hybrid (LH) frequency ranges the wave field is often calculated using ray tracing techniques, though more recently some full wave calculations have been done. Ray tracing provides a simpler way of proceeding, but the problem arises of dealing with the situation in which there is not a single well defined beam and diffraction and beam divergence are important. Since an LH antenna produces a complicated spectrum, launching waves in a range of directions, the problem is particularly acute there. In this paper we suggest a way of calculating the wave field from tracing of multiple rays using a technique based on the stationary phase approximation. We demonstrate how it can be used and its effectiveness through a number of simple examples.

The optimization of resonant magnetic perturbation spectra for the COMPASS tokamak

The COMPASS tokamak, recently transferred from UKAEA Culham to IPP Prague, is equipped with a set of saddle coils for producing controlled resonant magnetic perturbations (RMPs). In the future experimental programme of COMPASS we plan to focus on studies of RMPs, especially in view of their application as an ELM control mechanism and their considered use in ITER. In the present contribution we describe the preparatory calculations for the planned experiments. We computed the spectra of perturbations for several different equilibria predicted by MHD simulations and determined the positions and sizes of the resulting islands. It is shown how the saddle coils of COMPASS can be adapted to our equilibria to obtain good island overlap at the edge, which is believed to be a key component in the ELM mitigation effect. The techniques used for adapting the coils to achieve this result are described. Those are fairly general and could be used in the design of RMP coils on other machines.

Simulations of current density profile control using lower hybrid current drive in the TdeV Tokamak

The physics basis of a simulation model for lower hybrid current drive (LHCD) is discussed. Issues associated with LH power deposition-wave propagation, mode conversion and cut-offs in toroidal geometry, as well as linear and quasi-linear Landau damping-are analysed. A simulation model (ACCOME) is applied to the LHCD experiment now operating on the Tokamak de Varennes (TdeV). The profiles and values of density and temperature needed as inputs to ACCOME are taken from the experiment. The predictions of current density and loop voltage from ACCOME are then compared with experimental LHCD results. Possible LH current profile control experiments are also analysed for TdeV using composite LH spectra to control the location of RF power deposition. Finally the relevance of these current profile control results to future devices is discussed and an example is shown for ITER-like parameters

A full wave theory of high-harmonic fast wave absorption in high-beta plasmas

A theory of fast wave absorption in a high-beta plasma is given. A reduced, second-order, ordinary differential equation has been used which includes all collisionless electron dissipation mechanisms and ion cyclotron damping over many harmonics. This is relevant to the high-harmonic fast wave heating scheme proposed by Ono [Phys. Plasmas 2, 4075 (1995)]. The parameters appropriate to the National Spherical Tokamak Experiment NSTX [J. Spitzer et al., Fusion Technol. 30, 1337 (1996)] have been used to investigate the absorption characteristics of electrons and ions under high-beta, high-harmonic conditions.