N. Bertelli

Full wave simulations of fast wave heating losses in the scrape-off layer of NSTX and NSTX-U

Full wave simulations of fusion plasmas show a direct correlation between the location of the fast-wave cut-off, radiofrequency (RF) field amplitude in the scrape-off layer (SOL) and the RF power losses in the SOL observed in the National Spherical Torus eXperiment (NSTX). In particular, the RF power losses in the SOL increase significantly when the launched waves transition from evanescent to propagating in that region. Subsequently, a large amplitude electric field occurs in the SOL, driving RF power losses when a proxy collisional loss term is added. A 3D reconstruction of absorbed power in the SOL is presented showing agreement with the RF experiments in NSTX. Loss predictions for the future experiment NSTX-Upgrade (NSTX-U) are also obtained and discussed.

The effects of the scattering by edge plasma density fluctuations on lower hybrid wave propagation

Scattering effects induced by edge density fluctuations on lower hybrid (LH) wave propagation are investigated. The scattering model used here is based on the work of Bonoli and Ott (1982 Phys. Fluids 25 361). It utilizes an electromagnetic wave kinetic equation solved by a Monte Carlo technique. This scattering model has been implemented in GENRAY, a ray-tracing code which explicitly simulates wave propagation, as well as collisionless and collisional damping processes, over the entire plasma discharge, including the scrape-off layer that extends from the separatrix to the vessel wall. A numerical analysis of the LH wave trajectories and the power deposition profile with and without scattering is presented for Alcator C-Mod discharges. Comparisons between the measured hard x-ray emission on Alcator C-Mod and simulations of the data obtained from the synthetic diagnostic included in the GENRAY/CQL3D package are shown, with and without the combination of scattering and collisional damping. Implications of these results on LH current drive are discussed.

Paraxial Wentzel–Kramers–Brillouin method applied to the lower hybrid wave propagation

The paraxial Wentzel–Kramers–Brillouin (pWKB) approximation, also called beam tracing method, has been employed in order to study the propagation of lower hybrid waves in a tokamak plasma. Analogous to the well-know ray tracing method, this approach reduces Maxwell’s equations to a set of ordinary differential equations, while, in addition, retains the effects of the finite beam cross-section, and, thus, the effects of diffraction. A new code, LHBEAM (lower hybrid BEAM tracing), is presented, which solves the pWKB equations in tokamak geometry for arbitrary launching conditions and for analytic and experimental plasma equilibria. In addition, LHBEAM includes linear electron Landau damping for the evaluation of the absorbed power density and the reconstruction of the wave electric field in both the physical and Fourier space. Illustrative LHBEAM calculations are presented along with a comparison with the ray tracing code GENRAY and the full wave solver TORIC-LH.

The contribution of radio-frequency rectification to field-aligned losses of high-harmonic fast wave power to the divertor in the National Spherical Torus eXperiment

The National Spherical Torus eXperiment (NSTX) can exhibit a major loss of high-harmonic fast wave (HHFW) power along scrape-off layer (SOL) field lines passing in front of the antenna, resulting in bright and hot spirals on both the upper and lower divertor regions. One possible mechanism for this loss is RF sheaths forming at the divertors. Here, we demonstrate that swept-voltage Langmuir probe characteristics for probes under the spiral are shifted relative to those not under the spiral in a manner consistent with RF rectification. We estimate both the magnitude of the RF voltage across the sheath and the sheath heat flux transmission coefficient in the presence of the RF field. Although precise comparison between the computed heat flux and infrared (IR) thermography cannot yet be made, the computed heat deposition compares favorably with the projections from IR camera measurements. The RF sheath losses are significant and contribute substantially to the total SOL losses of HHFW power to the divertor f...

Coupling of alpha channeling to parallel wavenumber upshift in lower hybrid current drive

Although lower hybrid (LH) waves have been shown to be effective in driving plasma current in present-day tokamaks, they are predicted to strongly interact with the energetic α particles born from fusion reactions in eventual tokamak reactors. However, in the presence of the expected steep α particle birth gradient, this interaction can produce wave amplification rather than wave damping. Here, we identify the flexibilities and constraints in achieving this amplification effect through a consideration of symmetries in the channeling interaction, in the wave propagation, and in the tokamak field configuration. Interestingly, for standard LH current drive that supports the poloidal magnetic field, we find that wave amplification through α channeling is fundamentally coupled to the poorly understood |k∥| upshift. In so doing, we show that wave launch from the tokamak high-field side is favorable both for α-channeling and for achieving the |k∥| upshift.

Simulations towards the achievement of non-inductive current ramp-up and sustainment in the National Spherical Torus Experiment Upgrade

One of the goals of the National Spherical Torus Experiment Upgrade (NSTX-U) (Menard et al 2012 Nucl. Fusion 52 083015) is the demonstration of fully non-inductive start-up, current ramp-up and sustainment. This work discusses predictive simulations where the available heating and current drive systems are combined to maximize the non-inductive current and minimize the solenoidal contribution. Radio-frequency waves at harmonics higher than the ion cyclotron resonance (high-harmonic fast waves (HHFW)) and neutral beam injection are used to ramp the plasma current non-inductively starting from an initial Ohmic plasma. An interesting synergy is observed in the simulations between the HHFW and electron cyclotron (EC) wave heating. Furthermore, time-dependent simulations indicate that, depending on the phasing of the HHFW antenna, EC wave heating can significantly increase the effectiveness of the radio-frequency power, by heating the electrons and increasing the current drive efficiency, thus relaxing the requirements on the level of HHFW power that needs to be absorbed in the core plasma to drive the same amount of fast-wave current.

The effects of finite electron temperature and diffraction on lower hybrid wave propagation

In this paper we show that the commonly used cold plasma dispersion relation for plasma waves in the lower hybrid range of frequencies (LHRF) produces a wave trajectory that is notably different than when thermal corrections to the Hermitian part of the dielectric tensor are retained. This is in contrast to the common implementation in LH simulation codes in which thermal effects are retained only for the anti-Hermitian part of the dielectric tensor used for damping calculations. We show which term is the critical one to retain in the dielectric tensor and discuss implications for modeling of LHRF waves in present day and future devices. We conclude with some observations on the effects of diffraction that may be isolated once thermal effects are retained in both ray tracing and full-wave approaches.

Quasilinear diffusion coefficients in a finite Larmor radius expansion for ion cyclotron heated plasmas

In this paper, a reduced model of quasilinear velocity diffusion by a small Larmor radius approximation is derived to couple the Maxwells equations and the Fokker Planck equation self-consistently for the ion cyclotron range of frequency waves in a tokamak. The reduced model ensures the important properties of the full model by Kennel-Engelmann diffusion, such as diffusion directions, wave polarizations, and H-theorem. The kinetic energy change ( W) is used to derive the reduced model diffusion coefficients for the fundamental damping (n = 1) and the second harmonic damping (n = 2) to the lowest order of the finite Larmor radius expansion. The quasilinear diffusion coefficients are implemented in a coupled code (TORIC-CQL3D) with the equivalent reduced model of the dielectric tensor. We also present the simulations of the ITER minority heating scenario, in which the reduced model is verified within the allowable errors from the full model results.

Full-wave simulations of ICRF heating regimes in toroidal plasma with non-Maxwellian distribution functions

At the power levels required for significant heating and current drive in magnetically-confined toroidal plasma, modification of the particle distribution function from a Maxwellian shape is likely (Stix 1975 Nucl. Fusion 15 737), with consequent changes in wave propagation and in the location and amount of absorption. In order to study these effects computationally, both the finite-Larmor-radius and the high-harmonic fast wave (HHFW), versions of the full-wave, hot-plasma toroidal simulation code TORIC (Brambilla 1999 Plasma Phys. Control. Fusion 41 1 and Brambilla 2002 Plasma Phys. Control. Fusion 44 2423), have been extended to allow the prescription of arbitrary velocity distributions of the form . For hydrogen (H) minority heating of a deuterium (D) plasma with anisotropic Maxwellian H distributions, the fractional H absorption varies significantly with changes in parallel temperature but is essentially independent of perpendicular temperature. On the other hand, for HHFW regime with anisotropic Maxwellian fast ion distribution, the fractional beam ion absorption varies mainly with changes in the perpendicular temperature. The evaluation of the wave-field and power absorption, through the full wave solver, with the ion distribution function provided by either a Monte-Carlo particle and Fokker–Planck codes is also examined for Alcator C-Mod and NSTX plasmas. Non-Maxwellian effects generally tend to increase the absorption with respect to the equivalent Maxwellian distribution.

Investigation of ion and electron heat transport of high-Te ECH heated discharges in the large helical device

An analysis of the radial electric field and heat transport, both for ions and electrons, is presented for a high-