Toroidal torque generated by neoclassical viscosity caused by external non-resonant, nonaxisymmetric perturbations has a significant influence on toroidal plasma rotation in tokamaks.In this article, a derivation for the expressions of toroidal torque and radial transport in resonant regimes is provided within quasilinear theory in canonical action-angle variables. The proposed approach treats all low-collisional quasilinear resonant NTV regimes including superbanana plateau and drift-orbit resonances in a unified way and allows for magnetic drift in all regimes. It is valid for perturbations on toroidally symmetric flux surfaces of the unperturbed equilibrium without specific assumptions on geometry or aspect ratio. The resulting expressions are shown to match existing analytical results in the large aspect ratio limit. Numerical results from the newly developed code NEO-RT are compared to calculations by the quasilinear version of the code NEO-2 at low collisionalities. The importance of the magnetic shear term in the magnetic drift frequency and a significant effect of the magnetic drift on drift-orbit resonances are demonstrated.
NEO-2 is a linearized drift kinetic equation solver for three-dimensional toroidal magnetic fields. It has been designed in order to treat besides all other regimes effectively the long mean free path regime avoiding any simplifications on device geometry or on the Coulomb collision model. The code is based on the field line integration technique combined with a multiple domain decomposition approach, which allows for introduction of an adaptive grid in velocity space. This makes NEO-2 capable to resolve effectively all boundary layers between various classes of trapped particles and passing particles and also allows for a straightforward code parallelization. In stellarators, NEO-2 is used mainly for computations of neoclassical transport coefficients in regimes with slow plasma rotation and for the evaluation of the generalized Spitzer function, which plays the role of a current drive efficiency. In tokamaks with small ideal non-axisymmetric magnetic field perturbations, NEO-2 is used for evaluation of the toroidal torque resulting from these perturbations (neoclassical toroidal viscosity). The limitation to slow plasma rotation pertinent to usage in stellarators has been removed in this case with help of a quasilinear approach, which is valid due to the smallness of the perturbation field.
The toroidal torque due to the non-resonant interaction with external magnetic perturbations (TF ripple and perturbations from ELM mitigation coils) in ASDEX Upgrade is modelled with help of the NEO-2 and SFINCS codes and compared to semi-analytical models. It is shown that almost all non-axisymmetric transport regimes contributing to neoclassical toroidal viscosity (NTV) are realized within a single discharge at different radial positions. The NTV torque is obtained to be roughly a quarter of the NBI torque. This indicates the presence of other important momentum sources. The role of these momentum sources and possible integral torque balance measurements are briefly discussed.
The Electron Cyclotron Current Drive (ECCD) efficiency is usually modeled in collisionless limits. While such models are sufficient for plasmas with rather low collisionality, they might underestimate the current drive in plasmas at low temperatures as they occur at an initial phase of device operation. In this paper, the impact of finite collisionality effects on the wave-induced current drive is studied for a highmirror configuration of Wendelstein 7-X using a combination of the drift kinetic equation solver NEO-2 and the ray-tracing code TRAVIS for a realistic set of plasma parameter profiles. The generalized Spitzer function, which describes the ECCD efficiency in phase space, is modeled with help of NEO-2, which uses the full linearized Coulomb collision operator including energy and momentum conservation. Within this approach the linearized drift kinetic equation is solved by means of the field line integration technique without any simplifications on device geometry. Results of the ray-tracing code TRAVIS using the ECCD efficiency from NEO-2 within the adjoint approach show a significant difference of the driven current as compared to commonly used collisionless models for the ordinary as well as the extraordinary second harmonic mode. a)
Abstract. The generalized Spitzer function, which determines the current drive eciency in tokamaks and stellarators is modelled for nite plasma collisionality with help of the drift kinetic equation solver NEO-2 [1]. The eect of nite collisionality on the global ECCD eciency in a tokamak is studied using results of the code NEO-2 as input to the ray tracing code TRAVIS [2]. As it is known [3], specic features of the generalized Spitzer function, which are absent in asymptotic (collisionless or highly collisional) regimes result in current drive from a symmetric microwave spectrum with respect to parallel wave numbers. Due to this eect the direction of the current may become independent of the microwave beam launch angle in advanced ECCD scenarii (O2 and X3) where due to relatively low optical depth a signicant amount of power is absorbed by trapped particles.
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