Ivan B. Ivanov

Kinetic estimate of the shielding of resonant magnetic field perturbations by the plasma in DIII-D

Effects of linear plasma response currents on non-axisymmetric magnetic field perturbations from the I-coil used for edge localized mode mitigation in DIII-D tokamak are analysed with the help of a kinetic plasma response model developed for cylindrical geometry. It is shown that these currents eliminate the ergodization of the magnetic field in the core plasma and reduce the size of the ergodic layer at the edge. A simple balance model is proposed which qualitatively reproduces the evolution of the plasma parameters in the pedestal region with the onset of the perturbation. It is suggested that the experimentally observed density pump-out effect in the long mean free path regime is the result of a combined action of ion orbit losses and magnetic field ergodization at the edge.

Magnetic reconnection with space and time varying reconnection rates in a compressible plasma

Fast magnetic reconnection of Petschek-type including moving shock waves and discontinuities in a compressible plasma is studied. Magnetic flux tubes of finite size are reconnected by a localized dissipative electric field pulse. This process generates nonlinear perturbations propagating along the initial current surface. The linear wave problem in the outer regions is solved analytically in terms of the reconnection induced sources which move in different directions and with different speeds along the surface. The time-coordinate representation of the solution is given in form of convolution integrals over the reconnection initializing electric field. As an example, reconnection of flux tubes in a sheared magnetic field geometry is analyzed.

Kinetic modelling of the interaction of rotating magnetic fields with a radially inhomogeneous plasma

The interaction of rotating magnetic fields (RMFs) with a plasma is modelled in the linear approximation. A kinetic Hamiltonian model for the rf plasma conductivity is used. A radially inhomogeneous periodic cylindrical plasma with a rotational transform of the magnetic field is studied with parameters relevant to the dynamic ergodic divertor (DED) of TEXTOR. For the case of a finite electron diamagnetic velocity it is shown that the torque resulting from the RMF tends to bring the electron fluid approximately to the rest frame of this field. This result is in qualitative agreement with long mean-free path drift MHD theory. In contrast to that theory where a resonant behaviour is found at electron and ion diamagnetic frequencies, in the present kinetic analysis, the RMF frequency where the torque passes through zero is smaller than the electron diamagnetic frequency if there is an electron temperature gradient present. The relation of these results with recent experimental measurements of the DED-induced plasma rotation in TEXTOR is discussed.

Numerical testing in determination of sound speed from a part of boundary by the BC-method

Abstract We present the results of numerical testing on determination of the sound speed c in the acoustic equation utt - c2Δu = 0 by the boundary control method. The inverse data is a response operator (a hyperbolic Dirichlet-to-Neumann map) given on controls, which are supported on a part of the boundary. The speed is determined in the subdomain covered by acoustic rays, which are emanated from the points of this part orthogonally to the boundary. The determination is time-optimal: the longer the observation time is, the larger the subdomain is, in which c is recovered. The numerical results are preceded with a brief exposition of the relevant variant of the BC-method.

Kinetic linear model of the interaction of helical magnetic perturbations with cylindrical plasmas

The linear kinetic model of the interaction of helical rotating magnetic perturbations (resonant and nonresonant) with a tokamak plasma developed in [M. F. Heyn et al., Nucl. Fusion 46, S159 (2006)] is extended by a Galilean invariant collision operator and a different finite Larmor radius expansion scheme of particle current density. The model is applied to study the plasma screening effect on resonant magnetic perturbations and the resulting torques acting on the plasma at various orders of Larmor radius expansion.

Quasilinear modelling of RMP interaction with a tokamak plasma: application to ASDEX Upgrade ELM mitigation experiments

First experiments on edge-localized mode (ELM) mitigation with the help of ITER-like coils on ASDEX Upgrade are analysed using linear and quasilinear kinetic models to describe the interaction of resonant magnetic field perturbations (RMP) with the plasma. The gyrokinetic derivation of RMP-driven transport coefficients is given in detail. The role of fluid resonances is studied, in particular the role of the resonance associated with the equilibrium electric field reversal point Er = 0. Like the electron fluid resonance associated with the zero of the total perpendicular electron fluid velocity, the Er = 0 resonance may lead to enhanced transport due to the reduction of RMP shielding in the pedestal region where the RMP field can even be amplified by this resonance. The conditions on the RMP coil spectrum resulting from the analysis are discussed.

On the confinement of passing alpha particles in a tokamak-reactor with resonant magnetic field perturbations shielded by plasma currents

Alpha-particle losses due to the resonant magnetic field perturbations (RMPs) created by the coil system for edge-localized mode mitigation in ITER are studied numerically. If shielding of RMPs by the plasma is not taken into account, passing α-particles are the main loss channel which, together with the trapped particle contribution leads to a loss of more than 5% of fusion alpha particle power. Shielding of RMPs practically eliminates this channel so that the overall losses are reduced to about 1%.

Kinetic versus ideal magnetohydrodynamic modelling of the resistive wall mode in a reversed field pinch plasma

Resistive wall modes (RWMs) are studied within the kinetic model proposed by Heyn et al. [Nucl. Fusion 46, S159 (2006); Phys. Plasmas 18, 022501 (2011)], which accounts for Landau damping, transit-time magnetic pumping, and Coulomb collisions in cylindrical geometry. Results for the reversed field pinch plasma are compared to the magnetohydrodynamic results obtained by Guo et al., [Phys. Plasmas 6, 3868 (1999)]. Stabilization of the external kink mode by an ideal wall as well as stabilization of the resistive wall mode by toroidal plasma rotation is obtained. In contrast to MHD modelling, which predicts a stability window for the resistive wall position, kinetic modelling predicts a one sided window only, i.e., the resistive wall must be sufficiently close to plasma to achieve rotational stabilization of the mode but there is no lower limit on the wall position. Stabilizing rotation speeds are found somewhat smaller when compared to MHD results. In addition, for the present plasma configuration, the kinet...

Effect of energy and momentum conservation on fluid resonances for resonant magnetic perturbations in a tokamak

In this paper, the impact of momentum and energy conservation of the collision operator in the kinetic description for Resonant Magnetic Perturbations (RMPs) in a tokamak is studied. The particle conserving differential collision operator of Ornstein-Uhlenbeck type is supplemented with integral parts such that energy and momentum are conserved. The application to RMP penetration in a tokamak shows that energy conservation in the electron collision operator is important for the quantitative description of plasma shielding effects at the resonant surface. On the other hand, momentum conservation in the ion collision operator does not significantly change the results.