R. B. White

Hamiltonian guiding center drift orbit calculation for plasmas of arbitrary cross section

A Hamiltonian guiding center drift orbit formalism is developed which permits the efficient calculation of particle trajectories in magnetic field configurations of arbitrary cross section with arbitrary plasma β. The magnetic field is assumed to be a small perturbation from a zero‐order ‘‘equilibrium’’ field possessing magnetic surfaces. The equilibrium field, possessing helical or toroidal symmetry, can be modeled analytically or obtained numerically from equilibrium codes. The formalism is used to study trapped particle precession. Finite banana width corrections to the toroidal precession rate are derived, and the bounce averaged trapped particle motion is expressed in Hamiltonian form. Particle drift‐pumping associated with the ‘‘fishbone’’ oscillation is investigated. A numerical code based on the formalism is used to study particle orbits in circular and bean‐shaped tokamak configurations.

Saturation of the tearing mode

A quasi‐linear analytical model is used to describe the nonlinear growth and saturation of tearing modes with mode number m⩾2. The saturation of the magnetic island growth is the quasi‐linear development of a single mode rather than a mode coupling process. The saturation amplitude, which is dependent on the form of the resistivity, is in good agreement with results obtained previously by numerically advancing the full set of nonlinear equations.

Excitation of zonal flow by drift waves in toroidal plasmas

An analytical dispersion relation is derived which shows that, in toroidal plasmas, zonal flows can be spontaneously excited via modulations in the radial envelope of a single-n coherent drift wave, with n the toroidal mode number. Predicted instability features are verified by three-dimensional global gyrokinetic simulations of the ion-temperature-gradient mode. Nonlinear equations for mode amplitudes demonstrate saturation of the linearly unstable pump wave and nonlinear oscillations of the drift-wave intensity and zonal flows, with a parameter-dependent period doubling route to chaos.

Principal physics developments evaluated in the ITER design review

As part of the ITER Design Review and in response to the issues identified by the Science and Technology Advisory Committee, the ITER physics requirements were reviewed and as appropriate updated. The focus of this paper will be on recent work affecting the ITER design with special emphasis on topics affecting near-term procurement arrangements. This paper will describe results on: design sensitivity studies, poloidal field coil requirements, vertical stability, effect of toroidal field ripple on thermal confinement, material choice and heat load requirements for plasma-facing components, edge localized modes control, resistive wall mode control, disruptions and disruption mitigation.

Reconnection rates of magnetic fields including the effects of viscosity

The Sweet–Parker and Petschek scalings of the magnetic reconnection rate are modified to include the effect of the viscosity. The modified scalings show that the viscous effect can be important in high‐β plasmas. The theoretical reconnection scalings are compared with numerical simulation results in a tokamak geometry for three different cases: a forced reconnection driven by external coils, the nonlinear m=1 resistive internal kink, and the nonlinear m=2 tearing mode. In the first two cases, the numerical reconnection rate agrees well with the modified Sweet–Parker scaling when the viscosity is sufficiently large. When the viscosity is negligible, a steady state which was assumed in the derivation of the reconnection scalings is not reached and the current sheet in the reconnection layer either remains stable through sloshing motions of the plasma or breaks up to higher m modes. When the current sheet remains stable, a rough comparison with the Sweet–Parker scaling is obtained. In the nonlinear m=2 teari...

On resonant heating below the cyclotron frequency

Resonant heating of particles by electrostatic and Alfven waves propagating in a confining uniform magnetic field is examined. It is shown that, with a sufficiently large wave amplitude, significant perpendicular stochastic heating can be obtained with wave frequency at a fraction of the cyclotron frequency. This result may have relevance for the heating of ions in the solar corona, and is a generic phenomenon, independent of the type of wave considered.

Alpha particle losses from toroidicity induced Alfven eigenmodes: Part II: Monte Carlo simulations and anomalous alpha loss processes

Fusion‐born α particles moving parallel to the magnetic field can resonate with toroidal Alfven eigenmodes (TAE) leading to anomalous α‐orbit diffusion across the α‐loss boundaries in a tokamak. This is analyzed using the Hamiltonian guiding center code orbit in conjunction with the kinetic magnetohydrodynamics (MHD) eigenmode solving code nova‐k. Resonant single α orbits are studied below and above the threshold for orbit stochasticity and Monte Carlo randomized ensembles of alphas subjected to a finite amplitude time‐dependent TAE are followed with respect to their radial losses using realistic MHD equilibria and numerically computed toroidal Alfven eigenfunctions for one toroidal eigenmode n=1 and the full Fourier spectrum of poloidal harmonics m involved in the ‘‘gap mode.’’ The α‐loss mechanisms are resonant drift motion across the loss boundaries of alphas born near these boundaries and stochastic diffusion to the boundaries in constants of the motion (phase) space. After a first transient of resona...

Numerical studies of nonlinear evolution of kink modes in tokamaks

A set of numerical techniques for investigating the full nonlinear unstable behavior of low‐β kink modes of given helical symmetry in tokamaks is presented. Uniform current density plasmas display complicated deformations including the formation of large vacuum bubbles provided that the safety factor q is sufficiently close to integral. Fairly large m=1 deformations, but not bubble formation, persist for a plasma with a parabolic current density profile (and hence shear). Deformations for m⩾2 are, however, greatly suppressed.

Theory of mode-induced beam-particle loss in tokamaks

Large‐amplitude rotating magnetohydrodynamic modes are observed to induce significant high‐energy beam particle loss during high‐power perpendicular netural beam injection on the poloidal divertor experiment (PDX). A Hamiltonian formalism for drift orbit trajectories in the presence of such modes is used to study induced particle loss analytically and numerically. Results are in good agreement with experiment.

Canonical Hamiltonian guiding center variables

A simplification of the canonical Hamiltonian variables for the guiding center motion of a charged particle in a general toroidal field is obtained using the Lagrangian formalism.