Computational studies have been performed for fast ion behavior in a Tokamak with toroidal field ripple. Collisionless behavior of fast ions relating to rippletrapping, ripple-detrapping and banana drift is of essential importance in fast ion loss processes in case of quasi-perpendicular neutral beam injection. The collisionless ripple trapping and ripple-enhanced banana drift produce a large number of loss bands in velocity space and enhance the loss of fast ions. The fast ion loss associated with ripple can be categorized into two groups; ripple-trapped loss and banana-drift loss. The amount of loss particles due to the respective loss process is significantly influenced by the effect of finite banana size of fast ions. The ripple-trapped loss particles are localized in a specific region on the first wall surface.

Effect of Toroidal Field Ripple on Fast Ion Behavior in a Tokamak

The author reviews the theoretical work on those properties of a thermonuclear plasma that relate to the charged products of nuclear fusion reactions – α-particles. Three basic lines of research – on classical mechanisms of α-particle loss in tokamaks, collective processes in the plasma initiated by α-particles, and the energy balance stability of a thermonuclear plasma – are considered.

https://iopscience.iop.org/article/10.1088/0029-5515/20/6/008/pdf

The role of alpha particles in tokamak reactors

The paper constitutes a review of the neoclassical theory of transport processes in the different types of toroidal magnetic configuration now being used to study the possibility of producing a controlled thermonuclear reaction. Owing to the abundance of the material that has accumulated in recent years and the large number of parameters involved in the problem, it has not been possible to present all the mathematical calculations in detail while confining the results to a few definitive expressions. The general approach to a solution of the problem and its key aspects have been discussed as fully as possible, and a number of definitive results are presented. In the review, a history of the subject and an account of its present status are given, the problem itself is formulated, the basic equations are discussed and analytical solution methods are described. Definitive expressions are given for cross-field particle and energy fluxes, the bootstrap current and conductivity, all of which are required to solve the particle and heat balance equations in magnetic confinement devices. The results are presented in a relatively simple form which is convenient for analysis of the experimental data and are accompanied by tables containing numerical values for the universal coefficients in the definitive expressions. The review is aimed at both theoreticians and experimenters working in high-temperature plasma physics and controlled thermonuclear fusion.

Neoclassical theory of transport processes in toroidal magnetic confinement systems, with emphasis on non-axisymmetric configurations

The ion velocity distributions of tokamak plasmas sustained by injected fast atomic beams fall into three categories, according to the partial pressure of the energetic-ion population, which in turn is determined by the plasma nτE, the injection energy, and the fraction of plasma fuelling performed by the beams. There are correspondingly three regimes of beam-driven reactor operation in D-T or D-D: thermonuclear; beam-target or TCT; and plasmas with ion pressure/electron pressure 1. This review treats the physical basis and plasma engineering parameters of beam-driven tokamak reactors. The theories of energetic-ion velocity distributions, stability, injection, and orbits are summarized. The many-faceted role of the energetic ions in plasma heating, fuelling, and current maintenance, as well as in the direct enhancement of fusion power multiplication and power density, is discussed in detail for the three reactor types. The relevant implications of recent experimental results from several beam-injected tokamaks are examined. The behaviour of energetic ions is found to be in accordance with classical theory, large total ion energy densities are readily achieved, and plasma equilibrium and gross stability are preserved. The status of neutral-beam injectors and of conceptual design studies of beam-driven reactors is reviewed briefly. The principal plasma-engineering problems are those associated directly with achieving quasi-stationary operation, particularly the problem of high-throughput particle exhaust. An especially attractive feature of beam-driven tokamak plasmas is their capability for useful application in devices of relatively small size.

https://iopscience.iop.org/article/10.1088/0029-5515/17/2/015/pdf

Neutral-beam-driven tokamak fusion reactors

The differences among the various scalings in the transport calculations associated with the collisionless detrapping/retrapping orbits in a nonaxisymmetric torus are clarified. A simple random walk argument indicates that these differences are mainly due to an implicit assumption made about the retrapping rate of the toroidally trapped particles.

Transport associated with the collisionless detrapping/retrapping orbits in a nonaxisymmetric torus

The magnetic field modulation due to the discrete nature of the field coils in a Tokamak leads to additional particle trapping. The resulting diffusion is evaluated and compared with the neoclassical diffusion. The two diffusion rates are found to be comparable in existing Tokamaks. The limit on the field ripple below which ripple diffusion should be negligible in the next generation of machines is evaluated.

https://iopscience.iop.org/article/10.1088/0029-5515/12/6/010/pdf

T.E. Stringer

Papers

Effect of the magnetic field ripple on diffusion in Tokamaks