Tokamak plasmas are inherently comprised of multiple ion species. This is due to wall-bred impurities and, in future reactors, will result from fusion-born alpha particles. Relatively small densities nI, of highly charged non-hydrogenic impurities can strongly influence plasma transport properties whenever . The determination of the complete neoclassical Onsager matrix for a toroidally confined multispecies plasma, which provides the linear relation between the surface averaged radial fluxes and the thermodynamic forces (i.e. gradients of density and temperature, and the parallel electric field), is reviewed. A closed set of one-dimensional moment equations is presented for the time evolution of thermodynamic and magnetic field quantities which results from collisional transport of the plasma and two-dimensional motion of the magnetic flux surface geometry. The effects of neutral-beam injection on the equilibrium and transport properties of a toroidal plasma are consistently included.

https://iopscience.iop.org/article/10.1088/0029-5515/21/9/003/pdf

Neoclassical transport of impurities in tokamak plasmas

New techniques for calculating heat and particle source rates due to neutral beam injection in axisymmetric tokamaks

The Fokker-Planck equation is studied for an energetic ion beam injected into a magnetized plasma consisting of Maxwellian ions and electrons with υthi ≪υb≪ υthe. The time evolution of the fast ion distribution is given in terms of an infinite sum of Legendre polynomials for distributions that are axisymmetric about the magnetic field. The effect of charge exchange is included. The resulting ion distribution is somewhat isotropic for velocities much less than the injection velocity, however, the distribution is sharply peaked in both energy and pitch angle for velocities near the injection velocity. Approximate asymptotic expressions are given for the distribution in the vicinity of the injected beam and for velocities greater than the injection velocity. The effect of a weak parallel electric field is also given.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022377800020134

Energetic ion distribution resulting from neutral beam injection in tokamaks

Tokamak plasma diagnostics is reviewed. Subjects are classified according to the physical quantities to be measured. Instrumental techniques and theoretical considerations are developed at length only when the development in question is relatively new. Present trends are emphasized, as well as diagnostic limitations and needs for future large tokamaks.

https://iopscience.iop.org/article/10.1088/0029-5515/18/5/004/pdf

Tokamak plasma diagnostics

Reviews the neutron measurement techniques that are applied to the study of tokamak plasmas. The range of neutron energies of primary interest is limited to narrow bands around 2.5 and 14 MeV, and the variety of measurements that can be made for plasma diagnostic purposes is also restricted. To characterize the plasma as a neutron source, it is necessary only to measure the total neutron emission, the relative neutron emissivity as a function of position throughout the plasma, and the energy spectra of the emitted neutrons. In principle, such measurements might be expected to be relatively easy. That this is not the case is, in part, attributable to practical problems of accessibility to a harsh environment but is mostly a consequence of the time scale on which the measurements have to be made and of the wide range of neutron emission intensities that have to be covered; for tokamak studies, the time-scale is of the order of 1 to 100 ms and the neutron intensity ranges from 1012 to 1019 s-1.

https://iopscience.iop.org/article/10.1088/0741-3335/36/2/002/pdf

Neutron measurement techniques for tokamak plasmas

The energetic ion distribution resulting from the injection of high‐energy neutrals into a toroidal plasma has been derived. An appropriate kinetic equation which contains the angular scattering, friction, and diffusion of the energetic ions by the background particles, charge exchange on the background neutrals, and acceleration of the ions by the electric field has been solved analytically by use of the WKBJ method. Collisions of the energetic ions with the faster moving electrons results in some of the ions increasing their energy above the injection energy. The width of this ``high‐energy tail'' is shown to depend upon the electron temperature and the electric field. An estimate of the effect upon the width of this tail of collisions between the energetic ions themselves is also given. Finally, illustrated examples of the various significant physical processes are presented.

W. G. F. Core

Papers

Energetic particle distribution in a toroidal plasma with neutral injection heating