Physical problems

The physics of toroidal plasma in the most general case is described by Maxwell’s equations, kinetic equations and equations of charged particles motion. The general model is intractable for both analytic and numerical study due to high dimensionality of the phase space and presence of processes with substantially different time scales. However, the general model can be substantially simplified for particular processes, for example using symmetry or averaging over fast processes.

Classification of processes in toroidal plasma and characteristic time scales are given, for example, in the book "Днестровский Ю.Н., Костомаров Д.П. Математическое моделирование плазмы. - М: Наука, первое издание 1982, 320 с., второе издание 1993, 336 с. (Issue in English: Yu.N. Dnestrovskij, D.P. Kostomarov. Numerical Simulations of Plasmas. Springer-Verlag, New-York, 1986.)"

Reduced physical models can be divided in several main groups:

  • Kinetic models, in which magnetic and electric fields are considered as given functions of space and time. These include description of single particle motion.
  • Equilibrium models with prescribed kinetic parameters.
  • Self-consistent equilibrium evolution models, in which two previous items are coupled.
  • Magnetohydrodynamic models for plasma stability analyses giving fluid description of plasma.
  • Radial transport models.
  • Fluid models for particular processes, such as turbulence.
  • Adaptive models, derived from experimental data.
  • Various hybrid models consisting of composition of mentioned above.

Although thermonuclear synthesis with substantial amount of fusion products can be achieved on tokamaks since 1991, there are still unresolved physical problems. One of the them is inconsistency between radial transport models and experimental data.