Energetic ion distribution resulting from neutral beam injection in tokamaks

The Fokker-Planck equation is studied for an energetic ion beam injected into a magnetized plasma consisting of Maxwellian ions and electrons with υ thi ≪υ b ≪ υ the . 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.

[1]  Tihiro Ohkawa,et al.  New methods of driving plasma current in fusion devices , 1970 .

[2]  R. Fowler,et al.  Particle-orbit loss regions and their effects on neutral-injection heating in axisymmetric tokamaks , 1976 .

[3]  J. Cordey,et al.  Problems associated with the injection of a high-energy neutral beam into a plasma , 1973 .

[4]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[5]  Melville Clark,et al.  Plasmas and Controlled Fusion , 1961 .

[6]  D. A. Tidman,et al.  Plasma Kinetic Theory , 1964 .

[7]  P. Rutherford,et al.  ION RUNAWAY IN TOKAMAK DISCHARGES. , 1972 .

[8]  G. G. Kelley,et al.  Neutral Injection Heating Experiments on the Oak Ridge Tokamak Device , 1975 .

[9]  R. Kulsrud,et al.  Runaway electrons in a plasma , 1973 .

[10]  R. Goldston.  Charge-exchange spectra near the injection energy in tokamaks equipped with tangential neutral beams – experiment and theory , 1975 .

[11]  Microinstability theory of two-energy-component toroidal systems , 1975 .

[12]  T. H. Stix.  Stability of a toroidal plasma subject to neutral injection , 1973 .

[13]  Burton D. Fried,et al.  The Plasma Dispersion Function , 1961 .

[14]  William M. MacDonald,et al.  Fokker-Planck Equation for an Inverse-Square Force , 1957 .

[15]  Subrahmanyan Chandrasekhar,et al.  Dynamical friction. I. General considerations: the coefficient of dynamical friction , 1943 .

[16]  T. H. Stix,et al.  Heating of toroidal plasmas by neutral injection , 1972 .

[17]  J. Cordey,et al.  Energetic particle distribution in a toroidal plasma with neutral injection heating , 1974 .

[18]  H. Dreicer,et al.  Electron and Ion Runaway in a Fully Ionized Gas. I , 1959 .