Fast-ion thermalization in non-circular tokamaks with large-banana-width effects

Fusion-product thermalization and heating are calculated on the assumption of collisional slowing-down. The present analytical model describes fast-ion orbits and their distribution function in realistic, high-beta, non-circular tokamak equilibria. The Fokker-Planck equation is bounce-averaged over the large banana-width orbits after the variables have been transformed to the constants-of-motion space. First-orbit losses, trapping effects, and slowing-down drifts are fully treated. By solving a 3-D (+ time) partial differential equation, it is possible to obtain an invariant of the slowing-down process, μ/E = (magnetic moment)/energy = constant, and explicit expressions for the slowing-down drifts. Large banana-width effects give rise to a net co-going alpha-particle current. The large banana-width orbits smear the energy deposition over large regions of the plasma. This causes the in-situ heating rates to be 20–25% above theflux-surface-averagedrates on axis but enhances the edge heating 10-fold over in-situ deposition. While this result implies reduced alpha 'ash' accumulation on axis, the reduced heating rate makes start-up and maintenance of ignition more difficult.

[1]  E. M. Jones,et al.  A kinetic theory of beam-induced plasma currents , 1979 .

[2]  J. G. Cordey,et al.  Effects of particle trapping on the slowing-down of fast ions in a toroidal plasma , 1976 .

[3]  E. M. Jones,et al.  The effect of trapped electrons on beam driven currents in toroidal plasmas , 1980 .

[4]  Y. Kolesnichenko.  Distribution function for nuclear fusion reaction products in a stationary thermonuclear reactor , 1975 .

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

[6]  Marshall N. Rosenbluth,et al.  Transport properties of a toroidal plasma at low‐to‐intermediate collision frequencies , 1973 .

[7]  D. P. Kostomarov,et al.  Role of impurities and electric field in plasma heating by an injected neutral beam in tokamaks , 1977 .

[8]  M. Rensink,et al.  The Solution of the Kinetic Equations for a Multispecies Plasma , 1976 .

[9]  D. Sweetman.  Ignition condition in Tokamak experiments and role of neutral injection heating , 1973 .

[10]  T. W. Petrie,et al.  New Techniques for Studying Some Effects of Suprathermal Alpha Particles , 1977 .

[11]  J. Rand McNally,et al.  Alpha-driven, steady-state tokamak , 1978 .

[12]  V. Yavorskij,et al.  The current generated by alpha-particle loss in tokamak reactors , 1980 .

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

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

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

[16]  W. Stacey,et al.  Response of a tokamak plasma to particle and momentum sources , 1978 .

[17]  M. Ohnishi,et al.  Loss of alpha particles during slowing-down in an axisymmetric tokamak reactor , 1978 .

[18]  T. Stringer,et al.  Radial profile of alpha -particle heating in a Tokamak , 1974 .

[19]  D. J. Rose.  Engineering feasibility of controlled fusion: A Review , 1969 .

[20]  G. Joyce,et al.  Plasma heating by energetic particles , 1971 .

[21]  The topology of tokamak orbits , 1979 .

[22]  S. T. Butler,et al.  ENERGY LOSS OF A FAST ION IN A PLASMA , 1962 .

[23]  E. G. Hope,et al.  Frequency of the Hydrogen Maser , 1971, Nature.

[24]  L. Spitzer.  Physics of fully ionized gases , 1956 .

[25]  G. Miley,et al.  Prompt and non-prompt contributions to fusion product bombardment of a tokamak first wall , 1980 .

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

[27]  M. Katsurai,et al.  An approximate theory of steady-state and dynamic characteristics of alpha-particle-heated DT-fusion reactors , 1977 .

[28]  M. Rensink,et al.  A radial transport/Fokker-Planck model for a Tokamak plasma☆ , 1977 .

[29]  D. Sigmar,et al.  Bootstrap equilibria in tokamaks with neutral injection, including the energy balance , 1973 .

[30]  J. D. Strachan,et al.  Confinement of fusion-produced tritium in the Princeton Large Torus , 1979 .

[31]  D. L. Galbraith,et al.  Energy loss of charged particles in Maxwellian plasmas , 1973 .

[32]  J. D. Callen,et al.  Magnetohydrodynamic Equilibria in Sharply Curved Axisymmetric Devices , 1972 .

[33]  M. Katsurai,et al.  Time-dependent solution of Fokker-Planck equation for alpha-particles and its effect on alpha-particle heating characteristics in a D-T fusion reactor , 1976 .

[34]  L. Hively.  Fusion-Product Transport in Axisymmetric Tokamaks: Losses and Thermalization , 1980 .

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

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

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

[38]  S. P. Hirshman,et al.  Classical collisional theory of beam‐driven plasma currents , 1980 .

[39]  D. McAlees.  Alpha particle energetics and neutral beam heating in tokamak plasmas , 1974 .

[40]  John D. Gaffey,et al.  Energetic ion distribution resulting from neutral beam injection in tokamaks , 1976, Journal of Plasma Physics.

[41]  J. G. Cordey,et al.  Effects of neutral injection heating upon toroidal equilibria , 1974 .

[42]  L. M. Hively,et al.  Convenient computational forms for maxwellian reactivities , 1977 .