Neoclassical transport of impurities in tokamak plasmas

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.

[1]  K. Burrell,et al.  Transport of a trace impurity in a dirty plasma in the Pfirsch–Schlüter regime , 1981 .

[2]  R. Hazeltine,et al.  Impurity transport in the collisional regime for large poloidal variations , 1980 .

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

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

[5]  A. Boozer.  Enhanced transport in tokamaks due to toroidal ripple , 1980 .

[6]  Impurity transport in tokamak plasmas containing momentum sources , 1980 .

[7]  W. Stacey,et al.  Impurity control by neutral-beam injection , 1979 .

[8]  Neoclassical transport in plasmas containing ions with multiple charge states , 1979 .

[9]  S. C. Jardin,et al.  Two‐dimensional transport of tokamak plasmas , 1979 .

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

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

[12]  K. Burrell,et al.  Experimental Observation of the Impurity-Flow-Reversal Effect in a Tokamak Plasma , 1978 .

[13]  W. Stacey.  Effect of sources upon collisional transport in tokamaks , 1978 .

[14]  Y. Pao.  Classical diffusion in large‐aspect toroidal plasmas , 1978 .

[15]  S. Hirshman.  The ambipolarity paradox in toroidal diffusion, revisited , 1978 .

[16]  G2M, a two-dimensional diffusion time scale tokamak code , 1978 .

[17]  Modification of Pfirsch–Schlüter transport by poloidally asymmetric sources , 1978 .

[18]  S. Hirshman.  Neoclassical current in a toroidally‐confined multispecies plasma , 1977 .

[19]  F. Engelmann,et al.  Transport properties of a tokamak plasma with impurities in the collision-dominated regime , 1977 .

[20]  S. Hirshman.  Moment equation approach to neoclassical transport theory , 1977 .

[21]  F. Engelmann,et al.  Transport properties of axisymmetric toroidal low-beta plasmas in the collision-dominated regime , 1977 .

[22]  Temperature screening effect in two-ion-species Pfirsch-Schlüter transport , 1977 .

[23]  P. H. Rutherford,et al.  A computer model of radial transport in tokamaks , 1977 .

[24]  Two-dimensional multi-fluid tokamak transport code , 1977 .

[25]  R. J. Hawryluk,et al.  Neoclassical conductivity of a tokamak plasma , 1977 .

[26]  K. Tsang.  Neoclassical transport in an elliptic tokamak , 1977 .

[27]  S. P. Hirshman,et al.  Neoclassical transport of a multispecies toroidal plasma in various collisionality regimes , 1977 .

[28]  F. Werkoff,et al.  Diffusion in tokamaks with impurities in the Pfirsch-Schlüter regime , 1977 .

[29]  J. F. Clarke,et al.  High-Pressure Flux-Conserving Tokamak Equilibria , 1977 .

[30]  Impurity transport in tokamaks in the plateau to Pfirsch-Schlüter regimes , 1977 .

[31]  E. Gelbard,et al.  Multispecies transport in collisional tokamaks , 1976 .

[32]  S. Hirshman.  Transport of a multiple-ion species plasma in the Pfirsch-Schlüter regime , 1976 .

[33]  F. Engelmann,et al.  Effect of energy transfer between electrons and ions on collision-dominated transport of a toroidal, axisymmetric plasma , 1976 .

[34]  S. P. Hirshman,et al.  Approximate Fokker–Planck collision operator for transport theory applications , 1976 .

[35]  Y. Pao.  Classical diffusion in toroidal plasmas , 1976 .

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

[37]  R. Hazeltine,et al.  Detailed ambipolar balancing in tokamak diffusion , 1976 .

[38]  J. F. Clarke,et al.  Neoclassical transport theory of a multispecies plasma in the low collision frequency regime , 1976 .

[39]  E. Frieman,et al.  Toroidal plasma rotation in axisymmetric and slightly nonaxisymmetric systems , 1976 .

[40]  J. Callen,et al.  Smooth transition of neoclassical diffusion from the banana to Pfirsch–Schlüter regime , 1976 .

[41]  G. Emmert,et al.  Removal of impurities from tokamaks by neutral-beam injection , 1976 .

[42]  F. Hinton,et al.  Theory of plasma transport in toroidal confinement systems , 1976 .

[43]  K. Burrell.  Effect of particle and heat sources on impurity transport in tokamak plasmas , 1976 .

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

[45]  M. Wakatani.  Diffusion of an elliptic tokamak in the plateau regime , 1976 .

[46]  S. Hirshman.  Transport properties of a toroidal plasma in a mixed collisionality regime , 1976 .

[47]  R. Hazeltine,et al.  Effects of electrostatic trapping on neoclassical transport in an impure plasma , 1976 .

[48]  V. Fomenko.  Excitation of a current in a Maxwellian plasma by means of an ion beam , 1975 .

[49]  D. Shumaker,et al.  Improved variational method for axisymmetric plasmas , 1975 .

[50]  H. Grad,et al.  Adiabatic evolution of plasma equilibrium. , 1975, Proceedings of the National Academy of Sciences of the United States of America.

[51]  A. Boozer.  Orthogonal conductivity of a toroidal plasma , 1975 .

[52]  F. Hinton,et al.  Transport properties of a toroidal plasma at intermediate‐to‐high collision frequencies , 1975 .

[53]  Exact equilibria of axisymmetric magnetic configurations , 1975 .

[54]  M. Dobrowolny,et al.  Neoclassical transport theory of a toroidal axisymmetric plasma with impurities , 1974 .

[55]  J. F. Clarke,et al.  Hot-ion distribution function in the Oak Ridge tokamak , 1974 .

[56]  Impurity transport in tokamaks in the banana-plateau regime , 1974 .

[57]  P. Rutherford.  Impurity transport in the Pfirsch-Schluter regime , 1974 .

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

[59]  R. Hazeltine,et al.  Rotation of a toroidally confined, collisional plasma , 1974 .

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

[61]  I. Bernstein.  Transport in axisymmetric plasmas , 1974 .

[62]  T. Ohkawa.  Impurity Pumping by Beam Injection , 1974 .

[63]  T. Stringer.  Growth of ambipolar electric field in a toroidal plasma , 1973, Journal of Plasma Physics.

[64]  A universal Ohm's law for tokamak plasmas , 1973 .

[65]  F. Hinton,et al.  Collision-dominated plasma transport in toroidal confinement systems , 1973 .

[66]  W. Horton,et al.  Equilibrium and electrostatic stability theory of tokamaks from the drift-kinetic equation , 1973 .

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

[68]  Marshall N. Rosenbluth,et al.  Plasma transport in a torus of arbitrary aspect ratio , 1973 .

[69]  J. Connor,et al.  The neo-classical transport theory of a plasma with multiple ion species , 1973 .

[70]  B. Coppi,et al.  Collisional resistivity in low aspect ratio tori , 1973 .

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

[72]  P. M. Keeping,et al.  The conductivity of a toroidal plasma , 1973 .

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

[74]  J. Connor,et al.  Neoclassical diffusion arising from magnetic-field ripples in Tokamaks , 1973 .

[75]  D. Sigmar.  Bootstrap current in Tokamaks with neutral injection , 1973 .

[76]  R. Hazeltine.  Recursive derivation of drift-kinetic equation. , 1973 .

[77]  T. Stringer.  The diffusion-driven current in a toroidal resistive plasma , 1972 .

[78]  R. Bickerton.  Dissipation picture of neo-classical diffusion , 1972 .

[79]  R. Grimm,et al.  Viscosity and thermal conductivity effects on the containment of a toroidally confined resistive plasma with flow , 1972 .

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

[81]  Marshall N. Rosenbluth,et al.  Plasma Transport in Toroidal Confinement Systems , 1972 .

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

[83]  E. Maschke.  Classical diffusion of a stationary toroidal plasma , 1971 .

[84]  A. Ware,et al.  Pinch Effect for Trapped Particles in a Tokamak , 1970 .

[85]  H. Wimmel.  Energy-balance equation and enhanced collisional plasma diffusion , 1970 .

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

[87]  Harold Grad,et al.  Classical Diffusion in a Tokomak , 1970 .

[88]  Harold P. Furth,et al.  Adiabatic Compression of Tokamak Discharges , 1970 .

[89]  T. Stringer.  Equilibrium Diffusion Rate in a Toroidal Plasma at Intermediate Collision Frequencies , 1970 .

[90]  P. Rutherford.  COLLISIONAL DIFFUSION IN AN AXISYMMETRIC TORUS. , 1970 .

[91]  F. Hinton,et al.  Electrical conductivity of plasma in a spatially inhomogeneous magnetic field , 1969 .

[92]  H. Grad.  Magneto-Fluid and Plasma Dynamics , 1967 .

[93]  I. Bernstein,et al.  A VARIATIONAL DESCRIPTION OF TRANSPORT PHENOMENA IN A PLASMA , 1962 .

[94]  J. Taylor.  Diffusion of Plasma Ions across a Magnetic Field , 1961 .

[95]  John L. Johnson,et al.  Determination of Hydromagnetic Equilibria , 1961 .

[96]  M. Cotsaftis,et al.  Equilibrium and stability of an axially symmetric plasma with anisotropic pressure , 1961 .

[97]  B. Liley,et al.  Dynamical Equations and Transport Relationships for a Thermal Plasma , 1960 .

[98]  M. Kruskal,et al.  Equilibrium of a Magnetically Confined Plasma in a Toroid , 1958 .

[99]  M. Rosenbluth,et al.  Plasma Diffusion in a Magnetic Field , 1958 .

[100]  F. Low,et al.  The Boltzmann equation an d the one-fluid hydromagnetic equations in the absence of particle collisions , 1956, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[101]  L. Spitzer,et al.  TRANSPORT PHENOMENA IN A COMPLETELY IONIZED GAS , 1953 .

[102]  L. Spitzer.  Equations of Motion for an Ideal Plasma. , 1952 .

[103]  L. Spitzer,et al.  The Stability of Isolated Clusters , 1940 .

[104]  T. G. Cowling,et al.  The mathematical theory of non-uniform gases , 1939 .