Gyrofluid turbulence models with kinetic effects

Nonlinear gyrofluid equations are derived by taking moments of the nonlinear, electrostatic gyrokinetic equation. The principal model presented includes evolution equations for the guiding center n, u∥, T∥, and T⊥ along with an equation expressing the quasineutrality constraint. Additional evolution equations for higher moments are derived that may be used if greater accuracy is desired. The moment hierarchy is closed with a Landau damping model [G. W. Hammett and F. W. Perkins, Phys. Rev. Lett. 64, 3019 (1990)], which is equivalent to a multipole approximation to the plasma dispersion function, extended to include finite Larmor radius effects (FLR). In particular, new dissipative, nonlinear terms are found that model the perpendicular phase mixing of the distribution function along contours of constant electrostatic potential. These ‘‘FLR phase‐mixing’’ terms introduce a hyperviscositylike damping ∝k⊥2‖Φkk×k’‖, which should provide a physics‐based damping mechanism at high k⊥ρ which is potentially as important as the usual polarization drift nonlinearity. The moments are taken in guiding center space to pick up the correct nonlinear FLR terms and the gyroaveraging of the shear. The equations are solved with a nonlinear, three‐dimensional initial value code. Linear results are presented, showing excellent agreement with linear gyrokinetic theory.

[1]  Bruce W. Char,et al.  Maple V Language Reference Manual , 1993, Springer US.

[2]  A. Hasegawa,et al.  Stationary spectrum of strong turbulence in magnetized nonuniform plasma , 1977 .

[3]  A. Aydemir Linear studies of m=1 modes in high‐temperature plasmas with a four‐field model , 1991 .

[4]  E. Frieman,et al.  Nonlinear gyrokinetic equations for low-frequency electromagnetic waves in general plasma equilibria , 1981 .

[5]  W. W. Lee,et al.  Gyrokinetic approach in particle simulation , 1981 .

[6]  W. Lee,et al.  Gyrokinetic particle simulation of ion temperature gradient drift instabilities , 1988 .

[7]  Stephen Wolfram,et al.  Mathematica: a system for doing mathematics by computer (2nd ed.) , 1991 .

[8]  B. Lehnert Phase-mixing by the guiding-centre drifts of charged particles in a plasma , 1989 .

[9]  J. Krommes Renormalized Compton scattering and nonlinear damping of collisionless drift waves , 1980 .

[10]  Satoshi Hamaguchi,et al.  Fluctuation spectrum and transport from ion temperature gradient driven modes in sheared magnetic fields , 1990 .

[11]  M. N. Rosenbluth,et al.  Instabilities due to Temperature Gradients in Complex Magnetic Field Configurations , 1967 .

[12]  Tadashi Sekiguchi,et al.  Plasma Physics and Controlled Nuclear Fusion Research , 1987 .

[13]  J. Dong,et al.  Finite beta effects on ion temperature gradient driven modes , 1987 .

[14]  Patrick H. Diamond,et al.  Theory of ion‐temperature‐gradient‐driven turbulence in tokamaks , 1986 .

[15]  G. Hammett,et al.  Ion‐temperature‐gradient‐driven transport in a density modification experiment on the Tokamak Fusion Test Reactor , 1992 .

[16]  J. Callen,et al.  Unified fluid/kinetic description of plasma microinstabilities. Part I: Basic equations in a sheared slab geometry , 1992 .

[17]  R. Sudan,et al.  Considerations of ion‐temperature‐gradient‐driven turbulence , 1991 .

[18]  T. H. Dupree,et al.  Renormalized dielectric function for collisionless drift wave turbulence , 1978 .

[19]  R. Hazeltine,et al.  Hamiltonian four-field model for nonlinear tokamak dynamics , 1987 .

[20]  W. Lee,et al.  Gyrokinetic Particle Simulation Model , 1987 .

[21]  Gregory W. Hammett,et al.  Gyro‐Landau fluid models for toroidal geometry , 1992 .

[22]  Alain J. Brizard,et al.  Nonlinear gyrokinetic theory for finite‐beta plasmas , 1988 .

[23]  H. Wilhelmsson,et al.  Review of plasma physics: Vol. 1 (ed. M. A. Leontovich, Consultants Bureau, New York, 1965) pp. 326, $ 12.50 , 1966 .

[24]  W. Dorland,et al.  Fluid models of phase mixing, Landau damping, and nonlinear gyrokinetic dynamics , 1992 .

[25]  J. N. Leboeuf,et al.  Landau fluid equations for electromagnetic and electrostatic fluctuations , 1992 .

[26]  A. Brizard Nonlinear gyrofluid description of turbulent magnetized plasmas , 1992 .

[27]  Perkins,et al.  Fluid moment models for Landau damping with application to the ion-temperature-gradient instability. , 1990, Physical review letters.

[28]  S. Orszag,et al.  Advanced Mathematical Methods For Scientists And Engineers , 1979 .

[29]  H. Ching Large‐amplitude stabilization of the drift instability , 1973 .

[30]  R. Linsker Integral-equation formulation for drift eigenmodes in cylindrically symmetric systems , 1981 .

[31]  J. Callen,et al.  Unified fluid/kinetic description of plasma microinstabilities. Part II: Applications , 1992 .