Nonlinear saturation of the trapped-ion mode by mode coupling in two dimensions

Technical Report · Wed Jul 20 04:00:00 EDT 1977

DOI:https://doi.org/10.2172/7315970· OSTI ID:7315970

Cohen, B. I.; Tang, W. M.

A study of the nonlinear saturation by mode coupling of the dissipative trapped-ion mode is presented in which both radial and poloidal variations are considered. The saturation mechanism consists of the nonlinear coupling via E x B convection of energy from linearly unstable modes to stable modes. Stabilization is provided at short poloidal wavelengths by Landau damping from trapped and circulating ions, at short radial wavelengths by effects associated with the finite ion banana excursions and at long wavelengths by ion collisions. A one-dimensional, nonlinear partial differential equation for the electrostatic potential derived in earlier work is extended to two dimensions and to third order in amplitude. Included systematically are kinetic effects, e.g., Landau damping and its spatial dependence due to magnetic shear. The stability and accessibility of equilibria are considered in detail for cases far from as well as close to marginal stability. In the first case three-wave interactions are found to be important when the spectrum of unstable modes is sufficiently narrow. In the latter case, it is found that for a single unstable mode, a four-wave interaction can provide the dominant saturation mechanism. Cross-field transport is calculated, and the scaling of results is considered for tokamak parameters.

• Research Organization: California Univ., Livermore (USA). Lawrence Livermore Lab.
• DOE Contract Number: W-7405-ENG-48; EY-76-C-02-3073
• OSTI ID: 7315970
• Report Number(s): UCID-17529
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700107* -- Fusion Energy-- Plasma Research-- Instabilities
COUPLING
DAMPING
INSTABILITY
LANDAU DAMPING
NONLINEAR PROBLEMS
PLASMA INSTABILITY
PLASMA MACROINSTABILITIES
PLASMA WAVES
SCALING LAWS
STABILIZATION
THERMONUCLEAR REACTORS
TOKAMAK TYPE REACTORS
TRAPPED-PARTICLE INSTABILITY
TWO-DIMENSIONAL CALCULATIONS