Showing papers by "Herbert L Berk published in 1986"

Existence and calculation of sharp boundary magnetohydrodynamic equilibrium in three‐dimensional toroidal geometry

Abstract: The problem of sharp boundary, ideal magnetohydrodynamic equilibria in three‐dimensional toroidal geometry is addressed. The sharp boundary, which separates a uniform pressure, current‐free plasma from a vacuum, is determined by a magnetic surface of a given vacuum magnetic field. The pressure balance equation has the form of a Hamilton–Jacobi equation with a Hamiltonian that is quadratic in the momentum variables, which are the two covariant components of the magnetic field on the outer surface of the plasma. The condition of finding a unique solution on the outer surface is identical with finding phase‐space tori in nonlinear dynamics problems, and the Kolmogorov–Arnold–Moser (KAM) theorem guarantees that such solutions exist for a wide band of parameters. Perturbation theory is used to calculate the properties of the magnetic field just outside the plasma. Special perturbation theory is needed to treat resonances and it is explicitly shown that there are bands of pressure where there are no solutions.

Tandem‐mirror trapped‐particle modes at arbitrary collisionality

Abstract: Tandem‐mirror trapped‐particle modes are studied in a model system consisting of two connected square wells representing the solenoid and the end cells. Collisions are described by a Lorentz operator. A dispersion relation that is valid for arbitrary ν/ω (ω=wave frequency, ν=collision frequency) is derived. Four limits are investigated. When e≡νRam/ω ≪1+pi/pe, where Ram is the mirror ratio separating electrons trapped in the anchor from those passing to the solenoid and pe and pi are the fractions of passing electrons and ions, collisions destabilize a trapped‐particle mode that is stable in the collisionless limit; the growth rate is proportional to e1/2 for e≪1 and e/ln e for 1+pi/pe ≫e≫1. When e ≫1+pi/pe, the trapped‐particle mode becomes a weakly growing drift wave with growth rate proportional to e−1 ln e for ν/ω≪1 and ν−1 for ν/ω≫1; additionally identified are two flute modes, one of which is unstable for some parameters, and a strongly damped high‐frequency mode.