Showing papers by "Herbert L Berk published in 1985"

Dissipative trapped particle modes in tandem mirrors

Abstract: The theory for the dissipative trapped particle modes is developed for a tandem mirror taking into account equilibrium rotational effects, electron temperature gradients, and an axial ambipolar potential, for a broad range of collisional parameters. The electrons are treated as a Maxwellian plasma that occupies the central cell and anchor cell regions. It is assumed that the eigenfunction is piecewise constant with abrupt transitions between the anchor and central cell regions. It is found that when ω/νp≳1, with ω the mode frequency and νp the Pastukhov loss rate, that the energy conservation structure of the collision operator produces important changes to previously developed theories. A solution to the problem is achieved by using the solution for the lifetime of an electron in an ambipolar trap, taking into account the global energy conservation. The energy conservation structure also allows a self‐consistent description of dissipative instabilities when thermal gradient and electric fields are presen...

Stability of high‐energy particle plasmas to magnetohydrodynamic‐like modes

Abstract: The stability of symmetric mirror systems, such as tandem mirrors and multiple mirrors (or equivalently, bumpy tori of large aspect ratio), is investigated when stabilization is attempted with high‐energy particles The analysis is derived from a zero Larmor radius variational form, and the stability criteria for eikonal and long wavelength layer modes are obtained For eikonal modes it is shown that line bending can stabilize the low l‐number modes and together with finite Larmor radius effects discussed elsewhere, complete stabilization is possible For disk‐shaped plasma pressure profiles it is shown that currents induced by conducting walls can stabilize the l=1 layer mode, while the higher‐l layer modes require finite Larmor radius effects for stabilization For thin, ring‐like pressure profiles, wall stabilization of the l=1 mode cannot be achieved, although the line bending term reduces the core beta limit and the growth rate of low l‐number layer modes The coupling of the precessional mode of a plasma ring to the surface Alfven wave in a multiple mirror plasma is also discussed

Interaction of the precessional wave with free‐boundary Alfvén surface waves in tandem mirrors

Abstract: A symmetric tandem mirror plugging a long central cell, with plugs stabilized by a hot‐component plasma is considered. The system is taken to have a flat pressure profile with a steep edge gradient. The interaction of the precessional mode with Alfven waves generated in the central cell is then considered. This analysis is noneikonal and is valid when mΔ/r<1 (m is the azimuthal mode number, r the plasma radius, and Δ the radial gradient scale length) for long‐wavelength radial modes. Without finite‐Larmor‐radius (FLR) effects the precessional mode is always destabilized by the excitation of the Alfven waves for m≥2. For m=1, it is possible to achieve stabilization with conducting walls. A discussion is given of how FLR affects stabilization of the m≥2 long‐wavelength modes and of FLR stabilization of modes described in the eikonal approximation.