Abstract Details
Abstracts
Author: Peter J Catto
Requested Type: Consider for Invited
Submitted: 2025-02-18 11:17:00
Co-authors:
Contact Info:
MIT Plasma Science and Fusion Center
167 Albany Street
Cambridge, MA 02139
USA
Abstract Text:
Landau (1946) first realized that the singular behavior of the collisionless linearized kinetic equation describing weakly damped plasma waves could be resolved by Laplace transforming in time to solve a causal initial value problem. Subsequent collisionless work by Dawson (1961) and O'Neil (1965) provided additional insights into the linear and nonlinear temporal behavior of the resonant electrons. Here the focus is on steady state plasmas where weak collisions must be retained to avoid singular behavior. Such situations occur for current drive with a monochromatic applied wave, and collisional transport in an axisymmetric tokamak or quasisymmetric stellarator with a single helicity imperfection. In the weak collision limit a narrow boundary layer resolves the singular behavior, and exactly recovers the collisionless Landau results as long as the wave amplitude is small and the collision frequency finite. However, these Landau results are shown to be inappropriate once the collision frequency becomes small enough and/or wave amplitude becomes large enough, that a nonlinear treatment is required. The nonlinear solution found for a monochromatic wave retains the island structure (Hamilton et al. 2023), but Landau's results (1946) are no longer valid as the collision frequency goes to zero for a non-vanishing plasma wave amplitude. Similar behavior happens for intense current drive, and in the presence of a single helicity error field in a quasisymmetric stellarator (Catto 2025). The seemingly "collisionless" Landau (1946) limit is actually a weakly collisional plateau (or resonant plateau) regime, located between the nonlinear regime and a fully collisional plasma regime.
Supported by DOE grant DE-FG02-91ER-54109.
CATTO, P. J. 2025 Journal of Plasma Physics 91.
DAWSON, J. 1961 Phys. Fluids 4, 869.
HAMILTON, C., TOLMAN, E. A., ARZAMASSKIY, L. & DUARTE, V. N. 2023
AJ 954:12.
LANDAU, L. 1946 J. Phys. 10, 25-34.
O'NEIL T. 1965 Phys. Fluids 8, 2255.
Characterization: 4.0
Comments: