Landau damping

In physics, Landau damping, named after its discoverer, Soviet physicist Lev Davidovich Landau (1908–68), is the effect of damping (exponential decrease as a function of time) of longitudinal space charge waves in plasma or a similar environment. This phenomenon prevents an instability from developing, and creates a region of stability in the parameter space. It was later argued by Donald Lynden-Bell that a similar phenomenon was occurring in galactic dynamics, where the gas of electrons interacting by electrostatic forces is replaced by a "gas of stars" interacting by gravitational forces. Landau damping can be manipulated exactly in numerical simulations such as particle-in-cell simulation. It was proved to exist experimentally by Malmberg and Wharton in 1964, almost two decades after its prediction by Landau in 1946. Landau damping occurs because of the energy exchange between an electromagnetic wave with phase velocity and particles in the plasma with velocity approximately equal to , which can interact strongly with the wave. Those particles having velocities slightly less than will be accelerated by the electric field of the wave to move with the wave phase velocity, while those particles with velocities slightly greater than will be decelerated losing energy to the wave: particles tend to synchronize with the wave. This is proved experimentally with a traveling-wave tube. In an ideal magnetohydrodynamic (MHD) plasma the particle velocities are often taken to be approximately a Maxwellian distribution function. If the slope of the function is negative, the number of particles with velocities slightly less than the wave phase velocity is greater than the number of particles with velocities slightly greater. Hence, there are more particles gaining energy from the wave than losing to the wave, which leads to wave damping. If, however, the slope of the function is positive, the number of particles with velocities slightly less than the wave phase velocity is smaller than the number of particles with velocities slightly greater.