Landau Damping

Landau damping is a phenomenon that occurs in plasma physics and describes the damping of waves or oscillations in a plasma due to the resonant interaction between the waves and the particles in the plasma. It is named after the Russian physicist Lev Landau, who first explained this damping mechanism.

In a plasma, particles have random thermal motion, characterized by a velocity distribution known as the Maxwellian distribution. When waves or oscillations with a certain frequency interact with the plasma particles, there can be a resonance between the wave frequency and the natural frequency of particle motion. This resonance allows energy transfer between the wave and the particles.

Landau damping occurs when the wave frequency matches the real part of the particle's wave-particle interaction frequency, which is determined by the properties of the plasma, such as the plasma density and temperature. When this resonance condition is satisfied, the wave can transfer energy to the particles or vice versa.

As the wave transfers energy to the particles, the wave amplitude decreases, resulting in damping of the wave. The energy transfer occurs through the process of wave-particle interactions, where the particles gain or lose energy by interacting with the wave.

Landau damping is an important mechanism in plasma physics as it affects the behaviour and stability of plasma waves. It plays a crucial role in various plasma phenomena, such as the damping of Langmuir waves in electron-ion plasmas and the damping of plasma waves in the presence of velocity gradients or velocity anisotropies.

The concept of Landau damping is derived mathematically from kinetic theory and can be described using the Vlasov equation, which governs the evolution of the particle distribution function in phase space. Analytical and numerical techniques are used to study the effects of Landau damping on plasma waves and to understand its impact on plasma behaviour and dynamics.

Landau Damping is a characteristics of collisionless plasmas, but is may also have application in other fields eg kinetic treatment of galaxy formation, stars. To interpret this Landau Damping, consider a graph of the potential energy (qΦ) of an electron in the waves as shown

Region like a are region of acceleration

Region like b are region of deacceleration

At t= 0, the electrons are in thermal (i.e Boltmann equilibrium)

If an electron is not traveling, it just oscillates up and down with the wave as it passes, gaining minimal energy.

If an electron is moving much more quickly than a wave, it is pushed by the wave since it cannot exchange energy.

An electron can be grabbed and pushed away by a wave if it is moving at almost the same speed as the wave.

A wave will accelerate an electron if it is moving somewhat more slowly than the wave (gain energy).

If an electron is moving more quickly than a wave, the electron will be decelerated by the wave, lose energy (in region b), and then the wave may gain energy.

There are electrons in a plasma that are both faster and slower than the wave. However, in plasma with a Maxwellian distribution, slow electrons outnumber fast ones. As a result, the wave is dampened as air wave particles absorb wave energy.

This note is a part of the Physics Repository.