Some basic concepts of wave‐particle interactions in collisionless plasmas

Abstract

Abstract. The physical concepts of wave-particle interactions in a collisionless plasma are developed from first principles. Using the Lorentz force, starting with the concepts of particle gyromotion, particle mirroring and the loss cone, normal and anomalous cyclotron resonant interactions, pitch angle scattering, and cross-field diffusion are developed. To aid the reader, graphic illustrations are provided. INTRODUCTIONWave-particle interactions play crucial roles in many phenomena occurring in the laboratory [Gill, 1981] and in space plasmas [Gary, 1992]. In laboratory plasmas, wave-particle interactions come into play in several important applications, including beat wave acceleration, plasma heating by radio waves at ion and electron cyclotron frequencies, and transport losses due to edge turbulence. In space plasmas, wave-particle interactions are thought to be important for the formation of the magnetopause boundary layer, generation of electromagnetic outer zone chorus and plasmaspheric hiss emissions, precipitation of particles causing auroras, etc. Further, low-frequency waves can interact with charged particles over long spatial scale lengths and within the magnetosphere can transport energy from one region to another. For example, the interaction of ion cyclotron and whistler mode waves with Van Allen belt particles can scatter energetic protons and electrons into the loss cone and thus lead to the ring current decay during a magnetic storm recovery phase. Similarly, pitch angle scattering resulting from cyclotron resonance between outer zone whistler mode chorus and 10-to 100-keV trapped substorm electrons can lead to the loss of electrons by precipitation. These precipitating electrons cause ionospheric phenomenon such as diffuse aurorae, enhanced ionization in the ionospheric D and E regions, and bremsstrahlung X rays.In space plasmas the collision time between charged particles is generally very long in comparison with the characteristic timescales of the system, namely, the inverse of the plasma frequency or cyclotron frequencies, and therefore the plasma can be treated as collisionless. This would imply that there is virtually no dissipation in space plasmas, as particle-particle collisions are infrequent. This statement is correct provided that there are no wave-particle interactions.The presence of waves can introduce finite dissipation in a collisionless plasma. Charged particles are scattered by the wave fields, and the particles' momenta and energies change through this process. The interaction between a wave and a charged particle becomes strong when the streaming velocity of the particle is such that the particle senses the Doppler-shifted wave at its cyclotron frequency or its harmonics. This is the so-called cyclotron resonance interaction between the waves and particles. The special case of the Doppler-shifted wave frequency being zero (i.e., zero harmonics of the cyclotron frequency) corresponds to the well-known Landau resonance. Landau [1946] showed that plasma waves in unmagnetiz...

Anisotropic pitch angle distribution of ~100 keV microburst electrons in the loss cone: measurements from STSAT-1

“…Here, we assumed a plasma density of 2/cm 3 at the equatorial region (Carpenter and Anderson, 1992) and L is 5.5. When ω − k v − n c γ = 0, a resonance condition is satisfied and wave-particle interactions alter the electron's pitch angle (Tsurutani and Lakhina, 1997). As shown in Fig.…”

Electromagnetic cyclotron waves in the dayside subsolar outer magnetosphere generated by enhanced solar wind pressure: EMIC wave coherency

“…The particle pitch angle scattering rates due to incoherent electromagnetic or electrostatic waves have been derived by Kennel and Petschek [1966] and Tsurutani and Lakhina [1997]. However, since the observed EMIC waves are coherent or quasi-coherent, the wave-particle interaction is considerably stronger.…”

“…In the expression for , v is the particle speed and c is the speed of light. For positive (negative) values of n, equation (1) represents the normal (anomalous) cyclotron resonance condition [Tsurutani and Lakhina, 1997]. For normal (n = 1, 2, 3, …) Doppler shifted cyclotron resonance, the waves and particles travel in opposite directions from each other along the magnetic field and the waves will be Doppler shifted up to the particle cyclotron frequency or its harmonics in the proton reference frame.…”

“…For example, ions interact with RH waves and sense them as LH polarized and vice versa, electrons interact with LH waves and sense them as RH. However, in the later case, because the LH waves have frequencies much below the electron cyclotron frequencies, resonant electrons must have relativistic parallel kinetic energies (E ∥ > MeV) [Tsurutani and Lakhina, 1997]. For the fundamental anomalous electron cyclotron resonance (n = −1) with a left-hand wave, equation (1) can be simplified for resonant particle velocity:…”

“…However, electrons drift from midnight through dawn, in the opposite sense as the protons. It has been shown that chorus is generated close to the geomagnetic equatorial plane or in minimum B field pockets Smith, 1974, 1977;LeDocq et al, 1998;Lauben et al, 2002;Omura et al, 2008] by the electron temperature anisotropy instability [Kennel and Petschek, 1966;Tsurutani and Lakhina, 1997].…”