Theoretical plasma physics

Abstract

These lecture notes were presented by Allan N. Kaufman in his graduate plasma theory course and a follow-on special topics course (Physics 242A, B, C and Physics 250 at the University of California Berkeley). The notes follow the order of the lectures. The equations and derivations are as Kaufman presented, but the text is a reconstruction of Kaufman’s discussion and commentary. The notes were transcribed by Bruce I. Cohen in 1971 and 1972, and word processed, edited and illustrations added by Cohen in 2017 and 2018. The series of lectures is divided into four major parts: (i) collisionless Vlasov plasmas (linear theory of waves and instabilities with and without an applied magnetic field, Vlasov–Poisson and Vlasov–Maxwell systems, Wentzel–Kramers–Brillouin–Jeffreys (WKBJ) eikonal theory of wave propagation); (ii) nonlinear Vlasov plasmas and miscellaneous topics (the plasma dispersion function, singular solutions of the Vlasov–Poisson system, pulse-response solutions for initial-value problems, Gardner’s stability theorem, gyroresonant effects, nonlinear waves, particle trapping in waves, quasilinear theory, nonlinear three-wave interactions); (iii) plasma collisional and discreteness phenomena (test-particle theory of dynamic friction and wave emission, classical resistivity, extension of test-particle theory to many-particle phenomena and the derivation of the Boltzmann and Lenard–Balescu equations, the Fokker–Planck collision operator, a general scattering theory, nonlinear Landau damping, radiation transport and Dupree’s theory of clumps); (iv) non-uniform plasmas (adiabatic invariance, guiding-centre drifts, hydromagnetic theory, introduction to drift-wave stability theory).

The challenge to understand the zoo of particle transport regimes during resonant wave-particle interactions for given survey-mode wave spectra

“…The separation between slow and fast is essentially determined by a transition from deterministic to stochastic trajectories (achieved via decorrelation of particle dynamics), and will usually occur after 'many' wave-/gyro-periods, leading to validity of the so-called random-phase approximation (Karpman, 1974;Lemons, 2012), as discussed in Section 2.1. As described and/or demonstrated in Chirikov (1960); Smith and Kaufman (1978); Smith et al (1980); Matsoukis et al (1998); Lichtenberg and Lieberman (1992); Karimabadi et al (1992); Sigov and Levchenko (1996); Neishtadt (1999); Wykes et al (2001); Kaufman (2009); Ukhorskiy and Sitnov (2013); Artemyev et al (2015); Escande (2018); Kaufman and Cohen (2019), the notion of the Chirikov resonance overlap is fundamental to this entire philosophy, despite the fact that it is rarely mentioned in respective derivations of the quasilinear theory.…”

Hamiltonian formulations for perturbed dissipationless plasma equations

“…As an application of the perturbative evolution of the Vlasov-Maxwell equations, we consider the simple example of the linearized Vlasov-Maxwell equations obtained in the absence of background electric and magnetic fields [36]. Here, using the Fourier space-time decomposition of the first-order fields…”

Hamiltonian formulations of quasilinear theory for magnetized plasmas

“…The complex interaction between charged particles and electromagnetic-field wave fluctuations in a magnetized plasma represents a formidable problem with crucial implications toward our understanding of magnetic confinement in laboratory and space plasmas (Kaufman and Cohen, 2019). These wave-particle interactions can be described either linearly, quasi-linearly, or nonlinearly, depending on how the background plasma is affected by the fluctuating wave fields and the level of plasma turbulence associated with them (Davidson, 1972).…”