Quantum kinetic theory of plasmas

Abstract

As is well known, for plasmas of high density and modest temperature, the classical kinetic theory needs to be extended. Such extensions can be based on the Schrödinger Hamiltonian, applying a Wigner transform of the density matrix, in which case the Vlasov equation is replaced by the celebrated Wigner–Moyal equation. Extending the treatment to more complicated models, we investigate aspects such as spin dynamics (based on the Pauli Hamiltonian), exchange effects (using the Hartree–Fock approximation), Landau quantization, and quantum relativistic theory. In the relativistic theory, we first study cases where the field strength is well-beyond Schwinger critical field. Both weakly relativistic theory (gamma factors close to unity) and strongly relativistic theory are investigated, using assumptions that allow for a separation of electron and positron states. Finally, we study the so-called Dirac–Heisenberg–Wigner (DHW) formalism, which is a fully quantum relativistic theory, allowing for field strengths of the order of the Schwinger critical field or even larger. As a result, the quantum kinetic theory is extended to cover phenomena such as Zitterbewegung and electron–positron pair creation. While the focus of this review is on the quantum kinetic models, we illustrate the theories with various applications throughout the manuscript.

Compton scattering of plasmons

“…The simple quantum model considered here can eventually be extended to a more complete quantum kinetic description of electron plasma waves [24]. In a recent work, this kinetic approach revealed the existence of multi-plasmon resonances associated with electron Landau damping [25].…”

Editorial : Reviews of Modern Plasma Physics: Volume 6

“…Topical collection "New Aspects of Quantum Plasma Physics (QP)" is organized by A.A. Mamun and published one article in 2021 (Manfredi et al 2021) and six articles in 2022 (Hossain and Mandal 2022;Mannan 2022;Brodin and Zamanian 2022;Misra and Brodin 2022;Haas and Mahmood 2022;Masood et al 2022).…”

The impact of quantized magnetic pressure on the stimulated Brillouin scattering of electromagnetic waves

“…It was shown by Landau [17] that SSH field leads to the Landau diamagnetism owing to quantization of the gyratory motion of Fermi electrons, also known as the Landau quantization (LQ), and the intrinsic or spin magnetic moment of electrons gives rise to Pauli paramagnetism. In this scenario, Hussain et al [18] pointed out that both LQ and spin effects may introduce interesting outcomes in the kinetic treatment of the quantum plasmas.Quite recently, Brodin et al [19] have developed a quantum kinetic theory of plasmas while taking into account Pauli Hamiltonian based spin dynamics and Hartree-Fock exchange effects, new quantum theories and the associated applications were presented in this paper. A modified kinetic model for the plasma embedded in a relativistically strong magnetic field is formulated in [20], where the usual relativistic γ factor is replaced by an energy operator (in Vlasov equation) to depict that the energy eigenstates in a magnetic field can be calculated as eigenfunctions of this operator.…”