Al-Naseri Haidar, Zamanian Jens, Ekman Robin, Brodin Gert
Department of Physics, Umeå University, SE-901 87 Umeå, Sweden.
Centre for Mathematical Sciences, University of Plymouth, Plymouth PL4 8AA, United Kingdom.
Phys Rev E. 2020 Oct;102(4-1):043203. doi: 10.1103/PhysRevE.102.043203.
When the Zeeman energy approaches the characteristic kinetic energy of electrons, Landau quantization becomes important. In the vicinity of magnetars, the Zeeman energy can even be relativistic. We start from the Dirac equation and derive a kinetic equation for electrons, focusing on the phenomenon of Landau quantization in such ultrastrong but constant magnetic fields, neglecting short-scale quantum phenomena. It turns out that the usual relativistic γ factor of the Vlasov equation is replaced by an energy operator, depending on the spin state, and also containing momentum derivatives. Furthermore, we show that the energy eigenstates in a magnetic field can be computed as eigenfunctions of this operator. The dispersion relation for electrostatic waves in a plasma is computed, and the significance of our results is discussed.
