Harris dispersion relation and Bernstein modes in dense magnetized quantum plasmas

The Bernstein mode is a well-known electrostatic mode in magnetized plasmas, and it has applications in many fields. This paper extends the Bernstein mode from classical plasmas to quantum plasmas by means of the quantum kinetic theory in a self-consistent manner. A quantum version of the Harris dispersion relation is derived. The pseudodifferential operator obtained in the formula is calculated by a numerical method and hence the nonrelativistic Bernstein modes including quantum recoil, finite-temperature, and Landau quantization effects are calculated. These results are important for plasma physics in extreme astrophysical environments and fundamental high-energy-density physics.