Jeanette I. Weise

Quantum correction to the linear response for a magnetized electron gas

It is shown how the fully relativistic quantum expression for the response of an arbitrary magnetized electron (plus positron) gas reproduces its nonquantum counterpart. In the relativistic quantum case the dispersion is due to both gyromagnetic absorption and one-photon pair creation. Although one-photon pair creation has no classical counterpart, somewhat surprisingly it needs to be retained to reproduce the nonquantum limit correctly. For unpolarized electrons it is shown that the first quantum correction (order ℏ) to the nonquantum limit for the dispersion vanishes when one sums over all excited states, as for an unmagnetized electron gas. However, in the magnetized case there is a contribution of order ℏ from the ground state, which is the only state with a specific spin.

Dispersion in a relativistic degenerate electron gas

Relativistic effects on dispersion in a degenerate electron gas are discussed by comparing known response functions derived relativistically (by Jancovici) and nonrelativistically (by Lindhard). The main distinguishing feature is one-photon pair creation, which leads to logarithmic singularities in the response functions. Dispersion curves for longitudinal waves have a similar tongue-like appearance in the relativistic and nonrelativistic case, with the main relativistic effects being on the Fermi speed and the cutoff frequency. For transverse waves the nonrelativistic treatment has a nonphysical feature near the cutoff frequency for large Fermi momenta, and this is attributed to an incorrect treatment of the electron spin. We find (with two important provisos) that one-photon pair creation is allowed in superdense plasmas, implying relatively strong coupling between transverse waves and pair creation.

Relativistic quantum plasma dispersion functions

Relativistic quantum plasma dispersion functions (RQPDFs) are defined and the longitudinal and transverse response functions for an electron (plus positron) gas are written in terms of them. The dispersion is separated into Landau- damping, pair-creation and dissipationless regimes. Explicit forms are given for the RQPDFs in the cases of a completely degenerate distribution and a nondegenerate thermal (Jdistribution. Particular emphasis is placed on the relation between dissipation and dispersion, with the dissipation treated in terms of the imaginary parts of RQPDFs. Comparing the dissipation calculated in this way with the existing treatments leads to the identification of errors in the literature, which we correct. We also comment on a controversy as to whether the dispersion curves in a superdense plasma pass through the region where pair creation is allowed.

Response of a relativistic quantum magnetized electron gas

The response 4-tensor is derived for a spin-independent, relativistic magnetized quantum electron gas. The sum over spins is carried out both directly and using a procedure due to Ritus. The 4-tensor components are written in terms of a sum over the two solutions of the resonance condition for the particle 4-momentum. It is shown that the dispersive properties may be described in terms of a single plasma dispersion function, for arbitrary occupation numbers for electrons and positrons in each Landau level. The plasma dispersion function is evaluated explicitly in the completely degenerate and nondegenerate thermal limits. The perpendicular wave number appears in the arguments of J-functions, which are proportional to generalized Laguerre polynomials, but not in the plasma dispersion function. The result generalizes a known form for the response tensor for parallel propagation (in the completely degenerate case), when the J-functions are either zero or unity, to arbitrary angles of propagation.

Spin-dependent relativistic quantum magnetized electron gas

The covariant form of the response 4-tensor is derived for a spin-dependent, relativistic magnetized quantum electron gas. The electron gas is described by its occupation number, nϵns(pz), where ϵ = ±1 labels electron and positron states, n the Landau level, pz the parallel momentum, and s = ±1 the spin, which corresponds to the parallel component of the magnetic moment operator. A spin-dependent electron gas corresponds to nϵn +(pz) ≠ nϵn −(pz). We evaluate the spin-dependent contribution to the response tensor and show that it can be written such that its tensorial form is independent of the occupation number, which appears only in relativistic plasma dispersion functions that are independent of the perpendicular wave vector, k⊥. We discuss the special cases of parallel propagation, complete degeneracy, the synchrotron-emitting limit, and nϵns(pz)∝δ(pz). We expand the exact quantum result in powers of ℏ and find that the correction of order ℏ is nonzero for the spin-dependent part, with the lowest order correction for the spin-independent part being of order ℏ2. We find inconsistencies when the result is compared with quasi-classical calculations of the spin-dependent response. We conclude that until these inconsistencies are understood and resolved, the validity of the quasi-classically derived, spin-dependent results is uncertain.