Onsager symmetry for inhomogeneous magnetized plasmas

Abstract

The symmetry properties of the linear dielectric function for an inhomogeneous magnetized plasma are studied based on the local mode approximation as well as on the modified local mode approximation. In the local mode approximation applied to the electrostatic or electromagnetic waves, the dielectric tensor lacks both the Hermitian symmetry and the symmetry of the Onsager relations. The lack of the symmetry properties arises because Fourier decomposition into plane waves is not a correct method for an inhomogeneous medium. The modified local mode approximation completely recovers the symmetry properties for the electromagnetic waves. However, it still lacks the symmetry properties for the electrostatic waves, due to the diamagnetic current. Some of the controversies previously given for an inhomogeneous plasma are also discussed.

The effective dielectric tensor for electromagnetic waves in inhomogeneous magnetized plasmas and the proper formulation in the electrostatic limit

“…In fact, Ref. [17] obtained expressions which satisfy Onsager symmetry for the case of electromagnetic waves, corroborating our earlier results presented in Ref. [5].…”

“…The calculations which follow show that the non-symmetrical tensor obtained when following the procedure indicated in Ref. [17] is not the correct form to be used for the study of electrostatic fluctuations. We therefore point out that the proper dispersion relation for electrostatic waves can be obtained from the effective dielectric tensor for electromagnetic waves, which features adequated symmetry properties.…”

“…However, Ref. [17] also considered the case of electrostatic waves, concluding that in this particular case the Onsager symmetry is not satisfied by the effective dielectric tensor. This is a particularly puzzling feature, which motivates the present investigation.…”

“…(2), and also discuss the case of electrostatic (ES) fluctuations, according to the approach adopted in Ref. [17]. In section 4 we discuss the Onsager symmetry of the effective dielectric tensor, the validity of the approach adopted in section 3 for the case of ES fluctuations, and the proper application to the ES limit.…”

On the Onsager symmetry of the effective dielectric tensor for plasmas in inhomogeneous magnetic field

“…The Onsager symmetry of the effective dielectric tensor for electromagnetic waves has also been discussed in Ref. [9], for the case of homogeneous magnetic field and inhomogeneous plasma parameters.…”