New results for attenuation and damping of electromagnetic fields in rigid conducting media are derived under the conjugate influence of inertia due to charge carriers and displacement current. Inertial effects are described by a relaxation time for the current density in the realm of an extended Ohm's law. The classical notions of poor and good conductors are rediscussed on the basis of an effective electric conductivity, depending on both wave frequency and relaxation time. It is found that the attenuation for good conductors at high frequencies depends solely on the relaxation time. This means that the penetration depth saturates to a minimum value at sufficiently high frequencies. It is also shown that the actions of inertia and displacement current on damping of magnetic fields are opposite to each other. That could explain why the classical decay time of magnetic fields scales approximately as the diffusion time. At very small length scales, the decay time could be given either by the relaxation time or by a fraction of the diffusion time, depending whether inertia or displacement current, respectively, would prevail on magnetic diffusion.
An extension of Hagen-Rubens relation beyond the far-infrared region is proposed by taking into account inertial effects due to charge carriers. The influence of inertia is described by introducing a finite relaxation time τ for the current density in the framework of a generalized Ohm's law. A closed formula for τ as a function of metallic permittivity and radiation frequency is derived. Our approach is applied to aluminum for which it is found that τ ∼ 6.91 fs at room temperature. It is also shown that the behavior of the observed absorptivity by that metal is in excellent agreement with our formulation up to the near-infrared region. The macroscopic approach proposed here is totally independent of other microscopic formulations such as Drude's theory of metallic conduction. Applications of our theory to related problems can lead to progress in extending the classical theory for the optics of metals.
We provide a formulation that describes the propagation of solitons in a nondissipative, nonmagnetic plasma, which does not depend on the particular electron density distribution considered. The Poisson equation in the plasma sheath is expressed in terms of the Mach number for ions entering the sheath from the plasma and of a natural scale for the electrostatic potential. We find a class of reference frames with respect to which certain functions become stationary after arbitrary small variations of the Mach number and potential scale, that is, by determining the critical values of those quantities based on a variational method. It is shown that the critical Mach number defines the limits for the applicability of the reductive perturbation technique to a given electron density distribution. Based on our provided potential scale, we show that the Taylor expansion of the suprathermal electron distribution around equilibrium converges for all possible values of the spectral κ-index. In addition, owing to the admissible range for the critical Mach number, it is found that the reductive perturbation technique ceases to be valid for 3/2<κ≤5/2. In the sequel, we show that the technique is not valid for the deformation q-index of nonextensive electrons when q≤3/5. Furthermore, by assuming that the suprathermal and nonextensive solitons are both described with respect to the same critical reference frame, a relation between κ and q, which has been previously obtained on very fundamental grounds, is recovered.
A simple helical magnetohydrodynamic equilibrium with flow, in which the vorticity is proportional to the current density, is presented. It is argued that the helical magnetic structures, known as snakes, can be described as a local transition to this equilibrium, triggered by the large temperature drop, observed when a pellet crosses the q = 1 rational magnetic surface. One of the most interesting phenomena occurring in tokamak plasmas is the appearance of long-lived structures at the q = 1 rational magnetic surface, where q is the inverse rotational transform of the magnetic field lines. Usually, the appearance of these structures is triggered by the crossing of externally injected hydrogen/deuterium pellets through the rational surface. This phenomenon was first observed in JET and the structures were dubbed 'snakes', for the signature they impress on the soft x-ray emission profile of the plasma, as recovered by tomography [1]. The standard model to describe snakes is based on the formation of a m = 1 magnetic island at the resonant surface, where m is the poloidal mode number of the structure. Essentially, as the pellet crosses this surface, it should cause a strong local cooling, enhancing the plasma resistivity, thus implying a drop in the current density. This perturbation could lead to the formation of a magnetic island, depending on the local shear of the magnetic field lines [2]. This model, however, is not entirely consistent with experimental observations as well as with some physical arguments. First of all, the structure has a poloidal cross-section much narrower than that of a m = 1 island; indeed, it usually extends to no more than 10% of the poloidal circumference of the resonant surface. Secondly, it can persist much longer than the characteristic time for recovery of the initial temperature drop and survive many sawtooth crashes, in some discharges, in which a strong temperature pulse passes through the reconnecting island [1,2]. Furthermore, later experimental work has shown that snakes can be spontaneously driven in ohmic discharges without pellet injection, and also in electron runaway discharges [3,4]. From these results, and other observations presented in the literature, it seems
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