Additional microwave modes in systems with conductivity of metals and superconductors

Formal Dissipation-Dependent Effects of Nonlocality in the Electrodynamics of Surface Impedance for Conductors

“…So for a finite frequency ω of an external field the spatial inhomogeneity k ′′ is determined, according to Dresvyannikov et al [1] and Karuzskii et al [9], by the frequency and by the eigenvalue of permittivity operator k ′′ ∼ ω( εaµ0) 1/2 = ω/ v ph (2.3) That may be assigned to a mean field approximation. The conductivity in the extremely anomalous limit is determined by the frequency σ ∼ 1/ω also [10]. The substitution of k ′′ and σ into the expression (2.2) for εa results in the proportionality ( εa) 3/2 ∼ ω −2 that corresponds to the frequency dependence of the impedance modulus | Z| ∼ ω 2/3 for all solutions found for the conductor except that for the superconductor, as it was shown in [1].…”

“…A value of this spatial inhomogeneity will not depend on frequency values ω of any incident microwaves, while those could be considered as quasi-stationary when ω < ω ′′ kp0 ≪ ωp. This can be illustrated by an expression of a current density after the end of an external perturbation obtained with the account of the spatial dispersion [10]. If one substitutes the spatial factor in Eq.…”

“…(3) of Ref. [10] in the form of j0(θ, r) = j0(θ)e iκr , (2.6) where θ is the reduced temperature θ = T /Tc [10,11], it is reexpressed as the current density…”

Spatial-Dispersion Eigenvalues for Permittivity Operator of Conductors and Superconductors in a Microwave Field

“…A significant role of the spatial-type force resonances was demonstrated [9][10][11][12]. Due to the self-consistency of a kinetics problem, which is non-linear on the spatial parameters, spatial-type force resonances are added to and usually dominate over an influence of boundary conditions.…”

“…It was found recently [9,10] in the surface impedance ( Z ) approximation that the complex number ε a Z = μ 0 Z −2 is the eigenvalue of the absolute permittivity operator ε a . This finding leads to the statement of a general wave problem, which is formulated to search the possible eigenvalues ε a of the absolute permittivity operator ε a and the corresponding wave solutions of the Maxwell equations, similar to the problem of wave propagation in hollow waveguides and resonators.…”