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The response of clean (I > & where I is the electron mean free path and & is the pure superconductor coherence length) type-II superconductors to an external perturbing ac field has been calculated for the case when the applied dc magnetic field is of the order of Hc, , the upper critical field. The method used in the calculation relies on an expansion of the transport coefficients in powers of the average order parameter a(r). It is shown that when kel > I, where kc = 1/2eH is the characteristic wave vector of the vortex lattice when H 5 Hc, , such expansions converge even if w < d provided that (k#[(Hc,(T) -H)/Hc,] < 1. Particular attention is paid to a calculation of the attenuation coefficient of longitudinal sound. It is shown that resonant absorption associated with the periodic nature of the flux line lattice is of negligible amplitude. When the discrete lattice of the mixed state is replaced by a continuous distribution function, it is found that the calculated attenuation coefficient is consistent with experiment within the regime of validity of the theory. Finally, in the limit of infinite mean free path, the result previously derived by Cyrot and Maki is recovered.
Derivation of the Boltzmann Equation for a Dilute, Quantum Mechanical, Slightly Inhomogeneous
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