We show that the flux-flow transport of the Josephson vortex lattice (JVL) in layered high-temperature superconductors provides a convenient probe for both components of quasiparticle conductivity, sigma(c) and sigma(ab). We found that the JVL flux-flow resistivity, rho(ff), in a wide range of magnetic fields is mainly determined by the in-plane dissipation. In the dense lattice regime (B>1 T) the rho(ff)(B) dependence is well fitted by the theoretical formula for that limit. That allows us to independently extract from the experimental data the values of sigma(c) and of the ratio sigma(ab)/(sigma(c)gamma(4)). The extracted temperature dependence sigma(ab)(T) is consistent with microwave data. The shape of the current-voltage characteristics is also sensitive to the frequency dependence of sigma(ab), which allows us to estimate the quasiparticle relaxation time and relate it to the impurity bandwidth using data obtained for the same crystal.
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