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Electron-phonon heat transfer in giant vortex states

We examine energy relaxation of non-equilibrium quasiparticles in different vortex configurations in ``dirty'' $s$-wave superconductors. The heat flow from the electronic subsystem to phonons in a mesoscopic superconducting disk with a radius of the order of several coherence lengths is calculated both in the Meissner and giant vortex states using the Usadel approach. The recombination process is shown to be strongly affected by interplay of the subgap states, located in the vortex core and in the region at the sample edge where the spectral gap $E_{\rm g}$ is reduced by the Meissner currents. In order to uncover physical origin of the results, we develop a semiquantitative analytical approximation based on the combination of homogeneous solutions of Usadel equations in Meissner and vortex states of a mesoscopic superconducting disc and analytically calculate the corresponding spatially resolved electron-phonon heat rates. Our approach provides an important information about non-equilibrium quasiparticles cooling by the magnetic-field induced traps in various mesoscopic superconducting devices.