  We formulate a theory based on the time-dependent Ginzburg Landau (TDGL)
theory and Newtonian vortex dynamics to study the transverse acousto-electric
response of a type-II superconductor with Abrikosov vortex lattice. When
exposed to a transverse acoustic wave, Cooper pairs emerge from the the moving
atomic lattice and moving electrons. As in the Tolman-Stewart effect in a
normal metal, an electromagnetic field is radiated from the superconductor. We
adapt the equilibrium-based TDGL theory to this non-equilibrium system by using
a floating condensation kernel. Due to the interaction between normal and
superconducting components, the radiated electric field as a function of
magnetic field attains a maximum value occurring below the upper critical
magnetic field. This local increase in electric field has weak temperature
dependence and is suppressed by the presence of impurities in the
superconductor.
