  Nonequilibrium electrons in superconductors relax and eventually recombine
into Cooper pairs. Relaxation is facilitated by electron-boson interaction and
is accompanied by emission of nonequilibrium bosons. Here I solve numerically a
full set of nonlinear kinetic balance equations for stacked Josephson
junctions, which allows analysis of strongly nonequilibrium phenomena. It is
shown that nonlinearity becomes significant already at very small
disequilibrium. The following new, essentially nonlinear effects are obtained:
(i) At even-gap voltages $V=2n \Delta/e$ $(n=2,3,...)$ nonequilibrium bosonic
bands overlap. This leads to enhanced emission of $\Omega = 2 \Delta$ bosons
and to appearance of dips in tunnel conductance. (ii) A new type of radiative
solution is found at strong disequilibrium. It is characterized by the fast
stimulated relaxation of nonequilibrium quasiparticles. A stack in this state
behaves as a light emitting diode and directly converts electric power to boson
emission, without utilization of the ac-Josephson effect. This leads to very
high radiation efficacy and to significant radiative cooling of the stack. The
phenomenon can be used for realization of a new type of superconducting cascade
laser in the THz frequency range.
