  We report on the observation of complex nonlinear intensity dependence of the
circular and linear photogalvanic currents induced by infrared radiation in
compensated (Bi$_{0.3}$Sb$_{0.7}$)$_2$(Te$_{0.1}$Se$_{0.9}$)$_3$ 3D topological
insulators. The photocurrents are induced by direct optical transitions between
topological surface and bulk states. We show that an increase of the radiation
intensity results first in a highly superlinear raise of the amplitude of both
types of photocurrents, whereas at higher intensities the photocurrent
saturates. Our analysis of the observed nonlinearities shows that the
superlinear behavior of the photocurrents is caused by a heating of the
electron gas, while the saturation is induced by a slow relaxation of the
photoexcited carriers resulting in absorbance bleaching. The observed
nonlinearities give access to the Fermi level position with respect to the
Dirac point and the energy relaxation times of Dirac fermions providing an
experimental room temperature probe for topological surface states.
