  Dynamics of homogeneous moving vortex matter is considered beyond the linear
response. The framework is the time dependent Ginzburg - Landau equation within
the lowest Landau level approximation. Both disorder and thermal fluctuations
are included using the Martin-Siggia-Rose formalism. We determine the critical
current as function of magnetic field and temperature Jc(B,T). The surface in
the J-B-T space defined by the function separates between the dissipative
moving vortex matter regime(flux flow)and an amorphous vortex "glass". Both the
thermal depinning and the depinning by a driving force are taken into account.
The static irreversibility line, determined by Jc(B,T)=0 is compared to
experiments in layered HTSC, and is consistent with the one obtained using the
replica approach. The non-Ohmic I-V curve (in the depinned phase) is obtained
and compared with experiment in layered superconductors and thin films.
