  We calculate the upper critical field in superconductors without inversion
symmetry at arbitrary temperatures, in the presence of scalar impurities. Both
orbital and spin (paramagnetic) mechanisms of pair breaking are considered. The
superconducting phase transition at nonzero field occurs into a helical vortex
state, in which the order parameter is modulated along the applied field (in a
cubic crystal). The helical state is stable with respect to disorder. However,
if the difference between the densities of states in the electron bands split
by spin-orbit coupling is neglected, then the order parameter modulation is
present only at low temperatures, and only if the system is sufficiently clean
and paramagnetically limited. This state resembles the
Larkin-Ovchinnikov-Fulde-Ferrell state in centrosymmetric superconductors.
