  Larkin and Ovchinnikov established that the viscous flow of magnetic flux
quanta in current-biased superconductor films placed in a perpendicular
magnetic field can lose stability due to a decrease in the vortex viscosity
coefficient $\eta$ with increasing velocity of the vortices $v$. The dependence
of $\eta$ on $v$ leads to a $nonlinear$ section in the current-voltage
($I$-$V$) curve which ends at the flux-flow instability point with a voltage
jump to a highly resistive state. At the same time, in contradistinction with
the nonlinear conductivity regime, instability jumps often occur in $linear$
$I$-$V$ sections. Here, for the elucidation of such jumps we develop a theory
of local instability of the magnetic flux flow occurring not in the entire film
but in a narrow strip across the film width in which vortices move much faster
than outside it. The predictions of the developed theory are in agreement with
experiments on Nb films for which the heat removal coefficients and the
inelastic scattering times of quasiparticles are deduced. The presented model
of local instability is also relevant for the characterization of
superconducting thin films whose performance is examined for fast single-photon
detection.
