  Possible saturation of betatron acceleration of dust particles behind strong
shock fronts from supernovae is considered. It is argued that the efficiency of
the nonthermal dust destruction should be substantially lower than the value
estimated from a traditional description of betatron acceleration of dust
grains behind radiative shock waves. The inhibition of the nonthermal
destruction can be connected with the mirror instability developed in the dust
component behind strong shocks with the velocity 3 times exceeding the Alfv\'en
speed. The instability develops on characteristic time scales much shorter the
age of a supernova remnant, thus its influence on the efficiency of dust
destruction can be substantial: in the range of shock velocities 100 km
s$^{-1}<v_s<300$ km s$^{-1}$ the destruction efficiency can be an order of
magnitude lower that normally estimated.
