  In the leptonic scenario for TeV emission from a few well-observed shell-type
TeV supernova remnants (STTSNRs), very weak magnetic fields are inferred. If
fast-mode waves are produced efficiently in the shock downstream, we show that
they are viable agents for acceleration of relativistic electrons inferred from
the observed spectra even in the subsonic phase, in spite that these waves are
subject to strong damping by thermal background ions at small dissipation
scales. Strong collisionless non-relativistic astrophysical shocks are studied
with the assumption of a constant Aflven speed in the downstream. The
turbulence evolution is modeled with both the Kolmogorov and Kraichnan
phenomenology. Processes determining the high-energy cutoff of nonthermal
electron distributions are examined. The Kraichnan models lead to a shallower
high-energy cutoff of the electron distribution and require a lower downstream
density than the Kolmogorov models to fit a given emission spectrum. With
reasonable parameters, the model explains observations of STTSNRs, including
recent data obtained with the Fermi gamma-ray telescope. More detailed studies
of the turbulence generation and dissipation processes, supernova explosions
and progenitors are warranted for better understanding the nature of supernova
shocks.
