  We provide constraints on Fast Radio Burst (FRB) models by careful
considerations of radiation forces associated with these powerful transients.
We find that the induced-Compton scatterings of the coherent radiation by
electrons/positrons accelerate particles to very large Lorentz factors (LF) in
and around the source of this radiation. This severely restricts those models
for FRBs that invoke relativistic shocks and maser type instabilities at
distances less than about $10^{13}$ cm of the neutron star. Radiation traveling
upstream, in these models, forces particles to move away from the shock with a
LF larger than the LF of the shock front. This suspends the photon generation
process after it has been operating for less than ~0.1 ms (observer frame
duration). We show that masers operating in shocks at distances larger than
$10^{13}$ cm cannot simultaneously account for the burst duration of 1 ms or
more and the observed ~1 GHz frequencies of FRBs without requiring an excessive
energy budget ($10^{46}$ erg); the energy is not calculated by imposing any
efficiency consideration, or other details, for the maser mechanism, but is
entirely the result of ensuring that particle acceleration by induced-Compton
forces upstream of the shock front does not choke off the maser process. For
the source to operate more or less continuously for a few ms, it should be
embedded in a strong magnetic field - cyclotron frequency $\gg$ wave frequency
- so that radiation forces do not disperse the plasma and shut-off the engine.
