  A feasibility study of fusion reactors based on accelerators is carried out.
We consider a novel scheme where a beam from the accelerator hits the target
plasma on the resonance of the fusion reaction and establish characteristic
criteria for a workable reactor. We consider the reactions $ d + t \rightarrow
n + \alpha, d + {}^3H_e \rightarrow p + \alpha$, and $p + {}^{11}B \rightarrow
3 \alpha$ in this study. The critical temperature of the plasma is determined
from overcoming the stopping power of the beam with the fusion energy gain. The
needed plasma lifetime is determined from the width of the resonance, the beam
velocity and the plasma density. We estimate the critical beam flux by
balancing the energy of fusion production against the plasma thermo-energy and
the loss due to stopping power for the case of an inert plasma. The product of
critical flux and plasma lifetime is independent of plasma density and has a
weak dependence on temperature. Even though the critical temperatures for these
reactions are lower than those for the thermonuclear reactors, the critical
flux is in the range of $10^{22} - 10^{24}/\rm{cm^2/s}$ for the plasma density
$\rho_t = 10^{15}/{\rm cm^3}$ in the case of an inert plasma. Several
approaches to control the growth of the two-stream instability are discussed.
We have also considered several scenarios for practical implementation which
will require further studies. Finally, we consider the case where the injected
beam at the resonance energy maintains the plasma temperature and prolongs its
lifetime to reach a steady state. The equations for power balance and particle
number conservation are given for this case.
