  We investigated wave amplification through the Electron-Cyclotron-Maser
mechanism.
  We calculated absorption and emission coefficients without any
approximations, also taking into account absorption by the ambient thermal
plasma. A power-law energy distribution for the fast electrons was used, as is
indicated by X-ray and microwave observations.
  We developed a model for the saturation length and amplification ratio of the
maser, scanned a large parameter space, and calculated the absorption and
emission coefficients for every frequency and angle.
  Previous studies concluded that the unobservable Z-mode dominates in the nu_p
\~ nu_B region, and that millisecond spikes are produced in the region nu_p /
nu_B<0.25. We find that the observable O-mode and X-mode can produce emission
in the 0.8<nu_p / nu_B<2 region, which is expected at the footpoints of a
flaring magnetic loop.
  The important criterion for observability is the saturation length and not
the growth rate, as was assumed previously, and even when the Z-mode is the
most strongly amplified, less strongly amplified O-mode or X-mode are still
intense enough to be observed.
  The brightness temperature computed with our model for the saturation length
is found to be of order 10^{16} K and higher. The emission is usually at a
frequency of 2.06 nu_B, and at angles 30-60 degrees to the magnetic field. The
rise time of the amplified emission to maximum is a few tenths of a millisecond
to a few milliseconds, and the emission persists for as long as new fast
electrons arrive into the maser region.
