We investigate the influence of the variable plasma density on the
spatial growth of the beam-plasma instability, considering the
model of homogeneous cold beam-inhomogeneous warm plasma
system under the condition of the smallness of phase velocit
y of
waves compared to the beam velocity. We determine a direction
of the beam with unmagnatized plasma. Considering a one –
dimensional electrostatic oscillation when the directions of beam
propagation, plasma density gradient and wave electric field
coincide with X-axis. To formulate mathematical equation of beam
and plasma then we make studying equation linearized, and then
study the continuity equation and boundary conditions.
Formulating electric field density then study a case in which a
plasma is collisional because of its high density and the
temperature .Finally we drive absorbent energy and find solutions
of these equations then draw it.
