Figure 1: Comparison of linear growth rates obtained from 1D
simulations ( 
) and linear theory (continuous line)
for 
kV and 
.
Figure 2: Linear growth rates versus harmonic numbers obtained from 1D
simulations ( ) and linear theory (continuous line)
for kV, and
.
Figure 3: Profiles of 
(top curve),
(middle curve) and
(bottom curve), at saturation for
I=40 A, kV and 
.
Figure 4: The steady state frequency spectrum of the
electrostatic potential at the axis R=0 for
I=40 A, kV and .
Figure 5: The time and space Fourier transform of the
electrostatic potential at the axis R=0 for
I=40 A, kV and .
Figure 6: Comparison of saturated perpendicular velocity (upper
curves) and energy (lower curves)
spreads obtained from 1D (+) and 2D ( ) simulations
for kV and .
Figure 7: Profiles of the saturated spreads in gyrotron I
(a) and II (b). The origin of the z axis is chosen to be at
the center of the resonator. Only the beam tunnel is considered
in the simulation of the electrostatic instability.
Figure: The steady state frequency spectrum of the
electrostatic potential at the axis R=0 for gyrotron I
with I=10 A. The profile of the local electron cyclotron
frequency 
is represented by a thick
line on the horizontal plane.
Figure: Profiles of the normalized density 
in gyrotron I (solid line) for several beam currents and
gyrotron II (dashed line) for I=20 A.
Figure 10: The geometry considered in the simulation: the Dirichlet boundary
condition is applied to the cavity wall (thick lines)
while the Neumann
condition is assumed on the open boundaries (dashed lines).
Figure: The saturated spreads versus the beam current I for the case
shown in Fig. 10