In the statistical quasilinear theory of weak plasma turbulence,
charged particles
moving in electrostatic fluctuations diffuse in velocity, i.e. the velocity
variance
〈Δv2(t)〉 increases linearly
with time t, for times long compared with the auto-correlation time τac of the field,
which may be estimated as the reciprocal of the
spectral width of the fluctuations. Recent test-particle simulations have
revealed a
new regime at very long timescales t[Gt ]τac
where quasilinear theory breaks down,
for intermediate field amplitudes. As this behaviour is not consistent
with a diffusion
on quasilinear timescales, the problem of the motion of particles in a
broadband
wave field, for the case of a slowly growing field, is considered here
from a purely
dynamical point of view, introducing no statistics on the field and no
restriction on
the amplitude of this field. By determining, on a given timescale, and
in the frame of
wave–particle interaction, the spectral width over which waves interact
efficiently
with a particle, a new timescale is found: the nonlinear time of wave–particle
interaction τNL∝ (spectral density of
energy)−1/3[Gt ]τac. This is
the correlation
time of the dynamics. For times shorter than τNL,
the particles
trajectories remain globally regular, and do not separate: they follow
a quasifractal set of
dimension 2. For times long compared with τNL,
there appears a ‘true’ diffusive regime with
mixing and decorrelation, due to nonlinear mixing in phase space and the
localization
of the wave–particle interaction. These theoretical results are confirmed
by a
numerical study of the velocity variance as a function of time. In particular,
the
particle dynamics really do become diffusive on timescales several orders
of magnitude
longer than that predicted by quasilinear theory (namely
[Gt ]τNL[Gt ]τac).
Finally, deviations from the quasilinear value of the diffusion coefficient
and wave
growth rate, discussed in the literature, are explained.
WAKEFIELDS AND DRIVE ELECTRON BUNCHES DYNAMICS IN THREE-ZONE DIELECTRIC RESONATOR AT ASYMMETRICAL INJECTION
