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EDP Sciences, Società Italiana di Fisica, Springer-Verlag
Doi
Abstract
KEEN waves are non-stationary, nonlinear, self-organized asymptotic states in Vlasov
plasmas. They lie outside the precepts of linear theory or perturbative analysis, unlike
electron plasma waves or ion acoustic waves. Steady state, nonlinear constructs such as
BGK modes also do not apply. The range in velocity that is strongly perturbed by KEEN
waves depends on the amplitude and duration of the ponderomotive force generated by two
crossing laser beams, for instance, used to drive them. Smaller amplitude drives manage to
devolve into multiple highly-localized vorticlets, after the drive is turned off, and may
eventually succeed to coalesce into KEEN waves. Fragmentation once the drive stops, and
potential eventual remerger, is a hallmark of the weakly driven cases. A fully formed
(more strongly driven) KEEN wave has one dominant vortical core. But it also involves fine
scale complex dynamics due to shedding and merging of smaller vortical structures with the
main one. Shedding and merging of vorticlets are involved in either case, but at different
rates and with different relative importance. The narrow velocity range in which one must
maintain sufficient resolution in the weakly driven cases, challenges fixed velocity grid
numerical schemes. What is needed is the capability of resolving locally in velocity while
maintaining a coarse grid outside the highly perturbed region of phase space. We here
report on a new Semi-Lagrangian Vlasov-Poisson solver based on conservative non-uniform
cubic splines in velocity that tackles this problem head on. An additional feature of our
approach is the use of a new high-order time-splitting scheme which allows much longer
simulations per computational effort. This is needed for low amplitude runs. There, global
coherent structures take a long time to set up, such as KEEN waves, if they do so at all.
The new code’s performance is compared to uniform grid simulations and the advantages are
quantified. The birth pains associated with weakly driven KEEN waves are captured in these
simulations. Canonical KEEN waves with ample drive are also treated using these advanced
techniques. They will allow the efficient simulation of KEEN waves in multiple dimensions,
which will be tackled next, as well as generalizations to Vlasov-Maxwell codes. These are
essential for pursuing the impact of KEEN waves in high energy density plasmas and in
inertial confinement fusion applications. More generally, one needs a fully-adaptive
grid-in-phase-space method which could handle all small vorticlet dynamics whether pealing
off or remerging. Such fully adaptive grids would have to be computed sparsely in order to
be viable. This two-velocity grid method is a concrete and fruitful step in that
direction
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