29,118 research outputs found
On the nonlinear stability of a quasi-two-dimensional drift kinetic model for ion temperature gradient turbulence
We study a quasi-two-dimensional electrostatic drift kinetic system as a
model for near-marginal ion temperature gradient (ITG) driven turbulence. A
proof is given of the nonlinear stability of this system under conditions of
linear stability. This proof is achieved using a transformation that
diagonalizes the linear dynamics and also commutes with nonlinear
advection. For the case when linear instability is present, a corollary is
found that forbids nonlinear energy transfer between appropriately defined sets
of stable and unstable modes. It is speculated that this may explain the
preservation of linear eigenmodes in nonlinear gyrokinetic simulations. Based
on this property, a dimensionally reduced ()
system is derived that may be useful for understanding dynamics around the
critical gradient of Dimits
Frobenius-Perron Resonances for Maps with a Mixed Phase Space
Resonances of the time evolution (Frobenius-Perron) operator P for phase
space densities have recently been shown to play a key role for the
interrelations of classical, semiclassical and quantum dynamics. Efficient
methods to determine resonances are thus in demand, in particular for
Hamiltonian systems displaying a mix of chaotic and regular behavior. We
present a powerful method based on truncating P to a finite matrix which not
only allows to identify resonances but also the associated phase space
structures. It is demonstrated to work well for a prototypical dynamical
system.Comment: 5 pages, 2 figures, 2nd version as published (minor changes
- …