Area-preserving maps models of gyroaveraged E×B chaotic transport

Abstract

Discrete maps have been extensively used to model 2-dimensional chaotic transport in plasmas and fluids. Here we focus on area-preserving maps describing finite Larmor radius (FLR) effects on E × B chaotic transport in magnetized plasmas with zonal flows perturbed by electrostatic drift waves. FLR effects are included by gyro-averaging the Hamiltonians of the maps which, depending on the zonal flow profile, can have monotonic or non-monotonic frequencies. In the limit of zero Larmor radius, the monotonic frequency map reduces to the standard Chirikov-Taylor map, and, in the case of non-monotonic frequency, the map reduces to the standard nontwist map. We show that in both cases FLR leads to chaos suppression, changes in the stability of fixed points, and robustness of transport barriers. FLR effects are also responsible for changes in the phase space topology and zonal flow bifurcations. Dynamical systems methods based on recurrence time statistics are used to quantify the dependence on the Larmor radius of the threshold for the destruction of transport barriers. * Electronic address: jfonseca@if.usp.br † Electronic address: delcastillod@ornl.gov ‡ Electronic address: ibere@if.usp.br 1 arXiv:1409.3106v1 [physics.plasm-ph]

Symplectic Maps for Diverted Plasmas

“…All the maps introduced in this article are useful for studying different aspects of the field line dynamics and transport in tokamaks with divertor. Extensions of the presented maps could be derived to include additional effects not considered in this article, such as the particle's finite Larmor radius [34,35] and the screening caused by the plasma response to resonant magnetic perturbations [36,37].…”

Global Stability of Fractional Order Coupled Systems with Impulses via a Graphic Approach

“…For examples, one can refer to [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Besides, there are many results about fractional equations such as [16][17][18][19][20][21][22]. However, in the real world, at certain moments, many behaviors in neural networks may experience a sudden change.…”

Finite Larmor radius effects on weak turbulence transport

“…However, the transport along the flow direction has a superdiffusive scaling and increases with the Larmor radius. More recently, FLR effects have been studied in the context of Hamiltonian map models of transport in monotonic and non-monotonic flows with a continuum spectrum of drift waves with a one-dimensional spatial structure (da Fonseca, del Castillo-Negrete & Caldas 2014; da Fonseca et al. 2016).…”

“…This case was extended by da Fonseca et al. (2014) to include FLR effects where the gyroaveraged standard map (GSM) was introduced to study the resulting transport.…”