We analyze statistically the energization of particles in a large scale environment strong turbulence that is fragmented into number distributed current filaments. The turbulent generated through strongly perturbed, 3D, resistive magnetohydrodynamics simulations, and it emerges naturally from nonlinear evolution, without specific reconnection geometry being set up. Based on test-particle we estimate transport coefficients energy space for use classical Fokker-Planck (FP) equation, show...

Larger scale plasma instabilities not leading to an immediate termination of a discharge often result in periodic nonlinear perturbations the plasma. A minimal possible model is formulated for description system with drive and relaxation processes which have different time scales. The based on two equations: first being responsible dynamics second drive. can be generalized describe pellet injection.

Single trajectories of magnetic line motion indicate the persistence a central protected plasma core, surrounded by chaotic shell enclosed in double-sided transport barrier : latter is identified as being composed two Cantori located on successive "most-noble" numbers values perturbed safety factor, and forming an internal (ITB). Magnetic lines which succeed to escape across this begin wander wide sea extending up very robust (as long L<1) mathematically KAM surface at edge. In case shown be...

The paper studies the bifurcations that occur in T-system, a 3D dynamical system symmetric respect to Oz axis. Results concerning some local (pitchfork and Hopf bifurcation) are presented our attention is focused on special bifurcation, when has infinitely many equilibrium points. It shown that, at bifurcation limit, phase space foliated by invariant surfaces, each of them containing two points (an attractor saddle). For values parameter close study system’s dynamics done according singular...

The aim of this study is to localize and describe the transport barriers diffusion phenomena that appear in tokamak two Hamiltonian models for magnetic field line dynamics: a twist map (tokamap) non-twist one (rev-tokamap). New results obtained rev-tokamap will be compared already known ones on tokamap with those concerning standard model. analysis done terms stochasticity parameter describing perturbation amplitude ideal configuration, q-profiles.

The construction of explicit near-symplectic mappings for generic Hamiltonian systems with the utilization Lie transforms is presented. method mathematically rigorous and systematically extended to high order respect a perturbation parameter. are compared their implicit counterparts, which use mixed-variable generating functions, in terms conservation invariant quantities, calculation speed accurate Poincare surfaces sections. comparative study considers wide range parameters initial...

The dynamics of magnetic field lines and charged particles in toroidal chambers are commonly analysed by numerically solving the dynamical equations. They may also be using deterministic reduced models, i.e. low-dimensional discrete time approximations (maps) Hamiltonian continuous models. We report on accuracy latter method considering mapping technique derived from Hamilton–Jacobi equation. optimum stepping some models for study tokamaks is determined local criteria. Special attention...

The coexistence of stable limit cycles and chaotic attractors has already been observed in some 3D dynamical systems. In this paper we show, using the T-system, that unstable can also coexist. Moreover, by completing characterization existence invariant algebraic surfaces their associated global dynamics, give a better understanding on disappearance strange attractor studied system.

Gyrotrons are microwave sources whose operation is based on the stimulated cyclotron radiation of electrons oscillating in a static magnetic field. This process described by system two complex differential equations: nonlinear first order ordinary equation with parameter (averaged electron motion) and second partial for high frequency field (RF field) resonator (Schrödinger type wave amplitude). The stationary problem single mode gyrotron short time interval real initial conditions was...

The formation of internal transport barriers (ITB) in tokamaks has been experimentally associated with the region low magnetic shear and presence main rational surfaces. We study ITB from a mathematical point view Hamiltonian model (the rev-tokamap model) that describes field lines dynamics reversed tokamaks. non-twist properties map generates system are exploited order to explain analytically existence surrounding shearless curve (in zone) robustness invariant circles (corresponding closed...

The paper investigates some basic dynamical properties of a general system obtained from the Lorenz using non-linear feedback controller. We focus on bifurcation equilibrium points and existence description homoclinic heteroclinic orbits. present necessary conditions for anticontrol chaos in considered system.