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In this paper we analyze the motion of charged particles in a non-standard magnetic field that is of a Clebsch type representation where a magnetic perturbation is considered. The safety factor of ASDEX-Upgrade is used. Some aspects of the solutions of the guiding center system of equations are featured.

In our model the diffusion produced by a two-dimensional electrostatic stochastic field combined with a sheared magnetic field is analyzed numerically. We assumed, as in a lot of other papers, an isotropic spectrum of electrostatic fluctuations as a combination of a Gaussian one (for small wave-vectors) and a power-law k-3 (for large wave-vectors). The running and asymptotic diffusion coefficients of electrons are obtained for physically relevant parameter values.

The formation of internal transport barriers (ITB) in tokamaks has been experimentally associated with the region of low magnetic shear and the presence of main rational magnetic surfaces. We study the ITB from a mathematical point of view in a Hamiltonian model (the rev-tokamap model) that describes the magnetic field lines dynamics in reversed shear tokamaks. The non-twist properties of the map that generates the system are exploited in order to explain analytically the existence of ITB surrounding the shearless curve (in the low magnetic shear zone) and the robustness of invariant circles (corresponding to closed magnetic surfaces) situated in its proximity. We describe the location of the ITB for various q-profiles and perturbations of the (ideal) integrable system. We use an analytical method to estimate the maximum radius of magnetic field lines confinement, hence the position of the barrier, and we explain the destruction of invariant circles when the amplitude of the perturbation increases. The reconnection phenomena are also related with ITB and an explanation for the (experimentally observed) enlargement of ITB when the minimal value of the q-profile becomes close but less than a main rational is obtained.

Magnetic field lines behaviour in a reversed shear tokamak can be described by a one and a half degree of freedom Hamiltonian system. In order to get insights into its dynamics we study numerically a global model for a Poincare map associated to such a system. Mainly we investigate the scenario of reconnection of the invariant manifolds of two hyperbolic orbits of the same type n/m and show that it is a generic one. When the two Poincare–Birkhoff chains involved in this process are aligned in phase, i.e. they are in a nongeneric position, a sequence of two saddle–center bifurcations occur in one of the chains, interfering with the former elliptic orbit of that chain, such that at the reconnection threshold the two chains are in a generic position. Dynamics around the new created configuration at the reconnection appears to vary from a regular motion to a chaotic one. In connection with the study of this global bifurcation we give the first example of region of instability in the dynamics of a nontwist map.

International audience; The existence of transport barriers in 3/2 degrees of freedom degenerate Hamiltonian systems is studied using the associated stroboscopic maps. For small enough amplitudes of the perturbations, a transport barrier (formed by infinitely many invariant rotational circles) is proven to exist and to form in the degenerate annulus. These results are applied to Hamiltonian models which describe some magnetic configurations in tokamak plasmas. Read More: http://www.worldscientific.com/doi/abs/10.1142/S021812741350034X

Gyrotrons are microwave sources whose operation is based on the stimulated cyclotron radiation of electrons oscillating in a static magnetic field. This process is described by the system of two complex differential equations: nonlinear first order ordinary differential equation with parameter (averaged equation of electron motion) and second order partial differential equation for high frequency field (RF field) in resonator (Schrödinger type equation for the wave amplitude). The stationary problem of the single mode gyrotron equation in short time interval with real initial conditions was numerically examined in our earlier work. In this paper we consider the stationary and nonstationary problems in large time interval with complex oscillating initial conditions. We use the implicit finite difference schemes and the method of lines realized with MATLAB. Two versions of gyrotron equation are investigated. We consider different methods for modelling new and old versions of the gyrotron equations. The main physical result is the possibility to determine the maximal value of the wave amplitude and the electron efficiency coefficient.

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

Single trajectories of magnetic line motion indicate the persistence of a central protected plasma core, surrounded by a chaotic shell enclosed in a double-sided transport barrier : the latter is identified as being composed of two Cantori located on two successive "most-noble" numbers values of the perturbed safety factor, and forming an internal transport barrier (ITB). Magnetic lines which succeed to escape across this barrier begin to wander in a wide chaotic sea extending up to a very robust barrier (as long as L, TEX file, 84 pages including 32 color figures. Higher quality figures can be seen on the PDF file at http://membres.lycos.fr/fusionbfr/JHM/Tokamap/JSP.pdf

Using Hamiltonian models for the magnetic field lines, we propose a methodology to improve their confinement through the creation of transport barriers. A local modification of the safety profile creating a low-shear zone is shown to be sufficient to locally enhance drastically the regularity of the magnetic field lines without requesting a reversed shear. The optimal benefits of low-shear are obtained when the value q 0 of the safety profile in the low-shear zone is sufficiently far from the main resonance values m/n with low m and n, in the case of large enough values of those (m, n) mode amplitudes. A practical implementation in tokamak plasmas should involve electron cyclotron current drive to locally modify the magnetic shear.

The role of stochastization of magnetic field lines in fast reconnection phenomena occurring in magnetized fusion plasma is analyzed. A mapping technique is applied to trace the field lines of toroidally confined plasma where the perturbation parameter is expressed in terms of experimental perturbation amplitudes determined from the Axially Symmetric Divertor Experiment (ASDEX) Upgrade tokamak [S. Gunter, C. Angioni, M. Apostoliceanu et al., Nucl. Fusion 45, S98 (2005)]. It is found that fast reconnection observed during amplitude drops of the neoclassical tearing mode instability in the frequently interrupted regime can be related to stochastization.