Dana Constantinescu

Study of the interplay between magnetic shear and resonances using Hamiltonian models for the magnetic field lines

The issue of magnetic confinement in magnetic fusion devices is addressed within a purely magnetic approach. Using some Hamiltonian models for the magnetic field lines, the dual impact of low magnetic shear is shown in a unified way. Away from resonances, it induces a drastic enhancement of magnetic confinement that favors robust internal transport barriers (ITBs) and stochastic transport reduction. When low shear occurs for values of the winding of the magnetic field lines close to low-order rationals, the amplitude thresholds of the resonant modes that break internal transport barriers by allowing a radial stochastic transport of the magnetic field lines may be quite low. The approach can be applied to assess the robustness versus magnetic perturbations of general (almost) integrable magnetic steady states, including nonaxisymmetric ones such as the important single-helicity steady states. This analysis puts a constraint on the tolerable mode amplitudes compatible with ITBs and may be proposed as a poss...

Stochastization as a possible cause for fast reconnection during MHD mode activity in the ASDEX Upgrade tokamak

The role of stochastization of magnetic field lines is analysed in fast reconnection phenomena occurring in magnetized fusion plasma during various conditions in the ASDEX Upgrade tokamak. The mapping technique is applied to trace the field lines of toroidally confined plasma where perturbation parameters are expressed in terms of experimental perturbation amplitudes determined from the ASDEX Upgrade tokamak. 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. It is also shown that stochastization can explain the fast loss of confinement during the minor disruption. This demonstrates that stochastization can be regarded as a possible cause for different MHD events in the ASDEX Upgrade.

Modifying locally the safety profile to improve the confinement of magnetic field lines in tokamak plasmas

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 q0 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.

Reconnection in a global model of Poincaré map describing dynamics of magnetic field lines in a reversed shear tokamak

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.

Stochastization as a possible cause of fast reconnection in the frequently interrupted regime of neoclassical tearing modes

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.

A low-dimensional model system for quasi-periodic plasma perturbations

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

LOCALIZING TRANSPORT BARRIERS IN DEGENERATE 3/2 D.O.F. HAMILTONIAN SYSTEMS WITH APPLICATIONS TO MAGNETIC CONFINEMENT FUSION

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 t...

On the accuracy of some mapping techniques used to study the magnetic field dynamics in tokamaks

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.

Explicit near-symplectic mappings of Hamiltonian systems with Lie-generating functions

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

Numerical Experiments with Single Mode Gyrotron Equations

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 (Schrodinger 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...