Magnetic Field Lines In Tokamak Research Articles

Confining and escaping magnetic field lines in tokamaks: Analysis via symplectic maps

In magnetically confined plasma, it is possible to qualitatively describe the magnetic field configuration via phase spaces of suitable symplectic maps. These phase spaces are of mixed type, where chaos coexists with regular motion, and the complete understanding of the complex dynamical evolution of chaotic trajectories is a challenge that, when overcome, may provide further knowledge into the behaviour of confined fusion plasma. This work presents two numerical investigations into characteristics of mixed phase spaces which model distinct magnetic configurations in tokamaks under different perturbation regimes. The first approach relies on a recurrence-based analysis of ensembles of chaotic trajectories to detect open field lines that widely differ from the average. The second focuses on the transient dynamical behaviour of field lines before they escape the systems. These two methods provide insights into the influence of stickiness and invariant manifolds on the evolution of chaotic trajectories, improving our understanding of how these features affect transport and diffusion properties in mixed phase spaces. These theoretical and numerical approaches may enhance our comprehension of confined plasma behaviour and plasma-wall interactions.

Collisionless plasma transport mechanisms in stochastic open magnetic field lines in tokamaks

The collisionless plasma transport in stochastic magnetic fields connecting to wall boundary has been studied to understand the underlying mechanisms of thermal quench physics in tokamak disruption. In this study, we present a comprehensive understanding of the plasma dynamics in three-dimensional stochastic open magnetic field lines, taking into account the consistent coupling of electron and ion dynamics through the ambipolar electric field. The open stochastic field lines act as a 3D magnetic mirror consisting of the magnetic well and hill regions. It was found that the magnetic hill regions play a critical role in enhancing electron thermal transport. When the plasma collapses to the wall, the 3D ambipolar potential arises in the stochastic layer to maintain the quasi-neutrality of the plasma. The E × B vortices induced by the 3D ambipolar potential mix the plasma across stochastic field lines and enhance the radial transport. Particularly, the E × B mixing between the magnetic well and hill regions provides a collisionless detrapping mechanism that plays a major role in the loss of high-energy trapped electrons. As a result, the electron temperature steadily decreases at a rate of about −0.5 keV ms−1, comparable to the rate observed in thermal quench experiments.

Unveiling stickiness regions of magnetic field lines in tokamaks

Unveiling stickiness regions of magnetic field lines in tokamaks

Shearless bifurcation on symplectic maps of magnetic field lines in tokamaks with reversed current

We introduce two-dimensional symplectic maps to describe the Poincaré maps of magnetic field lines in large aspect ratio tokamak equilibria with reversed non-monotonic plasma current density profiles. For these maps, we investigate the effect of the symmetry breaking due to the toroidal correction with a peculiar invariant, namely, a magnetic surface with a null rotation number, enclosing a vanishing current. We find that this rotationless invariant surface is surrounded by many small island chains. Furthermore, near such invariant, the symmetry breaking gives rise to two magnetic shearless invariants surrounded by twin island chains. We also find chaotic lines adjacent to all the observed islands created by the considered structurally unstable equilibria.

Accuracy Assessment of Numerical Tracing of Three-Dimensional Magnetic Field Lines in Tokamaks with Analytical Invariants

We consider the problem of the accurate tracing of long magnetic field lines in tokamaks, which is in general crucial for the determination of the plasma boundary as well as for the magnetic properties of the scrape-off layer. Accurate field line tracing is strictly related to basic properties of ordinary differential equation (ODE) integrators, in terms of preservation of invariant properties and local accuracy for long-term analysis. We introduce and discuss some assessment criteria and a procedure for the specific problem, using them to compare standard ODE solvers with a volume-preserving algorithm for given accuracy requirements. In particular, after the validation for an axisymmetric plasma, a three-dimensional (3-D) configuration is described by means of Clebsch potentials, which provide analytical invariants for assessing the accuracy of the numerical integration. A standard fourth-order Runge-Kutta routine at fixed step is well suited to the problem in terms of reduced computational burden, with extremely good results for accuracy and volume preservation. Then we tackle the problem of field line tracing in the determination of plasma-wall gaps for a 3-D configuration, demonstrating the effective feasibility of the plasma boundary evaluation in tokamaks by tracing field lines with standard tools.

The non-twist standard map with robust tori

The non-twist standard map occurs frequently in many fields of science specially in modelling the dynamics of the magnetic field lines in tokamaks. Robust tori, dynamical barriers that impede the radial transport among different regions of the phase space, are introduced in the non-twist standard map in a conservative fashion. The resulting non-twist standard map with robust tori is an improved model to study transport barriers in plasmas confined in tokamaks.

Generic magnetic field model in poloidal divertor tokamaks in the presence of resonant magnetic perturbations

A generic analytical model for the description of magnetic field lines in poloidal divertor tokamaks in the presence of external resonant magnetic perturbations is proposed. It is based on the Hamiltonian description of magnetic field lines in tokamaks. The safety factor and the spectra of magnetic perturbations are chosen by the requirement to satisfy their generic behaviour near the magnetic separatrix and at the magnetic axis. The field line equations are integrated by the construction of two symplectic and computationally efficient mappings of field lines. The model for internal MHD modes is also proposed. The mapping procedure for field lines which includes the MHD modes is described. It is shown that the numerically calculated diffusion and convection coefficients of field lines are in close agreement with the quasilinear ones. It is found that in the presence of internal MHD modes at the plasma edge the convectional outward transport of field lines may reverse its direction to inward convectional transport.

Model of a magnetic field in poloidal divertor tokamaks affected by resonant magnetic perturbations

A generic analytical model for the description of magnetic field lines in poloidal divertor tokamaks in the presence of external resonant magnetic perturbations is proposed. It is based on the Hamiltonian description of magnetic field lines in tokamaks. The safety factor and the spectra of magnetic perturbations are chosen by the requirement to satisfy their generic behavior near the magnetic separatrix and at the magnetic axis. The field line equations of the model are integrated using symplectic efficient mappings of field lines. The analytical formulas for the quasilinear diffusion and convection coefficients of field lines are obtained. The latter describes the outwardly directed transport of field lines at the plasma edge. It was shown that they are in a good agreement with the corresponding numerically calculated coefficients.

Transport Barriers and Diffusion Phenomena for the Magnetic Field Lines in Tokamak

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

Control of chaotic magnetic fields in tokamaks

Chaotic magnetic field lines play an important role in plasma confinement by tokamaks. They can either be generated in the plasma as a result of natural instabilities or artifficially produced by external conductors, like resonant helical windings and ergodic magnetic limiters. This is a review of works carried out at the Universidade de Sao Paulo and Universidade Federal do Parana on theoretical and experimental aspects of generation and control of chaotic magnetic field lines in tokamaks.

Chaotic magnetic field lines in tokamaks with ergodic limiters

We consider a symplectic map for magnetic field lines in a tokamak with an ergodic limiter, whose function is to generate a perturbing magnetic field which causes the formation of chaotic field lines in the vicinity of the tokamak inner wall. We analyze numerically the onset of global chaos due to the interaction of adjacent magnetic islands, the size of the chaotic region, and investigate anomalous diffusion and loss of field lines due to their collisions with the tokamak wall.

Magnetic field lines, Hamiltonian dynamics, and nontwist systems

Magnetic field lines typically do not behave as described in the symmetrical situations treated in conventional physics textbooks. Instead, they behave in a chaotic manner; in fact, magnetic field lines are trajectories of Hamiltonian systems. Consequently the quest for fusion energy has interwoven, for 50 years, the study of magnetic field configurations and Hamiltonian systems theory. The manner in which invariant tori breakup in symplectic twist maps, maps that embody one and a half degree-of-freedom Hamiltonian systems in general and describe magnetic field lines in tokamaks in particular, will be reviewed, including symmetry methods for finding periodic orbits and Greene’s residue criterion. In nontwist maps, which describe, e.g., reverse shear tokamaks and zonal flows in geophysical fluid dynamics, a new theory is required for describing tori breakup. The new theory is discussed and comments about renormalization are made.

Chaotic magnetic field lines in a Tokamak with resonant helical windings

We use a Hamiltonian description for magnetic field lines in a large aspect ratio Tokamak for describing the effect of resonant helical windings in a perturbative way, taking into account the toroidal correction. We consider the formation of chains of primary (main and satellites) and secondary islands, analysing their interactions to describe the generation of chaotic magnetic field lines within a portion of the plasma column. This chaotic structure is responsible for disruptive instabilities that may spoil plasma confinement in the Tokamak. Results are compared with numerical integration of magnetic field line equations.

Determination of Pitch Angles of Magnetic Field Lines in Tokamak with Obliquely Injected Helium Beam

The pitch angles of magnetic field lines or q-profile in a high-density tokamak can be determined by the new method proposed here. Blobs of monoenergetic helium beam with different velocities are injected into the tokamak obliquely to the toroidal direction on a poloidal plane χ. Produced He+ ions move nearly along magnetic field lines, and their front emitting a Hell line crosses a different sight plane and forms a curve on it. An optically measured shift of the curve from χ leads to a distribution of pitch angle after correction for the perpendicular drift motion of He+ ions, using the velocity dependence of the drift.

Theory of "clumps" in drift-wave turbulence in tokamak plasma

Basing on the new method of trajectory stochastic treatment advanced by one of the authors of this paper, the theory of "clumps" in driftwave turbulence in tokamak plasmas has been developed. It is shown that, as a longer time behaviour, plasmas in tokamaks will have the same "clumps" effects as those in uniform magnetic fields, although the diffusion crossing magnetic field lines in tokamaks will be enhanced. The influence of the non-uniformity of the magnetic field, such as curvature, shear, etc., on the transverse diffusion and the "clump" life-time is discussed.