Equilibrium Plasma Configurations Research Articles

Magnetic field simulations of the GOLEM tokamak via the NICE code

In this paper, the direct and inverse equilibrium computation mode of the NICE code is put into operation for the case of the GOLEM tokamak. This enables, for the first time, simulations of GOLEM's magnetic field. The computation mode put into operation simulates the magnetohydrodynamic equilibrium of a tokamak plasma based on a given plasma position or given currents in poloidal magnetic field coils. In order to set up NICE, a virtual model of GOLEM is introduced that includes axially symmetrical approximations of GOLEM's iron core and primary transformer coils. The results of NICE simulations are compared with experimental measurements, and it is shown that NICE simulations produce plasma equilibrium configurations typical for GOLEM. Nevertheless, a more detailed validation of GOLEM's virtual model and of the results of NICE simulations is to be performed in the future.

Mathematical Model of Equilibrium Plasma Configurations in Magnetic Traps and Their Stability Analysis

The paper presents a review of numerical investigations of a special class of magnetic field-based plasma confinement traps in which current-carrying conductors are immersed in plasma. These traps are referred to as Galatea traps, as proposed by A. I. Morozov. The investigations are presented as applied to a cylinder with two conductors parallel to the axis, which is a straightened analog of a toroidal Galatea-belt trap. The mathematical model of equilibrium is based on a boundary value problem for the two-dimensional elliptic Grad–Shafranov equation, which is solved numerically. Of main interest are various approaches to the stability analysis of magnetoplasma configurations in a trap and the dependence of stability on the geometry and parameters of the problem. We analyze the linear-approximation stability of one-dimensional configurations surrounding a conductor and of two-dimensional configurations in a Galatea-belt trap. The main result of calculations in various problem statements is that the ratio of the characteristic gas and magnetic pressures under which stability occurs is bounded from above. We give a brief account of the main results published in recent years and present new results obtained recently.

Numerical Simulation of Equilibrium Plasma Configurations in Toroidal Traps Based on the Morozov–Solovyov Equations

Numerical Simulation of Equilibrium Plasma Configurations in Toroidal Traps Based on the Morozov–Solovyov Equations

Spatial Structure of the Plasma Flows in the Magnetic Fields of Laser Plasma

The results of studying the spatial structure of the plasma flows that appear when a laser pulse of relativistic intensity (above 1018 W/cm2) is incident on the surface of a solid target are presented. The ring structure experimentally observed in the cross section of a plasma flow is shown to correspond to the toroidal equilibrium plasma configuration that appears in the strong magnetic fields of laser plasma. A model is proposed to describe astrophysical current jets consisting of a discrete sequence of toroidal equilibrium plasma structures.

Controlled movement of lower strike points by applying a divertor coil on the EAST tokamak

A new in-vessel water-cooled coil has been placed below the lower tungsten-covered divertor in EAST, aiming at moving the strike points in the divertor and spreading the heat flow on the targets. To achieve controlled movement of the strike points by the plasma control system (PCS) when applying the in-vessel coil, the plasma equilibrium configurations are predicted by the tokamak equilibrium (TEQ) code. The divertor coil current is involved in these calculations. The shape control parameters in the PCS are adjusted according to the predesigned equilibria from the TEQ code. The strike point movement over a wide range has been achieved in the experiment while keeping the main plasma stable. Thus, this method for divertor strike point movement with the assistance of the divertor coil is feasible.

Application of integrated simulation environment SIEMNED to the analysis of the MEPHIST-0 tokamak operation

This paper presents the results of numerical simulation of plasma equilibrium and stability in the MEPHIST-0 tokamak with SIEMNED software and comparison of simulation results with experiments. The determined characteristics of the vacuum chamber show that it significantly affects the entire discharge. For various scenarios of the inductor operation, a comparison of experimental data and simulated currents and magnetic fields induced in the chamber was carried out. For steady-state tokamak operation, a numerical study of equilibrium plasma configurations was carried out depending on the currents in the poloidal magnetic field coils and plasma current. The vertical plasma instability was investigated. The limiting values of plasma ellipticity preventing the vertical plasma instability were numerically determined. Numerical simulations show that plasma equilibrium is supported by induced currents. It was shown numerically that magnetic configuration with ‘zero of higher order’ were obtained before the plasma shot, suggesting consistency between the simulation results and observations.

Mathematical Model and Numerical Simulation of Equilibrium Plasma Configurations in ‘‘Threeleaf’’ Magnetic Traps

Mathematical Model and Numerical Simulation of Equilibrium Plasma Configurations in ‘‘Threeleaf’’ Magnetic Traps

Exact Solution for Equilibrium Configurations of Two-Component Plasma Confined between Parallel Plates

It is the fifth part of the study published under the common umbrella of “The Gibbs Variational Method in Thermodynamics of Equilibrium Plasma”. In Parts 1 - 4, we formulated a novel approach to thermodynamics of one- and two-component heterogeneous systems completely or partially filled with a liquid substance in the plasma state. The approach is based on the use of Gibbs variational principles, and it enables efforts to address a variety of problems relating to the equilibrium and stability of such systems. In this fifth part, the results of Parts 1 - 4 are applied to the analysis of equilibrium configurations of a two-component charged plasma trapped between two parallel plates (the geometry often used in various applications).

Magnetostatic analysis of HCSB blanket under three different plasma equilibrium configurations of CFETR

Abstract The blanket system, as one of the most technically challenging components of CFETR, has to accommodate large thermal-mechanical and electromagnetic loads. The electromagnetic forces play a critical role in safety analysis. Although the preliminary electromagnetic analysis of helium cooled solid blanket (HCSB) has been carried out, the influence of plasma equilibrium configurations on the electromagnetic results has not been researched yet. For CFETR, there are three typical plasma equilibrium configurations, ITER-like, Super-X and Snowflake, corresponding to three plasma equilibrium configuration currents. In this paper, the finite element method (FEM) models of HCSB under these three plasma equilibrium configurations are developed and magnetostatic force as well as moment have been computed by the FEM software called MAXWELL. In order to take into account of the effects of surrounding ferromagnetic material on the typical blanket, three sections of blankets around the typical blanket and the vacuum vessel are established. The total forces and magnetic fields are similar among three configurations but the differences in moments and force distributions suggest that there could be a significant distinction in stress distribution, which will be explored and evaluated in future study.

Equilibrium Configuration Reconstruction of Multipole Galatea Magnetic Trap Based on Magnetic Measurement

Equilibrium reconstruction is an important basic work for the design and operation of a multipole Galatea magnetic trap device, and it is also a fundamental theoretical work for plasma equilibrium control. Based on the static equilibrium model of the multipole Galatea magnetic trap, an equilibrium reconstruction scheme based on solving the Grad–Shafranov equilibrium equation is proposed. In the proposed scheme, a plasma current density distribution model is established, and the combination of the Green function and the finite difference method is investigated to realize the fast solution to the Grad–Shafranov equilibrium equation. At the same time, the least-squares fitting method is employed, along with the magnetic probe measurement data, which realizes correction and iteration of the parameters of the plasma current density distribution model. Through simulation, the magnetic field distribution, plasma current density distribution, and plasma pressure distribution of multipole Galatea magnetic trap can be obtained, which confirms the effectiveness of the equilibrium reconstruction when compares with other experimental results. At the end of this paper, the influence of the magnetic field produced by the solenoid coil on the equilibrium configuration of plasma is studied.

Comparative Analysis of Plasma Equilibrium Computations in Toroidal and Cylindrical Magnetic Traps

Toroidal magnetic traps for plasma confinement make up an extended object of controlled nuclear fusion investigations. Mathematical simulation of equilibrium plasma configurations in the traps often deals with their analogues straightened into a cylinder. This paper presents a comparative analysis of their numerical investigations in both geometry variants. Mathematical tool of the models use two-dimensional boundary problems with the Grad-Shafranov differential equation for the magnetic flux function. As the investigation result, we present some quantitative characteristics of differences between toroidal and cylindrical configurations by two examples: a plasma torus with longitudinal electrical current and the Galathea-Belt toroidal trap with two ring-shaped current-carrying conductors immersed into the plasma.

Numerical models in applied plasmadynamic and plasmastatic problems

We present a review of mathematical models and computations in the two plasma physic projects: creation of powerful plasma accelerators and researches of equilibrium plasma configurations in magnetic traps. Steady-state transonic plasma flows in accelerators are investigated in the plasmadynamic models. The recent time works deal with studies of the longitudinal magnetic field influence on the plasma acceleration process in the channels of various geometry. Equilibrium magnetoplasma configurations in the traps are researched in plasmastatic models based on the numerical solution of problems with the Grad-Shafranov equation. Configurations are investigated in the galateya-traps with current carrying conductors immersed into the plasma. In the recent time works, configurations in toroidal magnetic traps are studied in comparison with their analogues straightened into the cylinder.

Comparison of different linearized plasma response models on the EAST tokamak

In this paper, experimental growth rates are positively compared to numerical predictions for the new geometry of the experimental advanced superconducting tokamak (EAST) and for a wide variety of plasma equilibrium configurations; hence, significantly extending the validation range as compared to previous works. The general results confirmthat the CarMa0 code is adequate to reproduce the experimental situation in EAST. In addition, we investigate the effects of different assumptions on the plasma response model, on the structures and on plasma boundary.

Overview of the Design Status of the Superconducting Magnet System of the CFETR

The concept design of the China Fusion Engineering Test Reactor (CFETR) was started in 2012 in two stages. For CFETR-Phase I, the major radius is 5.7 m, the minor radius is 1.6 m, and the magnetic field at the plasma region, BT , is 4–5 T. There were 16 toroidal field coils and six central solenoid coils designed by a Nb3Sn cable-in-conduit conductor (CICC) with the maximum operation current of 64 and 50 kA, respectively. Three types of plasma equilibrium configuration (ITER-like single null, super-X, and snowflake) were designed. The maximum flux provided by the central solenoid is set at 180 V⋅s. However, to get much higher operation parameters such as steady-state operation, particle and heat exhaust, disruption mitigation and avoidance, ELM control, and material damage by high heat flux and neutron, the superconducting magnet system of CFETR-phase II has been updated based on the larger machine with R = 6.7 m−7.0 m, a = 2.0 m, and BT = 6.5–7 T. Such a new design makes over 1-GW fusion power and better plasma performance possible. Hybrid TF coils are designed by a high-performance Nb3Sn conductor, since the maximum magnetic field can reach to 14–15 T. Besides, in order to save the space for the blanket system and get higher flux, a high-temperature superconducting Bi-2212 magnet with better current-carrying performance under high field is supposed to be employed for the CS coils of CFETR-phase II. The Bi-2212 CICC sample has been tested at 4.2 K with a critical current of 26.6 kA under its self-field.

Numerical simulation of equilibrium plasma configurations in toroidal magnetic traps and their cylindrical analogues

Some basic characteristics investigations of equilibrium magnetoplasma configurations in toroidal traps for plasma confinement often use mathematical models of their straightened into a cylinder analogues. The aim of this work is a comparative analysis of MHD-models in toroidal and cylindrical configurations. We consider the plasma cylinder with the electric current (Z-pinch) as a simpliest trap type and its toroidal analogue and then extend and define more exactly the cylindrical and toroidal models of the ‘Galatea-Belt’ trap with two current-carrying conductors, immersed into the plasma. Distinctions between configurations in the traps of different geometry are registered and some stability problems are considered.

Ideal relaxation of the Hopf fibration

Ideal magnetohydrodynamics relaxation is the topology-conserving reconfiguration of a magnetic field into a lower energy state where the net force is zero. This is achieved by modeling the plasma as perfectly conducting viscous fluid. It is an important tool for investigating plasma equilibria and is often used to study the magnetic configurations in fusion devices and astrophysical plasmas. We study the equilibrium reached by a localized magnetic field through the topology conserving relaxation of a magnetic field based on the Hopf fibration in which magnetic field lines are closed circles that are all linked with one another. Magnetic fields with this topology have recently been shown to occur in non-ideal numerical simulations. Our results show that any localized field can only attain equilibrium if there is a finite external pressure, and that for such a field a Taylor state is unattainable. We find an equilibrium plasma configuration that is characterized by a lowered pressure in a toroidal region, with field lines lying on surfaces of constant pressure. Therefore, the field is in a Grad-Shafranov equilibrium. Localized helical magnetic fields are found when plasma is ejected from astrophysical bodies and subsequently relaxes against the background plasma, as well as on earth in plasmoids generated by, e.g., a Marshall gun. This work shows under which conditions an equilibrium can be reached and identifies a toroidal depression as the characteristic feature of such a configuration.

Plasmastatic model of toroidal trap “Galatea-belt”

Magnetic galatea-traps for thermonuclear plasma confinement with current carrying conductors immersed into the plasma volume, are represented by an example of the toroidal trap “The Belt” with two circular conductors. Numerical models of equilibrium plasma and field configurations are investigated in straightened into cylinder analogues of some toroidal galateas in a series of works by the authors. This paper presents a plasmastatic model of configurations in the toroidal variant of “The Belt” in terms of a boundary problem with the Grad-Shafranov equation. Distinctions of their geometry and quantitative characteristics from the cylindrical analogues and their dependence of parameters are determined in computation.

Numerical study of ion orbits in EAST plasmas with a current-reversal equilibrium configuration

By solving the Grad-Shafranov equation in the cylindrical coordinate system, we numerically obtain the tokamak plasma equilibrium configurations of the conventional mode and the high-to-lowfield-side current-reversal equilibrium mode (HL-CREC) by using the discharge parameters for the Experimental Advanced Superconductor Tokamak (EAST). By coupling with the particle’s motion equation, we obtain the orbits of trapped particles and passing particles under both equilibrium configurations. We find that the orbit of the passing particle in the HL-CREC is wholly confined on the low-field side and that the half width of the banana orbit of trapped particles increases greatly compared with those in the conventional equilibrium configuration. In addition, the ion loss is studied based on the Monte Carlo method. The results show that for ions near the plasma edge, a much high ion loss rate can be obtained in HL-CREC than that in the conventional equilibrium configuration.

Concept design of the CFETR central solenoid

China Fusion Engineering Test Reactor (CFETR) superconducting tokamak is a national scientific research project of China with major and minor radius is 5.7m and 1.6m respectively. The magnetic field at the center of plasma with radius as R=5.7m is set to be 5.0T. The major objective of the project is to build a fusion engineering tokamak reactor with fusion power in the range of 50–200MW and should be self-sufficient by blanket. Six central solenoid coils of CFETR with same structure are made of Nb3Sn superconductor. Besides, the stray field in plasma area should be less than 20Gs with the operation current of CS coils for plasma heating phase. The maximum magnetic field of CS coil is 11.9T. It is calculated by the coils’ operation current based on plasma equilibrium configuration. The central solenoid needs to have enough stability margin under the condition of high magnetic field and strain. This paper discusses the design parameters, electromagnetic distribution, structure and stability analysis of the CS superconducting magnet for CFETR.

Stability of global magnetohydrodynamic modes in the L-5 compact torsatron

Global magnetohydrodynamic (MHD) modes in free-boundary plasma equilibrium configurations of the L-5 six-period compact torsatron (project of the Prokhorov General Physics Institute, Russian Academy of Sciences; G. M. Batanov et al., Plasma Dev. Operat. 11, 161 (2003)) have been investigated using the CAS3D code. It is shown that global internal ideal MHD modes can be found reliably only in Mercier unstable plasmas. In all cases under study, they are intrinsically ballooning in nature, i.e., the disturbance at the inner side of the torus is significantly lower in value than that at the outer side. Besides internal modes localized near low-order rational magnetic surfaces, external modes that are localized near the free plasma boundary and are not associated with any rational magnetic surface inside the plasma (the so-called peeling modes) have been found. In contrast to a tokamak with the same aspect ratio, in which pressure-gradient edge-localized modes are ballooning in nature, the peeling modes in the 3D currentless magnetic configuration investigated in the present work are quasi-cylindrical in the flux coordinate system. The problem of plasma boundary destruction under the action of magnetic fields generated by plasma currents is also briefly discussed.