MHD Equilibrium with Reversed Current Density and Magnetic Islands Revisited:the Vacuum Vector Potential Calculus

The solution of Grad-Shafranov equation determines the stationary behavior of fusion plasma inside a tokamak.To solve the equation it is necessary to know the toroidal current density profile.Recent works show that it is possible to determine a magnetohydrodynamic(MHD)equilibrium with reversed current density(RCD)profiles that presents magnetic islands.In this work we show analytical MHD equilibrium with a RCD profile and analyze the structure of the vacuum vector potential associated with these equilibria using the virtual casing principle.     

Influence of Precipitates to Superconducting Properties of Nb-Ti Alloy in Connection with Hardness

Principal properties of the magnetic helicity are reviewed with pointing out its basic roles in the fusion plasma theory. Approximate conservation of the total helicity in a toroidal plasma characterizes a typical MHD relaxation process which leads to a force-free plasma equilibrium. The distribution of the plasma current is determined by the helicity transport. Transformer induction injects helicity flux into a toroidal plasma system. Oscillating field can also transport the helicity with driving a parallel (force-free) current.     

Plasma Stability Evaluation Based on MHD Activity and Hard X-Ray Emission in the IR-T1 Tokamak

Determinations of the poloidal beta, internal inductance, plasma energy, plasma pressure, plasma temperature, plasma resistance, plasma effective atomic number, magneto-hydrodynamics (MHD) activity, Runaway electrons energy and energy confinement time are essential for tokamak experiments and optimized operation. Also some of the plasma information can be deduced from these parameters, such as plasma toroidal current profile, and MHD instabilities. In this contribution we investigated about measurements of some plasma parameters as well as MHD activity and Runaway electrons energy. For this purpose we used the magnetic diagnostics and a hard X-ray spectroscopy in IR-T1 tokamak. A hard X-ray emission is produced by collision of the Runaway electrons with the plasma particles or limiters. The mean energy was calculated from the slope of the energy spectrum of hard X-ray photons. In this paper in order to measure energy of the Runaway electrons, we obtained hard X-ray energy in every 5 ms intervals, from the beginning to the end of plasma. Results indicated mean energy of Runaway electrons is maximum during the 0–5 ms interval.     

The Experiment of Modulated Toroidal Current on HT-7 and HT-6M Tokamak

The Experiments of Modulated Toroidal Current were done on the HT-6M tokamak and HT-7 superconducting tokamak. The toroidal current was modulated by programming the Ohmic heating field. Modulation of the plasma current has been used successfully to suppress MHD activity in discharges near the density limit where large MHD m = 2 tearing modes were suppressed by sufficiently large plasma current oscillations. The improved Ohmic confinement phase was observed during modulating toroidal current (MTC) on the Hefei Tokamak-6M (HT-6M) and Hefei superconducting Tokamak-7 (HT-7). A toroidal frequency-modulated current, induced by a modulated loop voltage, was added on the plasma equilibrium current. The ratio of A.C. amplitude of plasma current to the main plasma current △Ip/Ip is about 12% ～ 30%. The different formats of the frequency-modulated toroidal current were compared.     

Numerical simulation of plasma response to externally applied resonant magnetic perturbation on the J-TEXT tokamak

Nonlinear magnetohydrodynamic (MHD) simulations of an equilibrium on the J-TEXT tokamak with applied resonant magnetic perturbations (RMPs) are performed with NIMROD (non-ideal MHD with rotation, open discussion). Numerical simulation of plasma response to RMPs has been developed to investigate magnetic topology, plasma density and rotation profile. The results indicate that the pure applied RMPs can stimulate 2/1 mode as well as 3/1 mode by the toroidal mode coupling, and finally change density profile by particle transport. At the same time, plasma rotation plays an important role during the entire evolution process.     

Effect of Equilibrium Current Profiles on External Kink Modes in Tokamaks

Based on a linearized MHD model, the effect of equilibrium current profiles on external kink modes in tokamaks is studied by MARS code. Three types of equilibrium current profiles are adopted in this work. Firstly, a set of parabolic equilibrium current profiles are chosen. In these profiles the maximum current values in the center of the plasma are fixed, and the currents have different gradient and jump at the plasma boundary. The effects of the current gradient and jump on the growth rate of external kink mode are investigated. It is found that the current jump which causes the q profiles to change plays an important role in the externM kink modes in tokamaks. Secondly, a set of step equilibrium current profiles with different jump positions are chosen. The effect of jump position on external kink modes is discussed. Thirdly, a set of parabolic equilibrium current profiles with current bumps are chosen for the case of off-axis heating. The effects of height~ width and position of the current bumps on external kink modes are analyzed. The fiat equilibrium current profiles are disadvantageous for the MHD stabilities of tokamaks, because of the large current jump at the plasma edge. The peaked equilibrium current profiles and a large and localized current bump near the plasma edge benefit the MHD stabilities of tokamaks.     

A Compact Torus Fusion Reactor Utilizing a Continuously Generated String of CT’s. The CT String Reactor, CTSR

A fusion reactor is described in which a moving string of mutually repelling compact toruses (alternating helicity, unidirectional Btheta) is generated by repetitive injection using a magnetized coaxial gun driven by continuous gun current with alternating poloidal field. An injected CT relaxes to a minimum magnetic energy equilibrium, moves into a compression cone, and enters a conducting cylinder where the plasma is heated to fusion-producing temperature. The CT then passes into a blanketed region where fusion energy is produced and, on emergence from the fusion region, the CT undergoes controlled expansion in an exit cone where an alternating poloidal field opens the flux surfaces to directly recover the CT magnetic energy as current which is returned to the formation gun. The CT String Reactor (CTSTR) reactor satisfies all the necessary MHD stability requirements and is based on extrapolation of experimentally achieved formation, stability, and plasma confinement. It is supported by extensive 2D, MHD calculations. CTSTR employs minimal external fields supplied by normal conductors, and can produce high fusion power density with uniform wall loading. The geometric simplicity of CTSTR acts to minimize initial and maintenance costs, including periodic replacement of the reactor first wall. Charles W. Hartman—LLNL retired; John Thomas—Privately employed.     

Point-Source Helicity Injection Current Drive System for the Pegasus Toroidal Experiment

Recent Pegasus experiments are developing solenoid-free startup techniques using point-source magnetic helicity injection. These plasma sources, called “plasma guns”, ionize a stream of gas in a discharge channel, and bias this channel with respect to an external electrode, driving current along the plasma stream, which relaxes into a tokamak-like equilibrium. The relaxed discharges formed by these injectors exhibit high current amplification, which is the ratio of total toroidal current to the gun-driven current. The development and present design of these injectors are described, and time traces from a typical discharge are presented.     

Plasma profile and shape optimization for the advanced tokamak power plant, ARIES-AT

An advanced tokamak plasma configuration is developed based on equilibrium, ideal MHD stability, bootstrap current analysis, vertical stability and control, and poloidal field coil analysis. The plasma boundaries used in the analysis are forced to coincide with the 99% flux surface from the free-boundary equilibrium. Using an accurate bootstrap current model and external current drive profiles from ray tracing calculations in combination with optimized pressure profiles, β_N values above 7.0 have been obtained. The minimum current drive requirement is found to lie at a lower β_N of 6.0. The external kink mode is stabilized by a tungsten shell located at 0.33 times the minor radius and a feedback system. Plasma shape optimization has led to an elongation of 2.2 and triangularity of 0.9 at the separatrix. Vertical stability could be achieved by a combination of tungsten shells located at 0.33 times the minor radius and feedback control coils located behind the shield. The poloidal field coils were optimized in location and current, providing a maximum coil current of 8.6 MA. These developments have led to a simultaneous reduction in the power plant major radius and toroidal field from those found in a previous study [S.C. Jardin, C.E. Kessel, C.G. Bathke, D.A. Ehst, T.K. Mau, F. Najmabadi, T.W. Petrie, the ARIES Team, Physics basis for a reversed shear tokamak power plant, Fusion Eng. Design 38 (1997) 27].     

High Field Tokamaks for Burning Plasma Experiments

A direct consequence of the ELMy H-mode regime of tokamaks is that, for a constant value of the energy gain Q, both the plasma linear dimension and the normalized plasma density and beta are decreasing functions of the toroidal magnetic field. In this paper, starting from the conditions foreseen for the latest versions of ITER, we derive the plasma parameters of three tokamak plasmas with a toroidal magnetic field of 8, 10, and 13 T.     

Experimental Measurement of Asymmetric Fluctuations of Poloidal Magnetic Field in Damavand Tokomak at Different Plasma Currents

Toroidal and Poloidal magnetic fields have an important effect on the tokomak topology. Damavand Tokomak is a small size tokomak characterized with k?=?1.2, B _t?=?1T, R ₀?=?36?cm, maximum plasma current is about 35?KA with a discharge time of 21?ms. In this experimental work, the variation of poloidal magnetic field on the torodial cross section is measured and analyzed. In order to measure the polodial magnetic field, 18 probes were installed on the edge of tokomak plasma with ?θ?=?18°, while a limiter was installed inside the torus. Plasma current, I _p, induces a polodial magnetic field, B _p, smaller than the torodial magnetic field B _t. Magnetic lines B produced as a combination of B _t and B _p, are localized on the nested toroidal magnetic surfaces. The presence of polodial magnetic field is necessary for particles confinement. Mirnov oscillations are the fluctuations of polodial magnetic field, detected by magnetic probes. Disrupted instability in Tokomak typically starts with mirnov oscillations which appear as fluctuations of polodial magnetic field and is detected by magnetic probes. Minor disruptions inside the plasma can contain principal magnetic islands and their satellites can cause the annihilation of plasma confinement. Production of thin layer of turbulent magnetic field lines cause minor disruption. Magnetic limiter may cause the deformation of symmetric equilibrium configuration and chaotic magnetic islands reveal in plasma occurring in thin region of chaotic field lines close to their separatrix. The width of this chaotic layer in the right side of poloidal profile of Damavand Tokomak is smaller than the width in the left side profile because of Shafranov displacement. Ergodic region in the left side of profile develops a perturbation on the magnetic polodial field lines, B _p, that are greater in magnitude than that in the right side, although the values of B _p on the left side are smaller than that on the right side of the profile. The Left side of profile is close to the principal magnetic axis and the right side is away from Z axis of Tokamak.     

Free-boundary plasma equilibria with toroidal plasma flows

Magnetohydrodynamic equilibrium schemes with toroidal plasma flows and scrape-off layer are developed for the 'divertor-type' and 'limiter-type' free boundaries in the tokamak cylindrical coordinate. With a toroidal plasma flow, the flux functions are considerably different under the isentropic and isothermal assumptions. The effects of the toroidal flow on the magnetic axis shift are investigated. In a high beta plasma, the magnetic shifts due to the toroidal flow are almost the same for both the isentropic and isothermal cases and are about 0.04a0 (a0 is the minor radius) for M₀ = 0.2 (the toroidal Alfvén Mach number on the magnetic axis). In addition, the X-point is slightly shifted upward by 0.0125a0. But the magnetic axis and the X-point shift due to the toroidal flow may be neglected because M0 is usually less than 0.05 in a real tokamak. The effects of the toroidal flow on the plasma parameters are also investigated. The high toroidal flow shifts the plasma outward due to the centrifugal effect. Temperature profiles are noticeable different because the plasma temperature is a flux function in the isothermal case.     

Design,simulation and construction of the Taban tokamak

This paper describes the design and construction of the Taban tokamak, which is located in Amirkabir University of Technology, Tehran, Iran. The Taban tokamak was designed for plasma investigation. The design, simulation and construction of essential parts of the Taban tokamak such as the toroidal field(TF) system, ohmic heating(OH) system and equilibrium field system and their power supplies are presented. For the Taban tokamak, the toroidal magnetic coil was designed to produce a maximum field of 0.7 T at R?=?0.45 m. The power supply of the TF was a130 kJ, 0–10 kV capacitor bank. Ripples of toroidal magnetic field at the plasma edge and plasma center are 0.2% and 0.014%, respectively. For the OH system with 3 kA current, the stray field in the plasma region is less than 40 G over 80% of the plasma volume. The power supply of the OH system consists of two stages, as follows. The fast bank stage is a 120 μF, 0–5 k V capacitor that produces 2.5 kA in 400 μs and the slow bank stage is 93 mF, 600 V that can produce a maximum of 3 kA. The equilibrium system can produce uniform magnetic field at plasma volume. This system's power supply, like the OH system, consists of two stages, so that the fast bank stage is 500 μF, 800 V and the slow bank stage is 110 mF, 200 V.     

MHD Instabilities and Their Effects on Plasma Confinement in Large Helical Device Plasmas with Intense Neutral Beam Injection

MHD stability of the Large Helical Device (LHD) plasmas produced with intense neutral beam injection is experimentally studied. When the steep pressure gradient near the edge is produced through L-H transition or linear density ramp experiment, interchange-like MHD modes whose rational surface is located very close to the last closed flux surface are strongly excited in a certain discharge condition and affect the plasma transport appreciably. In NBI-heated plasmas produced at low toroidal field, various Alfven eigenmodes are often excited. Bursting toroidal Alfven egenmodes excited by the presence of energetic ions induce appreciable amount of energetic ion loss, but also trigger the formation of internal and edge transport barriers.     

Numerical Modeling of a Magnetic Flux Compression Experiment

A possible plasma target for Magnetized Target Fusion (MTF) is a stable diffuse z-pinch in a toroidal cavity, like that in MAGO experiments. To examine key phenomena of such MTF systems, a magnetic flux compression experiment with this geometry is under design. The experiment is modeled with 3 codes: a slug model, the 1D Lagrangian RAVEN code, and the 1D or 2D Eulerian Magneto-Hydro-Radiative-Dynamics-Research (MHRDR) MHD simulation. Even without injection of plasma, high-Z wall plasma is generated by eddy-current Ohmic heating from MG fields. A significant fraction of the available liner kinetic energy goes into Ohmic heating and compression of liner and central-core material. Despite these losses, efficiency of liner compression, expressed as compressed magnetic energy relative to liner kinetic energy, can be close to 50%. With initial fluctuations (1%) imposed on the liner and central conductor density, 2D modeling manifests liner intrusions, caused by the m = 0 Rayleigh-Taylor instability during liner deceleration, and central conductor distortions, caused by the m = 0 curvature-driven MHD instability. At many locations, these modes reduce the gap between the liner and the central core by about a factor of two, to of order 1 mm, at the time of peak magnetic field.     

Equilibrium of a spatial plasma pinch in a longitudinal magnetic field under steady-state conditions

The equilibrium conditions of plasma in toroidal chambers of the figure-of-eight type are determined for the case in which the plasma is preserved for lpnger than the magnetic field takes to pass through the windings of the solenoid. In this case, some of the magnetic lines of force pass through the solenoid windings, closing outside it. Hence, the radius of the cross section of the extreme toroidal magnetic surface lying as a whole inside the chamber is always smaller than the radius of cross section of the solenoid. For a plasma pressure exceeding a certain critical value, toroidal magnetic surfaces are absent, and containment of the plasma is in principle impossible.Translated from Atomnaya Énergiya, Vol. 18, No. 5, pp. 443–446, May, 1965     

Magnetic ripple diffusion and stable INTOR equilibria

Under conditions representative of ignited tokamak operation, ion energy losses are likely to be dominated by transport due to deviation from toroidal field axisymmetry. This asymmetry, termed ripple, induces several distinct physical processes, all of which lead to enhanced ion thermal conduction above the neoclassical value. The net impact of these processes on ignition dynamics is analyzed for an INTOR-like plasma by means of a 1 1/2-D transport code. The radial shift of the plasma to regions of higher ripple during plasma heating results in a substantial broadening of the window of values of ripple consistent with favorable ignition and burn characteristics and also provides some measure of automatic burn control. Because-limiting processes are also prime candidates for burn control, the profiles obtained from the transport analyses are examined for stability with respect to ideal MHD modes. The MHD-limited value increases as the plasma is heated and in fact in the burn phase approaches the value characteristic of a shape-optimized MHD equilibrium. The sensitivity of the transport and MHD results to the choice of plasma density is examined, and it is found that hot-ion mode operation is precluded for devices such as INTOR unless present estimates of both ripple losses and-limits are highly pessimistic.     

Controlling the Diffusion of Runaway Electrons by Safety Factor Changes in IR-T1 Tokamak

The high-energy current of runaway electrons during a major disruption in tokamak reactors can cause serious damage to the first wall of the reactor and reduce its lifetime. Therefore, it is important to find methods for decreasing the generation of runaway electrons and their energy. The safety factor plays an important role in determining the stability criteria for a wide range of MHD modes. Since runaway electrons suffer only rarely from collisions and are hardly sensitive to electrostatic turbulence, their transport is governed by the magnetic lines structure. On the other hand, since the safety factor is related to the magnetic lines structure, changes in safety factor may have important effects on the diffusion of runaway electrons. In this paper, the generation of runaway electrons and their transport is investigated theoretically. Moreover, by changing the discharge voltage of ohmic and toroidal capacitors, different values of the edge safety factor is generated. In fact, in this experiment, the researchers try to increase the diffusion of runaway electrons by using safety factor changes in the IR-T1 tokamak.     

Compact toroid challenge experiment with the increasing in the energy input into plasma and the level of trapped magnetic field

The present work reports on compact toroid hydrogen plasma creation by means of a specially designed discharge system and results of magnetic fields introduction. Experiments in the compact toroid challenge (CTC) device at P.N. Lebedev Physical Institute (FIAN) have been conducted since 2005. The CTC device differs from the conventional theta-pinch formation in the use of an axial current for enhanced efficiency. We have used a novel technique to maximize the flux linked to the plasma. The purpose of this method is to increase the energy input into the plasma and the level of trapped magnetic flux using an additional toroidal magnetic field. A study of compact torus formation with axial and toroidal currents was done and a new method is proposed and implemented.     

Generalization of Solovev's approach to finding equilibrium solutions for axisymmetric plasmas with flow

Solovev's approach of finding equilibrium solutions was found to be extremely useful for generating a library of linear-superposable equilibria for the purpose of shaping studies.This set of solutions was subsequently expanded to include the vacuum solutions of Zheng,Wootton and Solano,resulting in a set of functions [SOLOVEV_ZWS] that were usually used for all toroidally symmetric plasmas,commonly recognized as being able to accommodate any desired plasma shapes (complete-shaping capability).The possibility of extending the Solovev approach to toroidal equilibria with a general plasma flow is examined theoretically.We found that the only meaningful extension is to plasmas with a pure toroidal rotation and with a constant Mach number.We also show that the simplification ansatz made to the current profiles,which was the basis of the Solovev approach,should be applied more systematically to include an internal boundary condition at the magnetic axis;resulting in a modified and more useful set [SOLOVEV_ZWSm].Explicit expressions of functions in this set are given for equilibria with a quasi-constant current density profile,with a toroidal flow at a constant Mach number and with specific heat capacity 1.The properties of [SOLOVEV_ZWSm] are studied analytically.Numerical examples of achievable equilibria are demonstrated.Although the shaping capability of the set [SOLOVE_ZWSm] is quite extensive,it nevertheless still does not have complete shaping capability,particularly for plasmas with negative curvature points on the plasmaboundary such as the doublets or indented bean shaped tokamaks.