Simulations of the Field-Reversed Configuration with the NIMROD Code

The recently formed Plasma Science and Innovation Center (PSI-Center) is refining the NIMROD code to simulate field-reversed configurations (FRCs). The NIMROD code can resolve highly anisotropic heat conduction and viscosity. This, combined with its ability to include two-fluid effects, allows us to capture more detailed physics than previous calculations. Some initial simulations are focused on 2D (n = 0 only) non-linear two-fluid simulations. We present initial validations of a translating FRC and note good conservation of density and magnetic flux. As a validation of the effects of anisotropic thermal conduction, we present a comparison of an FRC with standard thermal transport to one with anisotropic conduction. Two-fluid simulations are shown which produce significant spin-up due to the end-shorting boundary condition. Finally, simulations of the tilt instability are presented, which show that Hall physics significantly retards, but does not eliminate the growth rate.     

Internal Transport Barrier in Edge Plasma of Small Size Divertor Tokamak Using Neutral Beam Injection

We model the internal transport barrier “ITB” in edge plasma of small size divertor tokamak with B2SOLPS0.5.2D fluid transport code. The simulation results demonstrated the following: (1) we control the internal transport barrier by altering the edge particle transport through changes the edge toroidal rotation which agree with the result of Burrell et al. (Edge Pedestal control in quiescent H-mode discharges in DIII-D using co-plus counter-neutral beam injection, Nucl Fusion, 49, 085024 (9pp) in 2009). (2) The radial electric field has neoclassical nature near separatrix with discharge by co-injection NBI. (3) The toroidal plasma viscosity has strong influence on the toroidal velocity.     

High Flux FRC Facility for Stability and Confinement Studies

To provide a path for advancing the FRC concept into a more fusion-like regime, the existing TCSU facility will be modified to take advantage of the new FRC formation method of dynamic formation and merging of FRCs. Results from recent experiments have shown that this methodology provides appreciable increases in the key parameters of ion temperature, poloidal flux and FRC lifetime. FRC stability has been found in numerical calculations where a subpopulation of high energy particles is present in sufficient numbers. A critical goal of the high flux FRC facility will be to form FRCs with poloidal fluxes sufficiently large to fully confine high energy ion orbits introduced from neutralized ion beams injected during FRC formation. A key aspect of the experiments will be to validate theoretical models and simulation codes, such as the 3D extended-MHD code NIMROD, in a in a high beta regime with large two-fluid effects, plasma flows, and an energetic minority species.     

Simulation of the Radial Electric Field in the Small Size Divertor Tokamak for Discharge with Neutral Beam Injection (NBI)

The radial electric field in the edge plasma of small size divertor tokamak can be simulated by B2SOLPS0.5.2D fluid transport code. The simulation provides the follow results: (1) Switching on and off the part of the parallel plasma viscosity driven by parallel ion diamagnetic heat flux (Bekheit in J. Fusion Energ 27(4), 338–345, 2008; Schneider et al. in Nucl. Fusion 41:387, 2001) and Counter-NBI plasma heating change profile of radial electric field significantly. (2) Switching on and off the parallel plasma viscosity driven by parallel ion diamagnetic heat flux leads to the radial electric field is toroidal magnetic field dependence (3) For the case of counter-NBI plasma heating, the switching on and off the current driven by part parallel plasma viscosity depends on the ion diamagnetic heat flux leads to the ion poloidal velocity is toroidal magnetic field B_T dependence. (4) The profile of the radial electric field in edge plasma of small size divertor tokamak is consistent with poloidal rotation velocity.     

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.     

Physics Basis and Progress for a Translating FRC for MTF

We describe a physics scaling model used to design the high density field reversed configuration (FRC) at LANL that will translate into a mirror bounded compression region, and undergo Magnetized Target Fusion compression to a high energy density plasma. At Kirtland AFRL the FRC will be compressed inside a flux conserving cylindrical shell. The theta pinch formed FRC will be expelled from inside a conical theta coil. Even though the ideal FRC has zero helicity and toroidal magnetic field, significant non-ideal properties follow from formation within a conical (not cylindrical) theta coil. The FRC stability and lifetime properties may improve. Several experimental features will also allow unique scientific investigations of this high Lundquist number but collisional plasma.     

Proto-CIRCUS tilted-coil tokamak–torsatron hybrid: Design and construction

We present the field-line modeling, design, and construction of a prototype circular-coil tokamak–torsatron hybrid called Proto-CIRCUS. The device has a major radius R = 16 cm and minor radius a < 5 cm. The six “toroidal field” coils are planar as in a tokamak, but they are tilted. This, combined with induced or driven plasma current, is expected to generate rotational transform, as seen in field-line tracing and equilibrium calculations. The device is expected to operate at lower plasma current than a tokamak of comparable size and magnetic field, which might have interesting implications for disruptions and steady-state operation. Additionally, the toroidal magnetic ripple is less pronounced than in an equivalent tokamak in which the coils are not tilted. The tilted coils are interlocked, resulting in a relatively low aspect ratio, and can be moved, both radially and in tilt angle, between discharges. This capability will be exploited for detailed comparisons between calculations and field-line mapping measurements. Such comparisons will reveal whether this relatively simple concept can generate the expected rotational transform.     

Reversed-field pinch studies in the Madison Symmetric Torus

Studies of large-size (R=1.5 m,a=0.5 m), moderate current (I <750 kA) reversed-field pinch (RFP) plasmas are carried out in the Madison Symmetric Torus in order to evaluate and improve RFP confinement, study general toroidal plasma MHD issues, determine the mechanism of the RFP dynamo, and measure fluctuation-induced transport and anomalous ion heating. MST confinement scaling falls short of the RFP scaling trends observed in smaller RFPs, although the plasma resistance is classical. MHD tearing modes with poloidal mode numberm=1 and toroidal mode numbersn=5–7 are prevalent and nonlinearly couple to produce sudden relaxations akin to tokamak sawteeth. Edge fluctuation-induced transport has been measured with a variety of insertable probes. Ions exhibit anomalous heating, with increases of ion temperature occurring during strong MHD relaxation. The anomalous heating fraction decreases with increasing density, such that ion temperatures approach the lower limit given by electron-ion friction. The RFP dynamo has been studied with attention to various possible mechanisms, including motion-EMF drive, the Hall effect, and superthermal electrons. The toroidal field capacity of MST will be upgraded during Summer 1993 to allow low-current tokamak operation as well as improved RFP operation.     

Quasi-static magnetic compression of field-reversed configuration plasma: amended scalings and limits from two-dimensional MHD equilibrium

In this work, several key scaling laws of the quasi-static magnetic compression of field reversed configuration(FRC) plasma(Spencer et al 1983 Phys. Fluids 26 1564) are amended from a series of two-dimensional FRC MHD equilibriums numerically obtained using the Grad–Shafranov equation solver NIMEQ. Based on the new scaling for the elongation and the magnetic fields at the separatrix and the wall, the empirically stable limits for the compression ratio, the fusion gain, and the neutron yield are ...     

identification and Analysis of Magnetic Structures on HL-2A

A method for the identification and analysis of magnetic islands is presented based on the calculation of the perturbative current and magnetic field in plasmas. A cylindrical approximation is adopted and the toroidal effect on plasma equilibrium is also included. This method has been used on the HL-2A tokamak for analysing the magnetic island structures.     

Frequency multiplication with toroidal mode number of kink/fishbone modes on a static HL-2A-like tokamak

In the presence of energetic particles (EPs), the long-lived mode (LLM) frequency multiplication with n = 1, 2, 3, or higher is often observed on HL-2A, where n is the toroidal mode number. Hybrid kinetic-MHD model simulations of the energetic particle (EP) driven kink/fishbone modes on a static HL-2A-like tokamak using NIMROD code find that when the background plasma pressure is relatively high, and the EP pressure and the beam energy are relatively low, the mode frequency increases almost linearly with EP pressure, and the frequency is proportional to n ('frequency multiplication'), even in the absence of any equilibrium plasma rotation. In addition, the frequency multiplication persists as the safety factor at the magnetic axis q0 varies. In the absence of EPs, the growth rate of the 1/1 mode is the largest; however, as the EP pressure increases, the growth rate of 2/2 modes or 3/3 modes becomes dominant, suggesting that higher-n modes are more vulnerable to EPs. These results may shed light on the understanding of the toroidal mode number dependence of kink/fishbone modes in the advanced scenarios of tokamaks with weak or reversed central magnetic shear.     

Effects of helium massive gas injection level on disruption mitigation on EAST

In this study, NIMROD simulations are performed to investigate the effects of massive helium gas injection level on the induced disruption on EAST tokamak. It is demonstrated in simulations that two different scenarios of plasma cooling(complete cooling and partial cooling) take place for different amounts of injected impurities. For the impurity injection above a critical level, a single MHD activity is able to induce a complete core temperature collapse. For impurity injection below the critical level, a series of multiple minor disruptions occur before the complete thermal quench.     

Extended MHD Simulations of the Compression and Stability of Spheromaks for Current Drive

We examine the compression and stability of spheromaks for magnetic field generation and heating by use of the 3D extended MHD code, NIMROD [C.R. Sovinec, et al., J. Comp. Phys. 195, 355 (2004)]. The formation of compact tori (CT) plasmas with strong magnetic fields by use of repetitive CT injection is being investigated experimentally and serves as impetus for this computational study. To reach high fields, the injected CT will require compression before injection. Stability of the spheromak to tilt and shift modes is examined during compression, as is the amplification of flux during co-helicity spheromak merging.     

Research plan for divertor simulation making use of a large tandem mirror device

We are planning to start a study of divertor simulation under the closely resemble to actual fusion plasma environment making use of the advantage of open magnetic field configuration and to contribute the solution for realizing the divertor in ITER as a future research plan of Plasma Research Center of the University of Tsukuba. In the research plan, the concepts of two divertor devices are introduced. One has an axi-symmetric divertor configuration with the separatrix which is similar to toroidal divertor of torus systems and the other is a high heat flux divertor simulator by using an end-mirror exit of the existing tandem mirror device. Development of magnetic field configuration for ensuring the MHD stability is under way and a designed example is investigated under the optimal condition for plasma production. Consideration of plasma heating scheme using Fokker-Planck simulation code was successfully performed at both axi-symmetric divertor and end-mirror regions. Preparative experiments using calorimeter, Mach probe and high-speed camera have been started at the end-mirror region and the heat flux density of the level in 1-10 MW m⁻² was achieved in standard hot-ion mode plasma-confining experiments, which gives a clear prospect of generating the required heat flux density for divertor studies.     

Computer code for depth distribution of energy deposition by heavy ion bombardment

For bombardment by a heavy-ion beam, we have written a FORTRAN computer code which yields the distribution of energy deposited into elastic atomic collisions as a function of penetration depth. Our aim has been to develop a simple package, inexpensive to run, that could be operated with little or no previous experience. Our calculation is based on an approximation of Kulcinski et al., refined to include the theory of Lindhard et al. which accounts for cascade energy loss to electronic collisions. Range calculation are obtained from the code of Johnson and Gibbons, which our code incorporates. The results of our code are compared with existing calculations of Brice and of Sigmund et al.     

Predictive Simulations of Plasma Heating and Current Drive by Neutral Beam Injection on EAST

Long pulse and high performance steady-state operation is the main scientific mission of experimental advanced superconducting tokamak (EAST). In order to achieve this objective, high-power auxiliary heating systems are essential. Radio frequency (RF) wave heating and neutral beam injection (NBI) are two principal methods. NBI is an effective method of plasma heating and current drive, and it has been used in many magnetic confinement fusion devices. Based on the plasma equilibrium of EAST (Li et al., Plasma Phys Control Fusion 55:125008, 2013) plus previous EAST experimental data used as initial conditions, the NBI module (Polevoi et al., JAERI-Data, 1997) employed in automated system for transport analysis (ASTRA) code (Pereverzev et al., IPP-Report, 2002) is applied to predict the effects of plasma heating and current drive with different neutral beam injection power levels. At certain levels of plasma densities and plasma current densities, the simulation results show that the NBI heats plasma effectively, also increases the proportions of NB current and bootstrap current among total current significantly.     

Stable Spheromaks Sustained by Neutral Beam Injection

It is shown that spheromak equilibria, stable at zero-beta but departing from the Taylor state, could be sustained by non-inductive current drive at acceptable power levels. Stability to both ideal MHD and tearing modes is verified using the NIMROD code for linear stability analysis. Non-linear NIMROD calculations with non-inductive current drive and pressure effects could point the way to improved fusion reactors.     

Simulation of Low–High Transition by Neutral Beam Injection in Edge Plasma of Small Size Divertor Tokamak

This paper reports simulation of L–H transition by fluid transport code B2SOLPS0.5.2D at low ion plasma density on neutral beam injection (NBI) in the edge plasma of small size divertor tokamak. The simulation provides the following results: (1) the transition is possible at plasma density 2 × 10¹⁹ m^?3 with NBI at temperature heating T^heating 3.62 keV. (2) The simulation predicts the generation of large negative radial electric field E _r, which is thought to help L–H transition during NBI, is suggested in the edge plasma of small size divertor tokamak. (3) The toroidal current density in the edge plasma of small size divertor tokamak is plasma density and direction of NBI dependence. (4) Parallel flux transport by anomalous viscosity (turbulent) through separatrix leads to the variation of toroidal current density.     

Electromagnetic analysis of breakdown conditions in JET

This paper presents the breakdown studies carried out in the framework of JET Enhancement Projects for Plasma Control Upgrade (PCU) and Enhanced Radial Field Amplifier (ERFA), to obtain plasma formation with different sets of coil turns in the radial field circuit. The electromagnetic conditions to reach the plasma breakdown in the JET machine are strongly dependent on the properties of JET iron core and the effects of the eddy currents driven by the transient electric field on the present passive structures. The study has been carried out by using a linearized dynamic model of JET provided by 2D axisymmetric finite element code CREATE-L [R. Albanese, et al., Nucl. Fusion 38 (1998) 723–738]. The dynamic simulations have been compared with the experimental data. A new fast visible camera has been installed and has been used for the first time at JET for studies of plasma breakdown. The images show, coherently with the model, that the avalanche evolves dynamically towards a region where the stray field is perpendicular to the first wall.     

MHD stability analysis for advanced tokamak modes in the KSTAR device

The Korea Superconducting Tokamak Advanced Research (KSTAR) device aims to demonstrating the steady-state operation of high-performance advanced tokamak (AT) modes. In order to meet this research goal it is critical to have a good magnetohydrodynamic (MHD) stability, so that KSTAR adopted a strong plasma shape and a conducting wall close to plasma for such stability. An early calculation during the KSTAR design phase had shown that a target AT mode stable up to β_N above 5 can be then obtained. A recent work by Katsuro-Hopkins et al. [O. Katsuro-Hopkins, S.A. Sabbagh, J.M. Bialek, H.K. Park, J.G. Bak, J. Chung, et al., Equilibrium and global MHD stability study of KSTAR high beta plasmas under passive and active mode control, Nucl. Fusion 50(2010) 025019] showed, however, that the maximum β_N value can be substantially lower than 5, unlike the earlier result. In this work, we present a more detailed study on the MHD stability limit of the KSTAR target AT mode and try to clarify the discrepancy observed in the previous two works. It is shown that in the reverse-shear plasma the target mode with β_N above 5 can be obtained if the pressure profile is relatively peaked, but the maximum β_N value is substantially reduced below 5 if the pressure profile becomes broader. This result suggests the importance of a proper control of the pressure profile to get the high-beta AT mode in KSTAR.