Net Toroidal Current Research Articles

Non-resonant global mode in LHD partial collapse with net toroidal current

A transition from an interchange mode to a non-resonant mode is found in the nonlinear magnetohydrodynamic simulation for the partial collapse in a large helical device (LHD) plasma with a net toroidal current. This transition can occur when the magnetic shear is weak and the rotational transform is close to unity in the core region. In this transition, the mode number of the dominant Fourier component is reduced. As a result of the nonlinear evolution, the (m, n) = (1, 1) component can be dominant, where m and n are the poloidal and the toroidal mode numbers, respectively. This transition is considered to be a candidate to explain the observation in the LHD experiments with the net toroidal current that show partial collapses are caused by the (1, 1) mode.

Proof of concept of a fast surrogate model of the VMEC code via neural networks in Wendelstein 7-X scenarios

In magnetic confinement fusion research, the achievement of high plasma pressure is key to reaching the goal of net energy production. The magnetohydrodynamic (MHD) model is used to self-consistently calculate the effects the plasma pressure induces on the magnetic field used to confine the plasma. Such MHD calculations—usually done computationally—serve as input for the assessment of a number of important physics questions. The variational moments equilibrium code (VMEC) is the most widely used to evaluate 3D ideal-MHD equilibria, as prominently present in stellarators. However, considering the computational cost, it is rarely used in large-scale or online applications (e.g. Bayesian scientific modeling, real-time plasma control). Access to fast MHD equilibria is a challenging problem in fusion research, one which machine learning could effectively address. In this paper, we present artificial neural network (NN) models able to quickly compute the equilibrium magnetic field of Wendelstein 7-X. Magnetic configurations that extensively cover the device operational space, and plasma profiles with volume-averaged normalized plasma pressure ⟨β⟩ (β = ) up to 5% and non-zero net toroidal current are included in the data set. By using convolutional layers, the spectral representation of the magnetic flux surfaces can be efficiently computed with a single network. To discover better models, a Bayesian hyper-parameter search is carried out, and 3D convolutional NNs are found to outperform feed-forward fully-connected NNs. The achieved normalized root-mean-squared error, the ratio between the regression error and the spread of the data, ranges from 1% to 20% across the different scenarios. The model inference time for a single equilibrium is on the order of milliseconds. Finally, this work shows the feasibility of a fast NN drop-in surrogate model for VMEC, and it opens up new operational scenarios where target applications could make use of magnetic equilibria at unprecedented scales.

Non-Neutralized Electric Current of Active Regions Explained as a Projection Effect

Active regions (ARs) often possess an observed net electric current in a single magnetic polarity. We show that such "non-neutralized" currents can arise from a geometric projection effect when a twisted flux tube obliquely intersects the photosphere. To this end, we emulate surface maps of an emerging AR by sampling horizontal slices of a semi-torus flux tube at various heights. Although the tube has no net toroidal current, its poloidal current, when projected along the vertical direction, amounts to a significant non-neutralized component on the surface. If the tube emerges only partially as in realistic settings, the non-neutralized current will 1) develop as double ribbons near the sheared polarity inversion line, (2) positively correlate with the twist, and 3) reach its maximum before the magnetic flux. The projection effect may be important to the photospheric current distribution, in particular during the early stages of flux emergence.

Extension of Shafranov’s Equilibrium Theory to the Description of Current Quenches Affected by Resistive Wall Dissipation in Tokamaks

An equation for the plasma column position in a tokamak is derived with account of the resistive wall reaction on the changes in the plasma. A similar problem was considered by V.D. Shafranov [J. Nucl. Energy C 5, 521 (1963)] but for a fixed plasma current. Here, this current is treated as time-dependent, which allows to cover the current quenches and expand the study to the analysis of disruptions. It is shown that the net toroidal current induced in the wall during the current quench (which is not accounted for in the mentioned and related existing analytical models) can strongly affect the plasma equilibrium. A general algorithm applicable to arbitrary tokamaks is presented. For a large-aspect-ratio “circular” tokamak a full cycle of the step-by-step reduction of a problem is carried out down to the equation for the plasma shift evolution. The technique and results are ready for use with standard equilibrium solvers and models.

Ion temperature gradient turbulence modification in quasi-axisymmetry

The large flexibility of the proposed QUASAR facility [Gates et al., Nucl. Fusion 57, 126064 (2017)] is leveraged in order to explore the effect of magnetic shear on adiabatic Ion Temperature Gradient (ITG) turbulence. The QUASAR facility is a reimagining of the National Compact Stellarator Experiment utilizing and expanding upon the already constructed coil set. Recent work using fixed boundary optimization of the LI383 equilibrium (upon which QUASAR is based) has suggested possible improvements to ITG turbulence [Mynick et al., Plasma Phys. Controlled Fusion 56, 094001 (2014)]. In this work, a different approach is taken, wherein a series of self-consistent free boundary VMEC equilibria are developed for QUASAR. These equilibria assume temperature and density profiles consistent with 2% beta and ohmic current drive. In each configuration, the toroidal field coils are energized to different values and the STELLOPT code is used to vary the modular coil current and net toroidal current. The edge value of rotational transform is targeted in the optimization, producing a magnetic shear scan. All these configurations share similar neoclassical transport levels, while nonlinear GENE flux tube simulations show up to a factor of four change in adiabatic ITG turbulence at various radii. Comparisons of proxy functions and linear flux tube runs are also made. This work highlights the capability of the QUASAR experiment as a tool to explore transport in 3D magnetic fields and the possibility of the further improvements to stellarators through optimization.

Magnetic configuration effects on the Wendelstein 7-X stellarator

The two leading concepts for confining high-temperature fusion plasmas are the tokamak and the stellarator. Tokamaks are rotationally symmetric and use a large plasma current to achieve confinement, whereas stellarators are non-axisymmetric and employ three-dimensionally shaped magnetic field coils to twist the field and confine the plasma. As a result, the magnetic field of a stellarator needs to be carefully designed to minimize the collisional transport arising from poorly confined particle orbits, which would otherwise cause excessive power losses at high plasma temperatures. In addition, this type of transport leads to the appearance of a net toroidal plasma current, the so-called bootstrap current. Here, we analyse results from the first experimental campaign of the Wendelstein 7-X stellarator, showing that its magnetic-field design allows good control of bootstrap currents and collisional transport. The energy confinement time is among the best ever achieved in stellarators, both in absolute figures (τE > 100 ms) and relative to the stellarator confinement scaling. The bootstrap current responds as predicted to changes in the magnetic mirror ratio. These initial experiments confirm several theoretically predicted properties of Wendelstein 7-X plasmas, and already indicate consistency with optimization measures. Results from the first experimental campaign of the Wendelstein 7-X stellarator demonstrate that its magnetic-field design grants good control of parasitic plasma currents, leading to long energy confinement times.

Modification of the helical divertor footprint induced by the net toroidal plasma current in the LHD heliotron

In this study, the modification of the helical divertor footprint induced by the net toroidal plasma current was investigated in the Large Helical Device (LHD). The divertor footprint shifted a few centimetres when the net toroidal plasma current, as measured by Rogowski coils, was induced via the neutral-beam injection. The shift direction was related to the plasma current direction, and the shift width showed almost linear dependence on the plasma current divided by the toroidal field strength. Magnetic field line tracing calculation considering the plasma current within a simple model revealed that the modification of the edge field line structure causes the footprint shift. The predicted and experimental shift widths agreed qualitatively.

Stellerators

Stellarators are toroidal devices where the required rotational transform of the magnetic field lines is generated by external field coils and not via an induced net toroidal plasma current. This confinement scheme has the advantages that, in principle, steady-state plasma operation is possible and that it does not have to brace itself against disruptions of a toroidal plasma current. At the cost of having to give up toroidal symmetry the properties of the stellarator field can be tailored to suit reactor needs. Research focuses on the plasma confinement properties of different stellarator fields and investigates the problems arising when one extrapolates to reactor parameters.

Stellarators

Stellarators are toroidal devices where the required rotational transform of the magnetic field lines is generated by external field coils and not via an induced net toroidal plasma current. This confinement scheme has the advantages that, in principle, steady-state plasma operation is possible and that it does not have to brace itself against disruptions of a toroidal plasma current. At the cost of having to give up toroidal symmetry the properties of the stellarator field can be tailored to suit reactor needs. Research focuses on the plasma confinement properties of different stellarator fields and investigates the problems arising when one extrapolates to reactor parameters.

Stellarators

Stellarators are toroidal devices where the required rotational transform of the magnetic field lines is generated by external field coils and not via an induced net toroidal plasma current. This confinement scheme has the advantages that, in principle, steady-state plasma operation is possible and that it does not have to brace itself against disruptions of a toroidal plasma current. At the cost of having to give up toroidal symmetry the properties of the stellarator field can be tailored to suit reactor needs. Research focuses on the plasma confinement properties of different stellarator fields and investigates the problems arising when one extrapolates to reactor parameters.

Choice of coils for a fusion reactor

In a fusion reactor a hot plasma of deuterium and tritium is confined by a strong magnetic field to produce helium ions and release energetic neutrons. The 3D geometry of a stellarator provides configurations for such a device that reduce net toroidal current that might lead to disruptions. We construct smooth coils generating an external magnetic field designed to prevent the plasma from deteriorating.

Statistical analysis of the equilibrium configurations of the W7-X stellarator

Equilibrium magnetic configurations of W7-X stellarator plasma were analysed in this study. The statistical method of function parametrization was used to recover the physical properties of the magnetic configurations, such as the flux surface geometry, the magnetic field and the iota profile from simulated experimental data. The study was carried out with a net toroidal current. Idealized ‘measurements’ were first used to recover the configuration. These ‘ measurements’ were then perturbed with noise and the effect of this perturbation on the recovered configuration parameters was estimated. The noise was scanned over a range large enough to encompass that expected in the actual experiment. In the process, it was possible to ascertain the limit of tolerable noise that can be allowed in the inputs so as not to significantly perturb the outputs recovered with noiseless ‘measurements’. Generally, a cubic polynomial model was found to be necessary for noise levels below 10%. For higher noise levels, a quadratic polynomial performed as well as the cubic. The noise level of 10% was also the approximate limit up to which the recovery with ideal measurements was generally reproduced. For the flux geometry recovery, however, the quadratic model performed similarly to the cubic for any value of noise, with the latter model proving to be significantly better only for the noiseless case. Also, with noisy predictors the recovery error for the flux surfaces increases linearly with effective radius from the plasma core up to the edge.

Stellarators

Stellarators are toroidal devices where the required rotational transform of the magnetic field lines is generated by external field coils and not via an induced net toroidal plasma current. This confinement scheme has the advantages that, in principle, steady-state plasma operation is possible and that it does not have to brace itself against disruptions of a toroidal plasma current. At the cost of having to give up toroidal symmetry the properties of the stellarator field can be tailored to suit reactor needs. Research focuses on the plasma confinement properties of different stellarator fields and investigates the problems arising when one extrapolates to reactor parameters.

Stellarators

Stellarators are toroidal devices where the required rotational transform of the magnetic field lines is generated by external field coils and not via an induced net toroidal plasma current. This confinement scheme has the advantages that, in principle, steady-state plasma operation is possible and that it does not have to brace itself against disruptions of a toroidal plasma current. At the cost of having to give up toroidal symmetry the properties of the stellarator field can be tailored to suit reactor needs. Research focuses on the plasma confinement properties of different stellarator fields and investigates the problems arising when one extrapolates to reactor parameters.

Numerical computation of magnetic fields of two-and three-dimensional equilibria with net toroidal current

The MFBE_2001 code computes the magnetic field in a form suitable forfield line tracing inside and outside the plasma boundary of two- and three-dimensional finite-β equilibria. It is a modified version of the Magnetic FieldSolver for Finite-β Equilibria (MFBE) code whichwas developed for the investigation of stellaratorequilibria without net toroidal current. The numerical method used in MFBE_2001 is based on the `virtual casing' principle which also allows the computation of magnetic fields of equilibria with net toroidal current, such asquasi-axisymmetric and tokamak equilibria. The numerical accuracy of thecode is tested for an axisymmetric tokamak equilibrium and the correspondingthree-dimensional one including the toroidal field ripple. For this purpose,the results obtained with the code system VMEC/NEMEC+MFBE_2001+GOURDONare compared with those computed with the axisymmetric equilibrium code DIVA.

Bootstrap current analysis for neoclassical internal transport barrier discharge of CHS

The bootstrap current analyses have been carried out for two different kinds of discharges of compact helical system (CHS) heliotron/torsatron. One is the electron cyclotron resonance heating (ECRH) discharge with moderate density and without internal transport barrier (ITB) (ne(0)>0.5×1019 m-3, Te(0)<1.2 keV). Another is the neoclassical ITB (NC ITB) discharge, which has been achieved in the rather low electron density condition (ne<0.4×1019 m-3) with ECRH and co-NBI. The NC ITB mode is characterized by steeply peaked electron temperature profile (Te(0)>2.0 keV) in the core domain and large positive radial electric field (Er~ + 10 kV m-1). The dependence of toroidal net current on magnetic axis position Rax was investigated for ECRH discharges without ITB. There is good agreement in the tendency of Rax dependence of the net toroidal current between experiment and neoclassical calculation. In the NC ITB discharges, the experimental net current including both bootstrap and beam-driven current is largely reduced compared with that in the L-mode and it drops to almost zero. It seems as if the reversal of bootstrap current takes place in the NC ITB phase but such a view is inconsistent with neoclassical prediction. The observed reduction of the plasma current in the ITB phase is not explained by the neoclassical theory.

Stellarators

Stellarators are toroidal devices where the required rotational transform of the magnetic field lines is generated by external field coils and not via an induced net toroidal plasma current. This confinement scheme has the advantages that, in principle, steady-state plasma operation is possible and that it does not have to brace itself against disruptions of a toroidal plasma current. At the cost of having to give up toroidal symmetry the properties of the stellarator field can be tailored to suit reactor needs. Research focuses on the plasma confinement properties of different stellarator fields and investigates the problems arising when one extrapolates to reactor parameters.

Computational study of three-dimensional equilibria with the bootstrap current

The three-dimensional currentless equilibrium code, HINT is revised so that it can handle equilibria with a net toroidal current, for example the bootstrap current. The revised HINT code is applied to Large Helical Device-like equilibria with good nested flux surfaces.

Modular coils and finite-β operation of a quasi-axially symmetric tokamak

Quasi-axially symmetric tokamaks (QA tokamaks) are an extension of the conventional tokamak concept. In these devices the magnetic field strength is independent of the generalized toroidal magnetic co-ordinate even though the cross-sectional shape changes. An optimized plasma equilibrium belonging to the class of QA tokamaks has been proposed by Nührenberg. It features the small aspect ratio of a tokamak while allowing part of the rotational transform to be generated by the external field. In this article, two particular aspects of the viability of QA tokamaks are explored, namely the feasibility of modular coils and the possibility of maintaining quasi-axial symmetry in the free-boundary equilibria obtained with the coils found. A set of easily feasible modular coils for the configuration is presented. It was designed using the extended version of the NESCOIL code (Merkel, P., Nucl. Fusion 27 (1987) 867). Using this coil system, free-boundary calculations of the plasma equilibrium were carried out using the NEMEC code (Hirshman, S.P., Van Rij, W.I., Merkel, P., Comput. Phys. Commun. 43 (1986) 143). It is observed that the effects of finite β and net toroidal plasma current can be compensated for with good precision by applying a vertical magnetic field and by separately adjusting the currents of the modular coils. A set of fully three dimensional (3-D) auxiliary coils is proposed to exert control on the rotational transform in the plasma. Deterioration of the quasi-axial symmetry induced by the auxiliary coils can be avoided by adequate adjustment of the currents in the primary coils. Finally, the neoclassical transport properties of the configuration are examined. It is observed that optimization with respect to confinement of the alpha particles can be maintained at operation with finite toroidal current if the aforementioned corrective measures are used. In this case, the neoclassical behaviour is shown to be very similar to that of a conventional tokamak.

External kinks in plasmas with helical boundary deformation and net toroidal current

The global ideal magnetohydrodynamic (MHD) stability of plasmas with a prescribed helical boundary deformation and nonvanishing toroidal current is investigated with respect to the (m,n) external modes with n=1,2,3, and m=n+1. L= 2, 3 and mixtures (of both) configurations were studied by systematically varying parameters such as the aspect ratio, the number of equilibrium field periods, the toroidal current density, and the pressure profiles. The study focuses mainly on the q&amp;lt;2 area. It is shown that a fixed helical boundary deformation can stabilize the (m,n) external modes with n=1,2,3, and m=n+1 at values of β≃1%–2%. These modes are unstable in the circular tokamak at the same value of β. If δ is a measure of the plasma boundary deformation, then windows of stability [δminδmax] may exist depending strongly on equilibrium parameters. The results are described in terms of stability zones in the (qaxis,qedge) plane.