Plasma Current Density Profile Research Articles

Tokamak plasma equilibria with n=1 toroidal asymmetry

A general approach of how to construct plasma equilibrium in a tokamak with n=1 violation of toroidal symmetry is proposed. For an arbitrary axisymmetric tokamak plasma equilibrium, there exists the small n=1 deformation of the initial magnetic configuration that keeps the nesting of the magnetic surfaces (as in the initial configuration) and provides plasma equilibrium; such deformation and final equilibrium configuration are calculated analytically. The asymmetric analogue of the Solov'ev's equilibrium with non-degenerated plasma pressure and current density profiles is presented as an example of the application of the developed algorithm.

Optimisation of the poloidal field system for advanced divertor configurations in STEP

The power exhaust proves to be one of the most challenging and concept–defining aspects in the design of a commercial fusion power plant, while the magnetic coil system, capable of supporting advanced exhaust solutions, emerges as one of the main design and cost drivers. Consequently, much effort should be dedicated to the optimisation of a robust global magnetic configuration, which integrates both the plasma and edge scenarios, while ensuring engineering feasibility and compatibility with the available technology. Here we present a multidisciplinary framework employed to analyse, evaluate, and optimise the Spherical Tokamak for Energy Production (STEP) equilibrium configuration, coupled with a viable divertor solution, and a compatible poloidal field coil system. The complexity of this task leads to a multitude of potentially conflicting requirements and competing constraints. We identify interfaces and conflicts between the aspects of the design that were previously considered independently, and highlight the key benefits, trends, and trade–offs between alternative configurations. We demonstrate that advanced exhaust solutions, simultaneously applied to both inboard and outboard divertors, are accessible with feasible coil sets under conditions relevant for STEP. We show that the most promising inner–X geometry, paired with the outer super–X configuration, can significantly enhance divertor’s power handling capability, allowing access to stable detached regimes. The coil set feasibility is further assessed considering its compatibility with the assumed plasma initiation scenario, and with the most demanding plasma current density profiles utilising alternative heating and current drive schemes.

Deep learning approaches to recover the plasma current density profile from the safety factor based on Grad–Shafranov solutions across multiple tokamaks

Many magnetohydrodynamic stability analyses require generation of a set of equilibria with a fixed safety factor q-profile while varying other plasma parameters. A neural network (NN)-based approach is investigated that facilitates such a process. Both multilayer perceptron (MLP)-based NN and convolutional neural network (CNN) models are trained to map the q-profile to the plasma current density J-profile, and vice versa, while satisfying the Grad–Shafranov radial force balance constraint. When the initial target models are trained, using a database of semi-analytically constructed numerical equilibria, an initial CNN with one convolutional layer is found to perform better than an initial MLP model. In particular, a trained initial CNN model can also predict the q- or J-profile for experimental tokamak equilibria. The performance of both initial target models is further improved by fine-tuning the training database, i.e. by adding realistic experimental equilibria with Gaussian noise. The fine-tuned target models, referred to as fine-tuned MLP and fine-tuned CNN, well reproduce the target q- or J-profile across multiple tokamak devices. As an important application, these NN-based equilibrium profile convertors can be utilized to provide a good initial guess for iterative equilibrium solvers, where the desired input quantity is the safety factor instead of the plasma current density.

Characterization of early current quench time during massive impurity injection in JT-60SA

Characteristics of the early current quench (CQ) time in mitigated disruptions are studied for a full-current (5.5 MA) scenario in the JT-60SA superconducting tokamak. Self-consistent evolution of the plasma temperature and current density profiles during the early CQ phase before the plasma moves vertically is simulated using the axisymmetric disruption code INDEX for given impurity source profiles. It is shown that the hollow (flat) impurity density profiles peaks (flattens) the current density, and it causes a temporal change in the internal inductance in this phase. However the resultant CQ time is found to be insensitive to the impurity source profile for the same assimilated quantity. The simulation results are interpreted by the L/R model including the temporal change in the internal inductance as well as the effect of a gap between the plasma and the conducting vessel structures and stabilizing plates. This results will improve the accuracy to estimate the amount of impurity assimilated into plasma from the observed CQ rate in the massive gas injection (MGI) experiment planned in JT-60SA. The accessible range in which the CQ time can be scanned as well as the electron densities to suppress runaway electrons is also shown for different injected amounts of neon, argon, and their deuterium mixture under the limitation of the MGI gas amount. Mitigated disruptions in JT-60SA typically lead to the CQ time shorter than the vessel wall time, which is expected to produce relevant contributions to disruption mitigation in ITER and future reactors.

Numerical study on the peeling–ballooning modes with electron cyclotron wave injection

The influence of electron cyclotron wave (ECW) injection with different deposition positions and injection powers on the evolution of peeling–ballooning (P–B) modes is studied with the BOUT++ code, in which the energy deposition and current drive of the ECW are calculated using a ray tracing code. It is shown that the changes in the profiles of plasma pressure, current density, and resistivity induced by ECW injection can significantly influence the linear property and the nonlinear evolution of P–B modes. For the linear simulation, the ECW deposited at the top of the pedestal makes the high toroidal mode number (n) P–B modes more unstable; however, it stabilizes the medium-n to high-n P–B modes when the ECW is deposited at the middle of the pedestal, and the ECW deposited at the bottom of the pedestal decreases the growth rate of P–B modes with medium-n. Further investigation shows that the injected ECW influences the characteristic of linear P–B modes by changing the diamagnetic effect, magnetic shear, pressure gradient, current density, resistivity, and so on. It is known from the nonlinear simulation that the energy loss caused by the edge localized mode (ELM) with ECW injection deposited at the top of the pedestal is nearly the same as that in the case without ECW injection, while the ECW deposited at the middle and bottom of the pedestal is helpful to decrease ELM energy loss. According to the analyses of the time evolution of the P–B mode toroidal spectrum, the physical mechanism of the decrease in ELM energy loss in the simulation is that ECW injection suppresses the most unstable toroidal harmonic of the P–B mode. On the other hand, the influence of ECW injection on P–B modes becomes more obvious when the power of the injected ECW increases. Moreover, the influence of current driven by the ECW on P–B modes is studied separately in this paper, which plays a different role from the bootstrap current.

Real-time signal processing system based on FPGA for motional Stark effect diagnostic on EAST.

The plasma current density profile plays a key role in the development of a high poloidal beta scenario, which is essential for long-pulse and high-performance plasma operation on a tokamak. Based on the polarimetry technique, a Motional Stark Effect (MSE) diagnostic has been built on the Experimental Advanced Superconducting Tokamak. To be prepared for real-time (RT) feedback control of the plasma current density profile in the future, a RT signal processing system has been developed. The RT signal processing system is composed of three functional modules: analog-to-digital conversion (ADC) module, polarization information extraction module, and digital-to-analog conversion (DAC) module. The final objective of this system is to acquire the polarization information of the MSE. Based on the field-programmable gate array unit, fast Fourier transformation is adopted to process the Photoelastic Modulator (PEM) digital signal, which was converted from a PEM signal via the ADC module. By means of frequency spectrum separation, the components around double modulating frequencies are restored through inverse fast Fourier transformation. Furthermore, the two amplitudes of their corresponding components can be obtained through a digital harmonic analyzer technique. Afterward, the ratio of the two amplitudes is calculated by arc tangent so that the polarization angle is obtained. Finally, the information of this polarization angle is converted into a voltage signal by the DAC module and then output in RT. The test results based on the RT signal processing system are in good agreement with those based on the phase lock-in amplifiers. The working cycle of this system is shorter than 10ms, which meets the requirements of the MSE diagnostic as a RT controller. The algorithm of RT signal processing and the relevant technology applied for building this system are presented in the main body of this paper in detail.

Effect of resonant magnetic perturbations on local plasma current density gradients and neoclassical tearing modes

The effect of externally applied resonant magnetic perturbations (RMPs) on the local equilibrium plasma current density profile is studied numerically based on two-fluid equations in simplified cylindrical geometry. It is found that a moderate RMP below its penetration threshold, via non-linear mode coupling, induces a parallel electric field around its rational surface that can significantly change the local flux-surface-averaged current density gradient. At a given RMP amplitude, the modification of the current density profile increases with increasing electron temperature, and it significantly depends on the bi-normal electron fluid velocity at the resonant surface. The effect of this modification on the magnetic island growth is demonstrated by the example of small m/n = 2/1 islands (m/n being the poloidal/toroidal mode numbers), driven by an unfavorable plasma current density profile and bootstrap current perturbation. The 2/1 mode growth is stabilized by moderate static 4/2 or 6/3 RMPs if the local electron fluid velocity is in the ion drift direction or sufficiently large in the electron drift direction. These results reveal that a weakly three-dimensional equilibrium, containing a moderate 4/2 RMP and the associated shielding current, can be more stable against the 2/1 mode, which often causes tokamak plasma major disruptions.

Understanding the reduction of the edge safety factor during hot VDEs and fast edge cooling events

In the present work, a simple analytical approach is presented in order to clarify the physics behind the edge current density behavior of a hot plasma entering in contact with a resistive conductor. As has been observed in recent simulations [C. R. Sovinec and K. J. Bunkers, Plasma Phys. Controlled Fusion 61(2), 024003 (2019)], when a plasma comes in contact with a highly resistive wall, large current densities appear at the edge of the plasma. The model shows that this edge current originates from the plasma response, which attempts to conserve the poloidal magnetic flux (Ψ) when the outer current is being lost. The loss of outer current is caused by the high resistance of the outer current path compared with the plasma core resistance. The resistance of the outer path may be given by plasma contact with a very resistive structure or by a sudden decrease in the outer plasma temperature (e.g., due to a partial thermal quench or due to a cold front penetration caused by massive gas injection). For general plasma geometries and current density profiles, the model shows that, given a small change in minor radius (δa), the plasma current is conserved to first order [δIp=0+O(δa2)]. This conservation comes from the fact that total inductance remains constant (δL=0) due to an exact compensation of the change in external inductance with the change in internal inductance (δLext+δLint=0). As the total current is conserved and the plasma volume is reduced, the edge safety factor drops according to qa∝a2/Ip. Finally, the consistency of the resulting analytical predictions is checked with the help of free-boundary MHD simulations.

An inverse equilibrium tool to define axisymmetric plasma equilibria

In this paper, a numerical tool, called the inverse equilibrium tool (IET), for the solution of the inverse equilibrium engineering problem is presented. IET is developed in a MATLAB environment and allows for the computation of the coil currents needed to obtain a predetermined plasma shape with well defined plasma global parameters (i.e. total plasma current and total poloidal magnetic flux at the boundary) by solving a constrained minimization problem. IET can be used for the characterization of an existing plasma boundary or for the full design of a new one. Thus, it can be used to generate families of equilibrium configurations and to determine if the desired plasma shape is within the engineering capabilities of the device. The typical features of IET can be summarized as follows: (a) the plasma shape can be arbitrarily defined or characterized by means of a compact analytical functional form; (b) the fixed boundary plasma equilibrium solver allows the user to arbitrarily define the plasma current density profile for both tokamak and reversed field pinch magnetic configurations; (c) the minimization problem for the computation of the equilibrium coil currents is solved with both single and multi-objective optimization approaches. IET was validated considering both limiter and lower single null ITER-like plasma configurations and an upper single null experimental plasma in the RFX-mod tokamak. For all the cases under analysis, IET leads to accurate results for determining the currents that are able to reproduce the direct equilibrium reconstruction. The accuracy of the solution and the simplicity of both user interface and computational algorithm are the key features of the IET computational tool.

A novel code for the simulation of plasma equilibrium and evolution implemented in ANSYS

The simulation of the plasma equilibrium and its evolution is important for the study of plasma physics and for the correct design of fusion devices. For this purpose, a novel code, based on the solution of the Grad-Shafranov equation, has been fully implemented in ANSYS. It exploits the finite element method using the magnetic potential vector formulation. In this approach plasma pressure and current density profiles are described by means of two main parameters: the internal plasma inductance li and the poloidal beta βp. Several ITER equilibria of limiter and diverted plasma configurations have been reproduced and benchmarked with validated codes (e.g. DINA). Being fully implemented in ANSYS this code will easily allow the coupling of the 2D axisymmetric plasma equilibrium equations, describing the plasma behavior, with the full 3D eddy currents equations, describing the surrounding three-dimensional structures. Moreover it will also allow the coupling with the ANSYS mechanical module to perform self-consistent coupled electro-mechanical analyses.

Study of plasma equilibrium reconstruction on HL-2A

An equilibrium reconstruction code is a basic tool for determining the plasma position, boundary, shape and current density profile in a tokamak discharge. The equilibrium reconstruction code CPF has been written to make these calculations. It uses a polynomial to describe the spatial distribution of current density. The coefficients of the polynomial are determined by the best least squares fit to the internal and external magnetic measurement data. A finite difference method is used to solve the Grad-Shafranov equation. The equilibrium magnetic surfaces satisfying the convergence criterion is obtained by Picard iteration. The CPF equilibrium reconstruction is also checked by comparing to results obtained by the equilibrium code SWEQU. The CPF code is stable and has been used for several years.

Integrated modeling of plasma ramp-up in DIII-D ITER-like and high bootstrap current scenario discharges

Time-dependent integrated modeling of DIII-D ITER-like and high bootstrap current plasma ramp-up discharges has been performed with the equilibrium code EFIT, and the transport codes TGYRO and ONETWO. Electron and ion temperature profiles are simulated by TGYRO with the TGLF (SAT0 or VX model) turbulent and NEO neoclassical transport models. The VX model is a new empirical extension of the TGLF turbulent model [Jian et al., Nucl. Fusion 58, 016011 (2018)], which captures the physics of multi-scale interaction between low-k and high-k turbulence from nonlinear gyro-kinetic simulation. This model is demonstrated to accurately model low Ip discharges from the EAST tokamak. Time evolution of the plasma current density profile is simulated by ONETWO with the experimental current ramp-up rate. The general trend of the predicted evolution of the current density profile is consistent with that obtained from the equilibrium reconstruction with Motional Stark effect constraints. The predicted evolution of βN, li, and βP also agrees well with the experiments. For the ITER-like cases, the predicted electron and ion temperature profiles using TGLF_Sat0 agree closely with the experimental measured profiles, and are demonstrably better than other proposed transport models. For the high bootstrap current case, the predicted electron and ion temperature profiles perform better in the VX model. It is found that the SAT0 model works well at high IP (>0.76 MA) while the VX model covers a wider range of plasma current (IP > 0.6 MA). The results reported in this paper suggest that the developed integrated modeling could be a candidate for ITER and CFETR ramp-up engineering design modeling.

Suppressing magnetic island growth by resonant magnetic perturbation

The effect of externally applied resonant magnetic perturbations (RMPs) on the growth of magnetic islands is investigated based on two-fluid equations. It is found that if the local bi-normal electron fluid velocity at the resonant surface is sufficiently large, static RMPs of the same helicity and of moderate amplitude can suppress the growth of magnetic islands in high-temperature plasmas. These islands will otherwise grow, driven by an unfavorable plasma current density profile and bootstrap current perturbation. These results indicate that the error field can stabilize island growth, if the error field amplitude is not too large and the local bi-normal electron fluid velocity is not too low. They also indicate that applied rotating RMPs with an appropriate frequency can be utilized to suppress island growth in high-temperature plasmas, even for a low bi-normal electron fluid velocity. A significant change in the local equilibrium plasma current density gradient by small amplitude RMPs is found for realistic plasma parameters, which are important for the island stability and are expected to be more important for fusion reactors with low plasma resistivity.

Plasma equilibrium based on RF-driven current profile without assuming nested magnetic surfaces on QUEST

In the present RF-driven (ECCD) steady-state plasma on QUEST, the plasma current seems to flow in the open magnetic surface outside of the closed magnetic surface in the low-field region according to the plasma current fitting (PCF) method. The current in the open magnetic surface is due to the orbit-driven current by high-energy particles in the RF-driven plasma. High-energy particles guiding center orbits are calculated as contour plots of conserved variables in the Hamiltonian formulation considering particles in the initial position with different energies and pitch angles satisfying the resonance condition. A negative current appears near the magnetic axis, and a hollow current profile is expected even if the pressure driven current is considered. The equilibrium is fitted within nested magnetic surfaces by J-EFIT coded by MATLAB using the hollow current profile shift toward the low-field region. Although the plasma boundary shape reflects the plasma current density profile, the equilibrium shape fitted by J-EFIT does not coincide with the orbit-driven current profile. However, introducing an extension of the current profile without assuming nested contours into the J-EFIT code appropriately fits the plasma shape with the hollow current profile to the measured magnetic data.

Initial measurements of plasma current and electron density profiles using a polarimeter/interferometer (POINT) for long pulse operation in EAST (invited).

A double-pass, radially viewing, far-infrared laser-based POlarimeter-INTerferometer (POINT) system utilizing the three-wave technique has been implemented for diagnosing the plasma current and electron density profiles in the Experimental Advanced Superconducting Tokamak (EAST). POINT has been operated routinely during the most recent experimental campaign and provides continuous 11 chord line-integrated Faraday effect and density measurement throughout the entire plasma discharge for all heating schemes and all plasma conditions (including ITER relevant scenario development). Reliability of both the polarimetric and interferometric measurements is demonstrated in 25 s plasmas with H-mode and 102 s long-pulse discharges. Current density, safety factor (q), and electron density profiles are reconstructed using equilibrium fitting code (EFIT) with POINT constraints for the plasma core.

CORSICA modelling of ITER hybrid operation scenariosbbExtended from Proc. 24th Int. Conf. on Fusion Energy (San Diego, 2012) IT/P1-13.

The hybrid operating mode observed in several tokamaks is characterized by further enhancement over the high plasma confinement (H-mode) associated with reduced magneto-hydro-dynamic (MHD) instabilities linked to a stationary flat safety factor () profile in the core region. The proposed ITER hybrid operation is currently aiming at operating for a long burn duration (>1000 s) with a moderate fusion power multiplication factor, , of at least 5. This paper presents candidate ITER hybrid operation scenarios developed using a free-boundary transport modelling code, CORSICA, taking all relevant physics and engineering constraints into account. The ITER hybrid operation scenarios have been developed by tailoring the 15 MA baseline ITER inductive H-mode scenario. Accessible operation conditions for ITER hybrid operation and achievable range of plasma parameters have been investigated considering uncertainties on the plasma confinement and transport. ITER operation capability for avoiding the poloidal field coil current, field and force limits has been examined by applying different current ramp rates, flat-top plasma currents and densities, and pre-magnetization of the poloidal field coils. Various combinations of heating and current drive (H&CD) schemes have been applied to study several physics issues, such as the plasma current density profile tailoring, enhancement of the plasma energy confinement and fusion power generation. A parameterized edge pedestal model based on EPED1 added to the CORSICA code has been applied to hybrid operation scenarios. Finally, fully self-consistent free-boundary transport simulations have been performed to provide information on the poloidal field coil voltage demands and to study the controllability with the ITER controllers.

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.

Exploration of one-dimensional plasma current density profile for K-DEMO steady-state operation

Concept study for Korean demonstration fusion reactor (K-DEMO) is in progress, and basic design parameters are proposed by targeting high magnetic field operation with ITER-sized machine. High magnetic field operation is a favorable approach to enlarge relative plasma performance without increasing normalized beta or plasma current. Exploration of one-dimensional current density profile and its optimization process for the K-DEMO steady-state operation are reported in this paper. Numerical analysis is conducted with an integrated plasma simulation code package incorporating a transport code with equilibrium and current drive modules. Operation regimes are addressed with zero-dimensional system analysis. One-dimensional plasma current density profile is calculated based on equilibrium, bootstrap current analysis, and thermal transport analysis. The impact of self and external heating profiles on those parameters is considered self-consistently, where thermal power balance and 100% non-inductive current drive are the main constraints during the whole exploration procedure. Current and pressure profiles are identified as a reference steady-state profile by minimizing the external heating power with desired fusion power.

Coupling circuit model and discharge waveform prediction for Keda Torus eXperiment

A poloidal and toroidal magnetic field coupling circuit model is developed to simulate discharge waveforms of the Keda Torus eXperiment (KTX) reversed field pinch (RFP) to ensure that the design of the power supply systems is able to achieve the typical discharge parameters. The radial profiles of plasma current density and magnetic field used in the coupling model are characterized by modified Bessel function model (MBFM) derived from the well-known Taylor's theory. The power balance in the energy conservation of poloidal and toroidal fields is used to establish the connection between these two fields. The numerical solutions of the coupling show that the KTX power supply system is capable of achieving the designed discharge parameters, such as field reversal parameter (F), pinch parameter (Θ), magnetic field, plasma current and loop voltage. Furthermore, the delay of magnetic field penetration due to the effect of vacuum vessel is also considered in the model.

Application of visible bremsstrahlung to Z(eff) measurement on the Experimental Advanced Superconducting Tokamak.

The multi-channel visible bremsstrahlung measurement system has been developed on Experimental Advanced Superconducting Tokamak (EAST). In addition to providing effective ion charge Zeff as a routine diagnostic, this diagnostic can also be used to estimate other parameters. With the assumption that Zeff can be seen as constant across the radius and does not change significantly during steady state discharges, central electron temperature, averaged electron density, electron density profile, and plasma current density profile have been obtained based on the scaling of Zeff with electron density and the relations between Zeff and these parameters. The estimated results are in good coincidence with measured values, providing an effective and convenient method to estimate other plasma parameters.