Toroidal Plasma Research Articles

Investigations of Alfvén Modes at the Globus-M2 Tokamak Using a V-Band Multifrequency Doppler Reflectometer

We present new information on the development of Alfven modes on the Globus-M2 spherical tokamak. Data have been obtained using a V-band Doppler reflectometer with probing radiation frequencies from 50 to 75 GHz. Аs a multifrequency source of probing radiation, a microwave harmonic synthesizer has been used. As a result of using the new reflectometer, the toroidal Alfven mode localization in a magnetic field of 0.5 T has been obtained. The spectral components of the Alfven mode with Doppler frequency shifts caused by toroidal plasma rotation have been registered. In the central regions of the discharge, so-called “Alfven cascades” have been investigated.

Analysis of a magneto-inertial fusion concept with a field-reversed configuration for proton-boron fuel

The $$ p-^{11}B$$ reaction as much cleaner alternative in fusion reactors has been proposed in this paper. Since this reaction does not involve any radioactive material and also does not release neutrons, it has particularly become attractive for fusion research. Compared with the conventional inertial confinement fusion (ICF), magneto-inertial fusion (MIF) approaches take advantage of an embedded magnetic field to improve plasma energy confinement by reducing thermal conduction. Furthermore, Field Reversed Configuration (FRC) is a toroidal plasma configuration with toroidal current, poloidal magnetic field, and ideally no toroidal field. In this paper, the dynamics of liner compression and fusion burning for $$p-^{11}B$$ fuel have been analyzed and simulated in 2.4-dimensional mode under the initial physical conditions. Moreover, the fusion gain, liner parameters and the magnetized target parameters of $$p-^{11}B$$ fuel have been compared with those of the $$D-T$$ fusion fuel.

A sensitivity analysis of numerical predictions for beryllium erosion and migration in ITER

Abstract The present study addresses the uncertainties that affect the recently performed predictions of beryllium (Be) erosion and migration in ITER using the Monte-Carlo code ERO2.0. The focus of the study is a D–T baseline discharge with fusion power gain Q = 10 , scrape-off layer (SOL) input power P SOL = 100 MW , toroidal plasma current I p = 15 MA , and central toroidal field B t = 5.3 T . The parameter studies used to investigate uncertainties include variations of the radial extrapolation of plasma parameters in the far-SOL (scan A), the assumptions on impact angle distributions (scan B) and the anomalous transport of eroded Be (scan C). Variations by factors ∼ 3 , ∼ 18 and ∼ 2 for scans A, B and C, respectively, are found.

Systematic simulation studies on the penetration of resonant magnetic perturbations in an Experimental Advanced Superconducting Tokamak

The penetration properties of the n = 1 resonant magnetic perturbations (RMPs) with toroidal rotation are systematically studied by the upgraded three-dimensional toroidal magnetohydrodynamic code CLTx, through both linear and nonlinear simulations. It is found that in the presence of toroidal plasma rotation, the saturation state for high resonant harmonics is obtained in linear simulations due to the mode becoming unlocked from the internal magnetic islands. In nonlinear simulations, nonlinear effects become important when the toroidal plasma rotation is not included. The zonal component resulting from the nonlinear mode coupling is necessary for the saturation of the whole system including the internal kink mode and the m /n = 2/1 tearing mode. The simulations of RMP penetration demonstrate that the mode coupling is associated with the toroidal effect rather than nonlinear effects. With a low resistivity close to the experimental value, the single-harmonic-RMP is hard to penetrate the mode-rational surface because of the plasma screening effects, resulting in a truncation of the radial mode structure. On the other hand, the non-resonant components in the multiple-harmonic-RMP could largely reduce the effect of the plasma shielding, which leads to that the RMP is able to penetrate deeply into the central plasma region through the poloidal harmonic coupling.

A Data-Assimilation Based Method for Equilibrium Reconstruction of Magnetic Fusion Plasma and its Application to Reversed Field Pinch

Carbon-free energy sources are essential to avoid global warming, and nuclear fusion is expected to play a major role in achieving clean and sustainable energy. In the development of magnetic fusion, there exist a lot of issues related with plasma equilibrium to be studied extensively, typical representative of which is a problem of equilibrium reconstruction of plasma. In this paper we propose a new method of equilibrium reconstruction for fusion plasma based on the data assimilation. Aiming at dealing not only with axisymmetric toroidal plasmas but also with more general toroidal plasmas, we formulate the problems of equilibrium reconstruction in generalized forms and derive methods to solve them. We also propose a method for applying the equilibrium reconstruction method to the reversed field pinch (RFP), and it is applied to a real RFP experimental apparatus for its evaluation. It is shown through numerical experiments that the proposed equilibrium reconstruction method works well with reasonable accuracy. And it is also shown through real experiments applying the RFP apparatus that the equilibrium of RFP plasma is appropriately reconstructed.

Исследования альфвеновских мод на токамаке Глобус-М2 с использованием многочастотного допплеровского рефлектометра V-диапазона

New information on the development of Alfvén modes in the Globus-M2 spherical tokamak is presented. The data were obtained using a V-band Doppler reflectometer with probing radiation frequencies from 50 to 75 GHz. A microwave harmonic synthesizer was used as a multifrequency probing source. As a result of using a new reflectometer, the localization of the toroidal Alfvén eigenmode has been determined at a magnetic field of 0.5 T. The spectral components of the Alfvén mode with Doppler frequency shifts due to toroidal plasma rotation have been recorded. The so-called Alfvén cascades have been investigated in the central regions of the discharge.

Effect of ITER CS and PF magnets on EM loads outside vacuum vessel at plasma disruption events

One of the most crucial issues in the design of the ITER machine is the electromagnetic (EM) loads associated with eddy currents induced in the conducting structures during plasma disruptions. The ITER database contains tens of calculation scenarios for possible plasma disruption events. The duration of these scenarios is usually limited by the end of the plasma current quench when the toroidal plasma current decreases to zero. For further EM analysis, the currents in the poloidal field coils are conventionally assumed constant after the end of the current quench. Such approach is not good for estimation of electromagnetic loads acting on the tokamak components located outside vacuum vessel. A possible way to solve this problem is to employ pre-determined coil current variations over the entire period of observation including time interval after the current quench. This paper describes an approach to such electromagnetic calculations and comparative results for selected cases with/out an extended current-time specification.

Specific features of eddy current analysis with ANSYS® for fast plasma current decay event in W7-X

During the second operation phase (OP1.2) of the most advanced stellarator Wendelstein 7-X (W7-X), some events of fast plasma current decay with a time constant of about 1 ms were observed (for both toroidal and diamagnetic plasma currents). The events were triggered by Electron Cyclotron Current Drive (ECCD) and were much faster than the assumptions considered during the design phase of W7-X components: 100 kA and 2.7 MA plasma current discharge with the time constants of 140 and 50 ms for toroidal and diamagnetic currents respectively. During the observed 1 ms discharge of maximum expected plasma currents, significant eddy currents are expected to be induced in some components with resulting electro-magnetic (EM) forces. In order to avoid unnecessary changes on as-built components, evaluation of the eddy currents / EM forces with high accuracy is required, if the conservative simplified estimation shows criticality. As a result, a sophisticated EM model with plasma currents, superconducting (sc) coils, plasma vessel (PV) and multiple ports is developed in ANSYS® using the new element type SOLID236 / 237 (edge-based formulation), which is much more accurate than the legacy elements SOLID97 (vector potential formulation). The specific features of using SOLID236 elements for eddy current analysis are studied and presented in this paper. This includes the application of boundary conditions on sector EM model, modelling of excitation currents, field and eddy current accuracy, skin effect, shielding effect, voltage in conducting components, etc. Most of the issues are studied in comparison with SOLID97 elements. Finally, the pros and cons of SOLID236 and SOLID97 elements are summarized, and the experiences during the W7-X EM analyses are presented.

Influence of increased magnetic field on Alfvén eigenmodes on upgraded spherical tokamak Globus-M2

During modernization of the Globus-M tokamak, toroidal magnetic field and plasma current were increased, and a number of diagnostics were upgraded, which made it possible to study phenomena associated with the excitation of Alfvén waves in a spherical tokamak in a wider range of plasma parameters. In the experiments with neutral beam injection, the dependences of fast particle losses initiated by the toroidal Alfvén eigenmodes (TAE) on their magnitude in the magnetic field range of 0.4 – 0.7 T and currents of 180 – 330 kA were acquired. Resulting dependences confirm previously obtained results and indicate a decrease in losses with increasing magnetic field and plasma current. At the same time, a number of new phenomena, that have never been observed on Globus-M were detected. In experiments with neutral beam injection at the current ramp up stage, Alfvén cascades (AC) in the frequency range of 100 – 300 kHz were observed for the first time. By means of the Doppler backscattering diagnostics (DBS), it was shown that ACs are localized closer to magnetic axis unlike TAE. Also, during low hybrid wave current drive (LHCD) experiments, global Alfvén eigenmodes (GAE) were detected at a frequency close to 1 MHz, apparently driven in the resonance with runaway electron beam. Detected global eigenmodes are also able to arise in ohmic discharges, however, their magnitude is lower.

Anomalous transport due to large coherent structures in a magnetized toroidal plasma

Anomalous transport due to large coherent structures, or coherent events, is studied experimentally in a magnetized toroidal discharge plasma. The present analysis emphasizes anomalous plasma losses as well as transport of electron thermal energy density across magnetic field lines. The experiment was carried out in the Blaamann device at the University of Tromsø. The diagnostics are based on data for potential, density and electron temperature variations as detected by Langmuir probes. Most of the data analysis uses conditional sampling. The flux of thermal energy density can be broken down into several components which are analyzed separately. Experimental means for obtaining the space-time variation of the complete polarization drifts are demonstrated, and the results compared with the fluctuating -velocities. For the present conditions these polarization drifts contribute only little to the plasma losses, but for other discharge parameters in heavier gases they can be important. Our results show that while the density, the potential and the electric field variations are dominated by large scales, the vorticity of the -flow as well as the ion polarization drifts are strongly intermittent.

Persistent random walks of charged particles across magnetic field lines.

We investigate the time evolution of the mean location and variance of a charged particle subject to random collisions that are Poisson distributed. The particle moves on a plane and is subject to a magnetic field applied perpendicular to the plane, so it is constrained to move in circles in the absence of collisions. We develop a procedure that yields analytic expressions of the mean and variance. These results are valid for arbitrary times after the start of the walk, including early on when, on average, less than one collision is expected. As an example of their applicability, we use these expressions to model experimental results and simulations of suprathermal ions propagating in a turbulent plasma in TORPEX (the TORoidal Plasma EXperiment).

Progress of advanced transport modeling of toroidal plasmas

Integrated modeling is required for predicting the behavior of burning plasma in fusion devices. Core plasma transport modeling is a key component which describes the time evolution of plasma profile. Between the simple 1D diffusive transport model and the large-scale microscopic turbulent transport simulation, advanced transport modeling which requires decent computational resource is desired. Two approaches, 1D fluid transport modeling and 3D kinetic transport modeling, are discussed.

Pedestal electron collisionality and toroidal rotation during ELM-crash suppression phase under n = 1 RMP in KSTAR

Excellent reproducibility of KSTAR resonant magnetic perturbation (RMP)-driven, edge-localized mode (ELM)-crash suppression enables us to construct a database reliably for the study of ELM-crash suppression conditions. To establish a high-fidelity database, we have selected one of the frequently used RMP configurations in KSTAR, n = 1, +90° phasing RMP-coil configuration. A series of fitting curves based on edge profile diagnostics data is used for normalized electron collisionality (νe*) and plasma toroidal rotation (Vtor) at pedestal top. Since ITER is expected to employ slowly rotating, low-collisionality, high-density plasmas whose conditions are not readily accessible in the existing devices, the exploration and understanding of these two parameters would be important not only for RMP-driven, ELM-crash-suppression physics but also for the success of ITER. The data points for the ELM-crash suppression phase are in the range of 0.2 < νe,ped*< 1.1 with Zeff = 2 assumption and Vtor,ped> 40 km/s. Suppression thresholds or boundaries in νe,ped* or Vtor,ped are not confirmed in the investigated parameter ranges so far. The KSTAR database still needs additional experimental datasets in ITER-relevant conditions (νe,ped* ∼ 0.1 and low-torque low-rotation) to confirm the boundary of the ELM-crash suppression window in KSTAR and reduce the uncertainties of the RMP ELM-crash control technique in ITER. In both νe,ped* and Vtor,ped parameters, the phase-space distribution of the ELM-crash suppression has no clear distinction from that of the ELM-crash mitigation. Linear discriminant analysis provides a linear combination of parameters relevant to ELM-crash suppression, best separating two data categories. Recursive feature elimination indicates that ne,ped and IRMP, as well as νe,ped* and Vtor,ped, are critical variables in the separation of the data groups.

Nonlinear dynamics of the fishbone-induced alpha transport on ITER

The fishbone-induced transport of alpha particles is computed for the ITER 15 MA baseline scenario (ITER Physics Expert Group on Energy Drive 1999 Nucl. Fusion 39 2471) using the non-linear hybrid Kinetic-MHD code XTOR-K. Two limit cases have been studied, in order to analyse the characteristic regimes of the fishbone instability: the weak kinetic drive limit (Berk et al 1999 Phys. Plasmas 6 3102) and the strong kinetic drive limit (Zonca et al 2015 New J. Phys. 17 013052). In both those regimes, characteristic features of the n = m = 1 fishbone instability are recovered, such as a strong up/down-chirping of the mode frequency, associated with a resonant transport of trapped and passing alpha particles. The effects of the n = m = 0 sheared poloidal and toroidal plasma rotation are taken into account in the simulations. The shear is not negligible, which implies that the fishbone mode frequency has a radial dependency, impacting the wave-particle resonance condition. Phase space hole and clump structures are observed in both non-linear regimes, centered around the precessional and passing resonances. These structures remains attached to the resonances as the different mode frequencies chirp up and down. In the non-linear phase, the transport of individual resonant trapped particles is identified to be linked to mode-particle synchronization. On this basis, a partial mechanism for the non-linear coupling between particle transport and mode dominant down-chirping is proposed. The overall transport of alpha particles through the q = 1 surface is of order 2–5\\% of the initial population between the simulations. The loss of alpha power is found to be directly equal to the loss of alpha particles.

Destabilization of Alfvénic activity by non-axisymmetric magnetic field induced rotation braking in KSTAR tokamak

We report an experimental observation of destabilization of the Alfvénic activity by non-axisymmetric (3D) magnetic field induced toroidal rotation braking in the KSTAR tokamak. The toroidicity-induced Alfvén eigenmodes (TAEs) are destabilized when toroidal plasma rotation is reduced down to the minimum to approach near-zero rotational shear by 3D magnetic braking. This observation indicates that the stability of the TAEs is strongly correlated to the plasma rotation that modifies Alfvén continuum. The TAE frequency predicted by stability calculation with the reduced rotation is in a good agreement with the experimental measurement. It is suggested that the impact of 3D magnetic field and rotation on the Alfvénic modes and associated fast ion confinement should be considered for the operation of magnetic confinement fusion devices.

An Overview of the Hybrid Illinois Device for Research and Applications Material Analysis Test-stand (HIDRA-MAT)

The Hybrid Illinois Device for Research and Applications (HIDRA) at the University of Illinois at Urbana-Champaign is a toroidal plasma device that enables fusion plasma-material interaction testing with both stellarator and tokamak plasmas. HIDRA’s long-pulse steady state stellarator plasmas provide a testbed for plasma facing component (PFC) plasma exposures. The HIDRA Material Analysis Test-stand (HIDRA-MAT) is a material characterization module attached to HIDRA that is being designed and fabricated to include thermal desorption spectroscopy and laser induced breakdown spectroscopy systems for in-vacuo PFC characterization. A specialized rotatable sample holder positions the sample for liquid metal droplet application from a liquid metal droplet injector on HIDRA-MAT. Early experiments look to investigate the effect liquid lithium has on porous tungsten samples’ retention of H, D, and He after plasma exposure. Preliminary results from a dual residual gas analyzer system show the ability to differentiate D2 and He in HIDRA-MAT. This work aims to advance the understanding of liquid metal PFCs and further the design and development of new fusion PFCs and technologies.

Progress in extending high poloidal beta scenarios on DIII-D towards a steady-state fusion reactor and impact of energetic particles

To prepare for steady-state operation of future fusion reactors (e.g. the International Thermonuclear Experimental Reactor and China Fusion Engineering Test Reactor (CFETR)), experiments on DIII-D have extended the high poloidal beta (βP) scenario to reactor-relevant edge safety factor q95 ∼ 6.0, while maintaining a large-radius internal transport barrier (ITB) using negative magnetic shear. Excellent energy confinement quality (H98y2 > 1.5) is sustained at high normalized beta (βN ∼ 3.5). This high-performance ITB state with Greenwald density fraction near 100% and qmin ≥ 3 is achieved with toroidal plasma rotation Vtor ∼ 0 at ρ ≥ 0.6. This is a key result for reactors expected to have low Vtor. At high βP (≥1.9), large Shafranov shift can stabilize turbulence leading to a high confinement state with a low pedestal and an ITB. At lower βP (<1.9), negative magnetic shear in the plasma core contributes to turbulence suppression and can compensate for reduced Shafranov shift to continue to access a large-radius ITB and excellent confinement with low Vtor, consistent with the results of gyrofluid transport simulations. These high-βP cases are characterized by weak/no Alfvén eigenmodes (a.e.) and classical fast-ion transport. At high density, the fast-ion deceleration time decreases and Δβfast is lower; these reduce a.e. drive. The reverse-shear Alfvén eigenmodes are weaker or stable because the negative magnetic shear region is located at higher radius, away from the peaked fast-ion profile. Resistive wall modes can be a limitation at simultaneous high βN, low internal inductance, and low rotation. Analysis suggests that additional off-axis external current drive could provide a more stable path at reduced q95. Based on a DIII-D high-βP plasma with large-radius ITB, two scenarios are proposed for CFETR Q = 5 steady-state operation with ∼1 GW fusion power: a lower- ( ∼ 0.66) and a higher- ( ∼ 0.75) case. Using a Landau closure model, multiple energetic particle (EP) effects on the a.e. stability are analyzed modifying the growth rate of the a.e.s triggered by the neutral-beam-injection EPs and alpha particles, although the stabilizing/destabilizing effect is weak for the cases analyzed. The stabilizing effects of the combined EP species β, energy, and density profile in CFETR need further investigation.

On the polarization of shear Alfvén and acoustic continuous spectra in toroidal plasmas

In this work, the FALCON code is adopted for illustrating the features of shear Alfvén and sound continuous spectra in toroidal fusion plasmas. The FALCON codes employ the local Floquet analysis discussed in (Phys. Plasmas, vol. 26, issue 8, 2019, 082502) for computing global structures of continuous spectra in general toroidal geometry. As particular applications, reference equilibria for the divertor tokamak test and ASDEX Upgrade plasmas are considered. In particular, we illustrate the importance of mode polarization for recognizing the physical relevance of the various branches of the continuous spectra in the ideal magnetohydrodynamics limit. We also analyse the effect of plasma compression and the validity of the slow sound approximation.

Observation of helical m/n = 1/1 saturated steady mode in EAST pure electron heating scenario with q0 ≼ 1

We observed for the first time a helical m/n = 1/1 (m is the poloidal mode number and n is the toroidal mode number) saturated steady mode (SSM) in the center of the EAST electron heating dominant plasma where the core safety factor was close to but slightly below unity and the profile had an extreme peak at the plasma center ( is the electron temperature). An internal crash can be caused by the dynamics of the SSM, and its influence on the electron temperature profile is as large as that of a typical sawtooth crash (SC) in magnitude. Due to the weak magnetic shear in the core, the SSM regularly exhibits an m/n = 2/2 harmonic component. For low shear auxiliary heated plasma, the SSM cannot cause the degradation of plasma confinement ( or ), but an SC is indeed a harmful factor. Three-dimensional resistive magnetohydrodynamic simulations with a realistic EAST strong elongated magnetic configuration, a high Lundquist number () and a strong central peaked pressure profile, have been made to demonstrate the formation of the SSM in the case of and the destabilization of the SC in another case with . These nonlinear simulation results agree well with the observations of both the SSM and SC in EAST electron heating dominant discharges with an extreme central peaked . An M3D simulation found that the SC is caused by additional newly developed harmonics of the m/n = 1/1 helical instability. Nonlinear simulation also predicted a modulation of the SSM on current in the plasma core, which is favorable for maintaining in the plasma core. Furthermore, nonlinear simulation also showed that a small toroidal plasma flow can be generated by the SC.

Simultaneous feedback control of toroidal magnetic field and plasma current on MST using advanced programmable power supplies

Programmable control of the inductive electric field enables advanced operations of reversed-field pinch (RFP) plasmas in the Madison Symmetric Torus (MST) device and further develops the technical basis for ohmically heated fusion RFP plasmas. MST’s poloidal and toroidal magnetic fields (B p and B t) can be sourced by programmable power supplies (PPSs) based on integrated-gate bipolar transistors (IGBT). In order to provide real-time simultaneous control of both B p and B t circuits, a time-independent integrated model is developed. The actuators considered for the control are the B p and B t primary currents produced by the PPSs. The control system goal will be tracking two particular demand quantities that can be measured at the plasma surface (r = a): the plasma current, I p ∼ B p(a), and the RFP reversal parameter, F ∼ B t(a)/Φ, where Φ is the toroidal flux in the plasma. The edge safety factor, q(a) ∝ B t (a), tends to track F but not identically. To understand the responses of I p and F to the actuators and to enable systematic design of control algorithms, dedicated experiments are run in which the actuators are modulated, and a linearized dynamic data-driven model is generated using a system identification method. We perform a series of initial real-time experiments to test the designed feedback controllers and validate the derived model predictions. The feedback controllers show systematic improvements over simpler feedforward controllers.