Quasi-single Helicity Research Articles

Combined Capacitor–Resistor Energy Transfer System to Increase Plasma Current in RFX-Mod2

RFX-mod is an experimental fusion device, which contributes to plasma physics studies both in reversed field pinch (RFP) and tokamak configurations. Its high flexibility, due to an active magnetohydrodynamic (MHD) control system and the modular coils power supply (CPS) system, allowed operating RFX-mod in a wide range of experimental conditions with a plasma current up to 2 MA. Experiments with such high plasma current allowed the study on new promising confinement regimes, dominated by a self-organization process with the generation of a helical structure in the plasma core. Presently, RFX-mod is under a significant upgrade (RFX-mod2) to extend the operational scenarios increasing the proximity between the conductive shell and the plasma. This main modification of the magnetic front-end, together with other main improvements, is expected to increase the performance of the machine in both magnetic configurations. In the frame of the studies to exploit the new potential of RFX-mod2 achieving a higher plasma current and longer flat-top duration, a solution based on additional magnetic energy storage has already been proposed. The study of RFP physics at higher plasma current could be crucial to confirm positive trends, such as electron temperature and persistence of quasi single helicity states with the plasma current, and to explore and achieve improved confinement states. This article presents an alternative reconfiguration of the poloidal power supply system of RFX-mod2 based on a combined resistor–capacitor energy transfer system. This system allows to store energy in capacitor banks during the first phase of the plasma current ramp-up and release it to the plasma when the magnetizing current changes polarity, driving the plasma current over 2.5 MA. The proposed upgrade does not involve radical poloidal CPS modifications, maintaining the present converters number and ratings and remaining within the power limits of the main power transformers (300 MVA).

The isotope effects in RFP magnetic configuration

The comparison between deuterium and hydrogen plasmas at high current in the RFX-mod experiment proves that the reversed field pinch configuration experiences the isotope effect in a way analogous to tokamak experiments. Both energy and particle confinement exhibit a favourable scaling with the isotope mass M i , respectively, as and as . This effect is mainly due to the mitigation of transport at the edge, which is driven by electrostatic fluctuations, although a mitigation of the stochastic transport in the plasma core is also observed. As in tokamaks, the MHD properties are modified when the gas mass is changed. The most evident modification regards the spectrum of tearing modes that are more stable in deuterium, so that the duration and the purity of quasi single helicity (QSH) phases are enhanced. The thermal structures that develop during the QSH phases enclose a plasma volume that is wider in deuterium discharges than in hydrogen ones.

Robust analysis of space-, time-, and energy-resolved soft x-ray measurements of magnetically confined fusion plasmas (invited).

A novel compact multi-energy soft x-ray (ME-SXR) diagnostic based on the PILATUS3 100K x-ray detector has been developed in collaboration between the Princeton Plasma Physics Laboratory and the University of Wisconsin-Madison and tested on the Madison Symmetric Torus (MST) reversed-field pinch. This solid-state photon-counting detector consists of a two-dimensional array of ∼100 000 pixels for which the lower photon absorption cutoff energy can be independently set, allowing it to be configured for a unique combination of simultaneous spatial, spectral, and temporal resolution of ∼1cm, 100eV, and 500Hz, respectively. The diagnostic is highly versatile and can be readily adapted to diverse plasma operating conditions and scientific needs without any required downtime. New results from improved-confinement and quasi-single helicity plasmas in the MST demonstrate how the detector can be applied to study multiple aspects of the evolution of magnetically confined fusion-grade plasmas. These include observing the evolution of thermal emissivity, characterizing the energy of mid-Z excitation lines, extracting the Te profile, and observing the evolution of non-thermal populations. A technique for integrating the ME-SXR diagnostic into an integrated data analysis framework based on Bayesian inference is also presented. This allows ME-SXR measurements to be combined with data for complementary diagnostics in order to simultaneously infer Te and nZ from all available information.

Helical plasma-wall interaction in the RFX-mod: effects of high-n mode locking

The purpose of this paper is to analyse higher toroidal harmonics m = 1 with 7 < n < 23 (secondary modes) in the quasi single helicity, reversed field pinch plasma in the RFX-mod device. The quasi single helicity is an improved confinement state characterized by a dominant mode m/n = 1/7, rotating along the toroidal direction. The spectroscopic measurements in the boundary plasma show footprints of a localized plasma deformation called ‘phase locking’, which can be described as an interferential pattern of toroidal Fourier harmonics. In the locking region the magnetic field lines are deformed in large poloidal lobes hitting the plasma facing components, a mechanism similar to the ‘homoclinic lobes’ observed in the Tokamak divertor with RMP application. Correspondingly, the magnetic connection length to the wall presents a strong decrease (‘hole’) with increased plasma-wall interaction, which fortunately is not stationary, but jumps in the toroidal direction thanks to the effective action of the RFX-mod feedback system. The global plasma wall interaction is the superposition of a rotating helix and of the localized toroidal deformation due to the secondary modes, which mirrors the local emission and particle influx from the wall. The local edge perturbation impacts also on the global plasma performance: a threshold to obtain an electron transport barrier has been identified. An improvement in plasma performance is expected in the upgraded device RFX-mod2, where the magnetic boundary will be modified to decrease the edge field deformation by a factor about 2.

Coherent magnetic structures in self-organized plasmas

The concept of Lagrangian coherent structures (LCS) has been recently applied to complex magnetic configurations in plasmas in order to find and characterize their main structural features. LCS make it possible to separate regions inside these configurations where field lines exhibit a different kind of behavior. In the present article, first we review the main features and uses of this technique and then apply it to the study of configurations that evolve into a self-organized quasi-single helicity state referring in particular to results obtained in the reversed-field pinch experiment in Padua.

Electron thermal confinement in a partially stochastic magnetic structure

Using a high-repetition-rate Thomson scattering diagnostic, we observe a peak in electron temperature Te coinciding with the location of a large magnetic island in the Madison Symmetric Torus. Magnetohydrodynamic modeling of this quasi-single helicity plasma indicates that smaller adjacent islands overlap with and destroy the large island flux surfaces. The estimated stochastic electron thermal conductivity (≈30 m2/s) is consistent with the conductivity inferred from the observed Te gradient and ohmic heating power. Island-shaped Te peaks can result from partially stochastic magnetic islands.

Resistive MHD modelling of the quasi-single helicity state in the KTX regimes

The potential formation of a quasi-single-helicity (QSH) state in the Keda Torus eXperiment (KTX) is investigated in resistive MHD simulations using the NIMROD code. We focus on the effects of finite resistivity on the mode structure and characteristics of the dominant linear and nonlinear resistive tearing-mode in a finite β, cylindrical configuration of a reversed field pinch model for KTX. In the typical resistive regimes of KTX where the Lundquist number , the plasma transitions to a steady QSH state after evolving through an initial transient phase with multiple helicities. The dominant mode of the QSH state develops from the dominant linear tearing mode instability. In the lower β regime, the QSH state is intermittent and short in duration; in the higher β regime, the QSH state persists for a longer time and should be more easily observed in experiments.

Thermal properties of three sub-states of quasi-single helicity states on RFX-mod

Quasi-single helicity (QSH) state has been widely observed in reversed field pinch devices to sustain thermal structures, enclosed by steep temperature gradients interpreted as electron internal transport barriers (eITB). Within the evolution of a QSH cycle, three sub-states can be identified in the RFX-mod experiment, named DAx, SHAxn and SHAxw, where the subscript n and w indicate narrow and wide thermal structures, respectively. Such sub-states feature different magnetic topologies as well as different width of the thermal structures. This paper presents a characterization of the three QSH sub-states mainly devoted to describe the properties of the eITB temperature gradients. The analyses show a decreasing trend of the absolute value of the thermal gradient as the dominant mode increases. Further study on the thermal diffusivity confirms that these behaviors are essentially due to the local change of the heat transport. Besides, the thermal gradient in DAx and SHAxn groups shows an increasing trend with the decrease of secondary modes. Such behavior has been studied and it can be explained by stochastic transport in agreement with what found for SHAXw (Lorenzini et al 2012 Nucl. Fusion 52 062004). As for SHAxw group, the thermal gradient suddenly decreases with respect to DAx and SHAxn values. This behavior can still be explained in the framework of stochastic transport considering the structure of magnetic perturbations at the location of thermal gradients (Lorenzini et al 2016 Phys. Rev. Lett. 116 185002). The total energy confinement time has also been evaluated, adopting a more appropriate method. The result shows that the energy confinement time increases up to 40% from DAx to SHAxw.

Features of the Electron-Temperature Distribution in a Low-Aspect-Ratio Reversed Field Pinch Plasmas

The features of the two-dimensional (2D) line-averaged electron-temperature (Te) distribution in low-aspect-ratio (low-A) reversed field pinch (RFP) plasmas are reported. We successfully obtain the time evolution of line-averaged Te images in a low-A RFP plasma with a soft X-ray (SXR) camera with two pin-holes for two-kinds of absorber foils in cojunction with a high-speed camera. Our obtained line-averaged Te is positively correlated with plasma current (Ip), and data are consistent with core and edge Te obtained by other methods. In multi helicity (MH) discharge, up-down symmetry is not changed as time goes by. On the other hand, tilting of the high temperature region is observed quasi-periodically in quasi-single helicity (QSH) discharge, with a steeper Te gradient appearing during the QSH state.

Thermal transport dynamics in the quasi-single helicity state

A dynamical model describing oscillations between multiple and single helicity configurations in the quasi-single helicity (QSH) state of the reversed field pinch [P. W. Terry and G. G. Whelan, Plasma Phys. Controlled Fusion 56, 094003 (2014)] is extended to include electron temperature profile dynamics. It is shown that QSH dynamics is linked to the electron temperature profile because the suppression of mode coupling between tearing modes proposed to underlie QSH also suppresses magnetic-fluctuation-induced thermal transport. Above the threshold of dominant-mode shear that marks the transition to QSH, the model produces temperature-gradient steepening in the strong shear region. Oscillations of the dominant and secondary mode amplitudes give rise to oscillations of the temperature gradient. The phasing and amplitude of temperature gradient oscillations relative to those of the dominant mode are in agreement with experiment. This provides further evidence that the model, while heuristic, captures key physical aspects of the QSH state.

Magnetic fluctuation behavior during the transition between quasi-single helicity and multi helicity states in the reversed-field pinch plasma

We measured the variation of magnetic and electrostatic fluctuations observed during the transition between the quasi-single helicity (QSH) and multi helicity (MH) states in the edge region of the Toroidal Pinch Experiment-Reversed eXperiment reversed-field pinch plasma [Yagi et al., Fusion Eng. Des. 45, 421 (1999)]. The high-frequency magnetic fluctuations largely decrease at the start of the QSH state. During the QSH state, the toroidal and radial magnetic fluctuations slightly increase again between 12 and 18 kHz but the decrease in the poloidal magnetic fluctuation is maintained. The confinement of fast electrons may be improved in the period of the QSH state although the radial magnetic fluctuation increases between 12 and 18 kHz. It is suggested that the improved confinement of fast electrons may be obtained by the decrease in the fast radial magnetic fluctuation having the frequency higher than 20 kHz in the period of the QSH state. Contrarily, the transition from QSH to MH states occurs with the increase in the slow toroidal magnetic fluctuation having the frequency lower than 10 kHz. The QSH state may bring a good confinement of fast electrons by the reduced high-frequency magnetic fluctuation compared with the MH state.

The isotope effect in the RFX-mod experiment

The isotope effect in the reversed field pinch magnetic configuration is investigated for the first time comparing hydrogen and deuterium plasmas of the RFX-mod experiment. The picture which emerges has several similarities with the results of tokamak experiments, since plasma properties improve increasing the isotope mass Mi. The electron temperature is higher in deuterium than in hydrogen in a large fraction of the plasma volume (r/a < 0.9) and the energy confinement time scales . The particle influx is significantly reduced and the particle confinement time scales . The effect on confinement is mainly due to the mitigation of transport at the edge, internally to the scrape-off layer where long range correlations have been detected. Moreover a modification of magnetohydrodynamic properties is observed. Increasing Mi brings about a stabilizing effect on tearing modes, and increases the tendency of plasma to produce quasi-single helicity, which becomes longer, purer and more resilient to weak sawtoothing. Finally, the dynamo process that sustains the magnetic configuration becomes more discrete.

Light impurity transport studies with solid pellet injections in the RFX-mod reversed-field pinch

The transport of injected impurities is investigated in the multiple helicity (MH) and improved confinement quasi single helicity (QSH) magnetic regimes of RFX-mod reversed-field pinch. Impurities are introduced through injections of room temperature pellets of carbon (in MH and QSH) and lithium (in MH). Simulation of experimental spectroscopic measurements, including line and soft x-rays emission, electron density and radiated power is carried out with a 1D collisional-radiative impurity transport code, allowing to determine the transport parameters: diffusion coefficient and convective velocity. The transport coefficients were found close to those deduced in previous experiments through the introduction of Ni and Ne, confirming the existence of an external velocity barrier also for light impurities.

Time-dependent behavior in a transport-barrier model for the quasi-single helcity state

Time-dependent behavior that follows from a recent theory of the quasi-single-helicity (QSH) state of the reversed field pinch is considered. The theory (Kim and Terry 2012 Phys. Plasmas 19 122304) treats QSH as a core fluctuation structure tied to a tearing mode of the same helicity, and shows that strong magnetic and velocity shears in the structure suppress the nonlinear interaction with other fluctuations. By summing the multiple helicity fluctuation energies over wavenumber, we reduce the theory to a predator–prey model. The suppression of the nonlinear interaction is governed by the single helicity energy, which, for fixed radial structure, controls the magnetic and velocity shearing rates. It is also controlled by plasma current which, in the theory, sets the shearing threshold for suppression. The model shows a limit cycle oscillation in which the system toggles between QSH and multiple helicity states, with the single helicity phase becoming increasingly long-lived relative to the multiple helicity phase as plasma current increases.

Fast ion confinement in the three-dimensional helical reversed-field pinch

Fast ions are well confined in the stochastic magnetic field of the multiple-helicity (MH) reversed-field pinch (RFP), with fast ion confinement times routinely a factor of 5 to 10 higher than thermal confinement time. Recent experiments have examined the behavior and confinement of beam-born fast ions in the three-dimensional (3D) helical RFP state. In lower current discharges, where the onset of the helical state is uncertain, high power neutral beam injection (NBI) tends to suppress the transition to the single helicity mode. In high current discharges (Ip ∼ 0.5 MA), where the onset of n = 5 single helicity is quite robust, a short blip of NBI is used to probe the confinement of fast ions with minimal perturbation to the 3D equilibrium. The fast ion confinement time is measured to be substantially lower than fast ions in comparable MH RFP states, and there is a strong dependence on the strength of the helical perturbation. The established helical equilibrium is stationary in the laboratory frame but the locking occurs over the entire range of possible phase with respect to the Madison Symmetric Torus vessel. This effectively scans both the location of the NBI with respect to the helical structure and the pitch of the NBI-born fast ions. Fast ion confinement is observed to be insensitive to this angle, and in fact counter-NB injection into quasi-single helicity discharges shows fast ion confinement times similar to co-injection cases, in contrast to the MH RFP, where counter-injected fast ion confinement time is substantially lower.

Hall magnetohydrodynamic model of the quasi-single helicity self-organization of RFP

In the framework of two-fluids Hall magnetohydronynamic description of a paramagnetic z-pinch with the low safety factor (q≪1 on the pinch axis), the theoretical model of kink mode stabilization is developed. It is shown that global kink oscillations of paramagnetic pinch, whose instability had been found in the single-fluid MHD theory, generate due to the Hall effects a rotation of plasma, which, in turn, stabilizes the kinks of the plasma column. The fluctuations are considered in terms of the cylindrical boundary problem for the pinch equilibrium with arbitrary components of the magnetic field, (0,Bθ,BZ), hydrodynamic velocity, (0,Vθ,Vz), and the Hall parameter. The consideration is fulfilled in approximation of "cold" plasma when the Alfven magnetic activity plays the key role. The hydrodynamic velocities Vθ, Vz are determined numerically from momentum balance collision-free equations averaged over the helical fluctuations. The developed self-consistent quasi-linear magnetohydronynamic model of the marginally stable kink spectrum reflects some physical features of the quasi-single helicity regime in reversed field pinches.

2D electron temperature diagnostic using soft x-ray imaging technique

We have developed a two-dimensional (2D) electron temperature (T(e)) diagnostic system for thermal structure studies in a low-aspect-ratio reversed field pinch (RFP). The system consists of a soft x-ray (SXR) camera with two pin holes for two-kinds of absorber foils, combined with a high-speed camera. Two SXR images with almost the same viewing area are formed through different absorber foils on a single micro-channel plate (MCP). A 2D Te image can then be obtained by calculating the intensity ratio for each element of the images. We have succeeded in distinguishing T(e) image in quasi-single helicity (QSH) from that in multi-helicity (MH) RFP states, where the former is characterized by concentrated magnetic fluctuation spectrum and the latter, by broad spectrum of edge magnetic fluctuations.

Experimental-like Helical Self-Organization in Reversed-Field Pinch Modeling

We report the first nonlinear three-dimensional magnetohydrodynamic (MHD) numerical simulations of the reversed-field pinch (RFP) that exhibit a systematic repetition of quasisingle helicity states with the same dominant mode in between reconnection events. This distinctive feature of experimental self-organized helical RFP plasmas is reproduced in MHD simulations at low dissipation by allowing a helical modulation of the plasma magnetic boundary similar to the experimental one. Realistic mode amplitudes and magnetic topology are also found.

Advances in understanding RFX-mod helical plasmas

High current (Ip = 1–1.7 MA) operations in the ohmic reversed field pinch RFX-mod spontaneously access the quasi-single helicity (QSH) regime, in which the magnetic dynamics is dominated by the innermost resonant mode (m = 1, n = −7), the magnetic chaos level is reduced and the internal magnetic field configuration is close to a pure helix. During the QSH state strong electron temperature (Te) gradients can show up, identifying an electron transport barrier (Puiatti 2011 Nucl. Fusion 51 073038). Results and advancements obtained in recent RFX-mod high current campaigns are reported in this paper.The best plasma performances at high Ip (i.e. high power) in QSH regimes have been reached with marginally reversed values of the safety factor q at the edge (−0.01 < qa < 0) when the lowest amplitudes of secondary m = 0, 1 modes are obtained. The QSH magnetic states are not stationary and show back transitions to the multiple helicity regime; however, the total persistency of the QSH is found to increase with the plasma current and at Ip > 1.5 MA it exceeds 90% of the plasma current flat-top. The high electron temperature gradients (>2 keV m−1) do not persist throughout the magnetic QSH cycle, as documented by a new high time resolution SXR double-filter multichord system, however, they last 5 to 10 ms, more than the energy confinement time. In the barrier region the profile of the electron heat diffusivity χe falls around 2–20 m2 s−1, well below ∼40–100 m−2 s−1 typical of the outer regions. The experimental evaluation of χe across the thermal barrier is consistent with a microtearing mode driven heat transport.

Impact of helical boundary conditions on nonlinear 3D magnetohydrodynamic simulations of reversed-field pinch

Helical self-organized reversed-field pinch (RFP) regimes emerge both numerically—in 3D visco-resistive magnetohydrodynamic (MHD) simulations—and experimentally, as in the RFX-mod device at high current (IP above 1 MA). These states, called quasi-single helicity (QSH) states, are characterized by the action of a MHD mode that impresses a quasi-helical symmetry to the system, thus allowing a high degree of magnetic chaos healing. This is in contrast with the multiple helicity (MH) states, where magnetic fluctuations create a chaotic magnetic field degrading the confinement properties of the RFP. This paper reports an extensive numerical study performed in the frame of 3D visco-resistive MHD which considers the effect of helical magnetic boundary conditions, i.e. of a finite value of the radial magnetic field at the edge (magnetic perturbation, MP). We show that the system can be driven to a selected QSH state starting from both spontaneous QSH and MH regimes. In particular, a high enough MP can force a QSH helical self-organization with a helicity different from the spontaneous one. Moreover, MH states can be turned into QSH states with a selected helicity. A threshold in the amplitude of MP is observed above which is able to influence the system. Analysis of the magnetic topology of these simulations indicates that the dominant helical mode is able to temporarily sustain conserved magnetic structures in the core of the plasma. The region occupied by conserved magnetic surfaces increases reducing secondary modes' amplitude to experimental-like values.