Reversed Field Pinch Plasma Research Articles

Investigation of turbulence in reversed field pinch plasma by using microwave imaging reflectometry

Turbulence in the reversed field pinch (RFP) plasma has been investigated by using the microwave imaging reflectometry in the toroidal pinch experiment RX (TPE-RX). In conventional RFP plasma, the fluctuations are dominated by the intermittent blob-like structures. These structures are accompanied with the generation of magnetic field, the strong turbulence, and high nonlinear coupling among the high and low k modes. The pulsed poloidal current drive operation, which improves the plasma confinement significantly, suppresses the dynamo, the turbulence, and the blob-like structures.

Magnetic reconstruction of nonaxisymmetric quasi-single-helicity configurations in the Madison Symmetric Torus

Quasi-single-helicity (QSH) states, characterized by a magnetic spectrum dominated by the innermost resonant tearing mode, are common to all the reversed field pinch (RFP) experiments. The internal magnetic field structure produced by the dominant mode is investigated for the QSH observed in the Madison Symmetric Torus (MST) RFP in discharges with zero toroidal magnetic field at the plasma boundary. The reconstruction is based on an MHD model coupled to edge measurements of the magnetic field. The model discards pressure, which has little effect on the equilibrium magnetic profile of present RFP plasmas, but adopts a realistic toroidal geometry. The technique is the adaptation to the MST configuration of a procedure already applied in RFX-mod, but a more general radial profile for the current density is needed for an adequate reconstruction of the MST case. The emerging features are similar to those found in RFX-mod. The helical flux surfaces of the dominant mode provide, with a good degree of reliability, a basis for mapping kinetic quantities such as electron density and soft-x-ray emissivity.

Impurity effects on the ion temperature gradient mode in reversed-field pinch plasmas

Ion temperature gradient (ITG) driven modes in the presence of impurity ions are studied in reversed-field pinch plasmas by solving the gyrokinetic integral eigenmode equation. Detailed numerical studies for single and multiple impurity ion species indicate that the ITG modes are enhanced by impurity effects and the stability threshold values become higher than that in pure hydrogen plasmas when density gradients of the impurity ions are opposite to that of electrons and main ions. In addition, a mode is driven unstable by impurity ions no matter how low the main ion temperature gradient is when the destabilizing effect of the impurity ions is strong enough. These results resemble the effects of impurities in tokamak plasmas. Analysis of the typical RFX-mod experiments is performed and the results show that the ITG and impurity driven modes may be linearly unstable in the edge region of the plasmas when the observed radial profiles of the impurity ions are considered.

Correlation of electrostatic fluctuation and reversal of toroidal field in the reversed-field pinch plasma

The magnetic fluctuations and electrostatic probe potential have been measured in the Toroidal Pinch Experiment - RX (TPE-RX) reversed-field pinch plasma [Y. Yagi et al., Fusion Eng. Des. 45, 421 (1999)] (at the plasma surface r/a = 1.00). Fast electrons with energy comparable to or slightly higher than the core electron temperature are observed as many spikes in the electrostatic probe signal. These electrons are diffused by a fluctuating magnetic field from the core region. During the period of mild deepening of the reversal of the edge toroidal field, a significant reduction in the spike signal, increases in electron density and soft x-ray radiation, and a decrease in the Dα line radiation are observed, even though the reduction in magnetic fluctuations is not significant during the same period, which indicates that the mild deepening of the reversal of the toroidal field can improve the confinement of fast electrons.

Topology and transport in the edge region of RFX-mod helical regimes

New edge diagnostics and detailed analysis of magnetic topology have significantly improved the comprehension of the processes developing at the boundary of a reversed-field pinch (RFP) plasma in RFX-mod (a = 0.46 m, R = 2 m).An upper critical density nC ≈ 0.4 nG (nG Greenwald density) is found to limit the operational space for the improved quasi-single helical (QSH) regime: magnetic topology reconstructions and diagnostic observations suggest that this limit is due to a helical plasma–wall interaction which determines toroidally and poloidally localized edge density accumulation and cooling.The experimental evidence is provided by a variety of diagnostics: the magnetic boundary as reconstructed from equilibrium codes reveals a helical deformation, which is well correlated with the modulation of edge pressure profile as reconstructed from the thermal helium beam diagnostic. Correlations with the helical deformation are also observed on the space- and time-resolved patterns of the floating potential measured at the wall, and with the edge plasma flow, obtained from different diagnostics. The relevance of these findings is that understanding the mechanisms that limit the operational space of QSH is decisive in achieving the goal of high-density stationary helical RFP equilibrium.

Physical understanding of the instability spectrum and the feedback control of resistive wall modes in reversed field pinch

The cylindrical MHD model integrated with a feedback system is applied to the study of resistive wall mode (RWM) in reversed field pinch (RFP) plasmas. The model takes into account the compressibility, longitudinal flow, viscosity and resistive wall with a finite thickness. The study, via both analytical and numerical analyses, provides a physical understanding on the following subjects: firstly, on the nature of the instability spectrum of the RWM observed in RFP plasmas; specifically, the growth rates of the two groups of the RWMs (internally non-resonant and externally non-resonant) have opposite dependence on the variation of the field reversal. Secondly, on the response of the unstable plasmas to the feedback control in RFPs, the mode behaviour in plasmas under the feedback is clarified and discussed in detail. Finally, the linear solutions of time evolution of RWM instability in various feedback scenarios are given. The effects of the wall proximity, the sensor location and the system response time are discussed, respectively.

Equilibrium reconstruction for single helical axis reversed field pinch plasmas

Single helical axis configurations are emerging as the natural state for high-current reversed field pinch plasmas. These states feature the presence of transport barriers in the core plasma. Here we present a method for computing the equilibrium magnetic surfaces for these states in the force-free approximation, which has been implemented in the SHEq code. The method is based on the superposition of a zeroth-order axisymmetric equilibrium and of a first-order helical perturbation computed according to Newcomb's equation supplemented with edge magnetic field measurements. The mapping of the measured electron temperature profiles, soft x-ray emission and interferometric density measurements on the computed magnetic surfaces demonstrates the quality of the equilibrium reconstruction. The procedure for computing flux surface averages is illustrated, and applied to the evaluation of the thermal conductivity profile. The consistency of the evaluated equilibria with Ohm's law is also discussed.

Modelling the temperature plateau in RFX-mod single-helical-axis (SHAx) states

The core region of high-current RFX-mod reversed field pinch plasmas spontaneously organizes into high-temperature helical flux tubes with almost intact magnetic surfaces. Accordingly, radial diffusion due to magnetic chaos is expected to be vanishingly small. Notwithstanding this, the temperature profile within these structures is flat, suggesting instead a substantial level of heat transport inside them. In this work we propose a rather simplified model of two-dimensional electrostatic turbulence valid in the low-magnetic chaos region and suggest that the effective homogenization of temperature may come from self-consistently generated vortical drift motion.

Generation and confinement of hot ions and electrons in a reversed-field pinch plasma

By manipulating magnetic reconnection in Madison Symmetric Torus (MST) discharges, we have generated and confined for the first time a reversed-field pinch (RFP) plasma with an ion temperature >1 keV and an electron temperature of 2 keV. This is achieved at a toroidal plasma current of about 0.5 MA, approaching MST's present maximum. The manipulation begins with intensification of discrete magnetic reconnection events, causing the ion temperature to increase to several kiloelectronvolts. The reconnection is then quickly suppressed with inductive current profile control, leading to capture of a portion of the added ion heat with improved ion energy confinement. Electron energy confinement is simultaneously improved, leading to a rapid ohmically driven increase in the electron temperature. A steep electron temperature gradient emerges in the outer region of the plasma, with a local thermal diffusivity of about 2 m2 s−1. The global energy confinement time reaches 12 ms, the largest value yet achieved in the RFP and which is roughly comparable to the H-mode scaling prediction for a tokamak with the same plasma current, density, heating power, size and shape.

Differential interferometry for measurement of density fluctuations and fluctuation-induced transport (invited)

Differential interferometry employs two parallel laser beams with a small spatial offset (less than beam width) and frequency difference (1-2 MHz) using common optics and a single mixer for a heterodyne detection. The differential approach allows measurement of the electron density gradient, its fluctuations, as well as the equilibrium density distribution. This novel interferometry technique is immune to fringe skip errors and is particularly useful in harsh plasma environments. Accurate calibration of the beam spatial offset, accomplished by use of a rotating dielectric wedge, is required to enable broad application of this approach. Differential interferometry has been successfully used on the Madison Symmetric Torus reversed-field pinch plasma to directly measure fluctuation-induced transport along with equilibrium density profile evolution during pellet injection. In addition, by combining differential and conventional interferometry, both linear and nonlinear terms of the electron density fluctuation energy equation can be determined, thereby allowing quantitative investigation of the origin of the density fluctuations. The concept, calibration, and application of differential interferometry are presented.

Synthesis and operation of an FFT-decoupled fixed-order reversed-field pinch plasma control system based on identification data

Recent developments and applications of system identification methods for the reversed-field pinch (RFP) machine EXTRAP T2R have yielded plasma response parameters for decoupled dynamics. These data sets are fundamental for a real-time implementable fast Fourier transform (FFT) decoupled discrete-time fixed-order strongly stabilizing synthesis as described in this work. Robustness is assessed over the data set by bootstrap calculation of the sensitivity transfer function worst-case -gain distribution. Output tracking and magnetohydrodynamic mode m = 1 tracking are considered in the same framework simply as two distinct weighted traces of a performance channel output-covariance matrix as derived from the closed-loop discrete-time Lyapunov equation. The behaviour of the resulting multivariable controller is investigated with dedicated T2R experiments.

Equilibrium evolution in oscillating-field current-drive experiments

Oscillating-field current drive (OFCD) is a proposed method of steady-state toroidal plasma sustainment in which ac poloidal and toroidal loop voltages are applied to produce a dc plasma current. OFCD is added to standard, inductively sustained reversed-field pinch plasmas in the Madison Symmetric Torus [R. N. Dexter et al., Fusion Technol. 19, 131 (1991)]. Equilibrium profiles and fluctuations during a single cycle are measured and analyzed for different relative phases between the two OFCD voltages and for OFCD off. For OFCD phases leading to the most added plasma current, the measured energy confinement is slightly better than that for OFCD off. By contrast, the phase of the maximum OFCD helicity-injection rate also has the maximum decay rate, which is ascribed to transport losses during discrete magnetic-fluctuation events induced by OFCD. Resistive-magnetohydrodynamic simulations of the experiments reproduce the observed phase dependence of the added current.

Toroidal kinetic ηi-mode study in reversed-field pinch plasmas

The ion temperature gradient (ITG) driven electrostatic modes in reversed-field pinch (RFP) plasma are studied with the gyrokinetic integral equation. A systematic threshold study is carried out and the results are compared with that in tokamaks with similar geometry and reveal that the ITG modes in RFP configurations are more stable than in tokamaks. The physics mechanism for such difference is that shorter connection length in RFPs leads to stronger landau damping, which is dominant and ultimately determinant for the stability threshold. The results confirm and extend the previous conclusion obtained with the differential equation [S. C. Guo, Phys. Plasmas 13, 122510 (2008)]. In addition, the effects of magnetic gradient and curvature drifts, which induce important interaction driving the modes, are carefully investigated. The effects of safety factor, ratio of electron temperature to ion temperature, magnetic shear as well as finite Larmor radius are also studied.

Comparison between cylindrical model and experimental observation on the study of resistive wall mode in reversed field pinch plasmas

A cylindrical magnetohydrodynamic model including plasma pressure and longitudinal flow has been employed for the study of resistive wall mode (RWM) in reversed field pinch (RFP) plasmas. In order to validate the model, a careful comparison with the experimental measurements in RFX-mod [P. Sonato et al., Fusion Eng. Des. 66–68, 161 (2003)] on the mode growth rates has been made by well matching the equilibrium parameters F, Θ, and βp. The RWM instability spectrum, which varies with the equilibrium parameters, is also calculated for comparison. The sensitivity of the mode growth rate to the equilibrium parameters is studied in details. It is concluded that the model can provide consistent accuracy in studies of RWM in RFP plasmas. The analysis based on the balance of the potential energy components has been carried out in order to obtain the physical understanding on the mode behavior.

Temperature evolution in a magnetohydrodynamics simulation of a reversed-field pinch

The temperature evolution in a magnetohydrodynamics (MHD) simulation of a reversed-field pinch (RFP) is investigated including thermal conductivity. For numerical reasons, an isotropic thermal conductivity is used, even though in a RFP plasma the parallel conductivity is much larger than the perpendicular one so that magnetic field lines tend to become isothermal. The system shows alternating multiple helicity states and quasi-single helicity states. Single-helical-axis states are formed when the amplitude of the dominant mode is above a determined threshold, as observed in experiments. The relation between heat transport and magnetic field topology that is observed in RFP experiments cannot be found in the simulation, since thermal conductivity is independent of the magnetic field. This difficulty should be taken into account in the numerical investigation of the RFP dynamics. In this paper, the first description of the temperature evolution in a compressible MHD simulation of a RFP is given.

The plasma boundary in single helical axis RFP plasmas

Single helical axis states obtained in high current reversed field pinch plasmas display, aside from a dominant mode in the m = 1 spectrum, also a dominant m = 0 mode, with the same toroidal mode number as the m = 1 one. The two modes have a fixed phase relationship. The island chain created by the m = 0 mode across the reversal surface gives rise, at shallow reversal of the toroidal field, to an X-point structure which separates the last closed flux surface from the first wall, creating a divertor-like configuration. The plasma–wall interaction is found to be related to the connection length of the field lines intercepting the wall, which displays a pattern modulated by the dominant mode toroidal periodicity. This configuration, which occurs only for shallow toroidal field reversal, could be exploited to realize an island divertor in analogy to stellarators.

Density Regimes of Low-Aspect-Ratio RFP Plasmas in RELAX

The line-averaged electron density has been measured over a wide range of discharge conditions in a low-aspect-ratio reversed field pinch (RFP) machine RELAX. A 104 GHz heterodyne interferometer was mainly used throughout the experiments. The measured electron density ne varied from ∼0.3 × 1019 m−3 to ∼3 × 1019 m−3, depending upon the discharge conditions. A new 60 GHz homodyne interferometer, characterized by simplicity and low cost, has been developed for the density measurement particularly in low density regime. The results from the new homodyne interferometer have shown good agreement with those from the heterodyne system in low-density regime of ne up to ∼1019 m−3.

Recent Progress in Low-A RFP Plasma Research in RELAX

Recent results from a low-aspect-ratio (low-A) reversed field pinch (RFP) machine with an aspect ratio of 2 (R/a = 0.51/0.25) are reported. The discharge characteristics of low-A RFP plasmas are described. The discharge regime in F − Θ space indicates that lowering the aspect ratio expanded the operational F − Θ space to the extremely high-Θ (>3), deep-reversal (F 0) region. A rotating helical Ohmic equilibrium RFP state could be realized in shallow-reversal discharge on REversed field pinch of Low Aspect eXperiment (RELAX). A preliminary feedback system is developed that results in plasma current with a longer discharge duration of ∼2ms. c

Observation of energetic electron confinement in a largely stochastic reversed-field pinch plasma

Runaway electrons with energies >100 keV are observed with the appearance of an m=1 magnetic island in the core of otherwise stochastic Madison Symmetric Torus [Dexter et al., Fusion Technol. 19, 131 (1991)] reversed-field-pinch plasmas. The island is associated with the innermost resonant tearing mode, which is usually the largest in the m=1 spectrum. The island appears over a range of mode spectra, from those with a weakly dominant mode to those, referred to as quasi single helicity, with a strongly dominant mode. In a stochastic field, the rate of electron loss increases with electron parallel velocity. Hence, high-energy electrons imply a region of reduced stochasticity. The global energy confinement time is about the same as in plasmas without high-energy electrons or an island in the core. Hence, the region of reduced stochasticity must be localized. Within a numerical reconstruction of the magnetic field topology, high-energy electrons are substantially better confined inside the island, relative to the external region. Therefore, it is deduced that the island provides a region of reduced stochasticity and that the high-energy electrons are generated and well confined within this region.

Current filaments in turbulent magnetized plasmas

Direct measurements of current density perturbations associated with non-linear phenomena in magnetized plasmas can be carried out using in situ magnetic measurements. In this paper we report such measurements for three different kinds of phenomena. Current density fluctuations in the edge density gradient region of a fusion plasma confined in reversed field pinch configuration and in a density gradient region in the Earth magnetosphere are measured and compared, showing that in both environments they can be attributed to drift-Alfvén vortices. Current structures associated with reconnection events measured in a reversed field pinch plasma and in the magnetosheath are detected and compared. Evidence of current filaments occurring during ELMs in an H-mode tokamak plasma is displayed.