Reversed Field Pinch Experiment Research Articles

Magnetohydrodynamic dynamo effect from electrostatic drift velocity field on sustainment of reversed field pinch plasmas in three-dimensional KTX equilibrium

A dynamo is necessary for reversed field pinch (RFP) configuration sustainment in a continuous way or oscillation cycles by self-organization. A dynamo velocity field from electrostatic drift is studied in three-dimensional (3D) equilibrium for Keda Torus eXperiment RFP plasmas in quasi-multi-helical (QMH) and quasi-single-helical (QSH) states. The 3D equilibrium reconstruction is computed by VMEC code. It is found that the electrostatic potential provides helical modulation of plasma flow in QSH states. The electrostatic potential in QMH states is processed as a superposition of limited helical harmonics, and it shows an axisymmetric pattern. Non-axisymmetric components are negligible in QMH states because of flux surface averaging of the electrostatic field and corresponding electrostatic drift flow. The electrostatic drift velocity is comparable to the total plasma drift in QSH states; this implies that the electrostatic drift may play an important role in sustaining the helical configuration in RFP plasma.

Prediction of temperature barriers in weakly collisional plasmas by a Lagrangian coherent structures computational tool

Analysis of Lagrangian Coherent Structures (LCSs) has been shown to be a valid mathematical approach to explain the formation of transport barriers in magnetized plasmas. Such LCSs, borrowed from fluid dynamics theory, can be considered as the hidden skeleton of the system and can be used for studying a wide spectrum of transport mechanisms, even in plasmas. An LCS can be considered as a generalization for a finite time interval and for a general dynamical system of what manifolds are for Hamiltonian systems. In this paper, we demonstrate that such structures can be particularly useful for underlying the hidden paths governing the motion of magnetic field lines in chaotic magnetic fields.To perform such an analysis, we developed a numerical tool able to detect LCSs for a general dynamical system. The tool is able to deal with general coordinate systems and it is shown to match with other techniques already used to analyse chaotic magnetic fields, e.g. connection length. After the description of the computational tool, we focus on the heat transport equation and the comparison between temperature profile and topology of the LCSs. We provide evidence that numerical simulations are able to reproduce the temperature profiles similar to those observed in reversed field pinch experiments and that our tool successfully predicts the location of temperature gradients. The results suggest that, inside the chaotic region, the field-lines motion is far from stochastic and that the presence of hidden patterns allows the development of high temperature gradients.

Edge turbulence approaching the density limit in RFX-mod experiment

The boundary region of the RFX-mod reversed field pinch experiment is strongly influenced by the value of the electron density. With increasing density the magnetic topology in the plasma core and in the plasma edge changes, together with the statistical properties of the edge turbulent fluctuations. Using the density normalized to the Greenwald density (n/nG), two density regimes are identified: the low density regime at n/nG < 0.3–0.4, and the high density regime for n/nG > 0.4–0.5, without a clear threshold between them. At low density the plasma is dominated by the (m, n) = (1, −7) magnetic mode, which gives the same shape to the magnetic boundary; at higher density a strong (0, 1) mode rises. When increasing n/nG, edge fluctuations develop strong non-Gaussian tails, turbulent structures become larger and their radial velocity become measurable with the gas puff imaging diagnostic when n/nG > 0.3–0.4. This phenomenology is described in detail for the two density regimes of RFX-mod.

A power-balance model of the density limit in fusion plasmas: application to the L-mode tokamak

A power-balance model, with radiation losses from impurities and neutrals, gives a unified description of the density limit (DL) of the stellarator, the L-mode tokamak, and the reversed field pinch (RFP). The model predicts a Sudo-like scaling for the stellarator, a Greenwald-like scaling, , for the RFP and the ohmic tokamak, a mixed scaling, , for the additionally heated L-mode tokamak. In a previous paper (Zanca et al 2017 Nucl. Fusion 57 056010) the model was compared with ohmic tokamak, RFP and stellarator experiments. Here, we address the issue of the DL dependence on heating power in the L-mode tokamak. Experimental data from high-density disrupted L-mode discharges performed at JET, as well as in other machines, are taken as a term of comparison. The model fits the observed maximum densities better than the pure Greenwald limit.

RFP based Fusion-Fission Hybrid reactor model for nuclear applications

The Reversed Field Pinch (RFP) configuration looks to be an attractive option for fusion-fission hybrid reactors: the toroidal magnetic systems would be made of copper coils instead of more expensive superconductive magnets; fusion conditions could be reached by ohmic heating only, therefore additional heating systems would not be required; the fission blanket could be located in the most external part of the torus thus facilitating maintenance operations. The paper aims at assessing the potentialities, such as fuel fertilization and/or nuclear waste transmutation and electricity production of a hybrid reactor with a RFP fusion core (R = 6 m, a = 1) whose conceptual design and plasma performances are based on RFX-mod, the largest RFP experiment currently in operation. Fusion conditions can be reached by heating a D-T plasma up to 9.6 keV by ohmic heating, generated by a 20 MA plasma current induced and sustained by flux swing only. The neutron flux (2.1 × 1013 fast neutron/cm2/s) is used to breed tritium in both the inner and outer blanket sections and induce fission reactions in dedicated areas in the external blanket section where Pu + MA (60%)-Zr (40%) rods are located. Both neutronic and safety analyses corroborate the viability of a FFH reactor with a RFP core.

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.

Effects of oscillating poloidal current drive on magnetic relaxation in the Madison Symmetric Torus reversed-field pinch

Magnetic relaxation behavior in reversed-field pinch (RFP) experiments on the Madison Symmetric Torus device is modified by oscillating poloidal current drive (OPCD). We observe that OPCD modulates the nonlinear magnetic fluctuation dynamics of the RFP as it modulates the equilibrium and its linear stability properties. In particular, OPCD can entrain the RFP’s nonlinear magnetic relaxation cycle and can therefore modify the frequency of the discrete relaxation events called sawtooth crashes. These crashes, which are intermittent or quasiperiodic in standard RFP plasmas without oscillating voltages, can be entrained by OPCD to become nearly periodic. The entrainment of the RFP sawtooth cycle is investigated by varying OPCD amplitude and frequency, as well as plasma equilibrium magnetic field reversal. Impurity ion (C+4) heating induced and modulated by OPCD is measured by ion Doppler spectrometry and is ascribed to the modulation of magnetic reconnection activity.

Modeling of the mode dynamics generated by Madison Symmetric Torus machine utilizing a modified sine-Gordon equation

In this paper, a new dynamic model is presented for the experimental data generated by the Madison Symmetric Torus (MST) machine. The model is based on a modified sine-Gordon (SG) dynamic equation. The modified sine-Gordon equation model effectively captures the behavior of the slinky mode in reversed-field pinch experiments. In addition, this paper demonstrates how the derived model accurately describes the behavior of the localized magnetohydrodynamic mode (slinky mode) that appears in reversed-field pinch toroidal magnetic confinement systems. The modified SG equation model is solved analytically by using the perturbation method. The resulting model is fit to match a variety of experimental results in the MST reversed-field pinch experiment. The efficacy of the newly developed model in effectively representing the slinky mode is verified by comparing obtained analytical solution to experimentally measured data.

FLiT: a field line trace code for magnetic confinement devices

This paper presents a field line tracing code (FLiT) developed to study particle and energy transport as well as other phenomena related to magnetic topology in reversed-field pinch (RFP) and tokamak experiments. The code computes magnetic field lines in toroidal geometry using curvilinear coordinates (r, ϑ, ϕ) and calculates the intersections of these field lines with specified planes. The code also computes the magnetic and thermal diffusivity due to stochastic magnetic field in the collisionless limit. Compared to Hamiltonian codes, there are no constraints on the magnetic field functional formulation, which allows the integration of whichever magnetic field is required. The code uses the magnetic field computed by solving the zeroth-order axisymmetric equilibrium and the Newcomb equation for the first-order helical perturbation matching the edge magnetic field measurements in toroidal geometry. Two algorithms are developed to integrate the field lines: one is a dedicated implementation of a first-order semi-implicit volume-preserving integration method, and the other is based on the Adams–Moulton predictor–corrector method. As expected, the volume-preserving algorithm is accurate in conserving divergence, but slow because the low integration order requires small amplitude steps. The second algorithm proves to be quite fast and it is able to integrate the field lines in many partially and fully stochastic configurations accurately. The code has already been used to study the core and edge magnetic topology of the RFX-mod device in both the reversed-field pinch and tokamak magnetic configurations.

Sawtooth mitigation in 3D MHD tokamak modelling with applied magnetic perturbations

The effect of magnetic perturbations (MPs) on the sawtoothing dynamics of the internal kink mode in the tokamak is discussed in the framework of nonlinear 3D MHD modelling. Numerical simulations are performed with the pixie3d code (Chacón 2008 Phys. Plasmas 15 056103) based on a D-shaped configuration in toroidal geometry. MPs are applied as produced by two sets of coils distributed along the toroidal direction, one set located above and the other set below the outboard midplane, like in experimental devices such as DIII-D and ASDEX Upgrade. The capability of n = 1 MPs to affect quasi-periodic sawteeth is shown to depend on the toroidal phase difference between the perturbations produced by the two sets of coils. In particular, sawtooth mitigation is obtained for the phasing, whereas no significant effect is observed for . Numerical findings are explained by the interplay between different poloidal harmonics in the spectrum of applied MPs, and appear to be consistent with experiments performed in the DIII-D device. Sawtooth mitigation and stimulation of self-organized helical states by applied MPs have been previously demonstrated in both circular tokamak and reversed-field pinch (RFP) experiments in the RFX-mod device, and in related 3D MHD modelling.

Characterization of small thermal structures in RFX-mod electron temperature profiles

In the RFX-mod reverse field pinch (RFP) experiment, electron temperature profiles often feature structures and fluctuations at fine scale. The present work aims at characterizing their occurrence and their localization, in particular by linking them to underlying tearing modes magnetic islands. The confinement characteristics are discussed, identifying analogies with respect to high scale Te structures. Finally, high frequency magnetic activity (i.e. microtearing instabilities) is confirmed to be closely correlated to the presence and proximity of temperature gradients.

Control of 3D equilibria with resonant magnetic perturbations in MST

To aid in diagnosis of 3D equilibria in the Madison Symmetric Torus, it has become necessary to control the orientation of the equilibria. In reversed field pinch experiments a transition to a 3D equilibrium is common with sufficiently large plasma current (and Lundquist number). Diagnosis of this state is hampered by the fact that the helical structure is stationary but with an orientation that varies shot-to-shot. A resonant magnetic perturbation (RMP) technique has been developed to vary controllably the orientation of the 3D equilibria and optimized to minimize the plasma wall interaction due to its use. Application of an RMP now allows alignment of the structure with key diagnostics, including Thomson scattering and an interferometer-polarimeter.

Spontaneous versus induced hydrogen and deuterium helical shaped plasmas with electron internal transport barriers

Electron internal transport barriers (eITBs) in high current plasmas with helical equilibria of the reversed field pinch experiment RFX-mod are analyzed and characterized in detail thanks to a high time resolution double filter diagnostic for the electron temperature spatial profile determination. The large amount of data provided by this diagnostic has required the development of dedicated algorithms and the identification of suitable parameters, reported and described in this paper, in order to perform automatic statistical studies. These numerical tools have been used to examine the effect of three dimensional (3D) magnetic fields applied by the RFX-mod 192 active coils in deuterium and hydrogen discharges with the aim to improve the sustainment and control of helical equilibria with eITBs. It is shown that 3D fields partially increase the occurring of helical states but with only a moderate effect on the eITBs duration; moreover, they have a different impact on the confinement properties in hydrogen and deuterium discharges. Numerical simulations, by the Hamiltonian guiding center code ORBIT, investigate the effect of magnetic topology in plasmas with and without the application of 3D fields on deuterium and hydrogen test ions transport. Results from numerical studies are in agreement with estimates of the particle confinement times showing that particle transport is reduced in deuterium plasmas but not significantly affected by the application of helical boundary conditions.

Overview of results from the MST reversed field pinch experiment

An overview of recent results from the MST reversed field pinch programme is presented. With neutral beam injection, bursty energetic particle (EP) modes are observed. The profiles of the magnetic and density fluctuations associated with these EP modes are measured using a far infrared interferometer–polarimeter. Equilibrium reconstructions of the quasi-single-helicity 3D helical state are provided by the V3FIT code that now incorporates several of MST's advanced diagnostics. The orientation of the helical structure is controlled using a new resonant magnetic perturbation technique. Gyrokinetic simulations based on experimental equilibria predict unstable trapped-electron modes (TEMs), and small-scale density fluctuations are detected in improved-confinement plasmas with TEM-like features. Upgraded pellet injection permits study of density and beta limits over MST's full range of operation, and an MST-record line-average density of 0.9 × 1020 m3 (n/nG = 1.4) has been obtained. Impurity ion temperature measurements reveal a charge-to-mass-ratio dependence in the rapid heating that occurs during a sawtooth crash. Runaway of NBI-born fast ions during the impulsive sawtooth event agrees with test-particle theory. Magnetic self-organization studies include measurements of the dynamo emf with an applied ac inductive electric field using oscillating field current drive.

Lithium wall conditioning by high frequency pellet injection in RFX-mod

In the RFX-mod reversed field pinch experiment, lithium wall conditioning has been tested with multiple scopes: to improve density control, to reduce impurities and to increase energy and particle confinement time. Large single lithium pellet injection, lithium capillary-pore system and lithium evaporation has been used for lithiumization. The last two methods, which presently provide the best results in tokamak devices, have limited applicability in the RFX-mod device due to the magnetic field characteristics and geometrical constraints. On the other side, the first mentioned technique did not allow injecting large amount of lithium. To improve the deposition, recently in RFX-mod small lithium multi-pellets injection has been tested. In this paper we compare lithium multi-pellets injection to the other techniques. Multi-pellets gave more uniform Li deposition than evaporator, but provided similar effects on plasma parameters, showing that further optimizations are required.

PADC Detected External Neutron Field by Nuclear Tracks at RFX-mod

Measured neutron signals relevant for plasma diagnostics on Reversed Field pinch eXperiment, RFX-mod, are obtained by nuclear track methodology with PADC-NtD’s. this technique provides the external neutron field values around the RFX-mod installation during pulsed operation. Charged particles from (n, p) and (n, α) reactions are related to formed latent tracks. these are etched in a thermoregulated water bath with a 6.25M, KOh solution at 60oC. Observed tracks were analyzed to determine track density from which neutron fluence spatial values should be derived. Results indicate that the neutron density in the surrounding environment change at most 40%. the epithermal component is 60% higher than that corresponding to the thermal region. the estimated neutron fluence for the whole experiment is 7.5×1010 neutrons cm2/s.

Calculation of 3-D Magnetic Fields Produced by MHD Active Control Systems in Fusion Devices

An accurate control of the magnetic boundary of a thermonuclear plasma is an important issue in magnetic confinement research. The development of methods for the active control of magnetohydrodynamic instabilities and correction of error fields is mandatory in view of fusion reactors or experimental test reactors under design. Recently, a very effective control scheme, named clean mode control (CMC), has been proposed in a reversed field pinch experiment (RFX-mod). The CMC is based on the real-time correction (cleaning), under simplifying hypothesis, of the sideband harmonics in the magnetic field produced by the discrete local active coils. In this paper, we focus on the problem of carefully computing the penetration of sidebands through a realistic load assembly, but still with a simplified cylindrical geometry, to allow for a detailed comparison with the crude CMC algorithm without the additional complication of the coupling between the poloidal harmonics due to the toroidal geometry.

Characterization of temperature profiles in the outer region of RFX-mod

The onset of helical states has been shown to strongly affect the transport properties and the plasma performance of both the core region (|R − R0|/a ≲ 0.5) and the plasma edge (|R − R0|/a ≳ 0.95) in the RFX-mod reversed field pinch experiment. Both regions have been widely investigated and a strong effort is still dedicated to deepening the comprehension of the phenomena affecting them. Conversely, the region bounded between the plasma core and the plasma edge (0.6 ≲ |R − R0|/a ≲ 0.95) has been poorly analyzed, despite the large plasma volume enclosed in this domain. Improvements in RFX-mod global plasma performance are thus closely linked to the identification of the physical mechanisms occurring in this region, referred to as the outer region. A specifically conceived method of analysis, which gathers together data from a Thomson scattering system and two edge temperature diagnostics, allows the study of the entire temperature profile of RFX-mod. A statistical analysis performed on a large discharge database shows that the temperature profile in the central region of the plasma column is mainly established by the plasma current and the degree of stochasticity of the magnetic field. On the other hand, the temperature profile in the outer plasma region is found to vary with electron density and plasma equilibrium.

Overview of results from the MST reversed field pinch experiment

An overview of recent results from the MST programme on physics important for the advancement of the reversed field pinch (RFP) as well as for improved understanding of toroidal magnetic confinement more generally is reported. Evidence for the classical confinement of ions in the RFP is provided by analysis of impurity ions and energetic ions created by 1 MW neutral beam injection (NBI). The first appearance of energetic-particle-driven modes by NBI in a RFP plasma is described. MST plasmas robustly access the quasi-single-helicity state that has commonalities to the stellarator and ‘snake’ formation in tokamaks. In MST the dominant mode grows to 8% of the axisymmetric field strength, while the remaining modes are reduced. Predictive capability for tearing mode behaviour has been improved through nonlinear, 3D, resistive magnetohydrodynamic computation using the measured resistivity profile and Lundquist number, which reproduces the sawtooth cycle dynamics. Experimental evidence and computational analysis indicates two-fluid effects, e.g., Hall physics and gyro-viscosity, are needed to understand the coupling of parallel momentum transport and current profile relaxation. Large Reynolds and Maxwell stresses, plus separately measured kinetic stress, indicate an intricate momentum balance and a possible origin for MST's intrinsic plasma rotation. Gyrokinetic analysis indicates that micro-tearing modes can be unstable at high beta, with a critical gradient for the electron temperature that is larger than for tokamak plasmas by roughly the aspect ratio.

Helical equilibrium reconstruction with V3FIT in the RFX-mod Reversed Field Pinch

Helical states are routinely found in all reversed field pinch experiments. The inherently three-dimensional feature of these states requires an adequate equilibrium reconstruction. In this paper we present the use of the V3FIT code for the RFX-mod experiment. V3FIT uses VMEC as an equilibrium solver and varies reconstruction parameters to minimize the difference between experimental and modelled signals. Both magnetic (local field, saddle coils and flux loops) and kinetic diagnostics (Thomson scattering, interferometric and soft x-ray emissivity data) are used in order to properly deal with the problem of equilibrium degeneracy. From this point of view a sensitivity study of external magnetic measurements on the internal topological structure is presented.As the work deals with fixed-boundary equilibria, a solution to the issue of vacuum fields computation is also presented.A comparison with previous procedures for obtaining both axisymmetric and helical equilibria is presented, with particular attention to the role of pressure and thermal measurements—information which is missing in previous analyses.The results provide a good match with experimental data showing that indeed a consistent inclusion of pressure with temperature and density measurements is necessary. The equilibria obtained are suitable for both transport and stability analysis.