Reversed Field Pinch Configuration Research Articles

Estimation of wall forces solely from magnetic measurements: an application to RFX-mod experiment

The estimation of integral wall force using solely magnetic measurement in RFX-mod experiment is presented. The vertical and sideways forces are directly obtained from the magnetic field measured outside the vacuum vessel. Several theoretical predictions related to tokamak are also verified for the reversed field pinch configuration. The contribution of different modes to the force is also considered and analyzed. This method of calculation would be relevant for future nuclear fusion reactors where magnetic measurements will be located only outside the vacuum vessel.

Viscosity impact on 3D non-linear MHD simulations of RFP fusion plasmas

Several studies pointed out the joint role of resistivity η and viscosity ν in determining the dynamics and the emergence of helical regimes of reversed-field pinch (RFP) plasmas. In this framework, the self-consistent time evolution of the η and ν coefficients still lacks of a fully satisfying modeling, being constrained by many approximations. In this work, the hypothesis of a flat viscosity profile is relaxed: A viscosity profile inspired by the Braginskii perpendicular viscosity is implemented in the code. This choice is motivated by the fact that the magnetohydrodynamics field instabilities relevant for the RFP configuration dynamics (resistive-kink/tearing modes) are active in the direction perpendicular to the magnetic field. Such a non-monotonous profile causes a localized damping of plasma flow in the regions, where the viscosity is stronger, close to the plasma edge. This results in the reduction of the flow shear, in turn allowing the enhancement of edge magnetic field modes amplitude. The impact on the magnetic topology and on connection length to the wall is also analyzed.

Alfvén waves in reversed-field pinch and tokamak ohmic plasmas: nonlinear 3D MHD modeling and comparison with RFX-mod

The properties and possible triggering mechanisms of Alfvén waves in the reversed-field pinch (RFP) and circular tokamak configurations are discussed in the framework of nonlinear 3D magnetohydrodynamics (MHD) modeling. Numerical simulations are performed with the SpeCyl code (Cappello and Biskamp 1996 Nucl. Fusion) that solves the equations of the viscoresistive MHD model in cylindrical geometry. Configurations with increasing levels of complexity are analyzed. First, single-wave numerical solutions are compared with analytical ones in the simplest case of a uniform axial magnetic field: an excellent agreement is obtained for both the shear Alfvén wave (SAW) and the compressional Alfvén eigenmodes (CAEs). Then, tokamak and RFP configurations are studied. Phenomena such as phase mixing of SAW, resonant absorption of CAEs and the appearance of the global Alfvén eigenmode are described. Finally, the fully 3D RFP case with typical sawtoothing activity is investigated, showing for the first time in nonlinear RFP simulations the excitation of Alfvén waves by magnetic reconnection events. The modeling results appear to be consistent with the experimental characterization of Alfvénic activity observed in RFX-mod.

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.

Helically self-organized pinches: dynamical regimes and magnetic chaos healing

This paper deals with helical self-organization in current-carrying toroidal pinches for the magnetic confinement of fusion plasmas. We perform our study in the framework of 3D nonlinear visco-resistive magnetofluid modelling, where a large set of simulations is now available. A global picture is derived about how visco-resistive transport coefficients and magnetic boundary conditions rule the self-organized helical states for the reversed-field pinch configuration. Decreasing visco-resistive dissipation causes a transition from steady ohmic helical equilibria to intermittent states (sawtoothing activity), while selected helical magnetic perturbations applied at the boundary favor steady global quasi-helical solutions. The sawtoothing frequency decreases together with visco-resistive dissipation, while sawtoothing amplitude decreases when applying non-resonant magnetic perturbations. Simulations of the tokamak configuration allow us to draw a tight parallelism with reversed-field pinches: a similar role of dissipation and magnetic boundary conditions on the dynamics of the internal kink mode is found, with decreasing sawtoothing frequency and amplitude by decreasing dissipation and by applying suitable helical boundary conditions. Magnetic chaos healing is the topological feature of the transition from intermittent to quasi-quiescent helical states in reversed-field pinches. Bundles of Lagrangian coherent structures (LCS) in the weakly stochastic region surrounding the helical core constitute the skeleton of chaos healing, and behave as barriers to the transport of magnetic field lines. In this work, they are detected during the whole temporal evolution and it is proved that they can withstand the nonlinear dynamics even during sawtoothing activity. Furthermore, we show that LCS are connected to regions with strong gradients of the connection length of magnetic field lines to the edge. This provides a further indication of their possible role in the formation of electron temperature barriers. As a final result it is shown that a reasonable value of plasma rotation can further enhance the intensity of the dominant helical mode.

MEST: A new Magnetic Energy Storage and Transfer system for improving the power handling in fusion experiments

A new magnetic energy storage scheme is studied for improving the power handling in fusion experiments: it can be applied both to tokamak or RFP experiments to supply the poloidal superconducting coils and can efficiently support the operation of the Central Solenoid (CS), without the need for resistive switching networks, thus with the advantage of energy dissipation avoidance. The basic idea, presented with reference to the CS circuit, is to provide an additional Superconducting Magnetic Energy Storage coil (TC), pre-charged along with the CS one to the same current value and then to transfer step by step the energy from one to the other and vice versa during the different phases of the plasma pulse, via switched capacitor. The principle is applied to the case of a Fusion-Fission Hybrid Reactor, based on Reversed Field Pinch configuration operated exploiting the flux double swing.

Magnetohydrodynamics modelling successfully predicts new helical states in reversed-field pinch fusion plasmas

Nonlinear fluid modelling predictions of qualitatively new self-organized helical states in the reversed-field pinch configuration are confirmed by experiments in the RFX-mod device. The new states are realized by using a seed edge magnetic field, which can impose its helical pitch to the whole plasma. In simulations, we show increased magnetic order and reduced transport of magnetic field lines in regimes with the twist of a non-resonant mode. We reveal the existence of Cantori, encompassing the region characterized by conserved magnetic surfaces, which act as barriers to transport of magnetic field lines. This opens a new research line for transport studies in hot magnetized plasmas and highlights a path towards reversed-field pinches with high confinement at high current.

Comparative studies of electrostatic turbulence induced transport in presence of resonant magnetic perturbations in RFX-mod

Three-dimensional non-axisymmetric magnetic fields are purposely applied to toroidally symmetric fusion plasmas in order to modify transport of heat and particle fluxes to the plasma-facing components (PFCs), and specifically to control and suppress edge localized modes (ELMs) in H-mode tokamak plasmas. This paper presents a comparative study between two magnetic configurations available in the RFX-mod device, namely the original reversed-field pinch configuration and the more recent low-field circular ohmic tokamak. The paper presents a detailed analysis of the modulation of electrostatic turbulence and induced transport in the presence of an externally applied magnetic perturbation, as measured in both configurations. A detailed study of the underlying magnetic topology in both configurations is given through the field line tracing code FLiT. The electrostatic turbulence induced flux is observed to be modulated by the underlying topology, with an enhancement close to the O-point and a reduction at the X-point of the induced magnetic island. The transport modification are discussed in terms of relevant frequency and wavenumber spectrum.

Overview of the RFX-mod contribution to the international Fusion Science Program

The RFX-mod device is operated both as a reversed field pinch (RFP), where advanced regimes featuring helical shape develop, and as a tokamak. Due to its flexibility, RFX-mod is contributing to the solution of key issues in the roadmap to ITER and DEMO, including MHD instability control, internal transport barriers, edge transport and turbulence, isotopic effect, high density limit and three-dimensional (3D) non-linear MHD modelling. This paper reports recent advancements in the understanding of the self-organized helical states, featuring a strong electron transport barrier, in the RFP configuration; the physical mechanism driving the residual transport at the barrier has been investigated. Following the first experiments with deuterium as the filling gas, new results concerning the isotope effect in the RFP are discussed. Studies on the high density limit show that in the RFP it is related to a toroidal particle accumulation due to the onset of a convective cell. In the tokamak configuration, q(a) regimes down to q(a) = 1.2 have been pioneered, with (2,1) tearing mode (TM) mitigated and (2,1) resistive wall mode (RWM) stabilized: the control of such modes can be obtained both by poloidal and radial sensors. Progress has been made in the avoidance of disruptions due to the (2,1) TM by applying q(a) control, and on the general issue of error field control. The effect of externally applied 3D fields on plasma flow and edge turbulence, sawtooth control and runaway electron decorrelation has been analysed. The experimental program is supported by substantial theoretical activity: 3D non-linear visco-resistive MHD and non-local transport modelling have been advanced; RWMs have been studied by a toroidal MHD kinetic hybrid stability code.

Detection of magnetic barriers in a chaotic domain: first application of finite time Lyapunov exponent method to a magnetic confinement configuration

Magnetic field lines embedded in a plasma confinement system are often characterized by a chaotic motion. This weakens the confinement properties of any magnetic configuration. However, even in case of chaotic domains, magnetic barriers can emerge and limit the field line motion itself. In the context of the numerical simulation of a Reversed-Field Pinch configuration a new magnetic topology analysis, borrowed from previous fluid dynamic studies, is discussed. This methodology relies on the behavior of the Finite Time Lyapunov Exponent (FTLE) associated with the magnetic field. By referring to a previous work in which the magnetic field is given in terms of analytical function (Borgogno et al 2011 Phys. Plasmas 18 102307) the FTLE field shows the presence of ridges, special gradient lines normal to the direction of minimum curvature, forming magnetic barriers. These ridges can be recognized as Lagrangian Coherent Structures (LCSs) for the system, actually opposing the penetration of magnetic field lines across them. In this article a more general numerical scheme for the detection of the LCSs has been adopted that allows analysis of realistic cases in which the magnetic fields are numerically known on a discrete mesh. After a validation test performed on the analytical case, a first application to a numerical magnetohydrodynamics simulation of the RFP, characterized by a broad chaotic region, has been performed. A strong magnetic barrier has been observed that effectively limits the field lines motion inside the chaotic sea.

Simulation of feedback control on tearing modes using different sensors in a reversed field pinch and application to the Keda Torus eXperiment

Feedback control of dynamo tearing modes (TMs) in a reversed field pinch (RFP) using radial field sensors has been achieved in RFX-mod (Zanca et al 2012 Plasma Phys. Control. Fusion 54 124018). In this paper a simulation, performed with the RFXLocking code (Zanca 2009 Plasma Phys. Control. Fusion 51 015006), is presented with the purpose of discovering the dependence of TM feedback on the type (radial, poloidal and toroidal) and location of the sensors. An arrangement of the latter inside the stabilizing shell is considered. Moreover, the impact of different sensors of the sideband harmonics, produced by a uniform grid of active coils located outside the shell, is investigated. The simulations consider the layout of the Keda Torus eXperiment (KTX), a large device under construction in Hefei designed to operate in the RFP configuration. Therefore, this work can give important indications to the project of the feedback control system in the KTX. The most important result is that radial field sensors turn out to be equivalent to the poloidal and toroidal ones only upon the removal of the aliasing coming from the coils' sideband harmonics.

Transport asymmetry and release mechanisms of metal dust in the reversed-field pinch configuration

Experimental data on dust resident in the EXTRAP T2R reversed-field pinch are reported. Mobile dust grains are captured in situ by silicon collectors, whereas immobile grains are sampled post mortem from the wall by adhesive tape. The simulation of collection asymmetries by the MIGRAINe dust dynamics code in combination with the experimental results is employed to deduce some characteristics of the mechanism of intrinsic dust release. All evidence suggests that re-mobilization is dominant with respect to dust production.

Does shaping bring an advantage for reversed field pinch plasmas?

The MHD–kinetic hybrid toroidal stability code MARS-K (Liu et al 2008 Phys. Plasmas 15 112503) is applied to study the shaping effects on magnetohydrodynamic (MHD) stabilities in reversed field pinch (RFP) plasmas, where both elongation and triangularity are taken into account. The ideal wall β (the ratio of the gaso-kinetic to magnetic pressures) limit set by the ideal kink mode/resistive wall mode in shaped RFP is investigated first, followed by a study of the kinetic damping on the resistive wall mode. Physics understanding of the results is provided by a systematic numerical analysis. Furthermore, the stability boundary of the linear resistive tearing mode in shaped RFP plasmas is computed and compared with that of the circular case. Finally, bootstrap currents are calculated for both circular and shaped RFP plasmas. Overall, the results of these studies indicate that the current circular cross-section is an appropriate choice for RFP devices, in the sense that the plasma shaping does not bring an appreciable advantage to the RFP performance in terms of macroscopic stabilities. In order to reach a steady-state operation, future RFP fusion reactors will probably need a substantial fraction of external current drives, due to the unfavourable scaling for the plasma-generated bootstrap current in the RFP configuration.

Effects of the resistivity profile on the formation of a reversed configuration and single helicity states in compressible simulations of the reversed-field pinch

Compressible magnetohydrodynamics simulations of the reversed-field pinch (RFP) are presented. Previous simulations of the RFP, including density and pressure evolution, showed that a stationary state with a reversed toroidal magnetic field could not be obtained, contrary to the results produced with numerical codes neglecting density and pressure dynamics. The simulations described in the present paper show that including density and pressure evolution, a stationary RFP configuration can be obtained if the resistivity has a radial profile steeply increasing close to the wall. Such resistivity profile is more realistic than a uniform resistivity, since the temperature at the wall is lower than in the plasma core.

Phase Locking and Unlocking Associated with Transition to Quasi-Single Helicity State in the RELAX Reversed-Field Pinch

In a reversed-field pinch configuration, many m 1⁄4 1 internally resonant tearing modes grow. The phase relationship among the modes is usually random, while there are cases where the phases tend to align each other. This phaselocking structure causes local enhancement of the heat flux to the wall. In the low-aspect-ratio reversed-field pinch (RFP) machine RELAX (major radius R 1⁄4 0:508m, minor radius a 1⁄4 0:250m, aspect ratio A 1⁄4 2:032), it has been observed that the phase-locking is released when a dominant mode grows to a large extent with suppression of the remaining modes, which state is often referred to as the quasi-single helicity (QSH) state. It has been found that the experimental phase behavior can be described as a probability distribution in ð min; NsÞ space, where min is the minimum of the phase dispersion, and Ns the spectral index. RFP is a relatively high-beta magnetic confinement configuration with much higher toroidal current than in Tokamaks with comparable size. Due to its high toroidal current, magnetic field lines skew in the poloidal direction and at the edge the direction of the toroidal field reverses. The safety factor (q) profile in RELAX is a monotonically decreasing function of radius with on-axis value of 0:3. Therefore, m 1⁄4 1 internally resonant tearing modes with toroidal mode numbers n satisfying 1=n . 1=3 can be simultaneously unstable in RELAX. The operational regime of the RELAX RFP is characterized by a wide range of field-reversal parameter F , which is the ratio of edge toroidal field Bta to the averaged toroidal field hBti. There are two characteristic regimes, possibly characteristic to low-A RFP. One is a shallow-reversal regime where F > 0:1, characterized by frequent transitions to QSH states, which may be attributable to larger separations between mode rational surfaces in the core region and power distribution of the m 1⁄4 1 modes to fewer toroidal mode numbers; some equilibrium analyses and numerical simulations predicted those effect of low aspect ratio on the RFP configuration. The helical structure coinciding with the magnetic island of the dominant mode in QSH state has been clearly observed in RELAX. The other is a deep-reversal regime where F 6) aspect-ratio RFPs. Although the reason of the attainment of the deep-reversal regime is not clear so far, this regime seems attractive in terms of optimization of the aspect ratio in the RFP since the tearing mode amplitudes are lowered in this regime. In a wide range of operational regimes of RELAX, phaselocking phenomena have been observed. Phase-locking structure called slinky mode tends to be locked to the wall due to electromagnetic interaction with error fields, and causes locally enhanced heat flux on the wall. In RFXmod, by an elaborate feed-back control of tearing modes’ dynamics with 192 saddle coils covering all over the wall, they have successfully released the wall-locking and, recently, higher plasma current operation of 2MA was performed. In the following, we show a spontaneous release of wall-locking and/or phase-locking due to transition to QSH state observed in RELAX. Figure 1(a) shows time evolution of spectral index Ns defined as

Physics of resistive wall modes

The advanced tokamak regime is a promising candidate for steady-state tokamak operation which is desirable for a fusion reactor. This regime is characterized by a high bootstrap current fraction and a flat or reversed safety factor profile, which leads to operation close to the pressure limit. At this limit, an external kink mode becomes unstable. This external kink is converted into the slowly growing resistive wall mode (RWM) by the presence of a conducting wall. Reduction of the growth rate allows one to act on the mode and to stabilize it. There are two main factors which determine the stability of the RWM. The first factor comes from external magnetic perturbations (error fields, resistive wall, feedback coils, etc). This part of RWM physics is the same for tokamaks and reversed field pinch configurations. The physics of this interaction is relatively well understood and based on classical electrodynamics. The second ingredient of RWM physics is the interaction of the mode with plasma flow and fast particles. These interactions are particularly important for tokamaks, which have higher plasma flow and stronger trapped particle effects. The influence of the fast particles will also be increasingly more important in ITER and DEMO which will have a large fraction of fusion born alpha particles. These interactions have kinetic origins which make the computations challenging since not only particles influence the mode, but also the mode acts on the particles. Correct prediction of the ‘plasma–RWM’ interaction is an important ingredient which has to be combined with external field's influence (resistive wall, error fields and feedback) to make reliable predictions for RWM behaviour in tokamaks. All these issues are reviewed in this paper.

Initial Result of Successive SXR Imaging Measurement in Low-A RFP

A fast successive soft-X ray (SXR) imaging system where SXR camera and high-speed camera for the study of time evolution of magnetic islands has been constructed. A preliminary experimental result in which we observed tangential SXR images from quasi-periodic quasi-single helicity (QSH) state in low-aspect-ratio (low-A) reversed field pinch (RFP) is presented. We successfully obtained time evolution of SXR images from tangential port. By comparison obtained images with simulated images, we may conclude that the evolution of experimental SXR image suggests the rotating QSH RFP configuration. The filamentous configuration tends to be observed in QSH state rather than in multi-helicity (MH) state.

Measurements of impulsive reconnection driven by nonlinear Hall dynamics

The magnetic fields associated with reconnection in the edge of the reversed field pinch configuration have been measured in the Madison Symmetric Torus. The measured magnetic field structure is compared with theoretical predictions computed in both toroidal and cylindrical geometries. The summation of multiple modes has been accomplished to reveal a complex but still coherent edge structure. Key terms of relevant Ohm’s law are accessible from magnetic field measurement and reveal the ordering [(1/ne)J×B⪢E>ηJ], which implies that two fluid effects are important in the physics governing this reconnection. Further, it is seen that the nonlinear three-wave coupling of the Hall term acts as a driving mechanism for this linearly stable mode.

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.

Gyrokinetic simulations of ion temperature gradient modes in the reversed field pinch

Linear gyrokinetic calculations are applied to the reversed field pinch configuration to investigate the occurrence of ion temperature gradient instabilities. The analysis shows this type of instability to be only marginally responsible for particle and energy transport. The required gradients could be reached only in correspondence to the temperature slopes arising at the boundary of the helical structure in the quasisingle helicity states. The dependence of the instability threshold on the relevant macroscopic quantities is considered. A discussion on the main differences in the driving mechanisms existing between the reversed field pinch and the tokamak configuration is addressed.