Reversed Field Pinch Research Articles

An overview of diagnostic upgrade and experimental progress in the KTX

The Keda Torus eXperiment (KTX) is still operated in the commissioning phase, and preparation for the operation capability of the KTX phase II upgrade is underway. The diagnostics in the KTX have been greatly developed: (1) the terahertz interferometer has been upgraded to seven chords for electron density profile inversion; (2) a Thomson scattering system with a 5 Joule laser has been installed and commissioning is in progress; (3) a 3D movable probe system has been developed for the electromagnetic turbulence measurement; (4) double-foil soft x-ray imaging diagnostics have been set up and a bench test has been completed; (5) an edge capacitive probe has been installed for the radial electrical field measurement; (6) a multi-channel spectrograph system has been built for detecting impurities of carbon and oxygen. In addition, the design of a new compact torus injection system has been completed for feeding and momentum driving. Pilot research, such as the 3D reversed field pinch physics and electromagnetic turbulence, etc, have been conducted in the discharge status of the KTX. The 3D spectra characters of electromagnetic turbulence are firstly measured using a classical two-point technique by Langmuir probe arrays set on the 3D movable probe system and edge magnetic sensors. The forward scattering is collected by the interferometer system, which shows the potential for turbulence research. The electromagnetic turbulence is tentatively investigated in the KTX. The formation of a quasi-single-helicity state in the KTX regime is also preliminarily explored in simulation.

Intrinsic flow and tearing mode rotation in the RFP during improved confinement

We use charge exchange recombination spectroscopy to make the first localized measurements of impurity ion flow velocity profiles in the reversed field pinch. Measurements in improved confinement plasmas reveal an intrinsic flow profile that is peaked on the axis and mostly parallel to the equilibrium magnetic field. The toroidal flow decreases in time at off-axis locations where tearing modes are resonant, giving rise to a highly sheared flow profile near the axis. The tearing mode phase velocity correlates strongly with toroidal flow near the resonant surface and weakly with flow in other locations, providing an opportunity to verify the commonly held assumption that the plasma and mode move together at the resonant surface. Mechanisms for the observed momentum loss during the improved confinement period are evaluated, and it is found that eddy currents in the conducting shell caused by the rotation of the dominant tearing mode dominate over other losses.

A measure of fast ion beta at marginal stability in the reversed field pinch

Energetic ions are well confined in the core of the reversed field pinch and a substantial population develops rapidly during tangential neutral beam injection. A saturated fast ion density is observed within several milliseconds and coincides with the onset of energetic particle mode activity. First measurements of the fusion product profile determine the fast ion density and pressure profiles, the latter of which when combined with neutral particle analysis of the energy distribution. These are key measurements in explaining the limiting behavior of the fast ion profile in response to a combination of effects. Tearing mode activity affects the fast ion profile, and the fast ions noticeably influence the core-most tearing mode. The nonlinear situation settles into a marginally stable state where the EPM transports fast ions down a steep gradient to a region where their confinement is limited by stochastic orbit and charge exchange losses. In the state at marginal stability (achieved in one set of experimental conditions with full 1 MW neutral beam power), a critical fast ion beta gradient is measured that limits the core , or nearly four times the core thermal , but less than a strictly classical calculation predicts.

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.

A three-dimensional magnetohydrodynamic equilibrium in an axial coordinate with a constant curvature

Motivated by the superior confinement observed in the relaxed three dimensional (3D) states in the reversed field pinch, 3D plasma equilibria in coordinate systems based on space curves with a constant curvature as the axial coordinates are studied by using the method of metric perturbation. Constancy of the curvature allows the development of magnetohydrodynamic equilibrium with asymptotic good 2D flux surfaces near the coordinate axis. The perturbation parameter is the product of the torsion variation along the coordinate axis and the distance from it. The lowest order equilibrium with good 2D flux surfaces is symmetric with respect to translation along the space curve. It embodies the approximate toroidal-helical symmetry and is determined by a generalized Grad–Shafranov equation which includes information of the constant curvature and the average torsion of the space curve. Based on this fundamental equilibrium, a formal scheme is developed that allows us to find the ideal MHD equilibrium taking into account the full metric variation of the torsion along the spatial axis. In this limit, the flux surfaces are shown to exist for the full plasma. Numerical examples are given for the lowest order equilibria. It is suggested that equilibria based on this type of coordinates can allow easier evaluation of plasma shapes and magnetic boundary conditions that are more compatible with the relaxed central core. This could be the needed requirement for strongly self-organized equilibria with a large good confinement region.

Upgrades of the RFX-mod reversed field pinch and expected scenario improvements

RFX-mod is a Reversed Field Pinch device that allowed performing experiments in regimes with a plasma current up to 2 MA, thanks to its MHD active control system. Experiments have shown that improved plasma performances are obtained when in the resonant part of the m = 1 spectrum one dominant tearing mode is much higher than the other secondary ones (quasi single helicity states). Tearing modes play a crucial role in determining energy and particle transport. Based on the present understanding of the interplay between passive conductive boundaries and tearing modes in an RFP, an upgrade of RFX-mod machine assembly has been designed, dubbed RFX-mod2, and it is now being implemented. The highly resistive Inconel vessel will be removed, graphite tiles will be attached to the copper stabilizing shell and the stainless steel support structure will be modified in order to be vacuum tight. In RFX-mod2, the shell-plasma proximity decreases from b/a = 1.11 to b/a = 1.04 and copper, instead of Inconel, will be the continuous conducting structure nearest to the plasma. MHD non-linear simulations show that secondary tearing modes amplitude and the edge bulging due to their phase locking will decrease; moreover the plasma current threshold for tearing modes wall locking will also significantly increase.

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.

Forward Scattering Measurement Based on Terahertz Microwave Interferometer on KTX Reversed Field Pinch

Electron density fluctuation has been measured based on the collect forward scattering method using a single-chord microwave interferometer system on the Keda Torus eXperiment (KTX) reversed field pinch. The interferometer system is a heterodyne one with two terahertz solid-state sources with frequency around 650 GHz, and the transmitted beam and forward scattering beam are received simultaneously by a Schottky planar diode mixer with sensitivity about 500 mV/mW. Constrained by the beamwidth and geometry limitation, the measurable wave vector range is $k_{w}\le 5 {\mathrm {cm}}^{-1}$ with a resolution $\Delta k\approx 2.07\,{\mathrm {cm}}^{-1}$ . MHD activities are detected via this forward scattering technique. The results are consistent with other diagnostics, such as the chord averaged electron density, the edge magnetic probe, and high-speed charge-coupled device (CCD) camera.

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.

Electron temperature gradient driven instabilities in helical reversed-field pinch plasmas

We describe the occurrence of electron temperature gradient driven micro-instabilities in the helical states of RFX-mod reversed-field pinch plasmas. These plasmas are usually characterized by the presence of large, radially localized electron temperature gradients. Using realistic geometry and profiles, micro-tearing modes and electron temperature gradient modes turn out to regularly co-exist in the region of the temperature barrier. In the paper, we discuss the main features of such instabilities, especially focusing on the distinctive aspects of the helical geometry with respect to the toroidal symmetry.

Direct Measurement of a Toroidally Directed Zonal Flow in a Toroidal Plasma.

Zonal flow appears in toroidal, magnetically confined plasmas as part of the self-regulated interaction of turbulence and transport processes. For toroidal plasmas having a strong toroidal magnetic field, the zonal flow is predominately poloidally directed. This Letter reports the first observation of a zonal flow that is toroidally directed. The measurements are made just inside the last closed flux surface of reversed field pinch plasmas that have a dominant poloidal magnetic field. A limit cycle oscillation between the strength of the zonal flow and the amplitude of plasma potential fluctuations is observed, which provides evidence for the self-regulation characteristic of drift-wave-type plasma turbulence. The measurements help advance understanding and gyrokinetic modeling of toroidal plasmas in the pursuit of fusion energy.

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.

Fast ion transport in the quasi-single helical reversed-field pinch

The reversed-field pinch (RFP) can spontaneously transition from an axisymmetric magnetic topology to a 3D-helical geometry. Investigations on fast ion transport associated with energetic particle driven Alfven instabilities, tearing mode induced stochasticity, and neoclassical effects have been performed on the Madison Symmetric Torus. STELLGAP produced shear-Alfven continua seeded with V3FIT 3D-equilibrium reconstructions describe the response of Alfvenic bursting activity as a direct consequence of the equilibrium change on the fast ion resonance. Far infrared interferometry resolved electron density perturbations associated with the bursts provide a spatial measurement of the mode structure and support the reconstructions. The bursts produce no global resonant fast ion transport; however, their disappearance at a high core-resonant amplitude implies other transport mechanisms at play. Neutral particle analysis and neutron signals suggest fast ion losses at sufficient core tearing mode strength, supporting the lack of Alfvenic activity. The guiding-center code ORBIT corroborates rapid fast ion loss times in the helical state largely as a consequence of remnant tearing modes. Additionally, ORBIT simulations demonstrate little neoclassical enhancement of particle transport. While superbanana orbits may exist, the growth in the core-resonant fast ion island and the associated secondary mode overlap govern the largest transport process, leading to robust fast ion losses in the 3D-RFP.The reversed-field pinch (RFP) can spontaneously transition from an axisymmetric magnetic topology to a 3D-helical geometry. Investigations on fast ion transport associated with energetic particle driven Alfven instabilities, tearing mode induced stochasticity, and neoclassical effects have been performed on the Madison Symmetric Torus. STELLGAP produced shear-Alfven continua seeded with V3FIT 3D-equilibrium reconstructions describe the response of Alfvenic bursting activity as a direct consequence of the equilibrium change on the fast ion resonance. Far infrared interferometry resolved electron density perturbations associated with the bursts provide a spatial measurement of the mode structure and support the reconstructions. The bursts produce no global resonant fast ion transport; however, their disappearance at a high core-resonant amplitude implies other transport mechanisms at play. Neutral particle analysis and neutron signals suggest fast ion losses at sufficient core tearing mode strength, suppor...

The scale-to-scale energy transfers correlated with the development of turbulence in toroidal plasmas

Two different directions of scale-to-scale energy transfer that corresponds to forward and inverse energy cascades, respectively, were clarified in toroidal plasma turbulence by means of experimental analysis. In the present work we first report the evidence that the turbulence dominated by broad wavenumber spectrum was developed under the action of forward (direct) energy cascade in a reversed field pinch (RFP) plasma, while the generation of GAM zonal flow (ZF) was related with the energy concentrating into low frequency region from higher frequency region due to inverse energy cascade in a tokamak plasma. The two evidences are compared. The results indicate a modulation mechanism in turbulence which is relative to the generation or development of specific turbulent flows. This hints a correlation between energy transfer and the development of toroidal plasma turbulence.

Construction of an EBW Heating System for the MST RFP

The first observation of rf heating in a reversed field pinch (RFP) using the electron Bernstein wave (EBW) has been demonstrated on Madison Symmetric Torus (MST). The design of the RF heating system used in this experiment is described. Klystron and antenna limitations are examined during launch into the plasma.

Lagrangian Coherent Structures as a new frame to investigate the particle transport in highly chaotic magnetic systems

The concept of Lagrangian Coherent Structures (LCS) is here applied to investigate in a new perspective the particles transport in chaotic magnetic configurations. A paradigmatic and simplified magnetic configuration is revisited before extending the analysis to a more realistic one. Preliminary results concerning the typical dynamics of the Reversed Field Pinch (RFP) device are shown.

Role of resistivity and viscosity in the excitation of stable m = 0 modes during the RFP sawtooth crash

Visco-resistive magnetohydrodynamic simulations are used to investigate the role of resistivity and viscosity in the reversed field pinch sawtooth crash. Specifically, we examine the temporal behavior of the linearly stable (m, n) = (0, 1) mode. Both volume-averaged dissipation and dissipation levels in the region near the m = 0 resonance are found to influence characteristic time scales. Increasing resistivity causes the mode rise time, fall time, and total crash duration to decrease, while increasing viscosity has the opposite effect. Examination of energy flow during the sawtooth crash reveals that despite the linear stability of the (0, 1) mode, it receives most of its energy from the mean current profile during the crash rather than from nonlinear interactions with other modes. Resistivity and viscosity do not impact mode behavior directly through dissipative energy loss but rather through modification of the large scale current profile evolution and radial structure of the mode. Computational results are compared to experimental data from the Madison Symmetric Torus and found to largely agree when resistivity and viscosity are similar.

Measurements of Impurity Transport Due to Drift-Wave Turbulence in a Toroidal Plasma.

The first direct measurements of an impurity particle flux driven by drift-wave turbulence in a toroidal magnetized plasma are reported. The correlation between the impurity density and radial velocity fluctuations is measured using ion Doppler spectroscopy. The small, very fast radial velocity fluctuation is resolved with the aid of a new linearized spectrum correlation analysis method that rejects uncorrelated noise as the sample size increases. The measured C^{2+} turbulent impurity flux in the edge of the plasma is directed inward and is consistent with impurity density measurements. This is also the first direct evidence for fluctuation-induced transport due to trapped-electron-mode turbulence in reversed field pinch plasmas.

Simulation, design, and first test of a multi-energy soft x-ray (SXR) pinhole camera in the Madison Symmetric Torus (MST).

A multi-energy soft x-ray pinhole camera has been designed and built for the Madison Symmetric Torus reversed field pinch to aid the study of particle and thermal-transport, as well as MHD stability physics. This novel imaging diagnostic technique combines the best features from both pulse-height-analysis and multi-foil methods employing a PILATUS3 x-ray detector in which the lower energy threshold for photon detection can be adjusted independently on each pixel. Further improvements implemented on the new cooled systems allow a maximum count rate of 10 MHz per pixel and sensitivity to the strong Al and Ar emission between 1.5 and 4 keV. The local x-ray emissivity will be measured in multiple energy ranges simultaneously, from which it is possible to infer 1D and 2D simultaneous profile measurements of core electron temperature and impurity density profiles with no a priori assumptions of plasma profiles, magnetic field reconstruction constraints, high-density limitations, or need of shot-to-shot reproducibility. The expected time and space resolutions will be 2 ms and <1 cm, respectively.