Session GO4: Reversed-Field Pinch

Development of a Reliable Operational Scenario for High Current Operation in RFX-mod

The achievement of plasmas with current values close to the maximum design point of 2 MA for the operation of RFX-mod Reversed Field Pinch (RFP) involved acting on three key issues: the RFP start-up method, the MHD equilibrium control and the plasma-wall interaction mitigation. The most effective start-up scheme for high current operation consisted in ramping-up the plasma current in RFP configuration, with an initial weak toroidal bias field (less than 0.1 T). The additional poloidal flux required has been obtained by doubling the flat-top poloidal power supplies, using part of the former toroidal ones. Mitigation of the plasma wall interaction has been achieved either reducing the content of Hydrogen trapped into the graphite first-wall and avoiding wall locking of the tearing modes, by means of improved error field correction and phase gain tuning on the involved modes. The control of MHD equilibrium has been obtained with new real-time algorithms, implemented for the control of reversal parameter F and the flat-top plasma current. All such actions allowed the access and first experiments at regimes previously not accessible for RFP plasmas.   

Improved confinement at high density and high beta in the MST

Improved confinement plasmas in MST are routine using current profile control to reduce tearing instabilities. With pellet injection, the density of these plasmas has been increased to values well above the Greenwald limit. At 0.2 MA, the achieved density exceeds the limit by 50{\%}. At 0.5 MA, an MST-record density of 0.7 x 10$^{20}$ m$^{-3}$ is achieved that exceeds the limit by 10{\%}. While confinement is improved at high density, tearing instabilities are not reduced to the same degree as at lower density. This may be due to the larger beta at high density, with total beta reaching 26{\%}. The central pressure gradient violates the Mercier criterion, and linear stability calculations indicate that pressure-driven tearing could be important. The maximum MST energy confinement time of 12 ms, achieved at well below the density limit, is within a factor of two of expectations for a tokamak of the same size, current, and heating power. Supported by USDOE.   

3D magnetic fields and plasma flow in helical RFX-mod equilibria

A spontaneous transition to a helical equilibrium with electron internal transport barriers (ITB) is observed in RFX-mod as the plasma current is raised [R. Lorenzini et al. Nature Phys. 5, 570 (2009)]. The transition can be stimulated and controlled by means of 3D magnetic fields from a system of 192 active coils, providing at the same time proper helical boundary conditions and dynamic error field correction. A global helical flow develops in these states and is expected to play an important role in their formation: it generates a large portion of the dynamo electric field in a laminar way and it may contribute, through its shear, to the ITB sustainment. The origin of this flow, from resistive MHD and/or ambipolar electric fields, will be discussed, along with the possibility to control it by 3D magnetic fields. Its role in error field screening and in the suppression of MHD modes that perturb the helical equilibrium will be investigated. The commonality of the above 3D physics issues with tokamaks and stellarators will be also discussed.   

Plasma Braking Due to External Magnetic Perturbations

The RFP EXTRAP T2R is equipped with a comprehensive active feedback system (128 active saddle coils in the full-coverage array) and active control of both resonant and non-resonant MHD modes has been demonstrated. The feedback algorithms, based on modern control methodology such as reference mode tracking (both amplitude and phase), are a useful tool to improve the ``state of the art'' of the MHD mode control. But this tool can be used also to improve the understanding and the characterization of other phenomena such as the ELM mitigation with a resonant magnetic perturbation or the plasma viscosity. The present work studies plasma and mode braking due to static RMPs. Results show that a static RMP produces a global braking of the flow profile. The study of the effect of RMPs characterized by different helicities will also give information on the plasma viscosity profile. Experimental results are finally compared to theoretical models.   

Optimization for low-aspect-ratio RFP configuration in RELAX

Equilibrium analyses have shown that the aspect ratio A is one of the important parameters for optimization of the RFP configuration because it affects the q profile or fraction of the pressure-driven bootstrap current. RELAX (A=R/a=0.5m/0.25m) is a low-A RFP machine to explore the potential advantages of low-A configurations. The discharge and plasma parameters in RELAX to date are as follows: plasma current up to 100kA, discharge duration of up to 2.5ms, electron density in the range from 0.2 to 2.0 10$^{19}$ m$^{-3}$ from interferometer, and electron temperature $\sim$ 100eV from double-filtered soft- X ray (SXR) measurements. We will describe two extreme discharge regions, i.e., extremely deep reversal and very shallow reversal regions, attained in RELAX. Extremely high $\Theta$ (up to $\sim$ 3.5), deep reversal (F down to $\sim$ - 1.5 ) regions have been attained in RELAX without discrete relaxation events. Edge magnetic fluctuation level is lower for the discharges in the extremely deep reversal region. On the other hand, in very shallow-reversal region where F $\sim$ 0, helically deformed hot core has been identified using SXR imaging diagnostics. Behavior of the MHD instabilities in these two interesting regimes will be discussed.   

Neutral Beam Injection as a Tool for Momentum Transport Studies in MST

A new 1 MW Neutral Beam Injector is installed and in operation on MST. The deposition of fast hydrogen neutrals in the core of the reversed field pinch serves as an external source of momentum which can be used to study momentum transport. Viscous transport is inadequate to explain previous momentum transport measurements using a biased electrode to induce toroidal plasma rotation. Measurements of magnetic mode parallel velocity and impurity velocity show an increase in toroidal rotation during NBI in MST plasmas. Preliminary evidence suggests that in non-reversed plasmas the core resonant mode which normally slows the plasma due to an electromagnetic torque generated by wall currents is suppressed, resulting in longer periods of rotation. Examination of ensembles of core mode locking times confirm that while the plasma is rotating faster due to NBI, the torque balance is unchanged during locking.   

Anisotropic ion heating in the MST RFP

In the Madison Symmetric Torus reversed-field pinch, discrete bursts of magnetic reconnection liberate a large amount of energy ($\sim $20 kJ) from the equilibrium magnetic field, a significant fraction of which (10-25{\%}) becomes ion thermal energy, more than doubling T$_{i}$ in $<$ 100 $\mu $sec. Recent charge exchange recombination spectroscopy measurements of the C$^{+6}$ impurity ion temperature reveal that this heating is often anisotropic, such that the rise in perpendicular temperature is greater than or equal to the rise in parallel temperature. Furthermore, the magnitude of the rise in both temperatures is lessened as the plasma density increases, although this effect is more pronounced for the parallel temperature. Models of ion heating are reviewed in light of these observations.   

The scaling of micro-turbulence in Reversed Field Pinch Plasmas

Previous investigations on Reversed Field Pinch (RFP) plasmas have not convincingly explained observations of turbulence driven transport in improved confinement discharges, where tearing mode activity is suppressed through current profile control. The scaling of transport and linear growth rate with gradient scale-lengths, plasma $\beta$, shear, normalized ion sound gyro-radius $\rho _\ast =\rho _s /a$, radial profile and other parameters may help differentiate between various plausible theories for small scale turbulence. In this work, we examine the Ion Temperature Gradient (ITG) mode, the Trapped Electron mode (TEM), Kinetic Ballooning mode (KBM) and others using the gyrokinetic code GYRO in a collsionless limit with a real RFP geometry. We investigate the critical $\beta$ for the ITG to KBM and TEM transitions (which are well known for tokamaks), for Madison symmetric torus (MST) parameters. Linear and nonlinear characteristics of gyrokinetic simulations such as saturation level, mean wave-number $<$k$>$ have been investigated for possible correlations with experiment.   

Nonlinear 3D MHD verification study: SpeCyl and PIXIE3D codes for RFP and Tokamak plasmas

A strong emphasis is presently placed in the fusion community on reaching predictive capability of computational models. An essential requirement of such endeavor is the process of assessing the mathematical correctness of computational tools, termed verification [1]. We present here a successful nonlinear cross-benchmark verification study between the 3D nonlinear MHD codes SpeCyl [2] and PIXIE3D [3]. Excellent quantitative agreement is obtained in both 2D and 3D nonlinear visco-resistive dynamics for reversed-field pinch (RFP) and tokamak configurations [4]. RFP dynamics, in particular, lends itself as an ideal non trivial test-bed for 3D nonlinear verification. Perspectives for future application of the fully-implicit parallel code PIXIE3D to RFP physics, in particular to address open issues on RFP helical self-organization, will be provided. \\[4pt] [1] M. Greenwald, Phys. Plasmas \textbf{17}, 058101 (2010) \\[0pt] [2] S. Cappello and D. Biskamp, Nucl. Fusion \textbf{36}, 571 (1996) \\[0pt] [3] L. Chac\'{o}n, Phys. Plasmas \textbf{15}, 056103 (2008) \\[0pt] [4] D. Bonfiglio, L. Chac\'{o}n and S. Cappello, Phys. Plasmas \textbf{17} (2010)   

Flow, magnetic topology and transport in the edge region of RFX-mod device

Sheared flows are recognized to play an important role in regulating turbulent transport since the discovery of improved confinement regimes. Recently the interest in the relationship between flow and magnetic topology received great attention, also motivated by experiment with active MHD control of plasma instabilities through edge stochastization. We present a detailed comparison between edge flow and plasma topology in the edge region of the RFX-mod reversed field pinch experiment. Information on plasma flow is deduced both through insertable probes and a toroidally distributed array of langmuir probes. Different parallel and perpendicular flows are compared with different magnetic topology reconstructed through a Field Line Tracing codes. Hints on the relation between edge magnetic topology and the appearance of strong temperature gradients at the edge is also investigated.   

Origin of density fluctuations and particle transport in a stochastic magnetic field

We present an experimental investigation of the origin of density fluctuations and magnetic fluctuation-induced particle transport associated with tearing instabilities in the MST RFP. Our studies focus on plasma evolution during the sawtooth crash, when the stochastic magnetic field is strongest and density profile relaxation occurs. Measurements are accomplished by combining multiple interferometric techniques, including standard and differential interferometry, as well as Faraday rotation. Both the sign and amplitude of the nonlinearly-driven advection are measured in wavenumber space for the dominant core-resonant modes. Initial measurements show that density fluctuations result from both linear advection and nonlinear three-wave interactions. Observations also reveal the importance of the edge-resonant m=0 mode in mediating nonlinear three-wave interactions which serve to optimize the phase between density and magnetic fluctuations for maximum flux. By removing the m=0 mode resonant surface, density profile relaxation is no longer observed.   

Measurement of magnetic field using a spectral motional Stark effect diagnostic

We are continuing to develop a diagnostic based on the motional Stark effect (MSE) to provide internal magnetic field measurements in high-temperature plasmas. A high-energy beam of neutral hydrogen atoms is injected into the plasma, with a component of the atom velocity perpendicular to the magnetic field. The atoms experience a Lorentz electric field and emit Stark-split line spectra. The entire Stark spectrum is recorded and analyzed. This makes this diagnostic technique applicable to the measurement of low fields (down to 0.2 T), or to conditions in which polarization information may be compromised (e.g., burning plasma devices). A new analysis scheme has been developed to infer both the polarization direction and the magnitude of Stark splitting, from which both the direction and magnitude of the local magnetic field can be derived. Improved modeling of the relative magnitudes and positions of the Stark multiplets is underway using the Atomic Data and Analysis Structure (ADAS). This improvement is expected to reduce the systematic uncertainty of the measured magnetic field.   

Lithium wall conditioning in RFX-mod

The first wall of RFX-mod Reversed Field Pinch experiment is entirely covered by graphite tiles. This prevents plasma density control during pulses, because the graphite acts as a Hydrogen reserve providing an influx that depends mainly on the power loads on the wall. Different techniques of wall conditioning were used (He GDC, backing, etc.), but they were not able to provide both a good density control and better plasma performances. For this reason we tested the effect of wall conditioning with Lithium. After Lithium conditioning the wall adsorbs a larger fraction of Hydrogen with respect to the standard clean graphite, allowing a better control of plasma density and the achieving of the highest RFX-mod plasma current (over 1.9 MA). The main effects on plasma behavior are a higher density peaking factor, mostly due to a lower density at the edge in presence of a higher temperature. Particle confinement time increases while energy confinement time does not show significant improvement.   

Observation of Alfv\'{e}n eigenmodes in reversed-field pinch plasmas

High frequency (up to 1.5 MHz) Alfv\'{e}n eigenmodes have been detected in the RFX-mod reversed-field pinch (RFP) device by means of insertable edge magnetic probes. The Alfv\'{e}nic nature is deduced by the linear relation between the Alfv\'{e}n velocity of the investigated plasmas and the measured frequencies. A wide range of experimental conditions have been explored in terms of plasma current (0.4-1.8 MA), electron density (0.5-8 x 1019 m-3) and working gas (H and He). The coherent activity has been clearly observed on the parallel component of the magnetic field, which, at the edge of the RFP, is the poloidal one. Two distinct kinds of modes have been observed: the first consists of two modes together and continuously present during the discharges at two frequencies above 500 kHz; the second, at a lower frequency appears during the so-called Single Helical Axis states characterizing the high current discharges of RFX-mod.   

Impurity expulsion in an RFP plasma and the role of temperature screening

In the improved confinement discharges of the Madison Symmetric Torus reversed field pinch, the density profile of $C^{+6}$, measured using Charge-Exchange Recombination Spectroscopy, is hollow. The core impurity density decays in time after the transition to improved confinement, concurrent with an increase of impurity density outside mid-radius, indicating an outward convection of impurities from the core of the plasma. Our analysis using neoclassical impurity transport theory shows that the observed hollow profile could possibly be explained by a mechanism known as ``temperature screening,'' where a thermal force due to a strong ion temperature gradient and high collisionality of $C^{+6}$ ions expel impurities from the core of the plasma.