Quasi-single Helicity Research Articles

Dependence of Properties of Quasi-Single-Helicity States on Field Reversal Parameter in a Low-Aspect-Ratio Reversed Field Pinch

Dependence of several properties of Quasi-Single-Helicity (QSH) states on field reversal parameter F is investigated in low-aspect-ratio reversed-field-pinch (RFP) machine RELAX. QSH probability with dominant n = 5 or 6 (n is toroidal mode number) is higher in low F region than high F. QSH probability and duration with dominant n = 3 or 4 are higher in high F region. These suggest change of innermost resonant n with F as shown in an equilibrium reconstruction. QSH probability, duration and dominant mode amplitude with the dominant mode of possible innermost resonant n = 3, 4 or 5 are higher than other n, which is desirable for improved confinement. Averages of the spectral index NS for flat-topped plasma current phases are similar to that predicted by a simulation which has shown NS is lower as aspect ratio is lower. This agreement and the higher QSH probability of 2 - 3 % than another high aspect ratio RFP machine may show advantage of the low aspect ratio RFP in achieving QSH.

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

Characterization of Quasi-Single-Helicity States in a Low-Aspect-Ratio RFP

Characteristics of quasi-single-helicity (QSH) states have been studied in a low-aspect-ratio reversed field pinch (RFP) machine RELAX mainly by magnetic diagnostics. Internal profiles of the fluctuating radial, poloidal and toroidal magnetic fields have shown good agreement with eigenfunctions of a single helical mode. The edge magnetic fluctuation spectra are somewhat broader than what are expected from internal magnetic field profiles. In spite of these slight discrepancies, the usual measure for the QSH, the spectral index NS lower than 2, still provides a reasonable measure for QSH states in RELAX. The QSH persistence has been improved in RELAX by the reduction of the poloidal resistance of flanges at poloidal gaps, mainly due to the improved axisymmetry of the toroidal magnetic field. QSH persistence more than 30% of the flat-topped current phase has been realized with current density lower than in other RFP, and probability of spontaneous QSH is 12.8 ±7.3% which is higher than high-aspect-ratio RFP. It suggests the advantage of low-aspect-ratio configuration in attaining to the QSH. Comparison with recent experiments using active resonant perturbation may suggest the importance of further reduction of field errors to improve the quality of QSH. c

Design and Initial Result of Time-Resolved Vertical Soft X-Ray Imaging System in Low-<i>A </i>RFP

A time-resolved vertical soft X-ray (SXR) imaging system was constructed. To identify the structure of the magnetic island using the obtained SXR images, we calculated the two-dimensional (2-D) image expected from low-aspect-ratio (low-A) reversed field pinch (RFP) plasmas. The 2-D image was found to reflect the change in the radiation power caused by the magnetic island. A preliminary experimental result in which we observed vertical SXR images from the quasi-periodic quasi-single helicity (QSH) state in low-A RFP plasmas is presented. We successfully obtained the time evolution of SXR images from the vertical port. By comparing the observed images with simulated images, we found that the evolution of the experimental SXR image suggests a rotating helical configuration.

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.

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.

Impurity transport studies in RFX-mod multiple helicity and enhanced confinement QSH regimes

The transport of intrinsic and artificially introduced impurities is investigated in the multiple helicity (MH) and quasi-single helicity (QSH) plasma regimes of the RFX-mod reversed-field pinch. Impurities are introduced through Ni laser blow-off and Ne gas puffing in both magnetic confinement scenarios. Simulation of experimental spectroscopic measurements, including line and soft x-ray emission, electron density and radiated power is carried out with a one-dimensional collisional–radiative model. For both QSH and MH an outwardly directed pinch velocity with a large barrier in the edge and no reversal is determined, accompanied by a diffusion coefficient that is an order of magnitude greater in the core than at the edge. The established transport parameters are similar for the Ni and Ne injected impurities with the transition region and barrier less external and stronger in the QSH regime.

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.

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.

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.

Experiments and modelling of active quasi-single helicity regime generation in a reversed field pinch

The interaction of a static resonant magnetic perturbation (RMP) with a tearing mode (TM) is becoming a relevant topic in fusion plasma physics. RMPs can be generated by active coils and then used to affect the properties of TMs and of the corresponding magnetic islands. This paper shows how the feedback system of the EXTRAP T2R reversed field pinch (RFP) can produce a RMP that affects a rotating TM and stimulate the transition to the so-called quasi-single helicity (QSH) regime, a RFP plasma state characterized by a magnetic island surrounded by low magnetic chaos. The application of the RMP can increase the QSH probability up to 10% and enlarge the size of the corresponding island. Part of the experimental results are supported by a theoretical study that models the effect of the active coils on the magnetic island.

Numerical studies of transport mechanisms in RFX-mod low magnetic chaos regimes

The magnetic topology of quasi-single helicity (QSH) regimes, in the reversed field pinch experiment RFX-mod, is characterized by a helical magnetic structure surrounded by partially chaotic field lines. In this paper we investigate the transport mechanisms within these helical structures, in particular, the particle diffusion due to the residual magnetic chaos. The diffusion coefficients have been estimated for different plasma temperatures, collisionality and magnetic perturbation amplitudes. In the typical high temperature QSH regimes of RFX-mod, ambipolar transport between ions and electrons is found to be ensured by the non-zero but very low level of secondary modes and by the reduced collisionality. Trapped ions give the largest contribution to particles diffusion, while those passing are almost well confined within the helical structure. In the best QSH experimental performances, ion diffusion coefficients computed by numerical simulations are not affected significantly by the residual magnetic chaos and are very close to those expected in a regime with only helical conserved surfaces.

Improved confinement with internal electron transport barriers in RFX-mod

RFX-mod reliably operates at 1.5 MA, the highest current ever achieved on a reversed field pinch device thanks to the the feedback control on multiple magnetohydrodynamic modes.In these high current discharges magnetic topology spontaneously self-organizes in an Ohmic helical symmetry, the quasi single helicity (QSH) state, in which the magnetic dynamics is dominated by the innermost resonant mode, with the new magnetic axis helically twisting around the geometrical axis of the torus.Inside the helical structure energy confinement is enhanced and electron temperatures exceeding 1 keV are measured, with steep gradients, which identify an internal transport barrier. Separatrix expulsion and symmetric electron temperature profiles with high gradients are obtained for ratios between the dominant mode and total B above about 4%. The measured electron temperature peak involves a large fraction of the plasma cross section, corresponding to an improvement in the global electron energy confinement up to a factor 2. The steep temperature profiles obtained in QSH conditions correspond to an electron thermal diffusivity reduced by more than one order of magnitude.Perturbative experiments (pellets and impurity laser blow off injections) have been performed to study particle confinement inside and outside the thermal island. Inside the helical structure experimental evidence of main gas confinement increase has been obtained, while for impurities there is no evidence of confinement increase.

2D characterization of core thermal topology changes in controlled RFX-mod QSH states

In the reversed field pinch RFX-mod device, the achievement of high plasma currents (Ip ⩾ 1.3 MA) has allowed the appearance of a new kind of large thermal structures emerging in the plasma core during the so-called quasi-single helicity (QSH) regimes. These structures correspond to a helical equilibrium established in the plasma, which has been dubbed as the single helical axis (SHAx) state. The topological features of this new type of thermal structures covering most of the plasma core have been experimentally investigated here. Analyses have been performed by means of three diagnostics, simultaneously and routinely running on RFX-mod: the soft x-ray (SXR) camera, the Thomson scattering diagnostic for the electron temperature (Te) profile estimation and the SXR tomography. In particular, a 2D map reconstruction of Te has been performed: the core electron temperature asymmetries mostly account for the ones in the reconstructed SXR emissivity. The magnetic topology of these QSH thermal structures has also been analysed and numerically investigated by the Hamiltonian guiding centre code ORBIT: magnetic and thermal structures have been identified, in position and topological features. Also the Te profile temporal evolution, provided by the tomographic diagnostic and the SXR camera, has been investigated, showing that the transition to SHAx does not develop in a unique way.

Stability threshold of ion temperature gradient driven mode in reversed field pinch plasmas

For the first time in the reversed field pinch (RFP) configuration, the stability threshold of the ion temperature gradient driven (ITG) mode is studied by linear gyrokinetic theory. In comparison with tokamaks, the RFP configuration has a shorter connection length and stronger magnetic curvature drift. These effects result in a stronger instability driving mechanism and a larger growth rate in the fluid limit. However, the kinetic theory shows that the temperature slopes required for the excitation of ITG instability are much steeper than the tokamak ones. This is because the effect of Landau damping also becomes stronger due to the shorter connection length, which is dominant and ultimately determines the stability threshold. The required temperature slope for the instability may only be found in the very edge of the plasma and/or near the border of the dominant magnetic island during the quasi-single helicity state of discharge

MHD Properties of Low-aspect Ratio RFP in RELAX

The low-aspect-ratio (A) reversed field pinch (RFP) offers attractive properties such as enhanced bootstrap current and simpler MHD mode dynamics. The RELAX (REversed field pinch of Low-Aspect ratio eXperiment) machine with the world’s lowest A of 2 (R/a = 0.5 m/0.25 m) has been constructed to explore the RFP properties in low-A regime. In flat-topped low-A RFP discharges in RELAX, plasma current of ~50 kA has been attained with discharge duration of ~2 ms. In round-topped discharges with plasma current of ~70 kA, quasi-periodic growth of a single helical mode has been observed. When the dominant m = 1/n = 4 mode grows, the toroidal mode spectrum looks like that of the quasi-single helicity (QSH) RFP state with higher amplitude. MHD equilibrium analyses using a reconstruction code have shown that the bootstrap current fraction is lower than ~5% in the present RELAX plasmas, and it will be ~25% if we could achieve the plasma density of 4 × 1019 m−3 and electron temperature of 300 eV at plasma current of ~100 kA.

Mode coupling studies in the RFX-mod reversed field pinch

In this paper a linear model is presented and used to interpret the active applications of an external static or rotating poloidally symmetric perturbation to a reversed field pinch plasma. The plasma response is evaluated considering also the sidebands generated by the current distribution produced by the coils. We evaluate the plasma response, obtaining information about mode coupling. In ‘quasi-single helicity’ states—in contrast to ‘multiple helicity’ cases— the non-linear interaction between m = 1 dominant core-resonant modes seems not to adequately explain the (0, 1) mode evolution. Implications for the plasma dynamo mechanisms are accordingly deduced and discussed in comparison with previous findings, and mainly, we conclude that the (0, 1) mode could be an important factor in the torque balance rather than as an active dynamo driver.

Electron temperature profiles in RFX-mod

Electron temperature profiles have been measured by the main Thomson scattering (TS) diagnostic on the RFX-mod reversed field pinch experiment in Padova, Italy. The increased accuracy and spatial and temporal resolution permits one to measure in detail the improvements in Te profiles, obtained with the active saddle coil system, which allows one to obtain core temperature 30% higher and scaling stronger with plasma current, steeper gradients in the core (+30%) and at the edge (+60%). 1D power balance calculations show that the active control of MHD modes largely reduces the values of electron heat diffusivity along the whole plasma radius, with ∼50% reduction at the edge and ∼30% in the core. The resulting electron energy confinement time is doubled. Further improvements occur during quasi-single helicity (QSH) states: the new TS allows one to study in detail the hot island that develops in the core. A characterization of the island electron thermal profile is presented, in terms of width, temperature increase, gradients and asymmetry; the effect on density profile is also discussed. A 2D transport code has been applied to calculate the heat diffusivity inside the magnetic island corresponding to the QSH state, also considering the correlation between temperature increase and pressure gradient with the chaos level around the island. Finally, electron energy confinement time during QSH states is compared with that in MH states.

Microwave Imaging Reflectometry Experiment in TPE-RX

Microwave imaging reflectometry (MIR) was developed in TPE-RX, one of the world’s largest reversed field pinch (RFP) devices. The system optics are made of aluminum mirrors, Teflon lenses, and Plexiglas plates in order to reduce size. In this system, frequencies are stabilized so that noise can be reduced using narrow bandpass filters. A 4×4 2-D mixer array and phase detection system have also been developed. With this system, density fluctuations in the high-Θ RFP plasma, pulsed poloidal current drive (PPCD) plasma, and quasi-single helicity (QSH) plasma are observed in TPE-RX. This is the first MIR experiment in an RFP device.

Quasi-Periodic Growth of a Single Helical Instability in a Low-Aspect Ratio RFP

Quasi-periodic growth of a single core-resonant instability has been observed in a low-aspect ratio (low-A) reversed field pinch experiment in RELAX. In round-topped current discharges, the innermost core resonant m = 1/n = 4 mode grows with suppression of the neighboring m = 1/n = 5, 6 modes. The resultant toroidal mode spectrum of the m = 1 modes is similar to that of the quasi-single helicity (QSH) state with higher amplitudes. These phenomena are discussed along with the low-A characteristic of RELAX, indicating simpler MHD mode dynamics and easier access to the QSH state.