Single Helicity Research Articles

Electrostatically driven helical plasma state

A novel plasma state has been found in the presence of a uniformly applied axial magnetic field in periodic cylindrical geometry. This state is driven electrostatically by helical electrodes, providing a driving field that depends on the radius and mθ−nζ, where θ is the poloidal angle and ζ=z/R is the toroidal angle. We focus on m=n=1. The radial magnetic field at the wall is taken to be zero. With weak driving, the resulting distortion is very small, but for stronger driving, the mean field of the state has field line safety factor q0(r) just above the pitch of the electrodes m∕n = 1 except near the edge, where q0 increases monotonically. This state is characterized as a single helicity Ohmic equilibrium with the helical symmetry of the applied field. The plasma appears to be close to force-free in the interior, but current density crosses the magnetic flux surfaces near the edge, where current must enter and exit through the helical electrodes. This perpendicular current density drives large helical plasma flows. The sensitivity of this state to flow boundary conditions, plasma resistivity profile, the strength of electrostatic driving, and parameters such as the loop voltage and the Lundquist number is explored. The magnetic helicity is calculated for both the transient period and time-asymptotic state. Possible applications to current drive in toroidal confinement devices and to electrical transformers are discussed.

4D scattering amplitudes and asymptotic symmetries from 2D CFT

We reformulate the scattering amplitudes of 4D flat space gauge theory and gravity in the language of a 2D CFT on the celestial sphere. The resulting CFT structure exhibits an OPE constructed from 4D collinear singularities, as well as infinite-dimensional Kac-Moody and Virasoro algebras encoding the asymptotic symmetries of 4D flat space. We derive these results by recasting 4D dynamics in terms of a convenient foliation of flat space into 3D Euclidean AdS and Lorentzian dS geometries. Tree-level scattering amplitudes take the form of Witten diagrams for a continuum of (A)dS modes, which are in turn equivalent to CFT correlators via the (A)dS/CFT dictionary. The Ward identities for the 2D conserved currents are dual to 4D soft theorems, while the bulk-boundary propagators of massless (A)dS modes are superpositions of the leading and subleading Weinberg soft factors of gauge theory and gravity. In general, the massless (A)dS modes are 3D Chern-Simons gauge fields describing the soft, single helicity sectors of 4D gauge theory and gravity. Consistent with the topological nature of Chern-Simons theory, Aharonov-Bohm effects record the “tracks” of hard particles in the soft radiation, leading to a simple characterization of gauge and gravitational memories. Soft particle exchanges between hard processes define the Kac-Moody level and Virasoro central charge, which are thereby related to the 4D gauge coupling and gravitational strength in units of an infrared cutoff. Finally, we discuss a toy model for black hole horizons via a restriction to the Rindler region.

Nonlinear evolution of multi-helicity neo-classical tearing modes in rotating tokamak plasmas

Plasma perturbations from the core and/or boundary regions of tokamaks can provide seed islands for the excitation of neo-classical tearing modes (NTMs) with negative , where is the linear instability parameter of the classical tearing mode. In this work, by means of reduced magnetohydrodynamic simulations, we numerically investigate the nonlinear evolution of multi-helicity NTMs in rotating tokamak plasmas with these two types of plasma perturbations with different boundary conditions. In the first case of initial plasma perturbations from the core region with a zero boundary condition, the meta-stable property of seed-island triggered NTM with negative is verified in the single helicity simulation. Nevertheless in the multiple helicity simulation, this seed-island triggered NTM with negative can be suppressed by a spontaneous NTM with positive through the competitive interaction between NTMs with different helicities. If a fixed poloidal rotation is taken into account in the first case, two different helicity NTMs could coexist in the saturation stage, which is different qualitatively from the process without plasma rotation. In the second case of initial plasma perturbations from the boundary region with a nonzero boundary condition, as the amplitude of plasma perturbations on the boundary increases, the mode with negative gradually changes from the driven-reconnection state to the NTM state, accompanied by an enhancement of magnetic island width in the single helicity simulation. Nevertheless in the multi-helicity simulation, the spontaneous NTM with positive can make the driven-reconnection triggered NTM with negative transfer from the NTM state back to the driven-reconnection state again. The underlying mechanism behind these transitions is analyzed step by step. Effects of fixed and unfixed poloidal rotations on the nonlinear interaction processes are also investigated in detail. In addition, the appearance and disappearance of the magnetic stochasticity resulting from the nonlinear coupling among the multi-helicity NTMs are discussed in the second case.

Internal Transport Barrier Broadening through Subdominant Mode Stabilization in Reversed Field Pinch Plasmas.

The reversed field pinch (RFP) device RFX-mod features strong internal transport barriers when the plasma accesses states with a single dominant helicity. Such transport barriers enclose a hot helical region with high confinement whose amplitude may vary from a tiny one to an amplitude encompassing an appreciable fraction of the available volume. The transition from narrow to wide thermal structures has been ascribed so far to the transport reduction that occurs when the dominant mode separatrix, which is a preferred location for the onset of stochastic field lines, disappears. In this Letter we show instead that the contribution from the separatrix disappearance, by itself, is marginal and the main role is instead played by the progressive stabilization of secondary modes. The position and the width of the stochastic boundary encompassing the thermal structures have been estimated by applying the concept of a 3D quasiseparatrix layer, developed in solar physics to treat reconnection phenomena without true separatrices and novel to toroidal laboratory plasmas. Considering the favorable scaling of secondary modes with the Lundquist number, these results open promising scenarios for RFP plasmas at temperatures higher than the presently achieved ones, where lower secondary modes and, consequently, larger thermal structures are expected. Furthermore, this first application of the quasiseparatrix layer to a toroidal plasma indicates that such a concept is ubiquitous in magnetic reconnection, independent of the system geometry under investigation.

Aspect ratio scaling of the single helical states in the reversed field pinch plasmas

In this paper a new idea to help to predict the aspect ratio scaling law for the toroidal mode number of the so called Single Helicity states in reversed field pinch (RFP) plasmas is presented. In particular it is shown that the pure electromagnetic response of a toroidal shell is ‘optimal’ when currents with specific pitches are excited on it and that this response depends on the shell aspect ratio. The pure electromagnetic passive toroidal shell response model, cannot however, be useful in predicting the handedness of the current which is related, instead, to the plasma magnetic field profiles and their on-axis stability properties.

N-point amplitudes with a single negative-helicity graviton

We construct an expression for the n-point one-loop graviton scattering amplitude with a single negative helicity external leg using an augmented recursion technique. We analyse the soft-limits of these amplitudes and demonstrate that they have soft behaviour beyond the conjectured universal behaviour.

Light impurity transport studies with solid pellet injections in the RFX-mod reversed-field pinch

The transport of injected impurities is investigated in the multiple helicity (MH) and improved confinement quasi single helicity (QSH) magnetic regimes of RFX-mod reversed-field pinch. Impurities are introduced through injections of room temperature pellets of carbon (in MH and QSH) and lithium (in MH). Simulation of experimental spectroscopic measurements, including line and soft x-rays emission, electron density and radiated power is carried out with a 1D collisional-radiative impurity transport code, allowing to determine the transport parameters: diffusion coefficient and convective velocity. The transport coefficients were found close to those deduced in previous experiments through the introduction of Ni and Ne, confirming the existence of an external velocity barrier also for light impurities.

Time-dependent behavior in a transport-barrier model for the quasi-single helcity state

Time-dependent behavior that follows from a recent theory of the quasi-single-helicity (QSH) state of the reversed field pinch is considered. The theory (Kim and Terry 2012 Phys. Plasmas 19 122304) treats QSH as a core fluctuation structure tied to a tearing mode of the same helicity, and shows that strong magnetic and velocity shears in the structure suppress the nonlinear interaction with other fluctuations. By summing the multiple helicity fluctuation energies over wavenumber, we reduce the theory to a predator–prey model. The suppression of the nonlinear interaction is governed by the single helicity energy, which, for fixed radial structure, controls the magnetic and velocity shearing rates. It is also controlled by plasma current which, in the theory, sets the shearing threshold for suppression. The model shows a limit cycle oscillation in which the system toggles between QSH and multiple helicity states, with the single helicity phase becoming increasingly long-lived relative to the multiple helicity phase as plasma current increases.

Fast ion confinement in the three-dimensional helical reversed-field pinch

Fast ions are well confined in the stochastic magnetic field of the multiple-helicity (MH) reversed-field pinch (RFP), with fast ion confinement times routinely a factor of 5 to 10 higher than thermal confinement time. Recent experiments have examined the behavior and confinement of beam-born fast ions in the three-dimensional (3D) helical RFP state. In lower current discharges, where the onset of the helical state is uncertain, high power neutral beam injection (NBI) tends to suppress the transition to the single helicity mode. In high current discharges (Ip ∼ 0.5 MA), where the onset of n = 5 single helicity is quite robust, a short blip of NBI is used to probe the confinement of fast ions with minimal perturbation to the 3D equilibrium. The fast ion confinement time is measured to be substantially lower than fast ions in comparable MH RFP states, and there is a strong dependence on the strength of the helical perturbation. The established helical equilibrium is stationary in the laboratory frame but the locking occurs over the entire range of possible phase with respect to the Madison Symmetric Torus vessel. This effectively scans both the location of the NBI with respect to the helical structure and the pitch of the NBI-born fast ions. Fast ion confinement is observed to be insensitive to this angle, and in fact counter-NB injection into quasi-single helicity discharges shows fast ion confinement times similar to co-injection cases, in contrast to the MH RFP, where counter-injected fast ion confinement time is substantially lower.

Nonlinear evolution of double tearing modes in tokamak plasmas via multiple helicity simulation

Nonlinear evolution of multiple double tearing modes (multi-DTMs) with different helicities (DHs) in several reversed magnetic shear configurations is investigated by employing a reduced magnetohydrodynamic model in cylindrical geometry. It is found that the basic characterizations of the nonlinear evolution process of the system depend on the linear unstable spectrum of multi-DTMs with DHs. In the case that the linear growth rates of multi-DTMs with DHs are comparable to each other, continuous bursts occur one after another due to a sequence of magnetic energy release induced by multi-DTMs reconnections on different pairs of resonant surfaces with DHs. Moreover, the overlapping of the magnetic island chains of multi-DTMs during the continuous bursts process results in the strong magnetic stochasticity in the off-axis region. Such unique nonlinear evolution of multi-DTMs with DHs cannot be reproduced by the single helicity simulation. However, in the case that the linear growth rates of DTMs with the dominant helicity are much larger than the counterparts of DTMs with the other helicities, the main nonlinear physical process obtained by the multiple helicity simulation can be reproduced by the single helicity simulation.

Magnetic island evolution in the presence of ion-temperature gradient-driven turbulence

Turbulence is known to drive and sustain magnetic islands of width equal to multiples of the Larmor radius. The nature of the drive is studied here by means of numerical simulations of a fluid electrostatic model in 2D (single helicity) sheared-slab geometry. The electrostatic model eliminates the coalescence of short wavelength islands as a mechanism for sustaining longer wavelength islands. In quiescent islands, the polarization current, which depends on the propagation velocity of the island through the plasma, plays a critical role in determining the growth or decay of island chains. For turbulent islands, the unforced propagation velocity is significantly changed by strong zonal flow. The simulations show, however, that the turbulent fluctuations in the current density are much larger and faster than those in the zonal flow, and that they dominate the steady-state perturbed current density. In order to distinguish the roles of the zonal flow from the direct action of the fluctuations on the islands, a new diagnostic is implemented. This new diagnostic separates the effects of all the sources of parallel current. These are the curvature (which drives Pfirsch-Schlüter currents) and the divergences of the viscous and Reynolds stresses (the latter driving polarization currents). The new diagnostic also enables the contributions from short and long wavelengths to be separated for each term. It shows that in the absence of curvature, the drive is dominated by the contributions to the polarization current from the short wavelength fluctuations, while the long-wavelength fluctuations play a stabilizing role. In the presence of unfavorable curvature, by contrast, the effects of the short- and long-wavelength contributions of the polarization current reverse roles but nearly cancel, leaving the Pfirsch-Schlüter current as the dominant drive.

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.

Adaptive feedback control of rotating external kink modes in HBT-EP

An advanced adaptive control algorithm is used to study the control of external kink modes that are excited in the HBT-EP tokamak and have a natural toroidal rotation frequency near 8 kHz. The controller's system model is parametrized and the parameters are adjusted in real-time to match the measured plasma evolution. Depending upon a programmed phase angle, active feedback control is shown to either suppress or amplify the controlled amplitude by an amount comparable to the variations observed over a variety of plasma discharges. With negative feedback, the maximum amplitude is reduced to 40% of the uncontrolled value. With positive feedback, the amplitude increases to 155%. Intermediate feedback phases lead to an acceleration or deceleration of the mode rotation frequency in addition to changes in mode amplitude. As the feedback gain increases, the level of both mode suppression and mode amplification also increases. However, for sufficiently high gain, kink mode suppression becomes limited by the excitation of an additional, slowly rotating 1.4 kHz mode having the same helical structure as the uncontrolled kink. High gain amplification is limited by disruptive loss of plasma current. Experimental results are compared with numerical simulations based on a single helicity model, and qualitative agreement is found.

RFX-mod: A multi-configuration fusion facility for three-dimensional physics studies

RFX-mod [Sonato et al., Fusion Eng. Des. 66, 161 (2003)] exploits its 192 active coils in both reversed-field pinch (RFP) and tokamak configurations with varying degrees of 3D shaping, providing also a test bed for validating stellarator codes and 3D nonlinear magnetohydrodynamic codes. This makes RFX-mod a unique and flexible facility for comparative studies on 3D shaping and control. The paper discusses how 3D fields allow access to RFP and tokamak advanced regimes. 3D fields are used to feedback control Single Helicity (SH) RFP equilibria with 1/7 helicity up to ∼2 MA. They also allow accessing SH regimes with higher density (Greenwald fraction up to 0.5), presently inaccessible in spontaneous SH regimes. Feedback on the 2/1 resistive-wall mode in RFX-mod tokamak plasmas allows for safe operation at q(a)<2, an almost unexplored promising regime. Forcing the 2/1 mode to saturate at finite but small level, a helical tokamak equilibrium with significant n = 1 modulation is produced and a new way to tailor sawteeth is found. The effects of different levels of 3D shaping on momentum transport in both RFP and tokamak helical states are discussed.

Tearing mode stability in a toroidally flowing plasma

The effect of a sheared toroidal equilibrium flow on the tearing mode stability index, Δ′, is studied. A flow modified external kink equation for a single helicity mode is derived in a toroidal geometry. The corrections to Δ′ arising from flow contributions are estimated on the basis of a boundary layer calculation. Toroidal shear flow is seen to have a destabilizing influence on the tearing mode in a manner similar to pure axial flows in a cylindrical geometry. However, the increase in Δ′ as a function of increasing flow is seen to be smaller than the cylindrical case due to beneficial magnetic curvature effects. Shear flow associated stabilization, as observed in many recent experiments, might be arising from other physical effects such as toroidal mode couplings which are neglected in the present model.

Experimental Study of Repetitive ST Plasma Merging by use of Oscillating Poloidal Coil Currents

Repetitive merging of spherical tokamak (ST) plasma was demonstrated in the TS-4 device using oscillating poloidal field (PF) coil currents. The oscillating induction current is transformed into plasma currents of small ST plasmas, if its polarity satisfies the Shafranov condition. This natural rectification was found to form repetitively small ST plasmas with single helicity, and their merging gradually drives the plasma current of the main ST plasmas.

Inertial magnetic reconnection effects on the electron dynamics in a three-dimensional configuration

The three-dimensional response of a population of thermal electrons to a collision-less magnetic reconnection process is investigated through a relativistic Hamiltonian guiding centre formulation of the particle dynamics. The resulting electron equations have been implemented in a test-particle code that evolves the spatial position and the velocity of the electrons according to the fields calculated by the numerical solutions of a two-fluid reconnection model. In particular, we consider here reconnection events triggered by single helicity perturbations. By following the evolution of the electron distribution function we can quantify the number of suprathermal electrons generated during the nonlinear phase of reconnection and observe how the increase in the electron energy deforms the moments of the electron distribution function with respect to the corresponding fluid quantities.

Single Helicates of Dipalladium(II) Hexapyrroles: Helicity Induction and Redox Tuning of Chiroptical Properties

Hexapyrrole-α,ω-dialdehyde, which has eight donor atoms, afforded a dipalladium(II) single helicate (see picture; Pd pink, O red, N blue). A rapid interchange of the helical screw was slowed down by imine formation at the terminal aldehyde units with (R)-(−)-1-cyclohexylethylamine, leading to an overwhelming excess of a P-helical screw. This stable dinuclear single helicate has a redox-driven reversible change in chiroptical properties.

Co-assembly of Zn(SPh)2 and organic linkers into helical and zig-zag polymer chains

Two novel one-dimensional coordination polymers, single helicate [Zn(SPh)2(TPyTA)(EG)]n (EG=ethylene glycol) (1) and zig-zag structure [Zn(SPh)2(BPyVB)]n (2), were synthesized under solvothermal conditions at 150°C or room temperature by the co-assembly of Zn(SPh)2 and organic linkers such as 2,4,6-tri(4-pyridyl)-1,3,5-triazine (TPyTA) and 1,3-bis(trans-4-pyridylvinyl)benzene (BPyVB). X-ray crystallography study reveals that both polymers 1 and 2 crystallize in space group P21/c of the monoclinic system. The solid-state UV–vis absorption spectra show that 1 and 2 have maxium absorption onsets at 400nm and 420nm, respectively. TGA analysis indicates that 1 and 2 are stable up to 110°C and 210°C.

Magnetic coordinate systems for helical SHAx states in reverse field pinch plasmas

Single helical axis (SHAx) states are the improved confinement RFP helical states, which have been observed at high plasma currents (beyond 1 MA) in the RFX-mod device. A reconstruction of these equilibrium configurations has been implemented in a code named SHEq, where SHAx states are modelled as pure single helicity (SH) states. We consider the helical flux in this work, which happens to be a good flux function for SH equilibrium, and its contours give the shape of the flux surfaces in the helical equilibrium. New curvilinear and non-orthogonal ‘helical’ coordinate systems are defined in SHEq, with the fundamental request that angles are defined with respect to the helical axis. We look for helical coordinates beginning from the canonical form of the magnetic field B and the Hamiltonian mechanics theory enables us to obtain straight-field-line helical coordinates computing action–angle coordinates.These coordinate systems are used to determine the helical safety factor q, using the simple formula valid in action–angle coordinates. Very good agreement with the computation of the safety factor using the ORBIT code has been found.