Conventional Stellarators Research Articles

Plasma flow healing of magnetic islands in stellarators

Recent experiments from the large helical device (LHD) demonstrate a correlation between the “healing” of vacuum magnetic islands in stellarators and changes in the plasma flow. A model explaining this phenomenon is developed based on self-consistent torque balance and island evolution equations. In conventional stellarators, neoclassical flow damping physics plays an important role in establishing the flow profiles. The balance of neoclassical damping and cross-field viscosity produces a radial boundary layer for the plasma rotation profile outside the separatrix of a locked magnetic island. The width of this boundary layer decreases as the plasma becomes less collisional. Associated with these flow effects are plasma currents flowing in the island region that attempt to suppress island formation. These currents are enhanced as the collisionality drops making magnetic island healing occur more readily in high temperature conventional stellarators. The analytic theory produces a critical β for healing that scales monotonically with collisionality and is in qualitative agreement with LHD observations.

Healing of magnetic islands in stellarators by plasma flow

Recent experiments from the Large Helical Device indicate that plasma flow can play a primary role in ‘healing’ vacuum magnetic islands in stellarators. The observed elimination of magnetic islands tends to occur at low collisionality and high plasma β. A model explaining this phenomenon is developed reminiscent of ‘mode locking/unlocking’ physics of tokamak and reversed field pinch experiments. The theory describes transitions between two asymptotic solutions, a state with a large non-rotating island and a state where rotation shielding suppresses island formation. Transitions between these two states are governed by coupled torque balance and island evolution equations. In conventional stellarators, neoclassical damping physics plays an important role in establishing the flow profiles. The balance of neoclassical damping and cross-field viscosity produces a radial boundary layer for the plasma rotation profile outside the separatrix of a locked magnetic island. The width of this boundary layer decreases as the plasma becomes less collisional. This has the consequence of enhancing the viscous torque at low collisionality making healing magnetic islands occur more readily in high temperature conventional stellarators.

Effect of perturbations on magnetic fields as a possible problem for implementing toroidal magnetic configurations with a zero rotational transform

Approved reliable methods and a unified quasi-resonant approach are used to reproduce the results characterizing the effect of dangerous perturbations on three particular types of toroidal magnetic configurations with a zero rotational transform (ι/2π = 0). An analysis is made of the perturbations whose geometry and amplitudes correspond to imperfections and defects in the assembly of the actual magnetic systems of conventional stellarators. The effect of perturbations on magnetic configurations with ι/2π = 0 is of the same quasi-resonant nature as that for systems with ι/2π ≠ 0 and a zero magnetic shear. However, in contrast to shearless configurations with a nonzero rotational transform, the most dangerous perturbations are those with n = 0 and m = 1, 2, 3, … (where m is the poloidal mode number and n is the toroidal mode number) and the effect of harmonics with the smallest poloidal and toroidal numbers is more destructive and nonlocal even for the amplitudes corresponding to imperfections and defects in the assembly of conventional stellarators. Such an extremely high sensitivity of magnetic systems with ι/2π = 0 to the perturbations under consideration may be a serious obstacle for their practical implementation.

Effects of electron cyclotron resonance heating (ECRH)-induced direct loss flux on neoclassical transport in a bumpy stellarator

Energetic electron populations can substantially modify the neoclassical transport properties in stellarators. A model accounting for this change in transport is developed assuming the presence of electron cyclotron resonance heating (ECRH). The quasilinear diffusion coefficient for second-harmonic X-mode ECRH is developed for a stellarator. Care is taken in accounting for the pitch-angle dependence of the quasilinear diffusion coefficient since application to experiments with narrow resonance zones is of interest. Weakly relativistic effects are considered through the mass effect on the cyclotron frequency. For trapped particles in a three-dimensional configuration, collisionless loss zones exist in velocity space. Radio-frequency (rf) waves accelerate trapped electrons into the direct loss zone in conventional stellarators and produce a direct loss flux. An analytic expression for this loss flux is derived; it is proportional to the rf field strength and the value of the zeroth-order distribution functi...

Diagnostic development for ST plasmas on NSTX**Work supported by US DOE Contract DE-AC02-76CH03073.

Spherical tori (ST) have much lower aspect ratio (a/R) and lower toroidal magnetic field than conventional tokamaks and stellarators. This paper will highlight some of the challenges and opportunities these features pose in the diagnosis of ST plasmas in the National Spherical Torus Experiment (NSTX), and discuss some of the corresponding diagnostic development that is underway. The low aspect ratio necessitates a small centre stack, with tight space constraints and large thermal excursions, complicating the design of magnetic sensors in this region. The toroidal magnetic field on the NSTX is ⩽0.6 T, making it impossible to use ECE as a good monitor of electron temperature. A promising new development for diagnosing electron temperature is electron Bernstein wave radiometry, which is currently being pursued on the NSTX. A high-resolution charge exchange recombination spectroscopy system is being installed. Since non-inductive current initiation and sustainment are top-level NSTX research goals, measurements of the current profile J(R) are essential to many planned experiments. On the NSTX several modifications are planned to adapt the motional Stark effect (MSE) technique to lower field, and two novel MSE systems are being prototyped. Several high-speed two-dimensional imaging techniques are being developed for viewing both visible and x-ray emission. The toroidal field is equivalent to the poloidal field at the outside plasma edge, producing a large field pitch (>50°) at the outer midplane. The large shear in pitch angle makes some fluctuation diagnostics like beam emission spectroscopy very difficult, while providing a means of achieving spatial localization for microwave scattering investigations of high-k turbulence, which are predicted to be virulent for NSTX plasmas. A brief description of several of these techniques will be given in the context of the current NSTX diagnostic set.This article was due to appear in issue 7 of Plasma Physics and Controlled Fusion. To access this special issue please follow this link: http://www.iop.org/EJ/toc/0741-3335/45/7.

Physics and engineering design of the low aspect ratio quasi-axisymmetric stellarator CHS-qa

A low aspect ratio quasi-axisymmetric stellarator, CHS-qa, has been designed. An optimization code has been used to design a magnetic field configuration with evaluations of the following physical quantities: quasi-axisymmetry, rotational transform, MHD stability and alpha particle collisionless confinement. It is shown that the electron neoclassical diffusion coefficient is similar to that of tokamaks for the low collisional regime. A self-consistent equilibrium with bootstrap current confirms the global mode stability up to 130 kA for an R = 1.5 m and Bt = 1.5 T device. The neoclassical plasma rotation viscosity is greatly suppressed compared with that of conventional stellarators. The engineering design was completed with 20 main modular coils and auxiliary coils, which provide flexibility of configuration in experiments for confinement improvement and MHDstability.

A helically symmetric stellarator (HSX)

The Helically Symmetric Experiment (HSX) Is a quasi-helically symmetric (QHS) stellarator currently under construction at the Torsatron/Stellarator Laboratory of the University of Wisconsin-Madison. This device is unique in its magnetic design in that the magnetic field spectrum possesses only a single dominant (helical) component. This design avoids the large direct orbit losses associated with conventional stellarators. The restoration of an ignorable coordinate in the confining magnetic field makes this device analogous to an axisymmetric q=1/3 tokamak with respect to neoclassical confinement.

Control of Pfirsch-Schluter current by an external poloidal magnetic field in conventional stellarators

The problem is analysed of whether it is possible to create net-current-free equilibrium configurations without Pfirsch-Schluter current (jzeta =0) in conventional stellarators with a planar circular axis. Recently, such an analysis has been presented for the case when only the vertical magnetic field was a control parameter. Here, the external poloidal field is considered as arbitrary, and it must be found from the condition jzeta =0. It is shown that such suppression of Pfirsch-Schluter current by means of an external poloidal field is possible, theoretically, in shear-free systems and in stellarators with l>or=3 only, i.e. in ordinary l=2 stellarators with a shear plasma equilibrium with jzeta =0 it is impossible with any choice of external poloidal field. In these systems, nevertheless, the dipole component of Pfirsch-Schluter current can be suppressed or strongly reduced by the joint effect of vertical and quadrupole fields. It is shown that in this case phase inversion of the Pfirsch-Schluter current could be obtained under realistic conditions. These results explain, in particular, experimental observations of configurations almost insensitive to plasma pressure in Heliotron E

Suppression of Pfirsch-Schluter current by vertical magnetic field in conventional stellarators

The problem of whether a stellarator configuration can be made insensitive to the plasma pressure by using an external vertical magnetic field as a control parameter is discussed. Conventional stellarators with a planar circular axis are analysed. It is shown that for these systems the condition of Pfirsch-Schluter current suppression can be formulated as a two dimensional equation with all quantities expressed in terms of the vacuum magnetic field only. The major advantage of this formulation is that it allows the problem to be solved without solving the equilibrium equations. The formulation is used as a basis for showing that complete suppression of the Pfirsch-Schluter current by means of the vertical field is possible, in principle, both in shear free systems and in stellarators with l ⩾ 3. In l=2 stellarators with shear it is possible to obtain significant reduction of the current and to suppress the pressure induced plasma column shift. This phenomenon may be called `integral independence` of beta in contrast to true local independence in other cases. In all cases, a large inward shift of the plasma column is necessary, which is outside the operational range in all existing devices except Heliotron-E. In recent experiments in Heliotron-E, the state of being `integrally` independent of beta was almost fully achieved. The present study was stimulated by this result

On rotation of collisional plasmas in toroidal systems

This paper describes the poloidal and toroidal spin-up of an isothermal plasma in toroidal equilibria. The mechanism is the Stringer spin-up mechanism which will be generalized to an arbitrary toroidal equilibrium using the Hamada coordinate system. Viscous damping or magnetic pumping balances the accelerating forces and determines the threshold of spin-up. The accelerating forces arise from the Coriolis forces which couple the radial flow to the poloidal flow velocity. The magnetic pumping rate is computed for conventional stellarators and stellarators of the Helias type. Magnetic pumping depends on the specific structure of B on the magnetic surface and the results exhibit a smaller damping rate in Helias configurations than in conventional stellarators. The paper presents numerical results of viscous damping rates computed for conventional stellarators, the Wendelstein 7-AS and Wendelstein 7-X devices and a tokamak with a toroidal magnetic ripple.

Application of Quasi-Symmetry Concept to Conventional Stellarators

Quasi-symmetry condition, which demands that B{sup 2} does not depend on one from two angles in Boozer coordinates, is analyzed for stellarators with planar circular axis. In stellarator approximation this condition is reduced here to two equations. The first one imposes a restriction on the helical field which can be satisfied by a proper choice of satellite helical harmonics. At the same time problem remains to suppress poloidal asymmetry of B{sup 2} related with toroidicity, the condition described by the second equation. 9 refs.

Orbit topology in conventional stellarators in the presence of electric fields

Orbits are considered in conventional stellarators (i.e. with helical coils) using Boozer co-ordinates. The Advanced Toroidal Facility (ATF) in Oak Ridge, Tennessee, will be used as an example to study the effects of its configurational flexibility on orbit topology. It is shown that the symplectic integration technique yields superior results for single particle orbits. These orbits will be compared with predictions using the J* invariant. J* conservation allows examination and understanding of the global stellarator topology, both with and without radial electric fields

Ripple transport in helical-axis advanced stellarators: a comparison with classical stellarator/torsatrons

Calculations of the neoclassical transport rates due to particles trapped in the helical ripples of a stellarator's magnetic field are carried out, based on solutions of the bounce-averaged kinetic equation. These calculations employ a model for the magnetic field strength, B, which is an accurate approximation to the actual B for a wide variety of stellarator-type devices, among which are Helical-Axis Advanced Stellarators (Helias) as well as conventional stellarators and torsatrons. Comparisons are carried out in which it is shown that the Helias concept leads to significant reductions in neoclassical transport rates throughout the entire long-mean-free-path regime, with the reduction being particularly dramatic in the nu -1 regime. These findings are confirmed by numerical simulations. Further, it is shown that the behaviour of deeply trapped particles in Helias can be fundamentally different from that in classical stellarator/torsatrons; as a consequence, the beneficial effects of a radial electric field on the transport make themselves felt at a lower collision frequency than is usual.

Confinement improvement in H-mode-like plasmas in helical systems

The reduction of the anomalous transport due to the inhomogeneous radial electric field is theoretically studied for toroidal helical plasmas. The self-sustained interchange-mode turbulence is analysed for a system with magnetic shear and magnetic hill. The ballooning mode turbulence is studied for a system with magnetic well-like conventional stellarators. The influence of the radial electric field inhomogeneity on the transport coefficients and fluctuations is quantitatively shown. Unified theories of the transport coefficients in the L-mode- and H-mode-like plasmas are presented.

Theory of electron cyclotron heating in the AFT torsatron

The heating of torsatron devices by electron cyclotron waves has been investigated using ray tracing techniques. The geometry of the magnetic field and mod-B contours in torsatrons is very different from that found in tokamaks or in most conventional stellarators. The sensitivities of electron cyclotron heating to antenna position, antenna orientation, wave polarization and magnetic field strength are therefore correspondingly different. These sensitivities are identified and quantitative calculations of wave propagation, absorption and radial heating profiles are carried out to develop a systematic picture of heating in these devices. A simple model is introduced which statistically treats the effect of power reflected from the walls. Specific ray tracing calculations were performed using the RAYS geometrical optics code for the Advanced Toroidal Facility torsatron now under construction at Oak Ridge National Laboratory. Significant power absorption (up to 100% of incident wave power) can be obtained with an optimally placed and oriented beam. This is the case when the resonance is at the saddle point in the magnetic field. These results can be achieved through either ordinary mode waves at the fundamental resonance (high or low field launch) or extraordinary mode waves at the second harmonic resonance (low field launch). These results are quite sensitive to antenna placement, antenna orientation and the magnetic field level. Depending on experimental constraints (such as high field or inside accessibility), other considerations can come into play; for example, there are theoretical advantages to launching the waves horizontally in the equatorial plane. The qualitative results from the wall reflection model indicate that polarization control and maximization of the first-pass absorption are more important when the central plasma is resonant near the fundamental resonance thanwhen it is resonant at the second harmonic. Finally, a comparison of the calculations with data from the Heliotron-E torsatron is made and found to be in qualitative agreement.

Class of Model Stellarator Fields with Enhanced Confinement

A class of model stellarator fields has been found in which the transport is reduced by an order of magnitude from transport in conventional stellarators, by localizing the helical ripple to the inside of the torus. The reduction is observed in numerical experiments, and explained theoretically. Realizations of this class are achievable with use of modular coils.

Doublestar: a stellarator with three magnetic axes

Conventional stellarators utilize low-multipole-order helical windings, ℓ = 2 or 3, because a high-multipole-order helical winding results in localization of the rotational transform near the plasma surface. If, however, a carefully chosen axisymmetric poloidal magnetic field is added, high-shear, high-multipole-order (ℓ ≈ 6–9) stellarator configurations become possible without a vanishing rotational transform in the plasma interior. Because of the well-known potential advantage of non-circular cross-section plasmas, such as the Doublet configuration over the circular cross-section tokamak, the Doublestar was chosen for a numerical study. Included in this study was the question of the sensitivity of the Doublestar configuration to error fields. As expected, it was found that the size of islands produced by error fields is relatively small because of the large shear of the Doublestar.