Helical Ripple Research Articles

Control of the radial electric field shear by modification of the magnetic field configuration in LHD

Control of the radial electric field, Er, is considered to be important in helical plasmas, because the radial electric field and its shear are expected to reduce neoclassical and anomalous transport, respectively. In general, the radial electric field can be controlled by changing the collisionality, and positive or negative electric fields have been obtained by decreasing or increasing the electron density, respectively. Although the sign of the radial electric field can be controlled by changing the collisionality, modification of the magnetic field is required to achieve further control of the radial electric field, especially to produce a strong radial electric field shear. In the Large Helical Device (LHD) the radial electric field profiles are shown to be controlled by the modification of the magnetic field by (1) changing the radial profile of the effective helical ripples, εh, (2) creating a magnetic island with an external perturbation field coil and (3) changing the local island divertor coil current.

Dynamics of Zonal Flows in Helical Systems

A theory for describing collisionless long-time behavior of zonal flows in helical systems is presented and its validity is verified by gyrokinetic-Vlasov simulation. It is shown that, under the influence of particles trapped in helical ripples, the response of zonal flows to a given source becomes weaker for lower radial wave numbers and deeper helical ripples while a high-level zonal-flow response, which is not affected by helical-ripple-trapped particles, can be maintained for a longer time by reducing their bounce-averaged radial drift velocity. This implies a possibility that helical configurations optimized for reducing neoclassical ripple transport can simultaneously enhance zonal flows which lower anomalous transport.

The Configuration Dependence of Ripple Transport in LHD

The GIOTA code [1] has been applied to clarify the configuration dependence of ripple transport properties in LHD. The effective helical ripple (eeff), as a measure of the level of ripple transport, is calculated with a wide range scan of magnetic axis position, (Rax) and plasma beta value (β). Our results show that eeff takes a minimum value in a wide radial portion around the configuration with Rax = 3.53-3.55 m at vacuum. It is also revealed that eeff decreases as β is increased for configurations with Rax of less than the above mentioned range.

Dissipative Trapped Electron Modes in a Heliac

The objective of the present paper is to study the dissipative trapped electron modes (DTEM) in a stellarator configuration. A perturbative-iterative process is used to study the non-adiabatic response of the electrons in the dissipative regimes on the drift wave instability. A ballooning mode formalism is used to drive the drift eigenvalue equation for adiabatic electron which is solved numerically. The eigenmodes are marginally stable. The non-adiabatic response of the electrons is calculated perturbatively which is used to re-solve the eigenvalue equation. The process is iterated until electrons response converges. The effects of different parameters such as ηe, the ballooning angle θk, normalised density scale length ϵn, radial label s, and χ are studied. The mode localisation is correlated with the geometrical properties of the magnetic field. It is found that the wave functions of the most unstable modes are highly localised in a single helical ripple with the possibility of a variety of both helical and toroidal trapping. It is further fond that a perturbative calculations of the growthrate generally is not reliable and can give substantially lower or higher growthrate than the iterative method.

Small to mid-sized stellarator experiments: topology, confinement and turbulence

The very large stellarator experiments LHD (operating) and W7X (under construction) move stellarator-confined plasmas into the near-reactor regime. Continuing experiments on smaller devices operating at heating powers from kilowatts to a few megawatts are exploring the effects of magnetic configuration stability and turbulence on plasma confinement to improve stellarator performance and our understanding of general toroidal confinement physics. Key issues being explored are the relation of rational magnetic surfaces and magnetic configuration characteristics such as helical ripple to plasma transport, confinement scaling and turbulence. The robust macroscopic stability of currentless stellarator plasma is a major contributing factor to these studies. Many of the phenomena most clearly evident in stellarators are increasingly implicated in tokamak experiments as well.

Electron ITB Formation with Combination of NBI and ECH in LHD

The electron internal transport barrier (ITB) is formed with centrally focused electron cyclotron resonance heating superposed on plasmas heated by neutral beam injection in the Large Helical Device. The electron transport is investigated for the electron ITB plasmas observed in various magnetic axis positions of Rax = 3.6, 3.75, and 3.9 m, and it turns out that the core electron transport is reduced with suppression of the anomalous transport in all three magnetic axis positions. In the theoretical calculations, positive radial electric fields are generated in the improved transport region, implying that the electron ITB formation is correlated with the neoclassical electron root. At an outer-shifted configuration of Rax = 3.9 m, where the helical ripple is large, the thermal diffusivity is decreased with decreasing collisionality, suggesting the reduction of the ripple transport by the radial electric field. The temperature and density conditions for the ITB formation are consistent with the theoretical density dependence of the transition temperature to the neoclassical electron root from the ion root.

Relaxation of plasma rotation in toroidal magnetic confinement systems

A study is made of the relaxation of plasma rotation in nonaxisymmetric toroidal magnetic confinement systems, such as stellarators and rippled tokamaks. In this way, a solution to the drift kinetic equation is obtained that explicitly takes into account the time dependence of the distribution function, and expressions for the diffusive particle fluxes and longitudinal viscosity are derived that make it possible to write a closed set of equations describing the time evolution of the ambipolar electric field E and the longitudinal (with respect to the magnetic field) plasma velocity U0. Solutions found to the set of evolutionary equations imply that the relaxation of these two parameters to their steady-state values occurs in the form of damped oscillations whose frequency is about 2vT/R (where vT is the ion thermal velocity and R is the major plasma radius) and whose damping rate depends on the ion-ion collision frequency and on the magnetic field parameters. In particular, it is shown that, for tokamaks with a slightly rippled longitudinal magnetic field, the frequency of oscillations in the range q>2 (where q is the safety factor) is, as a rule, much higher than the damping rate. For stellarators, this turns out to be true only of the central plasma region, where the helical ripple amplitude ɛ of the magnetic field is much smaller than the toroidal ripple amplitude δ=r/R.

Magnetic field structure preferable to E×B shear flow generation in a quasi-axisymmetric stellarator CHS-qa

Viscous damping and effective helical ripple have been quantitatively estimated for a proposed quasi-axisymmetric stellarator CHS-qa configuration.It is predicted that viscous damping against plasma flow in CHS-qa is low enough to sustain large E×B shear as observed in the H-modesand internal transport barriers in many tokamaks. Effective helical ripple in CHS-qa is adjusted to be on the order of 10-2 or lower,which is suitable to trigger transport barriersdue to non-ambipolar neoclassical fluxes peculiar to conventional helical devices.For experimental flexibility, viscous damping and effective helical ripple in CHS-qacan be extensively controlled over a range of about one order by modifying modular coil currents.

Design of Quasi-Axisymmetric Stellarator CHS-qa.

A new compact helical system CHS-qa has been designed based on the advanced stellarator concept of the quasi-axisymmetry in the magnetic field configuration. This new concept of quasi-axisymmetry makes it possible to realize the two-dimensional vacuum magnetic field structure (a tokamak-like configuration) without using plasma current. In this system, the neoclassical transport is greatly reduced compared with conventional helical systems because the helical ripples are very small. Good MHD stability for the interchange and ballooning modes are obtained. The possibility of finding the confinement improvement is also discussed from the viewpoint of plasma rotation and maximum-J criterion.

The Helias reactor HSR4/18

The Helias reactor is an upgraded version of the Wendelstein 7-X experiment. A straightforward extrapolation of Wendelstein 7-X leads to HSR5/22, which has 5 field periods and a major radius of 22 m. HSR4/18 is a more compact Helias reactor with 4 field periods and an 18 m major radius. Stability limit and energyconfinement times are nearly the same as in HSR5/22, thus the same fusion power (3000 MW) is expected inboth configurations. Neoclassical transport in HSR4/18 is very low, and the effective helical ripple is below 1%. The article describes the power balance of the Helias reactor, and the blanket and maintenance concepts. The coil system of HSR4/18 comprises 40 modular coils with NbTi superconducting cables. The reduction from 5 to 4 field periodsand the concomitant reduction in size will also reduce the cost of the Helias reactor.

Configuration flexibility and extended regimes in Large Helical Device

Recent experimental results in the Large Helical Device have indicated that a large pressure gradient can be formed beyond the stability criterion for the Mercier (high-n) mode. While the stability against an interchange mode is violated in the inward-shifted configuration due to an enhancement of the magnetic hill, the neoclassical transport and confinement of high-energy particle are, in contrast, improved by this inward shift. Mitigation of the unfavourable effects of MHD instability has led to a significant extension of the operational regime. Achievements of the stored energy of 1 MJ and the volume-averaged beta of 3% are representative results from this finding. A confinement enhancement factor above the international stellarator scaling ISS95 is also maintained around 1.5 towards a volume-averaged beta, ⟨β⟩, of 3%. Configuration studies on confinement and MHD characteristics emphasize the superiority of the inward-shifted geometry to other geometries. The emergence of coherent modes appears to be consistent with the linear ideal MHD theory; however, the inward-shifted configuration has reduced heat transport in spite of a larger amplitude of magnetic fluctuation than the outward-shifted configuration. While neoclassical helical ripple transport becomes visible for the outward-shifted configuration in the collisionless regime, the inward-shifted configuration does not show any degradation of confinement deep in the collisionless regime (ν*<0.1). The distinguished characteristics observed in the inward-shifted configuration help in creating a new perspective of MHD stability and related transport in net current-free plasmas. The first result of the pellet launching at different locations is also reported.

A theory of the helical ripple-induced stochastic behavior of fast toroidal bananas in torsatrons and heliotrons

A theory of the helical ripple-induced stochastic behavior of fast toroidal bananas in torsatrons and heliotrons [K. Uo, J. Phys. Soc. Jpn. 16, 1380 (1961)] is developed. It is supplemented by an analysis of the structure of the secondary magnetic wells along field lines. Conditions, under which these wells are suppressed in torsatrons–heliotrons by poloidally modulated helical field ripple, are found. It is shown that inside the secondary magnetic well-free region, favorable conditions exist for a transition of fast toroidal bananas to stochastic trajectories. The analytical estimation for the value of an additional radial jump of a banana particle near its turning point, induced by the helical field ripple effect, is derived. It is found to be similar to the corresponding banana radial jump in a tokamak with the toroidal field ripple. Critical values of the helical field ripple dangerous from the viewpoint of a banana transition to stochastic behavior are estimated.

Splitting of the spectra of MHD waves and the structure of a satellite alfvén resonance in a cold plasma in a strong axial magnetic field and a weak helical field

The possibility is demonstrated of splitting the eigenfrequencies of MHD plasma waves in a stellarator with a weakly rippled helical confining magnetic field. The distribution of the fields of an Alfven wave in the satellite Alfven resonance region is investigated when the influence of the helical ripple in a confining magnetic field on the resonance structure is comparable with the effects of the finite ion Larmor radius, electron inertia, and collisions between plasma particles.

Direct losses of highly energetic trapped particles in torsatrons and heliotrons with a vertically asymmetric helical magnetic-field ripple

Direct losses of highly energetic helically trapped particles, especially of superbananas, are analytically investigated in torsatrons and heliotrons [Uo, J. Phys. Soc. Jpn. 16, 1380 (1961)] with a vertically asymmetric helical field ripple. It is found that the vertically asymmetric helical ripple causes an additional net radial drift of suprathermal superbananas, leading to convective losses of these particles from the confinement volume mainly in the vertical direction. For a vertically asymmetric rippled torsatron, a location of the particle loss region in the coordinate space and a dominated direction of the particle escape from the confinement volume is predicted on the basis of the probabilities of the particle trapping/detrapping in/from the helical ripple wells. Analytical predictions are confirmed by numerical computations of direct losses of highly energetic helically trapped particles for a number of torsatrons/heliotrons of today.

Vertical asymmetry of the helical magnetic-field ripple in torsatrons and heliotrons

Possible reasons are considered for the vertically asymmetric helical field ripple to occur in torsatrons and heliotrons [K. Uo, J. Phys. Soc. Jpn. 16, 1380 (1961)]. Vacuum magnetic configurations of present day l=2 torsatrons/heliotrons are analyzed using a harmonic expansion of the magnetic-field strength along a field line. It is shown that a typical feature of such configurations is a vertical asymmetry of their helical field ripple. This kind of vertical asymmetry of the ripple in torsatrons and heliotrons is caused by the presence of the helical satellite harmonics in a Fourier spectrum of the magnetic field. In configurations that are far from the quasihelically symmetric, due to these harmonics effects, the depth of the secondary magnetic wells along field lines can differ not only inside and outside the torus, but also in the upper and lower parts of the torus.

Helical post stellarator

A novel type of stellarator device, the helical post stellarator (HPS), is introduced. Calculations are given for a particular HPS configuration, the single-helix stellarator (SHS) featuring a single-helix centre post. This configuration is significantly different from all previously known stellarators due to the combination of its unique geometrical characteristics and physical properties. Among these are the facts that the helical magnetic field has only one toroidal period (N = 1), the plasma has an extremely low aspect ratio, , and the variation of the magnetic field, B, along field lines features a helical ripple entirely on the inside of the torus. Among the main advantages of an HPS for the fusion program are an extremely compact, modular, and simple design compatible with significant rotational transform, large plasma volume, and improved particle transport characteristics.

Extreme low aspect ratio stellarators

A novel class of stellarator configurations with unique and advanced characteristics is proposed. It features extreme low plasma aspect ratios (down to A M I), a simple coil system having a helical center post, extremely high p equilibria (PO N 90%, /3 N 20% is demonstrated) assisted by a strong positive bootstrap current, improved particle transport caused by the absence of an outboard helical ripple, and a natural divertor. The helical center post can be a single helix or may consist of a few helices. @ 1998 Elsevier Science B.V.

Modeling of the Mapping Experiments Based on the Diffusion Process

It is important in relation to the plasma confinement to understand the spatial variation of the impedance observed by the “stellarator diode method”. We develop a numerical code based on the collisional diffusion model and apply it to the various experimental conditions. It is shown that the ripple diffusion of electrons plays an important role in determination of the impedance between a magnetic surface and the vacuum vessel wall. The effects of the electron temperature, neutral pressure, helical ripple, and the magnetic island are also examined.

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.

First results from the 'URAGAN-2M' torsatron

The Uragan-2M (U-2M) (IPP, Kharkov) concept is the result of a search of torsatron system with a reduced helical ripple but still having a moderate shear and magnetic well. In this report the authors present the description of concept of the torsatron with an additional toroidal field, results of studies of confining properties of magnetic system of U-2M, design concept and its realization and first results of magnetic configuration studies for U-2M.