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The Large Helical Device (LHD), which is a heliotron/torsatron device with two helical coils, is designed so that the current in each helical coil can be controlled independently. Unbalancing these currents leads to spatial axis configurations. The bootstrap current is found to be strongly affected by any imbalance between these currents. When the ratio of the currents in the two helical coils is small enough, a bootstrap current flows in a direction so as to decrease the rotational transform because of the enhancement of the bumpiness component of the magnetic field as well as of the spatial axis component. This leads to improved stability

The Large Helical Device (LHD) is a plasma physics experimental device with a magnetic stored energy of 960 MJ, consisting of two superconducting (SC) helical coils and six SC poloidal coils. The trial operation and the first plasma discharge of the Phase I project for LHD were completed on 31 March 1998 as initially planned. The second experimental campaign was conducted with additional heating using two NBI devices. The third campaign started in June 1999 and was completed in January 2000. Many plasma heating tests with a plasma field of up to 2.90 T were carried out. Major test results on the SC magnet system for LHD are as follows: (1) The LHD cryogenic system was successfully operated for 13 400 h and proved its high reliability. (2) A central field of 2.91 T at a radius of 3.60 m was achieved at an inner helical coil current of 11.08 kA, a middle helical coil current of 11.83 kA and an outer helical coil current of 12.02 kA. (3) All six poloidal coils were excited stably. (4) Nine flexible SC bus lines with a total length of 497 m were operated stably and safely.

Toroidal effects on the outer magnetic surfaces of a configuration having a large toroidal plasma current that is stabilized by a pitch reversal produced by an external helical coil (OHTE) are investigated by both field-line tracing and an analytic expansion of the magnetic surfaces. Results of the two methods are compared. It is shown that both plasma position control and the helical coil winding law can be used to compensate undesired toroidal effects at both low and high beta.

Helicon is a new helical-axis configuration of the Heliac type in which the number of coils is minimized by replacing the numerous toroidal field coils by a single ? = 1 helical coil. Helicon has flexibility and potential high-beta properties similar to those of the Flexible Heliac as well as some of the characteristics of an ? = 1 torsatron. Devices with four, eight and twelve periods are discussed.

In an ultimate torsatron, magnetic surfaces are formed entirely from a single periodically modulated helical coil. Separatrix size and shape are determined by the winding poloidal multiplicity l, the number of field periods and the coil aspect ratio. The coil modulation principally determines the magnetic axis positioning in the radial direction, but does not directly affect the surface shape. An optimized l = 2 design demonstrates the desired magnetic properties of stable surfaces which are insensitive to winding perturbations, have high shear transform profiles and non-zero transform at the magnetic axis in addition to ample access to the plasma.

The size of a magnetic island driven by an error field or a helical coil depends strongly upon the plasma response aiming at the maintenance of equilibrium. Sample calculations for tokamaks within the context of a linear theory show that the island size is greatly augmented when the tearing mode is close to a marginally stable state.

A novel tokamak design with a new type of toroidal field (TF) coil and a central solenoid (CS) whose stress is reduced greatly to the theoretical limit determined by the virial theorem, has been devised, and plasma production and confinement experiments in a new small tokamak based on this design are presented. According to the virial theorem, the best TF coil for producing the strongest magnetic field under the weakest stress requires equal averaged principal stresses in all directions. Applying this condition to a helical coil, its pitch number is determined as a function of the aspect ratio. The helical winding according to this condition is modulated in such a way that the poloidal field exists only outside of the torus, which reduces the torsional force on the helical coil and makes plasma breakdown possible. Moreover, a helical coil with this modulation and a low aspect ratio is similar to CS and TF coil systems in conventional tokamaks since its helical winding is nearly vertical in the outer part of the torus. With the aspect ratio A = 2, our optimal coil theoretically reduces the working stress in the coil to about one-third less than that of conventional TF coils. On the basis of the design, a small prototype, 'Todoroki-II', with a major radius of 0.3 m, a minor radius of 0.08 m, toroidal magnetic field strengths of BT < 1.5 T and plasma currents of IP < 40 kA, was made. An external vertical field increased the plasma pulse length and the current to 1 ms and 11 kA, respectively, while they were restricted with no vertical field control. Using a Cauchy-condition surface method, the shape and displacement of the plasma boundary were reconstructed, and position control using the vetical field was confirmed.

A new numerical method for designing the external coils of a stellarator is presented. In this method, the shape of filamentary coils is expressed using fully three-dimensional B-spline curves that are not necessarily constrained on a winding surface. The control points of B-spline curves are optimized together with the coil position and current to minimize an objective function, which is defined using normal field components and engineering constraints. The genetic algorithm is employed to minimize the objective function for arbitrary combinations of modular, helical, and circular poloidal field coils without giving any specific initial guess of coil shapes. A new numerical code genetic optimizer using sequence of points for external coil is developed on the basis of this method, and successfully found optimized modular coils for the stellarators CFQS and Wendelstein 7-X. We also found a specific pattern of helical coil arrangement that can reproduce these optimized stellarators while creating divertor legs outside of the closed magnetic surfaces.

Segment fabrication is now a candidate for the design of superconducting helical magnets in the helical fusion reactor FFHR-d1, which adopts the joint winding of high-temperature superconducting (HTS) helical coils as a primary option and the 'remountable' HTS helical coil as an advanced option. This paper reports on recent progress in two key technologies: the mechanical joints (remountable joints) of the HTS conductors and the metal porous media inserted into the cooling channel for segment fabrication. Through our research activities it has been revealed that heat treatment during fabrication of the joint can reduce joint resistance and its dispersion, which can shorten the fabrication process and be applied to bent conductor joints. Also, heat transfer correlations of the cooling channel were established to evaluate heat transfer performance with various cryogenic coolants based on the correlations to analyze the thermal stability of the joint.

New design approaches are proposed for the LHD-type heliotron D–T demo-reactor FFHR2 to solve the key engineering issues of blanket space limitation and replacement difficulty. A major radius of over 14 m is selected to permit a blanket-shield thickness of about 1 m and to reduce the neutron wall loading and toroidal field, while achieving an acceptable cost of electricity. Two sets of optimization are successfully carried out. One is to reduce the magnetic hoop force on the helical coil support structures by adjustment of the helical winding coil pitch parameter and the poloidal coils design, which facilitates expansion of the maintenance ports. The other is a long-life blanket concept using carbon armour tiles that soften the neutron energy spectrum incident on the self-cooled flibe-reduced activation ferritic steel blanket. In this adaptation of the spectral-shifter and tritium breeder blanket (STB) concept a local tritium breeding ratio over 1.2 is feasible by optimized arrangement of the neutron multiplier Be in the carbon tiles, and the radiation shielding of the superconducting magnet coils is also significantly improved. Using constant cross sections of a helically winding shape, the 'screw coaster' concept is proposed to replace in-vessel components such as the STB armour tiles. The key R&D issues for developing the STB concept, such as radiation effects on carbon and enhanced heat transfer of Flibe, are elucidated.

Variation of the plasma position relative to the centre of the helical coil winding is a very effective means of controlling the MHD stability and the trapped particle confinement in heliotron/torsatron systems, but improving one of these two characteristics with this parameter simultaneously has a detrimental effect on the other. The inward shifted configuration is favourable for drift orbit optimization but is predicted to be unstable according to the Mercier criterion. Various physics problems, such as electric field structure, plasma rotation and MHD phenomena, have been studied in the Compact Helical System (CHS) with a compromise intermediate position. With this standard configuration, CHS has yielded experimental results that contribute to the understanding of general toroidal confinement physics and low aspect ratio helical systems. In the recent experiments, it was found that a wide range of inward shifted configurations give stable plasma discharges without any restriction to the special pressure profile. Such an enhanced range of operation made it possible to study experimentally the drift orbit optimized configuration in heliotron/torsatron systems. The effect of configuration improvement was studied with plasmas in a low collisionality regime.

A helical coil winding law has been found for a stellarator with many of the desirable properties of the Helias. High performance computer codes make it possible to optimize the configuration over a parameter space of large dimension. For reactor applications an ample gap is provided between the coils and the plasma. Line tracing shows that the magnetic surfaces are robust. Non-linear stability at high beta is verified by equilibrium calculations in three dimensions. A neoclassical theory of transport taking quasi-neutrality into account predicts that energy confinement times sufficient for ignition can be achieved economically. For power plant studies a more attractive modular version of this concept called the MHH stellarator is under investigation

For an analysis of the magnetic field configuration it is useful to represent the vacuum magnetic field by a set of harmonic functions. To exactly analyse a helical configuration, a harmonic function describing a pure helical mode of the configuration is desirable, especially in heliotrons, where good quasi-symmetry is regarded as an advantage for a built-in helical divertor. Owing to the specific mode numbers in the toroidal and the poloidal directions, toroidal harmonic functions are appropriate for a study of the helical field when a practical method for their numerical calculation is provided. In the paper, helical components are analysed by a numerical calculation with high accuracy. From a spectral analysis of the magnetic field generated by a continuous helical coil, the 'natural winding' law was found to be an excellent choice for the case where the components resonant with the helicity of the coil are dominant. A deviation from the natural winding law causes an enhancement of off-resonant components. The choice of unique toroidal co-ordinates and, hence, of a unique spectral representation follows naturally from the condition that the spectral series in which the magnetic field is expressed has the largest area for convergence. The high accuracy of the representation was used in a numerical investigation of the intricate structure of a helical divertor. A reticular structure of the scrape-off layer in a helical system was made visible by tracing an unclosed separatrix. The field line at the X-point is a nearly pure helix in the toroidal co-ordinates, and it was confirmed that the deviation due to perturbing fields is sufficiently small to allow a rigid divertor baffle to be installed.

The resonant interaction between magnetohydrodynamic (MHD) instability modes and the externally applied helical magnetic field is demonstrated in the Saskatchewan Torus-Modified (STOR-M) tokamak. The study is conducted both numerically and experimentally using a 2D MHD equilibrium code in the former and an (l = 2, n = 1) helical coil carrying a short current pulse in the latter. It is shown numerically that the resonant helical current can efficiently suppress the magnetic islands resonating on the (m = 2, n = 1) magnetic surface when the value of the safety factor at the plasma edge is relatively low (⩽4). It is also found numerically that (2, 1) islands are induced when the applied helical current exceeds a threshold. The experimental study is performed in STOR-M during low-q ohmic discharges with high MHD activities. The amplitude and frequency of (2, 1) Mirnov fluctuations are significantly reduced after the activation of the resonant field. Lesser suppression in sideband islands is also observed. Moreover, a phase of improved plasma confinement, characterized by a reduction in Hα emission level, a reduction in loop voltage and an increase in the soft x-ray emission, is induced after application of the resonant field.

Heliotron reactors have attractive features for fusion power plants such as having no need for current drive and a wide space between the helical coils for the maintenance of in-vessel components. Their main disadvantage was considered to be the necessarily large size of their magnet systems. According to the recent reactor studies based on the experimental results in the Large Helical Device, a major radius of plasma of 14–17 m with a central toroidal field of 6–4 T is needed to attain the self-ignition condition with a blanket space thicker than 1.1 m. The stored magnetic energy is estimated at 120–140 GJ. Although both the major radius and the magnetic energy are about three times as large as ITER, the maximum magnetic field and mechanical stress are comparable. In the preliminary structural analysis, the maximum stress intensity including the peak stress is less than the 1000 MPa that is allowed for strengthened stainless steel. Although the length of the helical coil is more than 150 m, that is about five times as long as the ITER TF coil, cable-in-conduit conductors can be adopted with a parallel winding method of five-in-hand. The concept of the parallel winding is proposed. Consequently, the magnet systems for helical reactors can be realized with a small extension of the ITER technology.

The structure of the magnetic surfaces in Heliotron DM is measured by the pulsed-electron-beam method. The shape of the observed magnetic island is described. By improving the helical-coil feeder and using compensation coils, the magnetic islands can be eliminated, and finally a value of the rotational transform that agrees well with the computed one up to ?/2? 2 is obtained.

The production of a highly ionized deuterium plasma at initial gas pressures of 0.5 to 2 mTorr has been investigated in a compact toroidal geometry (major radius of the torus vessel 20 cm, minor radius 10 cm). The gas, pre-ionized by a capacitively coupled RF-discharge, is further ionized (pre-heated) by toroidal and poloidal plasma currents which are induced by the discharge of a condenser bank (7.5 kJ maximum energy) into a helical coil system wound around the torus. At the end of the ionization phase, the current in the coil is crowbarred. Radial plasma density profiles are measured by using a movable 4-mm microwave probe. The plasma current, its energy, and the toroidal and poloidal magnetic field distributions are deduced from magnetic measurements, and the electron temperature from the Dβ-line-to-continuum-light-intensity ratio.At the low initial gas pressures studied here, the plasma formation occurs when the toroidal electric field amplitude on the torus axis lies below a critical value (< 6 V/cmmTorr). Using a programmed auxiliary perpendicular magnetic field, a plasma which is both highly ionized and well detached from the walls of the torus is obtained. Plasma equilibrium can be maintained during the time of observation (up to ≈ 40 μs after crowbar). Electron densities greater than 6 × 1013 cm−3 (cutoff density for 4-mm waves), a degree of ionization higher than 60%, and electron temperatures of 5 eV are reached starting from a pressure of 1 mTorr D2. The toroidal plasma current and the toroidal magnetic field are, respectively, 7 kA and 0.45 kG at the time of crowbar. The measured density and magnetic field profiles indicate that the magnetic axis lies significantly off the axis of the torus vessel.

The general expression of the l = 2 straight helical heliotron field is obtained by integrating Biot-Savart's formula after expanding the integrand. Solving the differential equation of the line of force, a general expression for the magnetic surfaces, which is in good agreement with the results of a computer calculation up to the separatrix, is obtained. The rotational transform and the shear of this field are calculated as functions of the average radius of the magnetic surface. For a certain range of α*, the ratio of the longitudinal field produced by the Bz–coil to the longitudinal component of the field produced by the helical coil, the field cannot form a closed magnetic surface. The width of this range, the forbidden zone, is a function of γ = 2πa/p, where a is the radius of the helical winding and p is the pitch. For small γ, the zone is wide and the closed magnetic surface has very small shear. For large γ, the zone is narrow and the magnetic surface has very small rotational transform and shear. Only for intermediate γ, the zone is narrow and rotational transform and shear are both large. These values of γ could be considered to be optimum values for plasma confinement.