The existence of the IIv regime, in which the neoclassical transport coefficients are inversely proportional to the collision frequency, increases the neoclassical particle and heat transport in nonaxisymmetric devices to levels far above those of axisymmetric tokamaks in the fusion-relevant longmean-free-path (lmfp) regime. Thus, the reduction of neoclassical transport is one of the key issues for any future fusion reactor based on a non-axisymmetric configuration.In this paper we study the neoclassical transport in strongly inward-shifted configurations of the LHD and find a neoclassical-transport-optimized configuration by evaluating a mono-energetic neoclassical transport coefficient. In order to compare the neoclassical transport properties of this optimized configuration with those of "advanced stellarators", an effective helical ripple, E eff , is also evaluated from the transport coefficients obtained. The neoclassical transport coefficient in the 1/v regime is proportional to Eeff and the neoclassical transport in the lmfp regime can be easily estimated by the value of E eff • We evaluate a mono-energetic local transport coefficient using DCOM (Diffusion COefficient calculator by Monte-carlo method)[2] in which test particle orbits are followed solving the equations of motion in Boozer coordinates and the transport coefficient is evaluated statistically from the mean square displacement of the particles. Figure 1 shows the mono-energetic transport coefficient evaluated by DCOM code normalized by the plateau value of the equivalent circular tokamak, Dp=(n/16)(YARwe3), where v, R, L, and We are the velocity, the major radius, the rotational transform, and the cyclotron frequency, respectively. With respect to 1/v transport, the optimum configuration is found when the magnetic axis has a major radius of 3.53m. In this case, the effective helical ripple is very small, remaining below 2 % inside 4/5 of the plasma radius (Fig. 2). This indicates that a strong inward 180 shift of the magnetic aXIS can optimized the neoclassical transport of the LHD configuration to a level typical of so-called"advanced stella-rators".

A general solution of the ripple-averaged kinetic equation, GSRAKE, is presented and used to investigate neoclassical transpolf in the model magnetic field of a simple stellarator. No assumptions are made as to the relative sizes of the collision frequency, Y, and poloidal precessional frequency, Re, so that the mlntion i s valid throughout the entire longmeon-freepath regime. Separate but fully self-consistent treatments of both localized and non-localized particles are provided: the interaction between these two classes of pmicles is accounted for through a set of appropriate physical boundary conditions. All drift terms present within the framework of the ripple-averaged theory are included: in particular, for localized particles Ro = RE + Rv, is comprised of both the E x B and VE precessional frequencies. The solution is thus equally valid in the RE >> Rvs and the RE = 0 limits of standard neoclassical theory. A detailed comparion of results with those of the FLOCS code is undertaken; estimates of neoclassical transport coefficients obtained from several codes are also presented. Good agreement of results is found in all of these comparisons, GSRAKE requiring but a tiny fraction of the computational time necessary for the other codes.Planck equation, FPSTEL [I91 and FL.OCS [20], and a solution of the drift-kinetic equation, DKES [21,22]. The principal disadvantage of these computational approaches lies in the

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 energy confinement times are nearly the same as in HSR5/22, thus the same fusion power (3000 MW) is expected in both 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 periods and the concomitant reduction in size will also reduce the cost of the Helias reactor.

The distribution function for ripple-trapped particles has been found in a series form valid for all low collision frequencies, for standard and transport-optimized stellarators. The diffusion coefficient obtained with this distribution function shows excellent agreement with the results of Monte Carlo and Fokker-Planck computer codes, in the cases studied.PACS numbers: 52.25.Fi, 52.55.HeOver the past several years there has been renewed interest in the toroidal stellarator as a possible fusion reactor. Much of this interest has centered on the transport properties of a stellarator at the low collision frequencies expected in a fusion plasma, since particles trapped in the local ripple wells of the stellarator's magnetic field are expected to introduce a significant loss mechanism above and beyond that predicted by neoclassical theory for an axisymmetric tokamak. The theory of ripple transport for a "standard" stellarator at low collision frequency, v, was introduced 1 and developed 2 as a number of distinct results, each of which applies in different circumstances. In these works, regimes were identified in which transport coefficients scaled as v~l, v 1/2 , and v.Since then it has been demonstrated 3 that a certain class of stellarators exhibits enhanced confinement, and parts of the existing theory have been extended to treat the more general case of a multiple-helicity stellarator in the -1 • 4 5 v regime. In the present work a series solution in k 2 of the bounce-averaged kinetic equation for ripple-trapped particles is presented. Here, k 2 is a quantity which describes a particle's trapping state, with ripple-trapped particles satisfying 0<£ 2 <1. The proper choice of boundary conditions makes this solution valid for all collision frequencies and for all of the classes of stellarators discussed above. Diffusion coefficients obtained using this series solution show excellent agreement with those obtained numerically.The bounce-averaged kinetic equationis of primary interest in the study of transport due to particles entrapping and detrapping in the local wells of the stellarator field B=B 0 ll+e t (r)cose-€ h (r)(\ ~ crcos0)cos(/0+/?0)].(2)The symbols in Eqs. (1) and (2) are standard, except for the constant 0, Eq.(2) describes a stellarator with reduced transport rates in the v _1 regime (the standard form for B, which closely approximates most experimental situations, has cr=0). The usual means of solution of Eq. (l) begins with assumptions as to the relative size of the characteristic frequencies present in the problem. 1,2 The two frequencies of primary interest are the frequency with which particles are collisionally detrapped from a local well, v / efT == vV2f/ I , which appears through the collision operator, C(/), and the poloidal precessional frequency, #~ -Ci E = -E r /rB 0 .It is assumed that a large ambipolar radial electric field, E r , provides the dominant contribution to 9 through the ExB drift. Solutions obtained in this way have the disadvantage that they are...