INTRODUCTION: One of the optimization criteria for the stellarator W7-X is the minimization of the bootstrap current [1], which is not needed for producing the magnetic field in W7-X and must be compensated. The plasma current alters the rotational transform and affects the magnetic configuration, especially near the edge area of plasma. Due to plasma current the last closed magnetic surface (LCMS), X-points, and islands change their spatial position. A simple estimation gives the following value of maximum displacement: dZ[cm] ~ 0.42IP[kA]. This represents a potential danger for the island divertor [2] used in W7-X, because the typical distance of target plates from LCMS is about 10cm. Preliminary calculations have shown that a tolerable value of current is about 10kA, while the maximum value of the bootstrap current for the expected plasma parameters of W7-X varies from 10kA to 40kA, depending on the magnetic configuration used. W7-X is not equipped with an Ohmic transformer, so the only means for compensating this current is electron cyclotron current drive (ECCD) and/or neutral beam current drive (NBCD). In this report we study the compensation of residual bootstrap current by using ECCD. METHOD: To model the control of the toroidal current we use a predictive 1D transport code, which is under development. The transport code is based on a system of equations, which consists of particle and power balance equations augmented by diffusion equations for the radial electric field and the toroidal current density:
A stellarator power plant is aimed to operate in a stable state, in the absence of thermal instability. This instability arises due to the strong increase of D-T fusion power with temperature. A thermally stable solution requires that the transport power losses increase more rapidly with temperature than the sum of the fusion power and auxiliary power, assuming a feedback loop that decreases auxiliary power (if any) as alpha particle power increases. The Helias reactor is expected to operate at high density (central electron density of 2 - 3·10 20 m -3 ) and moderate temperature (central temperature around 15 keV). Under these conditions, neoclassical theory predicts that only the “ion root” solution for the radial electric field exists with the stellarator specific 1/ν regime for electrons and ν regime for ions, demanding strong optimisation of the magnetic configuration to minimise losses. The Helias Reactor HSR4/18, which has 4-field periods and a major radius of 18m, with B = 5T, is very well optimised in this sense, having an effective helical ripple e eff ≤ 0.6% over the entire plasma cross-section [1]. At this level 1/ν losses pose no threat to ignition, however a stable steady-state burn can be maintained at very high central temperatures, with beta exceeding the MHD stability limit (which is about 4% for HSR4/18). In this article, the one-dimensional heat conduction equation is solved for the temperature profile taking into account alpha-particle heating and bremsstrahlung losses. The neoclassical coefficients, calculated for HSR4/18 magnetic field have been employed [2]. The non-linearity of the equation leads to multiple solutions. It is found that stable operation at moderate plasma temperatures can be achieved for some finite level of ripple losses (0.006 < e eff << e h ) or at some level of gyro-Bohm type transport. Below we solve energy balance equation, assuming that for reactor conditions (T = T i = T e ) : - 1 r ∂ ∂r rQ = h n,T
A rapid simulation of transport by trapped particles in stellarators, based on conservation of J, has been developed. At very low collision frequency the diffusion rates are not entirely in agreement with analytic theory. The potential importance of effects not described by an 'averaged' theory is discussed.
The bounce averaged Fokker-Planck equation for the distribution function of ripple trapped particles in a tokamak has been solved, for arbitrary collision frequencies, in the 'tokamak' limit in which ripple wells are localized close to the midplane. The equation includes the main terms contributing to collisionless (de)trapping. The solution employs power series expansions for the distribution function in the pitch angle variable k2 and the poloidal angle θ; the series in k2 and θ both terminate. The boundary conditions applied at the trapping/detrapping boundary, that f and ∂f/∂k2 be continuous, become the requirement that in the collisionless limit the derivative with respect to k2 reflect the scale length set by the motion in toroidally blocked orbits. The resulting series solutions reduce to the usual expressions in the high collision frequency limit, but they are considerably lower than the results of previous calculations (which neglect the collisionless detrapping effects), in the low collision frequency limit. Comparison with Monte Carlo calculations for INTOR parameters shows that, in all cases, the analytic results lie somewhat below the numerical results, which is to be expected since banana drift diffusion is also present in the Monte Carlo calculation. However, previous analytic calculations give diffusion coefficients which are much larger than the Monte Carlo results.
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 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, the effective helical ripple is below 1%. The paper describes the power balance of the Helias reactor, the blanket and maintenance concept. 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.
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