Monoenergetic Coefficients Research Articles

MONKES: a fast neoclassical code for the evaluation of monoenergetic transport coefficients in stellarator plasmas

MONKES is a new neoclassical code for the evaluation of monoenergetic transport coefficients in stellarators. By means of a convergence study and benchmarks with other codes, it is shown that MONKES is accurate and efficient. The combination of spectral discretization in spatial and velocity coordinates with block sparsity allows MONKES to compute monoenergetic coefficients at low collisionality, in a single core, in approximately one minute. MONKES is sufficiently fast to be integrated into stellarator optimization codes for direct optimization of the bootstrap current and to be included in predictive transport suites. The code and data from this paper are available at https://github.com/JavierEscoto/MONKES/.

A quasi-isodynamic configuration with good confinement of fast ions at low plasma β

A new quasi-isodynamic (QI) stellarator configuration optimized for the confinement of energetic ions at low plasma β is obtained. The numerical optimization is carried out using the STELLOPT suite of codes. New proxies to measure closeness to quasi-isodynamicity and quality of fast ion confinement have been included. The new configuration has poloidally closed contours of magnetic field strength, low magnetic shear and a rotational transform profile allowing an island divertor. It shows ideal and ballooning magnetohydrodynamic stability up to , reduced effective ripple, with in the plasma core. Even at low β, the configuration approximately satisfies the maximum-J property, and the confinement of fast ions is good at and becomes excellent at reactor values, . An evaluation of the D 31 neoclassical mono-energetic coefficient supports the expectation of a reduced bootstrap current for plasmas confined in QI configurations. A set of filamentary coils that preserve the good confinement of fast ions in the core is presented.

Calculation of the bootstrap current profile for the TJ-II stellarator

Calculations of the bootstrap current for the TJ-II stellarator are presented. DKES and NEO-MC codes are employed; the latter has allowed, for the first time, the precise computation of the bootstrap transport coefficient in the long-mean-free-path regime of this device. The low error bars allow a precise convolution of the monoenergetic coefficients, which is confirmed by error analysis. The radial profile of the bootstrap current is presented for the first time for the 100_44_64 configuration of TJ-II for three different collisionality regimes. The bootstrap coefficient is then compared with that of other configurations of TJ-II regularly operated. The results show qualitative agreement with toroidal current measurements; precise comparison with real discharges is ongoing.

Extended estimations of neoclassical transport for the TJ-II stellarator: The bootstrap current

This work extends previous Monte Carlo estimations of neoclassical transport for the TJ-II stellarator [V. Tribaldos, Phys. Plasmas 8, 1229 (2001)] to include, for the first time, the bootstrap current in low collisionality electron cyclotron resonance heated (ECRH) plasmas. The calculations are based on the mono-energetic coefficients calculated with DKES [W. I. van Rij and S. P. Hirshman, Phys. Fluids B 1, 563 (1989)] and MOCA codes. It is shown that despite the difficulties of calculating these coefficient in the long mean free path for TJ-II configurations, the bootstrap current can be accurately estimated based on the moderate temperatures measured in this device with and without enforcing momentum conservation [H. Maaßberg et al., Phys. Plasmas 16, 072504 (2009)]. The computed bootstrap current is found to be in fair agreement with the currents being measured in ECRH regimes. Finally, the effect of the bootstrap current on the rotational transform profile is discussed.

Neoclassical transport simulations for stellarators

The benchmarking of the thermal neoclassical transport coefficients is described using examples of the Large Helical Device (LHD) and TJ-II stellarators. The thermal coefficients are evaluated by energy convolution of the monoenergetic coefficients obtained by direct interpolation or neural network techniques from the databases precalculated by different codes. The temperature profiles are calculated by a predictive transport code from the energy balance equations with the ambipolar radial electric field estimated from a diffusion equation to guarantee a unique and smooth solution, although several solutions of the ambipolarity condition may exist when root-finding is invoked; the density profiles are fixed. The thermal transport coefficients as well as the ambipolar radial electric field are compared and very reasonable agreement is found for both configurations. Together with an additional W7-X case, these configurations represent very different degrees of neoclassical confinement at low collisionalities. The impact of the neoclassical optimization on the energy confinement time is evaluated and the confinement times for different devices predicted by transport modeling are compared with the standard scaling for stellarators. Finally, all configurations are scaled to the same volume for a direct comparison of the volume-averaged pressure and the neoclassical degree of optimization.

A convergence study for the Laguerre expansion in the moment equation method for neoclassical transport in general toroidal plasmas

The dependence of neoclassical parallel flow calculations on the maximum order of Laguerre polynomial expansions is investigated in a magnetic configuration of the Large Helical Device [S. Murakami, A. Wakasa, H. Maaßberg, et al., Nucl. Fusion 42, L19 (2002)] using the monoenergetic coefficient database obtained by an international collaboration. On the basis of a previous generalization (the so-called Sugama–Nishimura method [H. Sugama and S. Nishimura, Phys. Plasmas 15, 042502 (2008)]) to an arbitrary order of the expansion, the 13 M, 21 M, and 29 M approximations are compared. In a previous comparison, only the ion distribution function in the banana collisionality regime of single-ion-species plasmas in tokamak configurations was investigated. In this paper, the dependence of the problems including electrons and impurities in the general collisionality regime in an actual nonsymmetric toroidal configuration is reported. In particular, qualities of approximations for the electron distribution function are investigated in detail.

Analytical Methods to Calculate Flows and Diffusions Driven by Neoclassical Viscosities in Helical Plasmas

Methods to obtain monoenergetic viscosity coefficients by combining analytical approximations of the linearized drift kinetic equation are studied for a previously formulated full neoclassical transport matrix in general nonsymmetric toroidal plasmas. A unified analytical treatment of two coefficients due to the non-bounce-averaged radial drifts of guiding centers is shown. These coefficients were previously obtained by a direct numerical calculation of the kinetic equation in the three-dimensional (3-D) phase-space (pitch-angle, poloidal and toroidal angles). In a present study, the radial drift term in the equation is divided into three parts, and then the perturbed distribution and the resulting monoenergetic coefficients are expressed by superposed components, which can be calculated by combining analytical methods. An analytical expression for the boundary layer correction to the parallel viscosity in the 1/ν regime also is newly derived to complete the full matrix without a numerical calculation in 3-D phase-space. Analytical results given by adding these components approximately reproduce results of the direct numerical calculation of the kinetic equation.

Monte Carlo estimation of neoclassical transport for the TJ-II stellarator

The neoclassical transport properties of TJ-II stellarator [C. Alejaldre et al., Fusion Technol. 13, 521 (1988)] are studied with the monoenergetic Monte Carlo technique. A compromise between the number of modes and particles and the required computing time to obtain reliable estimates, from the computational point of view, of the monoenergetic diffusion coefficients is shown to be of one thousand particles and one hundred harmonics, because of the rich magnetic-field structure of TJ-II. Although, these requirements are probably too demanding in making the transport estimations. The data base containing the normalized monoenergetic diffusion coefficient for several radial positions, radial electric fields and collisionalities have been fitted using a neural network. This fit reduces the number of points necessary in the data base and allows a smooth interpolation and extrapolation to perform the convolutions of the monoenergetic coefficients with the Maxwellian. For two different typical TJ-II discharges the ambipolar radial electric field, and the neoclassical particle and heat fluxes are presented both showing rather large positive radial electric fields at the plasma core and small negative fields at the edge. The neoclassical particle and energy confinement time are in surprisingly good agreement with the experimental energy balance analysis and the international stellarator scaling. Although no satisfactory explanation is available yet the large neoclassical diffusion caused by the complex ripple structure of TJ-II magnetic field may be an important ingredient.