Benchmarking of the mono-energetic transport coefficients—results from the International Collaboration on Neoclassical Transport in Stellarators (ICNTS)

Abstract

Numerical results for the three mono-energetic transport coefficients required for a complete neoclassical description of stellarator plasmas have been benchmarked within an international collaboration. These transport coefficients are flux-surface-averaged moments of solutions to the linearised drift kinetic equation which have been determined using field-line-integration techniques, Monte Carlo simulations, a variational method employing Fourier-Legendre test functions and a finite difference scheme. The benchmarking has been successfully carried out for past, present and future devices which represent different optimisation strategies within the extensive configuration space available to stellarators.A qualitative comparison of the results with theoretical expectations for simple model fields is provided. The behaviour of the results for the mono-energetic radial and parallel transport coefficients can be largely understood from such theoretical considerations but the mono-energetic bootstrap current coefficient exhibits characteristics which have not been predicted.

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

“…The integral in kinetic energy, or speed, from zero to infinity (relativistic effect are negligible) translates into the mono-energetic coefficients' variation in inverse mean-free-path, ν/v, from collisionless (infinite mean free path) to fully collisional (zero mean free path). As shown in the literature [6,9] and also in Fig. 1 the dependence of the three coefficients on the mean free path is quite different.…”

“…See for example the NCSX (toroidally quasi-symmetric) and HSX (helical quasi-symmetric) in ref. [9]. The situation at intermediate collisionalities for purely symmetric fields is a transition from the null value at high collisionality to the plateau value in the collisionless limit.…”

“…The final step consists in linearizing the guiding center distribution function with respect to the drift ordering small parameter δ << 1 as f ≈ f 0 + δf 1 . The solution to order δ 0 is identically satisfied by a local maxwellian f 0 = f M = n(r)(m/2πT (r)) 3/2 exp(−mv 2 /2T (r)) and the resulting DKE equation to order δ 1 can be split into two independent equations [9], one forf I , with a parallel drive…”

“…(1) and (2), for several radial positions, normalized drift velocities, E r /vB 0 and mean-free-paths, R 0 ν/v. Several numerical techniques are nowadays available for the calculation of the mono-energetic diffusion coefficients [9] each with its strengths and drawbacks: i) analytical calculations [6,7]; ii) spectral decomposition [12,13] methods; iii) field line integration [14,15] techniques, and iv) Monte Carlo [16][17][18][19][20][21] simulations. However, not all of them are suited for the TJ-II stellarator because of its complex magnetic field structure; because they don't include the effect of the radial electric field; or because they can only compute one of the coefficients effectively.…”

Electron cyclotron current drive simulations for finite collisionality plasmas in Wendelstein 7-X using the full linearized collision model

“…In this code the kinetic equation is solved using the full linearized Coulomb collision operator including energy and momentum conservation 16 . Originally, NEO-2 was developed for the computation of mono-energetic neoclassical transport coefficients in stellarators 17 and for the computation of the distribution functions in tokamaks 11 . However, recent progress such as the development of a quasilinear version for non-axisymmetric tokamaks 18 as well as ongoing technical improvements such as parallelization for a more efficient computation of the generalized Spitzer function in stellarators 12,13 resulted in a more general version of the code.…”