Physical model assessment of the energy confinement time scaling in stellarators

The International Stellarator Confinement Database (ISCDB) is a joint effort of the helical device community. It is publicly available at http://www.ipp.mpg.de/ISS and http://iscdb.nifs.ac.jp. The validity of physics models is investigated employing ISCDB data. Bayesian model comparison shows differences in the confinement scaling of data subgroups. Theory-based assessment of pure neoclassical transport regimes, however, indicates scalability which is supported by experimental results in specific W7-AS scenarios. Therefore, neoclassical simulations are employed for predictive purposes, accounting for effects due to power deposition, plasma profiles, and the ambipolar radial electric field. Neoclassical case studies for W7-X are presented as examples for the neoclassical predictions to be considered as an upper limit of plasma performance. 1. The International Stellarator Confinement Database Stellarator/heliotron research aims at an alternative fusion reactor concept. For a conclusive physics basis a comprehensive exploration of the plasma performance in existing devices is required. With respect to magnetic configurations and operational regimes, varieties in stellarator operation were revealed in earlier studies [1,2]. Consequently, a permanent assessment of confinement in stellarators and its relevance for reactor scenarios are required. As part of this effort, the International Stellarator Confinement Database (ISCDB) was reinitiated in 2004 and the ISS95 [3] has been extended to roughly 3000 discharges from eight different devices. In a first step, a unified scaling law ISS04 [1] was derived from an ISCDB subset consisting of roughly 1700 data. ISS04 largely confirms ISS95, but reveals the impact of the magnetic configuration which is formally described by a confinement time enhancement factor. In addition to the data for global scaling considerations, ISCDB documents also special discharge scenarios, single parameter scans in power, density and rotational transform and even scans of the magnetic configuration (by variation of the major radius) in LHD [2]. The latter scan is also a case of neoclassical optimization due to inward shift of the plasma [4]. A second example is a density scan close to highest densities leading to the HDH bifurcation in Wendelstein 7-AS [5]. For HDH discharges the density scaling exponent was found to agree with the ISS04 scaling, however with a larger configuration factor which diminishes in the case of detached divertor plasmas. Third, the confinement in H-modes in W7-AS with broad density profiles compared to narrow density profile high-performance discharges is an example of profile effects on τE which is not reflected by the confinement scalings. Finally, 2 26.9.2006 – 7 version EX/P7-1 high-electron-temperature electron-root discharges governed by the beneficial effect of the radial electric field [6, 7] indicate the role of local transport properties in stellarator plasmas. The global confinement of nearly all discharges of the ISS04 database is dominated by anomalous transport. Only at fairly high temperatures does neoclassical transport become important due to its unfavorable temperature dependence in the long-mean-free-path regime. It is this small subset of discharges (mainly from W7-AS) which allows for the confirmation of neoclassical modeling for the confinement, and is an example for theory-based extrapolations for W7-X, and in a future step, to reactor scenarios. This paper is devoted to an assessment of physical models with respect to scaling laws. The first part deals with physical model comparison for global confinement data employing Bayesian model comparison techniques. In the second part purely neoclassical τE scalings are derived. The study is completed by predictive scans of neoclassical simulations for Wendelstein 7-X discharges which are compared with ISS95. 2. Model comparison for global confinement data scaling Scaling laws are used both as a reference and for extrapolation. The latter purpose requires a careful assessment of the validity of scaling laws. A powerful approach is the application of dimensional constraints due to Connor and Taylor [8], followed e.g. by Christiansen et al. [9]. The basic idea as applied in this paper is to test the compatibility of data with a physics model. Requiring the same invariance behavior of the basic equations determining confinement and the scaling relation under similarity transformations puts constraints on the scaling model. If the model is a power law, the constraints are restrictions in the exponents [8]. Our technique to identify the most valid model for experimental data given is Bayesian model comparison [10]. This technique automatically obeys Occam's Razor and thereby punishes models of higher complexity, i.e. it weights consistently the number of model parameters considered. However, a key for the application of Bayesian model comparison is reliable error estimates of all model parameters but as well as in the target quantity. Fig. 1: β vs. collisionality of confinement data subsets from ISCDB. The low-beta data are full squares for LHD and open circles for W7-AS. The high-beta data are open squares for LHD and full circles for W7-AS. An issue of particular reactor relevance is the beta scaling of global stellarator confinement. ISS04 indicates a small degradation of global stellarator confinement with the volume average plasma-β ( 17 . 0 − ∝ β τ E ). A caveat is due to the clustering of data in the beta-collisionality space. Therefore, a detailed statistical analysis of the data subsets is necessary. In previous 3 26.9.2006 – 7 version EX/P7-1 studies, early confinement data from W7-AS were identified to be consistent with a collisional low-β model [10]. The extension of ISCDB now allows us to test the model validity also for higher β data. Fig. 1 shows data from W7-AS and LHD widely spread in β and collisionality range. The data are separated into subgroups intuitively termed lowand high-β according to their relative appearance in Fig. 1 with respect to the β-axis. According to the Connor/Taylor invariance principle [8] the scaling law ansatz is (1) ∑ = − − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∝ E