No abstract

The B2‐Eirene code package was developed to give better insight into the physics in the scrape‐off layer (SOL), which is defined as the region of open field‐lines intersecting walls. The SOL is characterised by the competition of parallel and perpendicular transport defining by this a 2D system. The description of the plasma‐wall interaction due to the existence of walls and atomic processes are necessary ingredients for an understanding of the scrape‐off layer. This paper concentrates on understanding the basic physics by combining the results of the code with experiments and analytical models or estimates. This work will mainly focus on divertor tokamaks, but most of the arguments and principles can be easily adapted also to other concepts like island divertors in stellarators or limiter devices. The paper presents the basic equations for the plasma transport and the basic models for the neutral transport. This defines the basic ingredients for the SOLPS (Scrape‐Off Layer Plasma Simulator) code package. A first level of understanding is approached for pure hydrogenic plasmas based both on simple models and simulations with B2‐Eirene neglecting drifts and currents. The influence of neutral transport on the different operation regimes is here the main topic. This will finish with time‐dependent phenomena for the pure plasma, so‐called Edge Localised Modes (ELMs). Then, the influence of impurities on the SOL plasma is discussed. For the understanding of impurity physics in the SOL one needs a rather complex combination of different aspects. The impurity production process has to be understood, then the effects of impurities in terms of radiation losses have to be included and finally impurity transport is necessary. This will be introduced with rising complexity starting with simple estimates, analysing then the detailed parallel force balance and the flow pattern of impurities. Using this, impurity compression and radiation instabilities will be studied. This part ends, combining all the elements introduced before, with specific, detailed results from different machines. Then, the effect of drifts and currents is introduced and their consequences presented. Finally, some work on deriving scaling laws for the anomalous turbulent transport based on automatic edge transport code fitting procedures will be described. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The variational approach for electronic structure based on the two-body reduced density matrix is studied, incorporating two representability conditions beyond the previously used P, Q, and G conditions. The additional conditions (called T1 and T2 here) are implicit in the work of Erdahl [Int. J. Quantum Chem. 13, 697 (1978)] and extend the well-known three-index diagonal conditions also known as the Weinhold-Wilson inequalities. The resulting optimization problem is a semidefinite program, a convex optimization problem for which computational methods have greatly advanced during the past decade. Formulating the reduced density matrix computation using the standard dual formulation of semidefinite programming, as opposed to the primal one, results in substantial computational savings and makes it possible to study larger systems than was done previously. Calculations of the ground state energy and the dipole moment are reported for 47 different systems, in each case using an STO-6G basis set and comparing with Hartree-Fock, singly and doubly substituted configuration interaction, Brueckner doubles (with triples), coupled cluster singles and doubles with perturbational treatment of triples, and full configuration interaction calculations. It is found that the use of the T1 and T2 conditions gives a significant improvement over just the P, Q, and G conditions, and provides in all cases that we have studied more accurate results than the other mentioned approximations.