RESEARCH ON INTEGRATED MODELING
AND COUPLING WITH EXPERIMENTS

Integrated modeling is an important element of tokamak fusion research that contributes in an essential way to the interpretation and planning of experiments, validation of theory against experimental results, development of plasma control techniques, and the design of next step devices such as ITER. The following provides a summary of the recent research interests in integrated modeling research of the GA Theory Group and describes the tight coupling with the experimental DIII-D tokamak program. References are provided at the end.

An important component of tokamak research, particularly in the DIII-D program, is the simultaneous optimization of various physics elements toward advanced tokamak (AT) operation. Thus modeling necessarily involves the self-consistent integration of various physics elements from different topical science areas, such as transport, macroscopic equilibrium and stability, and heating and current drive.

In particular, a core or an edge transport barrier often leads to a large pressure gradient limited by MHD instabilities such as edge localized modes (ELM), which sets the edge boundary conditions in these configurations [Lao 2000, Snyder 2004]. The core performance depends strongly on the edge pedestal boundary conditions. On the other hand, the evolution of the edge pedestal pressure gradient also depends on the heat flux outflows from the core. Thus, a self-consistent integration of MHD stability and transport simulations is necessary to explore the ELM dynamics and its effects on core performance.

Furthermore, toroidal rotation and rotational shear have been shown to have many beneficial effects on the stabilization of MHD instabilities and suppression of turbulence that are crucial for high performance regimes. Magnetic field errors can interact with the plasma and slow down the rotation, that in turn can reduce the turbulence suppression and lead to further reduction of plasma rotation. In a high b plasma near the ideal no-wall limit, the plasma can also amplify the error magnetic field [Boozer 2001, Garofalo 2002, Chu 2003]. Lastly, experimental results from AUG [Gruber 2001] and DIII-D [Luce 2002] indicate that expulsion of magnetic flux from the plasma core due to fishbone and tearing instabilities may play a key role in maintaining qmin ~ 1 that is important for obtaining the stationary ITER-like hybrid-scenario discharges in these devices. Before accurate projections to ITER can be made, a self-consistent integration of MHD stability and transport simulations is needed.

A key DIII-D integrated modeling tool is the ONETWO transport code. Significant progress has recently been made to improve ONETWO. This includes development of various numerical solution schemes based on the use of a globally converged modified Newton approach to allow efficient coupling of the GLF23 transport model to ONETWO. Various new and improved NTCC RF and NBI source modules such as TORAY-GA, CURRAY, and the TRANSP derived NUBEAM have also been implemented into ONETWO. This new package of ONETWO tools has been extensively employed to model DIII-D experiments and AT scenarios with reasonable success [Murakami 2003]. It has also been recently applied to model ITER steady state AT scenario. An example of an ITER AT simulation using ONETWO with the GLF23 transport model is given in the figure below, showing a recent attempt to determine 100% non-inductive current drive operation for ITER.

Simulated profiles of toroidal current density components for an ITER steady state AT scenario using ONETWO and GLF23 (left). On the right is a comparison of simulated toroidal rotation profile computed using ONETWO with an inductive motor model against the experimental profile for DIII-D RWM discharge 106029.

Preliminary calculations to explore the resonant magnetic drag effects on plasma rotation using ONETWO with a simple inductive motor model [Fitzpatrick 1993] were also carried out. The results of a simulation for a DIII-D RWM discharge are given in the rightmost figure below. This also shows that the plasma rotation decreases strongly across the entire profile after the onset of a RWM at 1500 ms. The simulation shows a large local depression near r ~ 0.6 due to the resonant magnetic drag at the q = 3 surface, whereas the experimental profile has a smooth variation in that region. The discrepancy suggests that magnetic damping due to non-resonant effects also plays a role in the slowing down of plasma rotation and needs to be included.

Substantial contributions were also made to the Snowmass 2002 modeling Working Groups, both in transport (p4) and MHD (p3) [http:/conferences/snowmass/working/mfe/physics/p3/ and p4], to explore the effects of pedestal temperatures on ITER performance and the maximum pedestal temperature stable to the edge peeling-ballooning modes. The simulations were carried out using ONETWO and the XPTOR transport code with the GLF23 transport model and the ELITE edge stability code [Kinsey 2003ab, Snyder 2003, Lao 2003]. The results are summarized in the figure below, where the dependence of fusion power on the pedestal temperature and the maximum stable pedestal temperature against the intermediate n edge peeling-ballooning modes are shown. In these simulations, the core transport calculations and the edge stability analysis are separately computed. A key component of our proposed work is to self-consistently integrate these calculations to allow a more accurate projection to ITER.

Dependence of fusion power on pedestal temperature for an ITER reference scenario using XPTOR and GLF23 with different amount of input powers (left figure). Maximum pedestal temperature stable to edge peeling-ballooning modes as a function of the pedestal width (right figure).