An important progress in the understanding of the pedestal structure in the KSTAR discharge 7328 has been made during my visit. In particular:
- A new procedure to generate free boundary equilibrium for KSTAR discharges has been developed. This procedure is documented and is available online.
The improvements of the new equilibrium includes the following:
- The (R,Z) resolution has been increased by a factor of four. The stability analysis as well as extended MHD studies require well-resolved equilibrium;
- The central values of q has been reduced from 2 to more realistic values that takes into account episodic sawtooth crashes in this discharges;
- The pedestal is moved from the region (0.8:0.9) to (0.9:1);
- The densities and temperatures in the plasma core have more realistic values. Near the magnetic axis, the plasma pressure in the new equilibrium is significantly smaller comparing to the pressure in the old equilibrium;
- The new equilibria include vacuum field solutions and can be used for the nonlinear extended MHD studies of ELM crashes.
- Using the new equilibrium (case s17), a new peeling-ballooning diagram is generated. The diagram is also described and available online. Key features of the PB diagram include:
- The diagram indicates the toroidal mode numbers that are close to be modes observed in experiments. The modes identified on the PB diagram are n=5, n=9 and n=11;
- Both the peeling and ballooning boundaries were identified;
- The experimental pedestal conditions that are expected to correspond to n=5 and n=9 modes are determined;
- It is indicated that transition from n=9 to n=5 modes is likely to be associated with very small changes in the pedestal density and temperature, but rather significant changes in the parallel current density;
- The pedestal temperatures that are found to be associated with n=5 and n=9 are 800 eV and 775 eV correspondingly. These values are somewhat above the experimental temperatures that are expected to be in the range from 400 eV to 700 eV. The differences between temperature found in the stability analysis and experimental range for temperatures can be explained if the Sauter model, that has been used in this analysis for the bootstap current, over-predicts the values of the bootstrap current. The expected over-predict is about 20%.
- The kinetic neoclassical XGC0 code has been used to investigate the pedestal buildup dynamics. For this study, a KSTAR equilibrium with somewhat relaxed pedestal has been used. The results of this study are documented here and here.
- For the range of expected temperatures, it is noted that the pedestal buildup dynamics can be very different. The cases with lower plasma collisionality exhibit a faster pedestal buildup. For these case, the pedestal height is increasing and the pedestal width is decreasing faster comparing to the cases with higher plasma collisionality. The cases with lower collisionality are likely to be become unstable sooner for the PB modes.
- The kinetic predictions for the bootstrap currents are compared for these case. It is shown that the bootstrap current is significantly larger for the cases with lower plasma collisionality. Similar observations are made for the radial electric field and the poloidal velocity rotation profiles.
- The extended MHD simulations of the KSTAR discharge 7328 using the NIMROD and BOUT++ codes are compared here. It has been shown that
- The NIMROD and BOUT++ produce comparable growth rates;
- The resistivity profiles and a proper account for the diamagnetic effects are important;
- The parallel viscosity effects have relatively weak effect on the ELM dynamics at least during a linear stage of a crash.
Possible future studies can include:
- Improvements in the equilibrium solve in the vacuum region and further increase in the (R,Z) resolutions;
- Verification and validation of the bootstrap current models. It will be interesting to confirm one of the conclusions from the PB stability analysis that the Sauter model over-predicts the bootstrap currents in the KSTAR pedestal. The expected over-predict can be of order of 20%. The XGC0 code or some other new models for the bootstrap current can be compared with Sauter.
- The XGC0 simulations with impurities can be performed to compare with the available experimental measurements from KSTAR including rotation profiles etc.
- Comparison of NIMROD and BOUT++ results can be continued. The objective of this study can be the development of extended MHD model that includes necessary and essential physics to describe ELM. The importance of various two-fluid and FLR effects are still needs to be confirmed for the KSTAR plasma parameters. It is not completely clear if separate evolution of density will change linear or nonlinear results. Finally, the nonlinear dynamics of ELMs and the propagation of ELM filaments to the plasma wall including the associated heat loads can be investigated. As a near term objective of this NIMROD/BOUT++ study can be a test of hypothesis that the two-fluid effects nearly cancel the resistivity effects, and ideal stability analysis can be used for KSTAR.