# NERSC Initiative for Scientific Exploration (NISE) 2011 Awards

## Large Scale Numerical Study of Bootstrap Current in Edge Pedestal Plasma

### Choong-Seock Chang, Courant Institute of Mathematical Sciences - New York University

**Associated NERSC Project: Center for Plasma Edge Simulation: SciDAC FSP Prototype Center (m499)**

NISE Award: | 4,000,000 Hours |

Award Date: | March 2011 |

Accurate theoretical evaluation of the edge bootstrap current has recently become a central theme in the prediction for edge localized modes instability and the pedestal equilibrium. Edge localized modes must be controlled in ITER to meet its scientific goal. Accurate evaluation of the edge bootstrap current is also critical for the determination of the magnetic separatrix configuration and the location of the confined plasma edge in ITER, without which the experimental edge physics validation in the present tokamak devices and the divertor heat load prediction for ITER suffer a significant uncertainty.

Evaluation of the edge bootstrap current has been completely based upon simplified analytic formulas, which possess rather unknown accuracy due to various approximations required in the analytic formulation or due to inadequateness of the applied magnetic geometry and plasma profile for the trans-collisional pedestal plasma in diverted magnetic field. Self-consistent ExB drift motion is another issue. Even the most developed analytical formula by Sauter, et al [Physics of Plasmas , 2834 (1999)] uses drift orderings which are inadequate for the steep pedestal, adopt “homogeneous” electron collision operator which does not possess the electron-ion momentum conservation property in the collisional edge, magnetic geometry far away from the magnetic separatrix surface, and ignores the strongly sheared ExB flows in the edge pedestal. Bootstrap current is all about the difference in the parallel flow speed between electrons and ions and the nonlocal collisional dynamics between the neoclassical trapped-passing particles, which requires accurate particle guiding center orbit dynamics in the presence of momentum conserving collisions, especially in the plasma edge where the passing particle fraction becomes smaller, poloidal variation of the phase space Jacobian is large, and the collision frequency varies significantly across the pedestal. Besides the magnetic drift motions, the ExB drift motions need to be captured self-consistently. Recent experimental evidence on MAST [IAEA Fusion Energy Conference, October, 2010, Korea] showed a significant discrepancy (over 50%) between the experimentally inferred edge bootstrap current and the theoretically predicted values from the Sauter formula. A question naturally rises on how accurate the analytic formulas are in the pedestal of conventional and spherical tokamaks.

XGC0 is a kinetic particle code, which evaluates the 3D particle guiding center motions accurately according to the Lagrangian equation of motion in a realistic magnetic field geometry. XGC0 scales efficiently to extreme scale (> 1PF). The code calculates the electrostatic potential profile self-consistently in the plasma edge. Collision operators used in XGC0 code reproduces H-theorem and Maxwellian particle distribution function in the appropriate limit, and it conserves particle, momentum and energy. XGC0 has been verified to reproduce analytic neoclassical theories in the appropriate limits. XGC0 includes Monte Carlo neutral particles with ionization and charge exchange. In this research, XGC0 is being used to perform “numerical experiments” to measure the bootstrap current in steep pedestal profile in realistic diverted edge geometry of three major US tokamaks (DIII-D, C-Mod, and NSTX). It is found that the Sauter formula agrees quite well with the XGC0 simulation results in weakly collisional regime, in which the analytic bootstrap formalism is more faithfully developed, the “homogeneous” collision operator used in the development of equation is quite accurate, and the bounce-average calculations used to generate many of the curve-fitting data are more forgiving. However, Sauter formula does not agree well with the numerical results in the collisional pedestal plasma. In conventional tokamks (DIII-D and C-Mod) about 25% difference is common between the Sauter formula and the numerical results in collisional edge pedestal. In a spherical tokamak, such as NSTX, difference between the Sauter formula and the numerical results are found to be as large is 50% in collisional edge pedestal. A new bootstrap current formula will be developed using extensive XGC0 simulations on Franklin (and Hopper II) that can bring the agreement with the numerical results within simulation error bar.