Development and Validation of a Critical Gradient Energetic Particle Driven Alfv\'en Eigenmode Transport Model for DIII-D Tilted Neutral Beam Experiments*

Recent experiments on DIII-D with tilted neutral beam injection (NBI), which significantly vary the beam energetic particle (EP) source profiles, have provided strong evidence that unstable Alfv\'en eigenmodes (AE) drive stiff EP transport at a critical EP density gradient [1]. We hope to identify the critical gradient with the condition that the maximum local AE growth rate falls to the local ion temperature gradient (ITG)/trapped electron mode (TEM) rate at the same low toroidal mode number. This condition was supported by early nonlinear local GYRO simulations [2] and more is more optimistic than stiff EP transport at the AE marginal stability gradient used in a recent ITER projection of AE driven alpha confinement losses [3]. The AE and ITG/TEM growth rates are from GYRO with comparison of Maxwellian and slowing down beam-like EP distributions.\par \vskip6pt \noindent [1] W.W.\ Heidbrink, et al., Nucl.\ Fusion {\bf 53}, 093006 (2013).\par \noindent [2] E.M.\ Bass and R.E.\ Waltz, Phys.\ Plasmas {\bf 17}, 112319 (2010).\par \noindent [3] E.M.\ Bass, Bull.\ Am.\ Phys.\ Soc.\ {\bf 58}, 168 (2013).