7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Visualization of Fast Ion Phase-space Flow in Plasmas Well-below, Near andWell-above Alfven eigenmode Stability Threshold in Tokamak
X.D. Du1, W.W. Heidbrink2, M.A. Van Zeeland1, J. Gonzalez-Martin1,
M.E. Austin3, Z. Yan4, G.R. Mckee4
1

General Atomics, P.O. Box 85608, San Diego, California 92186-5608, USA
2
University of California, Irvine, California 92697, USA
3
University of Texas-Austin, Austin, Texas 78712, USA
4
Univeristy of Wisconsin-Madson, Madison, Wisconsin 53706-1687, USAe-mail (speaker): duxiaodi@fusion.gat.com

Transport of fast ions along certain local phase space paths,
referred to as fast ion phase-space flow, has beensystematically measured by an imaging neutral particle
analyzer (INPA) [1, 2] in three plasma regimes, which are
well-below, near, and well-above the Alfvén eigenmodestability threshold [3, 4].
(1) In plasmas well-below the AE stability threshold,fast ions are well-confined on passing particle orbits
without noticeable transport over the phase space. Theobserved INPA images agree well with the synthetic INPA
images, using the fast ion distribution predicted byneoclassical theory.
(2) In plasmas near the AE stability threshold, INPA
images in the presence of AE activity moderately deviate
from those without AE activity. The image difference canbe well interpreted by AE-driven, phase-space fast ionflow. As seen in Figs. 1 (a) and (b), paths of this flow overthe velocity space (or streamlines) is reconstructed by theintersection lines of curved E’ and μ surfaces, referred toas E’&μ line (where E’ = E-ω/n*Pζ; E, Pζ and μ are theenergy, canonical toroidal momentum and magnetic
moment of ions; ω and n are the angular frequency andtoroidal mode number of AEs, respectively). Resonant
fast ions move radially inward by gaining energy andmove radially outward by losing energy and the trajectory
well aligns with the E’&μ lines that pass through the mode
resonances near the injection energy of neutral beams.

(3) In plasmas well-above the AE stability threshold,fast ion phase-space dynamics show additional features.
Fast ions are transported out of the birth positions so
promptly along the streamlines that the slowing-down
process from the injection energy is not observable,
exhibiting strong critical gradient behavior at local phasespace. As a result, the increase of electron temperature isvery small, in spite of an increase of beam power by ~45%.
It should be emphasized that the directions of phase-spacetransport, induced by AEs with different frequencies,
structures and mode numbers, do not largely differ.
One of the interesting findings from this study is that,even though multiple small-amplitude AEs with a broad
range of frequencies and toroidal mode numbers aredestabilized in plasmas with very different safety factors
q and bulk plasma parameters, the direction of phase space
flow does not largely alter for fast ions on passing orbits.
This strongly indicates the possibility to develop a
computationally-efficient fast ion phase-space transportmodel, which flattens local fast ion density profiles atresonances along E’&μ lines. The radial widths offlattening are determined by AE amplitudes, which could
be obtained empirically from experiments.
This work was supported by the U.S. Department ofEnergy, Office of Science, Office of Fusion Energy Sciences under Award Numbers DE-SC0020337, DE-AC0500OR22725,
DE-FC02-04ER54698,
DE-AC0209CH11466, and DE-SC0015878.
References[1] Du X.D., Van Zeeland M.A., Heidbrink W.W. and Su
D. Nucl. Fusion 58 082006 (2018)[2] Van Zeeland M.A., Du X.D., Heidbrink W.W.,
Stagner L. and Su D. J. Instrum. 14 C09027 (2019)[3] Du X.D. et al Phys. Rev. Lett. 127 235002 (2021)[4] Du X.D. et al., Nucl. Fusion 63, 046020 (2023)

Figure 1. (a) Reconstructed constant μ = 18 keV T−1
surface and constant E′ surface. The intersection linesof two curved surfaces are the fast ion phase space flow
path, indicated by the black arrow. (b) The averaged
flow image from 0.37 s to 0.4 s, along with theprojection of the E′ and μ line from (a).