Visualization of Fast Ion Phase-Space Flow Driven by Alfvén Instabilities

Fast ion phase-space flow, driven by Alfvén eigenmodes (AEs), is measured by an imaging neutral particle analyzer in the DIII-D tokamak. The flow firstly appears near the minimum safety factor at the injection energy of neutral beams, and then moves radially inward and outward by gaining and losing energy, respectively. The flow trajectories in phase space align well with the intersection lines of the constant magnetic moment surfaces and constant $E-(\omega /n)P_{\zeta }$ surfaces, where $E$, $P_{\zeta }$ are the energy and canonical toroidal momentum of ions; $\omega$ and $n$ are angular frequencies and toroidal mode numbers of AEs. It is found that the flow is so destructive that the thermalization of fast ions is no longer observed in regions of strong interaction. The measured phase-space flow is consistent with nonlinear hybrid kinetic-magnetohydrodynamics simulation. Calculations of the relatively narrow phase-space islands reveal that fast ions must transition between different flow trajectories to experience large-scale phase-space transport.

Figure 1

(a) The neutral beam geometry, along with the INPA view. (b) The weight function of the INPA (circles) on the energy-radius plane, along with the measured pitch range. The orbit topology in the INPA-interrogated phase space is overlaid.

Figure 2

Frequency spectra of the density fluctuation for the low-power shot (a) and high-power shot (b), along with the waveforms of the neutral beams. (c) The time evolution of line-integrated $n_e$ and $T_e$. The measured INPA signal in the low-power shot (solid line) and high-power shot (dashed line) and the signal deficit to the expectation of the neoclassical theory (color map) for the velocity space ($E\sim 81\mathrm{keV}$, $R\sim 2.0\mathrm{m}$) (d) and ($E\sim 70\mathrm{keV}$, $R\sim 2.2\mathrm{m}$) (e).

Figure 3

INPA images of the modulated beam source during the weak AE activity (from 1.006 s to 1.019 s). (a1)–(a3) Low-power shot 179416. (b1)–(b3) High-power shot 179415. (c1)–(c3) Difference image. $T_e$ fluctuation in low-power shot (a4) and in high-power shot (b4) at $\sim 1.013\mathrm{s}$.

Figure 4

INPA images of the modulated beam source during strong AE activity (from 0.375 s to 0.388 s). (a1)–(a3) Low-power shot 179416. (b1)–(b3) High-power shot 179415. (c1)-(c3) Image difference. $T_e$ fluctuation in low-power shot (a4) and high-power shot (b4) at $\sim 0.381\mathrm{s}$.

Figure 5

(a) The measured flow images in (a), along with the streamlines; (b) the simulated flow image using MEGA-estimated fast ion distributions at INPA measured pitch of $\sim 0.78$; time evolution of the fast ion distributions in (c)–(f) by MEGA simulation.

Figure 6

(a) The averaged INPA signal along the streamlines $b1–b3$ in Fig. 5 in the LP shot (black) and in the HP shot (red), along with the $q$ profile. The estimated phase-space islands along these streamlines $b1–b3$ in (b1)–(b3), respectively.