Hybrid simulations for energetic particles interacting with a magnetohydrodynamic (MHD) fluid were conducted using the MEGA code [A, B] to investigate the spatial and the velocity distributions of lost fast ions due to the Alfvén eigenmode (AE) bursts in the Large Helical Device (LHD) [C, D]. It is found that the spatial distribution of lost fast ions in the divertor region during the AE burst is helically symmetric and peaks along the divertor location. Affected by the direction of grad-B and curvature drifts, the distribution of the co-going (counter-going) lost fast ions has two peaks in the outboard (inboard) side depending on fast-ion energy and pitch angle. The numerical fast-ion loss detector “numerical FILD” was constructed in the MEGA code. The velocity distribution of lost fast ions detected by the numerical FILD during AE burst is in good agreement with the experimental FILD measurements. This demonstrates that the MEGA is a useful tool for the prediction and the understanding of the fast-ion transport and losses brought about by AEs.
The LHD is one of the largest helical devices with non-axisymmetric 3-dimensional magnetic configuration. In the LHD, the fast-ion confinement has been investigated by using three tangentially injected neutral beams (NBs) with energy 180 keV and/or two perpendicularly injected NBs with energy 40-80 keV. The recurrent AE bursts were observed during the tangentially injected NB [C, D]. The fast-ion driven instabilities enhance the fast-ion transport and losses. It is important to identify the instabilities and clarify the properties of the fast-ion transport due to the instabilities. A hybrid simulation code for nonlinear MHD and energetic-particle dynamics, MEGA, has been developed to simulate recurrent bursts of fast-ion driven instabilities including the energetic-particle source, collisions and losses [A]. Since the equilibrium magnetic field in the real coordinates are used in MEGA, fast ion can be traced even in the peripheral region including the divertor region. The multi-phase simulation, which is a combination of classical simulation and hybrid simulation for energetic particles interacting with an MHD fluid, was applied to the LHD experiments #47645 [C] and #90090 [D] in order to investigate the AE bursts with beam injection, collisions, losses, and transport due to the AEs [A, B]. In the classical simulation, fast-ion orbits are followed in the equilibrium magnetic field with NBs and collisions while the MHD perturbations are turned off. The fast-ion loss rate brought about by the AE burst is proportional to the square of AE amplitude, which is consistent with the quadratic dependence of fast-ion loss observed in the LHD experiment [B].
In this work, the spatial and the velocity distributions of lost fast ions due to the AE bursts are investigated and compared with the experimental measurements. The multi-phase simulation was conducted for the LHD experiment #90090 where the 2-dimensional velocity distribution of lost fast ions is measured by scintillator-based FILD [D]. The AE bursts occur recurrently and then the fast ions are significantly lost during the AE bursts. Figure 1 shows the spatial distribution of lost fast ions in the divertor region during the AE burst. We see in Fig. 1 that the spatial distribution of lost fast ions in the divertor region during the AE burst is helically symmetric and peaks along the divertor trace. The lost fast ions reach the divertor region following the divertor magnetic field. There is a helical symmetry for the lost fast ion location even during the AE burst while some peaks are present in the number of lost fast ions in the poloidal direction. The time evolution of the spatial distributions of lost fast ions along the divertor trace is shown in Fig. 2. Affected by the direction of grad-B and curvature drifts, the distribution of the co-going (counter-going) lost fast ions has two peaks in the outboard (inboard) side depending on fast-ion energy and pitch angle. For the comparison with the lost fast-ion velocity distribution measured with the FILD, we have constructed the “numerical FILD” in the MEGA code. In the MEGA simulations, the guiding-center orbit is followed for fast ions. In the numerical FILD, when a fast ion approaches the FILD, we split the guiding-center particle into 64 particles around the guiding center with corresponding Larmor radius and 64 particles with different gyration phase are followed with Newton-Lorentz equation. The aperture of the numerical FILD is a circle with radius 6 mm. Only the fast ions passing through the aperture are detected by the numerical FILD. Figure 3 compares the pitch angle and energy distribution of the lost fast ions in the MEGA simulation and the FILD measurements in the experiment. Before the AE burst, fast ions with energy close to the injection energy are mainly detected by the numerical FILD. During the AE burst, we see in Fig. 3(b) that fast ions of 100-150 keV and 35-50 degree are detected by the numerical FILD. The velocity space region of the lost fast ions due to the AE burst is in good agreement with that observed in the experiment shown in Fig. 3(c) [D], although the two peaks observed in the experiment are not well resolved in the numerical FILD. The numerical FILD measurement is consistent with the experiment for the lost fast ions with pith angle = 30-40 degree which increased during the AE burst.
[A] Y. Todo, et al., Phys. Plasmas 24, 081203 (2017).
[B] R. Seki et al., Nucl. Fusion 59, 096018(2019).
[C] M. Osakabe et al., Nucl. Fusion 46 S911 (2006).
[D] K. Ogawa et al., Nucl. Fusion 52, 094013 (2012).
|Country or International Organization||Japan|
|Affiliation||National Institute for Fusion Science|