Prediction of the energetic particle redistribution by an improved critical gradient model and analysis of the transport threshold

Abstract

Based on the theory of critical gradient model (CGM) and following the simulation method proposed by Waltz et al. [Nucl. Fusion 55, 123012 (2015)], a combination of TGLFEP and EPtran code is employed to predict the energetic particle (EP) transport induced by Alfvén eigenmodes (AEs). To be consistent with the experiment, recent improvements to the simulation method include consideration of threshold evolution and orbit loss due to finite orbit width. The revised CGM is applied to simulate two DIII-D experimental discharges (#142111 and #153071). It well reproduces the experimental profiles with multiple unstable AEs and large-scale EP transport. Discharge #142111 had previously been simulated using a nonlinear MHD-kinetic code MEGA [Todo et al., Nucl. Fusion 55, 073020 (2015)] with a transport mechanism based on stochasticity induced by overlapping AE. By comparing the simulated EP profiles, we find that the AE transport threshold is approximated by both the MEGA nonlinear stability threshold and the proposed CGM threshold (error <5% for single n and <17% for multiple n simulation). Both of them are larger than the linear stability threshold of the most unstable AE mode by a quantity of the order of the flux needed to sustain EP transport by the background turbulence. We have also applied the improved CGM to simulate the α particle redistribution for a China Fusion Engineering Test Reactor steady state scenario. Because of the clear separation between the AE unstable region and the loss cone, only a moderate α particle loss of ∼9.6% is predicted.

Development of compact tokamak fusion reactor use cases to inform future transport studies

“…2022; Zou et al. 2022), one way to begin assessing its possible impact is to examine the stability of the predicted alpha density profile to the onset of such modes. Figures 9( c ) and 9( d ) show the alpha density gradient profiles for UCR-P and UCR-SS, respectively.…”

“…However, as shown in figure 9(b), the effective temperature of the hot alphas is so much larger than the background thermal temperatures that they provide approximately 20 % of the on-axis pressure, and thus contribute to both the overall magnetic equilibrium and stabilization of turbulence via increased Shafranov shift. While full and self-consistent predictions of AE-driven alpha transport remain an area of significant current research (Bass & Waltz 2017;Liu et al 2022;Zou et al 2022), one way to begin assessing its possible impact is to examine the stability of the predicted alpha density profile to the onset of such modes. Figures 9(c) and 9(d) show the alpha density gradient profiles for UCR-P and UCR-SS, respectively.…”

Energetic particle marginal stability profile for HL-2M integrated simulation based on neural network module

“…Compared to the H-mode scenario, the modification of the safety factor profile is larger and extends over a broader range because the fraction of beam current is higher. An interesting observation is that if one could design an H-mode plasma with off-axis unstable AE activity such as the DIII-D discharges discussed in [17], we could in principle create a flat or weakly reversed magnetic shear core. This presents a self-organized phenomenon that could replace the use of off-axis ECCD to produce a high confinement hybrid mode plasma [35].…”

“…In our previous work [17], the TGLFEP code was used to calculate the critical gradient and the ORBIT code was used to calculate EP loss cones. The critical gradient and loss cones are input into the EPtran code to calculate EP redistribution.…”

“…Zou et al [17] indicates that the coefficients k 1 and k 2 determine the local critical gradient evolution through the function a/L th nEP = k 1 /n EP + k 2 , where k 1 represents Landau damping of the bulk plasma, k 2 is the Landau damping of the EP itself as well as the temperature gradient drive of EP, L th nEP is critical characteristic length of the EP density, a is minor radius, and n EP is EP density. In our previous work, TGLFEP was used to estimate AE stability and calculate the two coefficients.…”