Role of Shafranov shift, zonal structures on the behavior of TAEs, AAEs and microinstabilities in the presence of energetic particles

TL;DR

The paper investigates how self-consistent Shafranov shift and self-generated zonal structures influence the stability and nonlinear transport of Alfvénic and drift-wave instabilities in burning plasmas with energetic particles. Using the ORB5 gyrokinetic code on CBC-based equilibria, it maps linear dispersions and continua across EP fractions and gradient cases, and then analyzes nonlinear saturation, zonal structures, and q-profile modification. Key findings include strong stabilization of KBMs and TAEs by the Shafranov shift and EPs, a weaker response for ITG, and the emergence of Axisymmetric Alfvén Eigenmodes that can enhance TAE transport. The results underscore the importance of self-consistent equilibria and zonal dynamics in predicting heat and particle fluxes in burning plasmas, with AAEs providing a potential link to EP transport.

Abstract

In future nuclear fusion reactors, even a small fraction of fusion-born energetic particles (EP) about 100 times hotter than the thermal bulk species, contributes substantially to the kinetic pressure and therefore affect the MHD equilibrium, mainly via the Shafranov shift. In this work, we perform first-principles numerical simulations using the gyrokinetic, electromagnetic, global code ORB5 to study the effect of a self-consistent finite $β$ equilibrium on the arising Alfvén Eigenmodes (destabilized by EPs), Ion Temperature Gradient (ITG), and Kinetic Ballooning Modes (KBM) microturbulence (destabilized by thermal species). Linearly, we explore the complex interplay between EP fraction, bulk gradients and a self-consistent Shafranov shift on the plasma stability. We choose single toroidal mode numbers to represent the system's instabilities and study the characteristic nonlinear evolutions of TAEs, KBMs and ITGs separately and including the axisymmetric field response to each mode separately. This study focuses on the impact of Shafranov shift equilibrium consistency, as well as the self-generated zonal ${E \times B}$ flows, the saturation levels and resulting heat and particle fluxes. In the ITG cases including the $n=0$ perturbations reduces turbulent fluxes, as expected, however, for the TAE cases including the $n=0$ perturbations is shown to enhance the fluxes. We show for the first time that Axisymmetric Alfvén Eigenmodes (AAEs) play a role in this mechanism.

Figures (26)

• Figure 1: On the left: initial temperature and density (flux-surface-averaged) logarithmic gradients, for ions, electrons, and EPs. The profiles of the bulk species (ions and electrons) change between the standard (ST) and peaked (PK) cases, while the EP profiles remain the same. The q profile is indicated by the black dashed line. The vertical gray dashed lines mark the mode rational surfaces $(nq = m + 1/2)$ of the $n = 2$ TAE. On the right: $\Delta^\prime$ and the $\beta$ profiles of the MHD equilibrium for the main 5 cases in this work: $\beta = 0$, not consistent ST and PK equilibria based on pressure arising solely from the bulk profiles, and consistent ST and PK equilibria which account for $1\%$ EP pressure as well.
• Figure 2: Linear growth rate $\gamma$ (top row) and real frequency $\omega$ (bottom row) vs. toroidal mode number $n$. On the left are ST cases, on the right cases with peaked (PK) and flat (FL) bulk gradients. Bottom plot left: frequency of the $n = 0$ Axisymmetric Alfvén eigenmodes (AAE). Color coding: Filled markers - Consistent (Cons.), Empty markers - Not Consistent (Not Cons.), and Gray - $\beta = 0$ MHD equilibria.
• Figure 3: Characteristic linear mode structure in $\phi$ ($1^{st}$ and $3^{rd}$ rows), and $A_{\parallel}$ ($2^{nd}$ and $4^{th}$ rows) of the $n = 2$ TAE (left column) and $n = 25$ ITG (right column) for cases with a self-consistent MHD equilibrium, and $n = 12$ KBM (middle column) in a case with a $\beta = 0$ MHD equilibrium. All cases are with peaked bulk gradients and include $1\%$ EPs. The dashed black curves are magnetic surfaces $s=[0;0.1;1]$. In the bottom two rows we see the radial structure of the poloidal harmonics. Here the black dashed line is the q profile referring to the y-axis on the right.
• Figure 4: On the left is the growth rate of an $n=2$ TAE as a function of the EP fraction. Color coding: Gray - $\beta=0$, Black - Not Consistent (Not Cons.), Colored - Consistent (Cons.), MHD equilibria. The colors match Figure \ref{['FIG:Linear_disperssion']}. The two plots on the right show the TAE's saturation level to growth rate ratio as a function of EP fraction.
• Figure 5: The Alfvén continuum with the slow-sound approximation for the $n = 0$$\&$$n = 2$ toroidal mode numbers, for standard and peaked profiles with consistent MHD equilibria. The labeled dashed lines indicate the frequency (in Alfvénic units), of either the $n = 2$ TAE or the $n = 0$ Axisymmetric Alfvén Eigenmode (AAE). Color coding: Dark gray - $n = 0$, Colored - $n = 2$ modes. The colors match Figure \ref{['FIG:Linear_disperssion']}.