Helical Core Formation and MHD Stability in ITER-Scale Plasmas with Fusion-born Alpha Particles

TL;DR

This work addresses how fusion-born alpha particles influence the formation and stability of a Helical Core (HC) in ITER-scale hybrid plasmas with $q ≳ 1$ by using nonlinear MHD-PIC simulations with MEGA and benchmarking against VMEC. It shows that HC can form with ITER-relevant alpha pressures; for $β_α(0) ≤ 1\%$, alpha pressure effectively adds to the MHD pressure without major profile flattening, while at higher $β_α$ the HC displacement $δ_{HC}$ grows but can saturate due to profile changes and non-ideal effects. A resistive pressure-driven secondary mode can emerge after HC formation, potentially causing magnetic chaos and degraded alpha confinement. VMEC–MEGA benchmarking indicates good agreement for low $β_α$, validating the approach, though non-ideal and kinetic alpha effects become important at higher $β_α$. Overall, alpha particles can strengthen the HC and maintain confinement in the ITER-scale regime provided secondary-instability risks are managed, offering guidance for HC-based confinement schemes and alpha-particle control.

Abstract

The effect of fusion-born alpha particles on the helical core (HC), a long-lived ideal saturation state of the $m/n=1/1$ kink/quasi-interchange mode, is studied in the ITER-scale hybrid scenario where a core plasma has a low magnetic shear $q\gtrsim1$. The HC state is determined by 3-D MHD force balance and all factors that contribute to it, such as plasma shaping, the safety factor profile, and the pressure profiles of all particle species. An incomplete but useful measure of the HC is the displacement of the magnetic axis, $δ_\mathrm{HC}$. Using MHD-PIC simulations, we find that $δ_\mathrm{HC}$ is enhanced by increasing alpha particle pressure $β_\mathrmα$. Within the ITER operating alpha pressure $β_\mathrmα(0) \lesssim 1\%$, $β_\mathrmα$ can be approximately treated as part of the total MHD pressure. In this regime, there is no notable flattening of the pressure profile, indicating that the HC preserves the omnigenity of the plasma. If one increases $β_\mathrmα(0)$ beyond $1\%$, $δ_\mathrm{HC}$ continues to increase with $β_\mathrmα$ until it reaches an upper limit at $β_\mathrmα(0)=3\%$ for our reference case. At this limit, both the bulk and alpha pressure profiles are partially flattened, indicating a reduction in omnigenity. After HC formation, a resistive pressure-driven MHD mode can become unstable, which is localized along the compressed magnetic flux region of the HC. This secondary mode consists of a broad spectrum of short-wavelength Fourier components that grow at same rates and are thus part of a single coherent entity. Our present simulation model is insufficient to adequately represent such a secondary mode; however, preliminary results suggest that it can facilitate magnetic chaos, which affects plasma confinement.

Figures (26)

• Figure 1: Illustrations of HC tokamak equilibrium in the (a) straight cylinder coordinate, and (b) Cartesian coordinate. The red surface represents an arbitrary magnetic flux surface that resides within the HC, the blue surfaces represents a flux surface located outside of the HC, and the LCFS appears in gray.
• Figure 2: ITER-scale HC MHD equilibria calculated with VMEC while varying (a-d) $q_\mathrm{0}$ and (e-h) $\rho_\mathrm{qmin}$: (a,e) prescribed $q$ profiles; magnetic Poincaré plots at (b,f) $\phi=180^\circ$ and (c,g) $\phi=0^\circ$. The radial coordinate at $\phi = 180^\circ$ is plotted with an inverted horizontal axis.; (d,h) $m/n=1/1$ radial displacement of the magnetic axis $\delta_\mathrm{HC}$.
• Figure 3: Bulk plasma $\beta_\mathrm{b}$ and alpha particle $\beta_\mathrm{\alpha}$ beta profiles. The blue solid line represents $\beta_\mathrm{b}$, which will remain unchanged. The red solid lines with markers represent the $\beta_\mathrm{\alpha}$ profiles that are used in our parameter scans.
• Figure 4: Helical core formation in the equilibria with (a-e) $q_\mathrm{0}/\rho_\mathrm{qmin}=1.06/0.575$, (f-j) $1.1/0.575$, and (k-o) $1.2/0.575$. The MEGA simulation was performed with $(N_R,N_Z)$=$(200,200)$, $\hat{\eta}=10^{-6}$, and $\beta_\mathrm{\alpha}=0\%$. Panels (a,f,k) show the cosine components of the $n=1$ radial MHD velocity harmonics. Panels (b,g,l) show the time evolution of $1\leq n\leq8$ mode energies $E_n$. Panels (c,h,m) show the time evolution of the radial displacement of the magnetic axis $\delta_\mathrm{HC}$. Panels (d,i,n) and (e,j,o) show the magnetic Poincaré plots before and after the excitation of secondary modes, respectively.
• Figure 5: (a, c) Poloidal variation of $\beta_\mathrm{b}$ along the traced magnetic field lines, and (b, d) $q$ profile of the $q_\mathrm{0}/\rho_\mathrm{qmin} = 1.1/0.575$ equilibrium simulated with $(N_R,N_Z)$=$(200,200)$, $\hat{\eta}=10^{-6}$, and $\beta_\mathrm{\alpha} = 0\%$. The colors used in this figure represent individual magnetic field lines. Panels (a-b) and (c-d) show the simulation results before and after the excitation of secondary modes, respectively.