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Description
In the ITER hybrid scenario, which is characterized by a centrally flat safety factor profile slightly above unity ($q > 1$), a bifurcated 3-D MHD equilibrium with a tilted magnetic axis—known as a helical core (HC)[1-4]—can form due to the ideal saturation of kink[2]/quasi-interchange[5] modes. Prior HC formation studies in ITER using VMEC[6], a 3-D equilibrium solver, have shown that the radial displacement of the magnetic axis (here denoted by $\delta_{\rm HC}$) can be as large as 0.4 m[3-4]. Such a large core displacement may affect not only plasma performance but also plasma control and diagnostics. Fusion-born alphas are expected contribute significantly to the plasma pressure in ITER and are known to have both stabilizing[7] and destabilizing[8] effects on the kink/quasi-interchange modes that also underlie the HC formation. Here, we study the interplay between a HC and alphas in ITER-like equilibria using MEGA[9], a nonlinear PIC-MHD hybrid code.
For normalized alpha pressures in the range $\beta_\alpha \leq 1\%$ that is expected to be accessible in ITER, the linear growth rate $\gamma$ of the kink/quasi-interchange mode is reduced by trapped alphas[7]. Although a reduced $\gamma$ often implies a lower saturation level, we find that this is not necessarily the case for the HC: In our initial setup (far from marginal stability) $\delta_{\rm HC}$ monotonically increases with $\beta_\alpha$ even when $\gamma$ is reduced. This decorrelation between $\gamma$ and $\delta_{\rm HC}$ implies that trapped-particle stabilization in this setup is capable of reducing only the rate of energy conversion but not its total cumulative amount. To confirm this result, we benchmarked MEGA against VMEC, where we included the alpha contribution to the scalar fluid pressure. The displacements $\delta_{\rm HC}$ and eigenfunctions obtained with the two codes are found to agree quantitatively when $\beta_\alpha \leq 1\%$, which suggests that $\delta_{\rm HC}$ is determined here by changes in the plasma configuration (known as quasi-linear effect), independently of the trapped-particle stabilization effect. The agreement also shows confirms that non-ideal effects captured by MEGA (namely, topology changes due to resistivity or resonances) are sufficiently weak for the bulk MHD fluid and alpha distribution to follow the HC’s 3-D distortion without radial mixing on macroscopic scales.
In addition to the HC formation, it is important to assess the stability of the resulting HC configuration. In MEGA’s MHD model, the HC is sometimes seen to destabilize a broad spectrum of secondary resistive pressure-driven MHD modes with multiple helicities. Their overlap can cause a stochastization of both the magnetic field and alpha particle trajectories, which facilitates in radial mixing. For the range of toroidal mode numbers studied ($n \leq 8$), these modes can be suppressed by reducing the size of the low magnetic shear region. Without these secondary modes, the alphas remain well-confined in the HC.
The results reported in this study, particularly the enhancement of $\delta_{\rm HC}$ by alphas and the secondary resistive modes, need to be considered in the design of plasma scenarios, the interpretation of line-of-sight diagnostic data, and feedback control systems. At least far from marginal stability, inexpensive VMEC calculations suffice for predicting the HC equilibrium state within ITER-relevant $\beta_\alpha \leq 1\%$. Its applicability near marginal stability is currently under investigation. The stability and impact of HC-induced secondary modes is also necessary, preferably using electromagnetic turbulence codes due to potentially short wavelengths. In HC equilibria where these secondary modes are stable, the effect of alpha-driven Alfvén eigenmodes and energetic particle modes is currently under investigation.
[1] Cooper, W. A., et al. Physical Review Letters 105.3 (2010): 035003.
[2] Cooper, W.A., et al. Nuclear Fusion 51.7 (2011): 072002.
[3] Cooper, W. A., et al. Plasma Physics and Controlled Fusion 53.2 (2011): 024002.
[4] Wingen, A., et al. Nuclear Fusion 58.3 (2018): 036004.
[5] Waelbroeck, F. L. Physics of Fluids B: Plasma Physics 1.3 (1989): 499
[6] Hirshman, S. P., and Whitson, J. C. Physics of Fluids 26.12 (1983): 3553-3568.
[7] Porcelli, F. Plasma Physics and Controlled Fusion 33.13 (1991): 1601.
[8] McGuire, K., et al. Physical Review Letters 50.12 (1983): 891.
[9] Todo, Y., and Sato, T. Physics of Plasmas 5.5 (1998): 1321-1327.
| Presentation type | Oral |
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