Turbulence Suppression by Energetic Particle Effects in Modern Optimized Stellarators

Turbulent transport is known to limit the plasma confinement of present-day optimized stellarators. To address this issue, a novel method to strongly suppress turbulence in such devices is proposed, namely the resonant wave-particle interaction of suprathermal particles—e.g., from ion-cyclotron-resonance-frequency heating—with turbulence-driving microinstabilities like ion-temperature-gradient modes. The effectiveness of this mechanism is demonstrated via large-scale gyrokinetic simulations, revealing an overall turbulence reduction by up to 65% in the case under consideration. Comparisons with a tokamak configuration highlight the critical role played by the magnetic geometry and the first steps into the optimization of fast particle effects in stellarator devices are discussed. These results hold the promise of new and still unexplored stellarator scenarios with reduced turbulent transport, essential for achieving burning plasmas in future devices.

Figure 1

Nonlinear main ion heat fluxes in GyroBohm $(Q_{\mathrm{gB}})$ units for different energetic particle temperatures $T_f/T_e$. The horizontal dotted lines denote the fluxes obtained without fast ions (w/o denotes without).

Figure 2

Nonlinear saturated (a) main and energetic ion heat flux spectra and (b) velocity space structure of $Q_f/Q_{\mathrm{gB}}$ averaged over $k_x$, $k_y$, and $z$ at $T_f/T_e=15$ (w/o denotes without). The black contour lines in (b) indicate the phase-space resonance positions ${\omega }_k={\omega }_{d,f}$ for $z=0$.

Figure 3

Field-line dependence of the (a) nonlinear main ion heat fluxes for different energetic particle temperatures and field lines and (b) ${\mathcal{K}}_y$ versus $z$ for both tokamak and stellarators.

Figure 4

Comparison of the ($z–\mu$) structure of the binormal curvature term ${\mathcal{K}}_y$ and the $v_{\parallel }$ averaged $Q_f/Q_{\mathrm{gB}}$ obtained from the bean-shaped and teardrop field lines at $T_f/T_e=10$. The area within the vertical gray boxes denotes the field-aligned values where ${\mathcal{K}}_y<0$.

Figure 5

Growth rates normalized to $c_s/a$ for different values of the amplitude $\mathcal{A}$ and inverse width $\mathcal{W}$ used in the ${\mathcal{K}}_y$ parametrization, obtained for the cases (a) without and (b) with energetic particles at $T_f/T_e=5$ for the bean-shaped flux tube. The red star denotes the optimized ${\mathcal{K}}_y$ configuration selected for the nonlinear analysis $(\mathcal{A},\mathcal{W})=(0.27,5.5)$.

Figure 6

Comparison of the (a) field-aligned structure of ${\mathcal{K}}_y$ and (b) time trace on the bulk ion heat flux for the nominal (blue line) and optimized (red line) W7-X geometry for the bean-shaped field line at $T_f/T_e=5$.