Role of the radial electric field in the confinement of energetic ions in the Wendelstein 7-X stellarator

TL;DR

This study demonstrates, using drift-kinetic simulations with ASCOT5 in the Wendelstein 7-X high-mirror configuration, that the radial electric field $E_r$ can have a confinement effect on fast ions that is quantitatively equivalent to increasing the plasma beta $\langle \beta \rangle$. The authors develop a theoretical framework for the bounce-averaged tangential drift $\overline{\mathbf{v}_d \cdot \boldsymbol{\nabla}\alpha}$, showing it depends linearly on $\langle \beta \rangle$ and $E_r$ through distinct integrals, and validate this with both an idealized (academic) scan and a realistic (experimental) scan. An analytic model for the contributing integrals $I_0$ and $I_{\langle \beta \rangle}$ corroborates the simulation results, illustrating that maximal losses occur when $\overline{\mathbf{v}_d \cdot \boldsymbol{\nabla}\alpha} \approx 0$ and losses decrease as either $\langle \beta \rangle$ or $|E_r|$ increases away from that region. The experimentally-based scan, using ambipolar $E_r$ profiles from a real discharge, confirms the qualitative trend on inner flux-surface regions where fast ions are more likely to be born near the axis, suggesting a viable path to validate W7-X’s optimization strategy through controlled $E_r$ variations. Overall, the work informs confinement optimization in quasi-isodynamic configurations and guides experimental validation strategies for reactor-relevant fast-ion behavior.

Abstract

Good fast-ion confinement is an essential requirement for a fusion reactor. The magnetic configuration of the Wendelstein 7-X (W7-X) stellarator is partially optimized in this regard in a reactor-relevant scenario: it is expected to show improved fast-ion confinement when $β$ is high and the effect of the radial electric field is negligible. The experimental validation of this optimization is difficult since, with the available power, achieving high $β$ under appropriate conditions for the validation is challenging and the effect of the radial electric field is inevitable. In this work, the confinement of fast ions in W7-X has been studied numerically for a variety of scenarios via the ASCOT5 code. The effect of the radial electric field on fast-ion losses is confirmed to be equivalent to the one produced by $β$, and this is characterized by means of scans on both parameters. Through a preliminary study with experimentally-based profiles, a viable scenario is identified that takes advantage of this effect for the experimental validation of the optimization strategy of W7-X.

Figures (9)

• Figure 1: Diagram of the workflow followed in the simulations scans from this work, both for the academic scan (top) and the experimentally-based scan (bottom).
• Figure 2: Density (left), temperature (center) and $\beta$ (right) profiles for the case $\left \langle \beta \right \rangle = 1 \%$.
• Figure 3: $E_s$ (left) and $E_r$ (right) profiles for several cases in the academic scan.
• Figure 4: Energy prompt loss fraction as a function of $\left \langle \beta \right \rangle$ and $E_r$ for $\rho_0 = 0.25$ (left), $\rho_0 = 0.50$ (center) and $\rho_0 = 0.71$ (right). The region of $\overline{\mathbf{v}_d \cdot \boldsymbol{\nabla} \alpha} \approx 0$, computed with the theoretical model explained above, is represented with lines for moderately-trapped (solid line), barely-trapped (dashed line) and deeply-trapped (dash-dotted line) particles.
• Figure 5: Energy prompt loss fraction as a function of $\left \langle \beta \right \rangle$ and $E_r$ for $\rho_0 = 0.50$ with several regions highlighted (top left), energy prompt loss fraction as a function of $\left \langle \beta \right \rangle$ in the absence of electric field (top right), energy prompt loss fraction as a function of $E_r$ for $\left \langle \beta \right \rangle = 0.5 \%$ for negative values of $E_r$ (bottom left) and for positive values of $E_r$ (bottom right). Values of $\left \langle \beta \right \rangle$ and $E_r$ for high-$\beta$ discharges are shown with a magenta ellipse in the top left plot.