Demonstration of reduced neoclassical energy transport in Wendelstein 7-X

Abstract

Research on magnetic confinement of high-temperature plasmas has the ultimate goal of harnessing nuclear fusion for the production of electricity. Although the tokamak¹ is the leading toroidal magnetic-confinement concept, it is not without shortcomings and the fusion community has therefore also pursued alternative concepts such as the stellarator. Unlike axisymmetric tokamaks, stellarators possess a three-dimensional (3D) magnetic field geometry. The availability of this additional dimension opens up an extensive configuration space for computational optimization of both the field geometry itself and the current-carrying coils that produce it. Such an optimization was undertaken in designing Wendelstein 7-X (W7-X)², a large helical-axis advanced stellarator (HELIAS), which began operation in 2015 at Greifswald, Germany. A major drawback of 3D magnetic field geometry, however, is that it introduces a strong temperature dependence into the stellarator's non-turbulent 'neoclassical' energy transport. Indeed, such energy losses will become prohibitive in high-temperature reactor plasmas unless a strong reduction of the geometrical factor associated with this transport can be achieved; such a reduction was therefore a principal goal of the design of W7-X. In spite of the modest heating power currently available, W7-X has already been able to achieve high-temperature plasma conditions during its 2017 and 2018 experimental campaigns, producing record values of the fusion triple product for such stellarator plasmas^3,4. The triple product of plasma density, ion temperature and energy confinement time is used in fusion research as a figure of merit, as it must attain a certain threshold value before net-energy-producing operation of a reactor becomes possible^1,5. Here we demonstrate that such record values provide evidence for reduced neoclassical energy transport in W7-X, as the plasma profiles that produced these results could not have been obtained in stellarators lacking a comparably high level of neoclassical optimization.

Fig. 1. Radial profiles of the effective helical ripple.

Radial profiles of ϵ_eff are shown for the W7-X standard (black continuous curve) and high-mirror (black broken curve) configurations as well as for the LHD R₀ = 3.6 m (red continuous curve) and R₀ = 3.75 m (red broken curve) configurations. In the last of these cases, the ‘missing’ portion of the curve that extends above the plot area increases roughly quadratically with normalized minor radius, ρ = r/a, to reach a value of 0.225 at ρ = 0.93.

Fig. 2. Density and temperature profiles for W7-X discharge 20180918.045 at t = 3.35 s.

Thomson scattering measurements of n^e and T^e are shown by red data points, ECE results for T^e are plotted in black and CXRS values of Tⁱ are given by blue circles. Error bars depict one standard deviation in the evaluation of the measurements. Fits to the experimental data used in the neoclassical analysis are depicted by the continuous curves with red used for the electron profiles and blue for the ions. The last closed flux surface of the equilibrium is at r = 0.508 m.

Fig. 3. Comparison of the neoclassical energy fluxes associated with the high-temperature experimental conditions of discharge 20180918.045 at t = 3.35 s, for stellarator configurations with different degrees of neoclassical optimization.

The plasma profiles used for this comparison are the fits of Fig. 2 and P_heat = 4.5 MW. b–e, Results are plotted for the configurations W7-X standard (b), W7-X high-mirror (c), LHD R₀ = 3.6 m (d), and LHD R₀ = 3.75 m (e). a, Radial profiles of the total neoclassical energy fluxes are provided for the four configurations (b–e) in a single plot to make direct comparison of the results straightforward. Physically impossible levels of the neoclassical energy fluxes are indicated by the appearance of regions with $V{}^{\prime }(Q_{\mathrm{n}\mathrm{e}\mathrm{o}}^{\mathrm{e}}+Q_{\mathrm{n}\mathrm{e}\mathrm{o}}^{\mathrm{i}})/P_{\mathrm{h}\mathrm{e}\mathrm{a}\mathrm{t}}>1$ (lying above the dotted horizontal line), which shows that the plasma profiles of Fig. 2 would not be attainable in the given configuration. More detailed results for each configuration are provided in the individual plots, where electron fluxes are shown in red, ion fluxes in blue and their sum appears as the black ball-and-chain curve. Also depicted are results for the sum of electron and ion fluxes obtained from a temperature-sensitivity study at constant pressure, that is, by replacing (n^e, T^α) with (gn^e, g⁻¹T^α) and varying g from 0.9 (upper extent of the shaded region) to 1.1 (lower extent).

Extended Data Fig. 1. Non-planar coil system of W7-X, viewed from above.

The complete set of superconducting coils also includes 20 planar coils, four in each field period, which are used to change the rotational transform and/or shift the plasma column; these are not shown as they remain current-free for the configurations considered here.

Extended Data Fig. 2. Time traces for W7-X discharge 20180918.045.

In the top frame, the launched ECRH power is shown, as well as the radiated power measured by bolometers (dotted curve). The second frame plots the line-integrated density measured by an interferometer. The third frame depicts ‘core’ electron (red) and ion (blue) temperatures from Thomson scattering and XICS measurements, respectively. The diamagnetic energy trace during this discharge is given in the bottom frame. A series of 28 pellets is injected into the plasma at a frequency of 30 Hz during the time phase indicated in grey. W_dia values exceeding 1.02 MJ are recorded during the phase indicated in yellow.

Extended Data Fig. 3. Profiles of the radial electric field as a function of the normalized plasma radius.

Experimental results from CXRS (blue) and XICS (red) measurements are compared to the theoretical expectations from the ambipolarity constraint (black) for the plasma profiles of Fig. 2. Error bars depict one standard deviation in the evaluation of the measurements. The XICS analysis is described in ref. ; documentation of the methodology used to evaluate the CXRS measurements is in preparation.