After a long device enhancement phase, scientific operation resumed in 2022. The main new device components are the water cooling of all plasma facing components and the new water-cooled high heat flux divertor units. Water cooling allowed for the first long-pulse operation campaign. A maximum discharge length of 8 min was achieved with a total heating energy of 1.3 GJ. Safe divertor operation was demonstrated in attached and detached mode. Stable detachment is readily achieved in some magnetic configurations but requires impurity seeding in configurations with small magnetic pitch angle within the edge islands. Progress was made in the characterization of transport mechanisms across edge magnetic islands: Measurement of the potential distribution and flow pattern reveals that the islands are associated with a strong poloidal drift, which leads to rapid convection of energy and particles from the last closed flux surface into the scrape-off layer. Using the upgraded plasma heating systems, advanced heating scenarios were developed, which provide improved energy confinement comparable to the scenario, in which the record triple product for stellarators was achieved in the previous operation campaign. However, a magnetic configuration-dependent critical heating power limit of the electron cyclotron resonance heating was observed. Exceeding the respective power limit leads to a degradation of the confinement.

We present recent highlights from the most recent operation phases of Wendelstein 7-X, the most advanced stellarator in the world. Stable detachment with good particle exhaust, low impurity content, and energy confinement times exceeding 100 ms, have been maintained for tens of seconds. Pellet fueling allows for plasma phases with reduced ion-temperature-gradient turbulence, and during such phases, the overall confinement is so good (energy confinement times often exceeding 200 ms) that the attained density and temperature profiles would not have been possible in less optimized devices, since they would have had neoclassical transport losses exceeding the heating applied in W7-X. This provides proof that the reduction of neoclassical transport through magnetic field optimization is successful. W7-X plasmas generally show good impurity screening and high plasma purity, but there is evidence of longer impurity confinement times during turbulence-suppressed phases.

The rush to build electricity producing tokamak reactors implies that empirically led physics basis must be increasingly replaced by theory and modelling. Particularly urgent is the design of robust scenarios that are stable to MHD instabilities, despite key differences in reactor plasma equilibria relative to present day machines. One approach is to deploy high fidelity codes, but very often this is at the cost of losing trace of individual physics effects, all of which should be understood for plasma scenario design. In addition large codes often neglect fundamental exotic details in favour of isolating the fastest growing instabilities. By considering toroidal coupling between modes, resistive dissipation and compressibility, we present a light approach to modelling long and moderate wavelength MHD instabilities. This allows a precise investigation into the implications of each of these effects on performance limiting instabilities, especially on resistive infernal modes. Reference [1] presented a unified and global analytic description of internal toroidal instabilities, and hinted at the development of a new reduced resistive eigenvalue solver. Here we present applications of this work to different kinds of advanced/hybrid scenarios. These scenarios typically have extended regions of low magnetic shear, and are therefore particularly sensitive to the details of toroidicity and other ordinarily weak driving effects. We extend [2] by initially investigating cases with low magnetic shear in regions of unfavourable average curvature. Well known stability criterion of interchange modes are modified strongly by the weak ballooning effects of global infernal drive. Stability properties of internal transport barriers in reversed shear configurations are also studied, revealing effects of infernal drive and damping by average good curvature in the face of resistive dissipation on the global eigenfunctions in regions of low and high shear. Taking a step further, we retrieve shorter radial wavelength modes (analytically described by [2]) ordinarily not obtainable with high fidelity codes. For the first time we show that a spectrum of unstable modes exists in the region of vanishing average curvature, which occurs at q = 1 in a toroidal plasma with circular cross sections. A novel analytical description of this resistive internal kink spectrum, with arbitrary m for non resonant q = 1 unstable spectra is also provided. Such cascades of modes could be connected with sawtooth crash events or the avoidance of the crash via long living modes with q ≈ 1 sustained. By extending some of the concept in [3] to include unstable short wavelength modes, we hope to gain fundamental understanding into key tokamak macroscopic reconnection events. References [1] Graves J P, Coste-Sarguet M and Wahlberg C (2021) Plasma Phys. Control. Fusion 64(1) 014001 [2] Wahlberg C and Graves J P (2007) Physics of Plasmas 14 110703 [3] Jardin S C, Krebs I and Ferraro N (2020) Physics of Plasmas 27(3) 32509 Kinetic ballooning modes as a constraint on plasma triangularity in commercial spherical tokamaks R. Davies1, D. Dickinson1, H. Wilson1 York Plasma Institute, University of York, Heslington, York, YO10 5DD, United Kingdom E-mail: bob.davies@york.ac.uk Abstract. To be economically competitive, spherical tokamak (ST) power plants require high β (plasma pressure/magnetic pressure) and sufficiently low turbulent transport to enable steadystate operation. A novel approach to tokamak optimisation is negative triangularity, with experimental results indicating this reduces transport in L-mode, and avoids the deleterious impact of Edge-Localised Modes (ELMs) experienced in standard H-mode operation. However, negative triangularity is known to close access to the “second stability” region for ballooning modes. Since second stability access is usually important in ST reactor design, this raises the question of whether negative triangularity is feasible. We address this by presenting a linear gyrokinetic study of three hypothetical (but reasonable) high β ST equilibria with similar size and fusion power in the range 500-800MW. We find that the negative triangularity equilibrium becomes strongly unstable to long-wavelength kinetic ballooning modes (KBMs) across the plasma, likely driving unacceptably high transport. By contrast, positive triangularity with reactor-relevant β can completely avoid the ideal MHD ballooning unstable region, provided the on-axis safety factor is sufficiently high. The dominant instability still appears to be KBM, but the growth rate is low; this could feasibly be stabilised by flow shear or may impose a soft β limit. To be economically competitive, spherical tokamak (ST) power plants require high β (plasma pressure/magnetic pressure) and sufficiently low turbulent transport to enable steadystate operation. A novel approach to tokamak optimisation is negative triangularity, with experimental results indicating this reduces transport in L-mode, and avoids the deleterious impact of Edge-Localised Modes (ELMs) experienced in standard H-mode operation. However, negative triangularity is known to close access to the “second stability” region for ballooning modes. Since second stability access is usually important in ST reactor design, this raises the question of whether negative triangularity is feasible. We address this by presenting a linear gyrokinetic study of three hypothetical (but reasonable) high β ST equilibria with similar size and fusion power in the range 500-800MW. We find that the negative triangularity equilibrium becomes strongly unstable to long-wavelength kinetic ballooning modes (KBMs) across the plasma, likely driving unacceptably high transport. By contrast, positive triangularity with reactor-relevant β can completely avoid the ideal MHD ballooning unstable region, provided the on-axis safety factor is sufficiently high. The dominant instability still appears to be KBM, but the growth rate is low; this could feasibly be stabilised by flow shear or may impose a soft β limit. Analytic model of m = 1 magnetic flux pumping H.J. de Blank, I. Krebs DIFFER – Dutch Institute for Fundamental Energy Research, De Zaale 20, 5612 AJ Eindhoven, Eindhoven, The Netherlands E-mail: h.j.deblank@differ.nl Abstract. Nonlinear MHD simulations of the m = n = 1 mode in the core of tokamak plasmas have demonstrated [1, 2] the possibility of a saturated mode with steady m = 1 convective motion balancing the resistive relaxation of the q-profile in a process dubbed “magnetic flux pumping”, giving rise to a central region with very low magnetic shear (q ≈ 1) despite the presence of a loop voltage and a peaked conductivity profile. It was noted [1, 2, 3] that such lowshear zone is unstable to the pressure-driven m = 1 quasi-interchange mode, and the numerically obtained flow pattern was found to be in agreement with the linear eigenfunction of the quasiinterchange [4]. The present paper follows up on the idea that the steady state flux pumping may be viewed as a resistive saturated state of the quasi-interchange mode. An analytic reduced MHD description is given of the saturated quasi-interchange mode, the saturation being the result of nonlinear deformation of the magnetic surfaces in the presence of a pressure gradient. In the presence of resistivity this state has a slow residual m = 1 flow. The flux pumping consists of two nonlinear effects by which the m = 1 perturbation affects the (m = 0) radial profiles: (1) the flow provides the radial transport of flux within the core q ≈ 1 region by the dynamo effect descibed in [1, 2, 3], and (2) the m = 1 deformed flux surfaces correspond to m = 1 perturbations of the current density, the resistive decay of which provides the necessary second step of removing flux from the core region. (Note that the dynamo term of effect (1) alone integrates to zero over the plasma core). Stability of this m = 1 state is analyzed, showing that it can be stable in cases where the axisymmetric equilibium with central q well below unity is stable to the quasi-interchange mode: a true bifurcated equilibrium. The m = 1 flow also causes convective heat transport. Inclusion of this transport in the model results in a smaller m = 1 amplitude due to reduced peaking of the conductivity profile and the pressure profile. Nonlinear MHD simulations of the m = n = 1 mode in the core of tokamak plasmas have demonstrated [1, 2] the possibility of a saturated mode with steady m = 1 convective motion balancing the resistive relaxation of the q-profile in a process dubbed “magnetic flux pumping”, giving rise to a central region with very low magnetic shear (q ≈ 1) despite the presence of a loop voltage and a peaked conductivity profile. It was noted [1, 2, 3] that such lowshear zone is unstable to the pressure-driven m = 1 quasi-interchange mode, and the numerically obtained flow pattern was found to be in agreement with the linear eigenfunction of the quasiinterchange [4]. The present paper follows up on the idea that the steady state flux pumping may be viewed as a resistive saturated state of the quasi-interchange mode. An analytic reduced MHD description is given of the saturated quasi-interchange mode, the saturation being the result of nonlinear deformation of the magnetic surfaces in the presence of a pressure gradient. In the presence of resistivity this state has a slow residual m = 1 flow. The flux pumping consists of two nonlinear effects by which the m = 1 perturbation affects the (m = 0) radial profiles: (1) the flow provides the radial transport of flux within the core q ≈ 1 region by the dynamo effect descibed in [1, 2, 3], and (2) the m = 1 deformed flux surfaces correspond to m = 1 perturbations of the current density, the resistive decay of which provides the necessary second step of removing flux from the core region. (Note that the dynamo term of effect (1) alone integrates to zero over the plasma core). Stabi

The optimized superconducting stellarator device Wendelstein 7-X (with major radius , minor radius , and plasma volume) restarted operation after the assembly of a graphite heat shield and 10 inertially cooled island divertor modules. This paper reports on the results from the first high-performance plasma operation. Glow discharge conditioning and ECRH conditioning discharges in helium turned out to be important for density and edge radiation control. Plasma densities of with central electron temperatures were routinely achieved with hydrogen gas fueling, frequently terminated by a radiative collapse. In a first stage, plasma densities up to were reached with hydrogen pellet injection and helium gas fueling. Here, the ions are indirectly heated, and at a central density of a temperature of with was transiently accomplished, which corresponds to with a peak diamagnetic energy of and volume-averaged normalized plasma pressure . The routine access to high plasma densities was opened with boronization of the first wall. After boronization, the oxygen impurity content was reduced by a factor of 10, the carbon impurity content by a factor of 5. The reduced (edge) plasma radiation level gives routinely access to higher densities without radiation collapse, e.g. well above line integrated density and central temperatures at moderate ECRH power. Both X2 and O2 mode ECRH schemes were successfully applied. Core turbulence was measured with a phase contrast imaging diagnostic and suppression of turbulence during pellet injection was observed.

An asymptotic expansion is performed to obtain quasi-axisymmetric magnetic configurations that are weakly non-axisymmetric. A large space of solutions is identified, which satisfy the condition of quasi-axisymmetry on a single magnetic flux surface, while (non-axisymmetric) globally quasi-axisymmetric solutions are shown to not exist, agreeing with the conclusions of previous theoretical work. The solutions found are shown to be geometrically constrained at low aspect ratio or high toroidal period number. Solutions satisfying the more general condition of omnigeneity (generalized quasi-axisymmetry) are also shown to exist, and it is found that quasi-axisymmetric deformations can be superposed with an omnigenous solution, while preserving the property of omnigeneity, effectively extending the space of "good" configurations. A numerical solution of the first order quasi-axisymmetry problem is demonstrated and compared with solutions found with a widely used MHD equilibrium solver, independently verifying that quasi-axisymmetry is satisfied at the appropriate order. It is thereby demonstrated that approximately quasi-axisymmetric solutions can be directly constructed, i.e. without using numerical search algorithms.

After completing the main construction phase of Wendelstein 7-X (W7-X) and successfully commissioning the device, first plasma operation started at the end of 2015. Integral commissioning of plasma start-up and operation using electron cyclotron resonance heating (ECRH) and an extensive set of plasma diagnostics have been completed, allowing initial physics studies during the first operational campaign. Both in helium and hydrogen, plasma breakdown was easily achieved. Gaining experience with plasma vessel conditioning, discharge lengths could be extended gradually. Eventually, discharges lasted up to 6 s, reaching an injected energy of 4 MJ, which is twice the limit originally agreed for the limiter configuration employed during the first operational campaign. At power levels of 4 MW central electron densities reached 3 x 10(19) m(-3), central electron temperatures reached values of 7 keV and ion temperatures reached just above 2 keV. Important physics studies during this first operational phase include a first assessment of power balance and energy confinement, ECRH power deposition experiments, 2nd harmonic O-mode ECRH using multi-pass absorption, and current drive experiments using electron cyclotron current drive. As in many plasma discharges the electron temperature exceeds the ion temperature significantly, these plasmas are governed by core electron root confinement showing a strong positive electric field in the plasma centre.