Nonlinear growth of zonal flows by secondary instability in general magnetic geometry
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70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
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Overview of physics studies on ASDEX Upgrade
The ASDEX Upgrade (AUG) programme, jointly run with the EUROfusion MST1 task force, continues to significantly enhance the physics base of ITER and DEMO. Here, the full tungsten wall is a key asset for extrapolating to future devices. The high overall heating power, flexible heating mix and comprehensive diagnostic set allows studies ranging from mimicking the scrape-off-layer and divertor conditions of ITER and DEMO at high density to fully non-inductive operation ( q 95 = 5.5, β N ≤ 2.8) at low density. Higher installed electron cyclotron resonance heating power ≤ 6 MW, new diagnostics and improved analysis techniques have further enhanced the capabilities of AUG.
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First divertor physics studies in Wendelstein 7-X
The Wendelstein 7-X (W7-X) optimized stellarator fusion experiment, which went into operation in 2015, has been operating since 2017 with an un-cooled modular graphite divertor. This allowed first divertor physics studies to be performed at pulse energies up to 80 MJ, as opposed to 4 MJ in the first operation phase, where five inboard limiters were installed instead of a divertor. This, and a number of other upgrades to the device capabilities, allowed extension into regimes of higher plasma density, heating power, and performance overall, e.g. setting a new stellarator world record triple product. The paper focuses on the first physics studies of how the island divertor works. The plasma heat loads arrive to a very high degree on the divertor plates, with only minor heat loads seen on other components, in particular baffle structures built in to aid neutral compression. The strike line shapes and locations change significantly from one magnetic configuration to another, in very much the same way that codes had predicted they would. Strike-line widths are as large as 10 cm, and the wetted areas also large, up to about 1.5 m 2 , which bodes well for future operation phases. Peak local heat loads onto the divertor were in general benign and project below the 10 MW m –2 limit of the future water-cooled divertor when operated with 10 MW of heating power, with the exception of low-density attached operation in the high-iota configuration. We report the most notable result was the complete (in all 10 divertor units) heat-flux detachment obtained at high-density operation in hydrogen.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Effects of collisional ion orbit loss on neoclassical tokamak radial electric fields
We report that ion orbit loss is considered important for generating the radially inward electric field E r in a tokamak edge plasma. In particular, this effect is emphasized in diverted tokamaks with a magnetic X point. In neoclassical equilibria, Coulomb collisions can scatter ions onto loss orbits and generate a radially outward current, which in steady state is balanced by the radially inward current from viscosity. To quantitatively measure this loss-orbit current in an edge pedestal, an ion-orbit-flux diagnostic has been implemented in the axisymmetric version of the gyrokinetic particle-in-cell code XGC. As the first application of this diagnostic, a neoclassical DIII-D H-mode plasma is studied using gyrokinetic ions and adiabatic electrons. The validity of the diagnostic is demonstrated by studying the collisional relaxation of E r in the core. After this demonstration, the loss-orbit current is numerically measured in the edge pedestal in quasisteady state. In this plasma, it is found that the radial electric force on ions from E r approximately balances the ion radial pressure gradient in the edge pedestal, with the radial force from the plasma flow term being a minor component. The effect of orbit loss on E r is found to be only mild.
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WEST full tungsten operation with an ITER grade divertor
The mission of WEST (tungsten-W Environment in Steady-state Tokamak) is to explore long pulse operation in a full tungsten (W) environment for preparing next-step fusion devices (ITER and DEMO) with a focus on testing the ITER actively cooled W divertor in tokamak conditions. Following the successful completion of phase 1 (2016-2021), phase 2 started in December 2022 with the lower divertor made entirely of actively cooled ITER-grade tungsten mono-blocks. A boronization prior the first plasma attempt allowed for a smooth startup with the new divertor. Despite the reduced operating window due to tungsten, rapid progress has been made in long pulse operation, resulting in discharges with a pulse length of 100 s and an injected energy of around 300 MJ per discharge. Plasma startup studies were carried out with equatorial boron nitride limiters to compare them with tungsten limiters, while Ion Cyclotron Resonance Heating assisted startup was attempted. High fluence operation in attached regime, which was the main thrust of the first campaigns, already showed the progressive build up of deposits and appearance of dust, impacting the plasma operation as the plasma fluence increased. In total, the cumulated injected energy during the first campaigns reached 43 GJ and the cumulated plasma time exceeded 5 h. Demonstration of controlled X-Point Radiator regime is also reported, opening a promising route for investigating plasma exhaust and plasma-wall interaction issues in more detached regime. This paper summarises the lessons learned from the manufacturing and the first operation of the ITER-grade divertor, describing the progress achieved in optimising operation in a full W environment with a focus on long pulse operation and plasma wall interaction.
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Introduction and overview: Chapter 1 of the special issue: on the path to tokamak burning plasma operation
The International Tokamak Physics Activity (ITPA) has developed a comprehensive overview of the results of its coordinated R&D activities in fusion physics and diagnostics implemented during the past two decades with the aim of developing an improved physics basis for the operation of tokamak burning plasma experiments. Here, an introduction is presented to key concepts in the physics of burning plasmas in tokamaks, together with an overview of the scope of the principal areas of physics R&D pursued by the ITPA Topical Physics Groups in which the critical issues, major areas of progress and most significant recent results are highlighted. This paper introduces the following collection of articles, which encompass detailed presentations of the progress achieved by the Topical Groups in preparing the physics basis for the operation of tokamak burning plasma experiments expected to come into operation in the 2030s.
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Verification of global gyrokinetic simulation of low frequency mode excited by thermal plasma in spherical tokamak
A low frequency Alfven eigenmode in the ST40 spherical tokamak (ST) is found to be resonantly excited by thermal ions from global gyrokinetic GTC simulations. The analyses of phase-space resonances and wave-particle energy exchanges show that the Beta-induced Alfvén-Acoustic Eigenmode (BAAE) is primarily driven unstable by thermal ions, but is stabilized by energetic particles (EPs). When all kinetic effects are artificially suppressed, GTC simulations in the ideal magnetohydrodynamic (MHD) limit confirm the existence of the MHD eigenmode with a frequency in the BAAEs gap, as previously found by the ideal MHD code NOVA. The kinetic effects of thermal ions induce a frequency downshift compared to the stable BAAE in the MHD simulations. These results support the verification for global gyrokinetic simulations of the BAAE in the ST. However, the simulations do not explain the experimental observations of the BAAE in the ST40, possibly owing to the limitation of the collisionless gyrokinetic Monte Carlo model for the EPs.
Alfvén eigenmode↗
Characterizing core and edge turbulence regimes with fluctuation imaging diagnostics in Wendelstein 7-X
Two density fluctuation imaging systems, phase contrast imaging (PCI) and gas puff imaging (GPI) measure spatially resolved density fluctuations with high time resolution throughout the core plasma (PCI) and in the scrape-off layer (GPI) of the Wendelstein 7-X (W7-X) stellarator. Both systems combined give a comprehensive overview of overall fluctuation levels, spectral properties such as their distribution in frequency and wavenumber space as well as their spatial distribution. These tools are used to assess changes in density turbulence in three representative discharges that transition into stable divertor detachment by different strategies (impurity seeding, density ramping and power starvation). Several general trends are identified when the radiated power fraction is systematically increased: In the plasma edge, the line emission observed by GPI shifts radially inward with a drop in electron temperature, and normalized intensity fluctuation profiles follow this inward shift. Skewness and kurtosis of these edge fluctuations are reduced, indicating a reduction of large intermittent transport events, and poloidal phase velocities decrease in magnitude. These observations are consistent with a reduced power input into the plasma edge and a general reduction of turbulent activity. Core density fluctuation levels remain nearly constant in the impurity seeding scenario, indicating that detachment does not significantly impact turbulence there. However, a strong reduction in the dominant outboard fluctuation phase velocity is observed that deviates from the previous interpretation of neoclassical radial electric field changes, showing that the core plasma is not completely unaffected. In the density ramp and power starvation scenarios, undesirable and irregular large-scale events arise clearly in both diagnostic systems as the radiative fraction is increased. Impurity seeding therefore seems to be a promising strategy on W7-X to achieve detachment without significantly altering core turbulence, especially when targeting a specific operating point in core density and heating power.
Wendelstein 7-X↗
Measuring the growth of Alfvén wave parametric decay instability using counter-propagating waves: Theory and simulations
The parametric decay instability (PDI) of Alfvén waves—where a pump Alfvén wave decays into a backward-propagating child Alfvén wave and a forward ion acoustic wave—is a fundamental nonlinear wave-wave interaction and holds significant implications for space and laboratory plasmas. However, to date there has been no direct experimental measurement of PDI. Here, we propose a novel and experimentally viable scheme to quantify the growth of Alfvén wave PDI on a linear device using a large pump Alfvén wave and a small counter-propagating seed Alfvén wave, with the seed-wave frequency tuned to match the backward Alfvén wave generated by standard PDI. Using hybrid simulations, we show that energy transfer from the pump to the seed reduces the latter's spatial damping. By comparing seed-wave amplitudes with and without the pump wave, this damping reduction can be used as a direct and reliable proxy for PDI growth. The method is validated in our simulations across a range of plasma and wave parameters and agrees well with theoretical predictions. Notably, the scheme exhibits no threshold for PDI excitation and is, in principle, readily implementable under current laboratory conditions. Finally, this scheme is a critical step toward solving the challenge of experimentally accessing Alfvén wave PDI and provides an elegant method that may be used to validate fundamental theories of parametric instabilities in controlled laboratory settings.
heliosphere↗
First Demonstration of Resonant Pitch-Angle Scattering of Relativistic Electrons by Externally Launched Helicon Waves
Helicon waves (a.k.a whistler waves) satisfying the normal wave-particle cyclotron resonance are observed to limit the growth and maximum energy of relativistic electrons (REs) in low-density Ohmic DIII-D tokamak plasmas. Following the application of helicon waves, pitch-angle scattering of high-energy REs causes an increase in both synchrotron and electron-cyclotron emissions. The hard x-ray emission, a proxy for the RE population, ceases to grow. Energy-resolved hard x-ray measurements also show a striking decrease in the number of high-energy REs (above the resonance at approximately 8MeV) to below the noise floor and an increase in low-energy (∼ 4 MeV) REs. This occurs despite the toroidal electric field remaining high enough to drive exponential RE growth in the absence of helicon waves. Furthermore, these results open new directions for limiting the maximum energy of RE populations in laboratory and fusion plasmas.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Observations of heteroclinic bifurcations in resistive magnetohydrodynamic simulations of the plasma response to resonant magnetic perturbations
A class of topological magnetic island bifurcations that has not previously been observed in toroidal plasmas is described. Increasing an externally applied three-dimensional magnetic field in resistive magnetohydrodynamic simulations results in the asymmetric elongation of resonant island flux surfaces followed by a sequence of heteroclinic bifurcations. Here, these bifurcations produce new sets of hyperbolic-elliptic fixed points as predicted by the Poincaré-Birkoff fixed point theorem. Field line calculations verify that the new fixed points do not connect to those of the prebifurcated islands as required for heteroclinic bifurcations on a torus with winding numbers composed of common integer factors.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Spontaneous and explicit parity-time-symmetry breaking in drift-wave instabilities
A method of parity-time- (PT) symmetry analysis is introduced to study the high-dimensional, complicated parameter space of drift-wave instabilities. Here, we show that spontaneous PT-symmetry breaking leads to the ion temperature gradient instability of drift waves, and the collisional instability is the result of explicit PT-symmetry breaking. A new unstable drift wave induced by finite collisionality is identified. It is also found that gradients of ion temperature and density can destabilize the ion cyclotron waves when PT symmetry is explicitly broken by a finite collisionality.
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Efficient electron cyclotron current drive regime for plasma current start-up in fusion reactors
We report an accessibility enhanced efficient fundamental X-mode electron cyclotron heating (ECH) current start-up regime was identified for a reactorlike toroidal magnetic field range which has more than 100 times higher current drive efficiency compared to more conventional ECH methods for the relevant start-up temperature range. Very high current drive efficiency is possible due to the strong cyclotron interaction only with unidirectional passing electrons constrained by the wave accessibility conditions. This efficient electron cyclotron current drive regime may help facilitate the design of innovative economical solenoid-free tokamak fusion reactor systems.
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Dynamics of potential vorticity staircase evolution and step mergers in a reduced model of beta-plane turbulence
A two-field model of potential vorticity (PV) staircase structure and dynamics relevant to both beta-plane and drift-wave plasma turbulence is studied numerically and analytically. The model evolves averaged PV whose flux is both driven by and regulates a potential enstrophy field, ε. The model employs a closure using a mixing length model. Its link to bistability, vital to staircase generation, is analyzed and verified by integrating the equations numerically. Long-time staircase evolution consistently manifests a pattern of metastable quasiperiodic configurations, lasting for hundreds of time units, yet interspersed with abrupt ( Δt << 1 ) mergers of adjacent steps in the staircase. The mergers occur at the staircase lattice defects where the pattern has not completely relaxed to a strictly periodic solution that can be obtained analytically. Other types of stationary solutions are solitons and kinks in the PV gradient and ε-profiles. The waiting time between mergers increases strongly as the number of steps in the staircase decreases. This is because of an exponential decrease in interstep coupling strength with growing spacing. The long-time staircase dynamics is shown numerically be determined by local interaction with adjacent steps. In conclusion, mergers reveal themselves through the explosive growth of the turbulent PV flux, which, however, abruptly drops to its global constant value once the merger is completed.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Theory of the Drift-Wave Instability at Arbitrary Collisionality
A numerically efficient framework that takes into account the effect of the Coulomb collision operator at arbitrary collisionalities is introduced. Such a model is based on the expansion of the distribution function on a Hermite-Laguerre polynomial basis to study the effects of collisions on magnetized plasma instabilities at arbitrary mean-free path. Focusing on the drift-wave instability, we show that our framework allows retrieving established collisional and collisionless limits. At the intermediate collisionalities relevant for present and future magnetic nuclear fusion devices, deviations with respect to collision operators used in state-of-the-art turbulence simulation codes show the need for retaining the full Coulomb operator in order to obtain both the correct instability growth rate and eigenmode spectrum, which, for example, may significantly impact quantitative predictions of transport. In conclusion, the exponential convergence of the spectral representation that we propose makes the representation of the velocity space dependence, including the full collision operator, more efficient than standard finite difference methods.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Reversal of Simple Hydrogenic Isotope Scaling Laws in Tokamak Edge Turbulence
The role of nonadiabatic electrons in regulating the hydrogenic isotope-mass scaling of gyrokinetic turbulence in tokamak fusion plasmas is assessed in the transition from ion-dominated core transport regimes to electron-dominated edge transport regimes. We propose a new isotope-mass scaling law that describes the electron-to-ion mass-ratio dependence of turbulent ion and electron energy fluxes. Here, the massratio dependence arises from the nonadiabatic response associated with fast electron parallel motion and plays a key role in altering—and in the case of the DIII-D edge, favorably reversing—the naive gyro-Bohm scaling behavior. In the reversed regime hydrogen energy fluxes are larger than deuterium fluxes, which is the opposite of the naive prediction.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Threshold Heat-Flux Reduction by Near-Resonant Energy Transfer
Near-resonant energy transfer to large-scale stable modes is shown to reduce transport above the linear critical gradient, contributing to the onset of transport at higher gradients. This is demonstrated for a threshold fluid theory of ion temperature gradient turbulence based on zonal-flow-catalyzed transfer. Furthermore, the heat flux is suppressed above the critical gradient by resonance in the triplet correlation time, a condition enforced by the wave numbers of the interaction of the unstable mode, zonal flow, and stable mode.
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Impact of Magnetic Field Configuration on Heat Transport in Stellarators and Heliotrons
We assess the magnetic field configuration in modern fusion devices by comparing experiments with the same heating power, between a stellarator and a heliotron. The key role of turbulence is evident in the optimized stellarator, while neoclassical processes largely determine the transport in the heliotron device. Gyrokinetic simulations elucidate the underlying mechanisms promoting stronger ion scale turbulence in the stellarator. Similar plasma performances in these experiments suggests that neoclassical and turbulent transport should both be optimized in next step reactor designs.
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