High Collisionality Research Articles

Benign termination of runaway electron beams on ASDEX Upgrade and TCV

This paper discusses the development of a benign termination scenario for runaway electron (RE) beams on ASDEX Upgrade and TCV. A systematic study revealed that a low electron density (n e) companion plasma was required to achieve a large MHD instability, which expelled the confined REs over a large wetted area and allowed for the conversion of magnetic energy to radiation. Control of the companion plasma ne was achieved via neutral pressure regulation and was agnostic to material injection method. The neutral pressure required for recombination was found to be dependent on impurity species, quantity and RE current. On TCV, n e increased at neutral pressures above 1 Pa, indicating that higher collisionality between the REs and neutrals may lead to an upper pressure limit. The conversion of magnetic energy to radiated energy was measured on both machines and a decrease in efficiency was observed at high neutral pressure on TCV. The benign termination technique was able to prevent any significant increase in maximum heat flux on AUG from 200 to 600 kA of RE current, highlighting the ability of this approach to handle fully formed RE beams.

Numerical minimization of neoclassical poloidal viscosity for supersonic equilibria in tokamak geometry

Extensive experimental evidence has shown that the presence of poloidal flow in tokamaks can dramatically improve transport properties. However, theory indicates that poloidal flows are damped by poloidal viscosity, thus necessitating external drivers, such as neutral beam injection or radio frequency heating. In this work, ideal magnetohydrodynamic equilibria are calculated via the FORTRAN code FLOW [Guazzotto et al., Phys. Plasmas 11, 604 (2004)] and a postprocessor is used to estimate the neoclassical poloidal viscosity. The equilibrium inputs, which correspond to intuitive physical quantities, are then numerically optimized to reduce a viscosity figure of merit. We present supersonic equilibria in tokamak geometry with minimized neoclassical poloidal viscosities for various velocity free function inputs, plasma aspect ratios, and collisionality regimes. Benchmarks are made against an analytic theory as well as a classical expression of poloidal viscosity. Numerical confirmation of the analytic theory is obtained in the high aspect ratio and high collisionality limit. Good agreement is also seen near the plasma core and edge, with discrepancies arising in the intermediate region. Outside of these limits, rotation input function profiles are found that provide ∼order of magnitude improvements over the analytic theory, with additional progress being made toward predictions for tokamak-relevant equilibria.

On the origin of the DIII-D L-H power threshold isotope effect

The increased low to high confinement mode (L to H-mode) power threshold PLH in DIII-D low collisionality hydrogen plasmas (compared to deuterium) is shown to result from lower impurity (carbon) content, consistent with reduced (mass-dependent) physical and chemical sputtering of graphite. Trapped gyro-Landau fluid (TGLF) quasilinear calculations and local non-linear gyrokinetic CGYRO simulations confirm stabilization of ion temperature gradient (ITG) driven turbulence by increased carbon ion dilution as the most important isotope effect. In the plasma edge, electron non-adiabaticity is also predicted to contribute to the isotope dependence of thermal transport and PLH , however its effect is subdominant compared to changes from impurity isotopic behavior. This L-H power threshold reduction with increasing carbon content at low collisionality is in stark contrast to high collisionality results, where additional impurity content appears to increase the power necessary for H-mode access.

Observation of long-radial-range-correlation in turbulence in high-collisionality high-confinement plasmas on DIII-D

We report on the observation of spatially asymmetric turbulent structures with a long radial correlation length in the core of high-collisionality H-mode plasmas on DIII-D tokamak. These turbulent structures develop from shorter wavelength turbulence and have a radially elongated structure. The envelope of turbulence spans a broad radial range in the mid-radius region, leading to streamer-like transport events. The underlying turbulence is featured by intermittency, long-term memory effect, and the characteristic spectrum of self-organized criticality. The amplitude and the radial scale increase substantially when the shearing rate of the mean flow is reduced below the turbulent scattering rate. The enhanced long-radial-range-correlated (LRRC) transport events are accompanied by apparent degradation of normalized energy confinement time. The emergence of such LRRC transport events may serve as a candidate explanation for the degrading nature of H-mode core plasma confinement at high collisionality on DIII-D tokamak.

Characterization of mesoscopic turbulent transport events with long-radial-range correlation in DIII-D H-mode plasmas

A dimensionless collisionality scan has been performed in H-mode plasmas on DIII-D tokamak, with detailed measurements of intermediate-to-high wavenumber turbulence using Doppler backscattering systems. It is found that the shorter wavelength turbulence develops into spatially asymmetric turbulent structures with a long-radial-range correlation (LRRC) in the mid-radius region of high collisionality discharges. Linear cgyro simulations indicate that the underlying turbulence is likely driven by the electron-temperature-gradient mode. The LRRC transport events are highly intermittent and show a power spectrum of Sñ(k⊥)∝k⊥−1 for density fluctuations, which is often associated with self-organized criticality. The magnitude and the radial scale of those turbulent structures increase significantly when the Er×B mean flow shearing rate decreases at higher collisionality. The enhanced LRRC transport events appear to be correlated with the degraded energy confinement time. The emergence of such LRRC transport events may serve as a candidate explanation for the degrading nature of H-mode core plasma confinement at high collisionality.

Parameter dependence of density pedestal width and correlation with pedestal turbulence in EAST type-I ELMy H-mode plasma

The density pedestal structures in a series of type-I ELMy H-mode discharges (0.6 MA/2.5 T) with upper single null (USN) divertor configuration have been studied in EAST. To obtain the pedestal width, density profiles are fitted via the modified hyperbolic tangent (mtanh) function and the two-line method. The pedestal widths from these two methods have a similar tendency. Significant impacts of pedestal poloidal beta and pedestal collisionality on the density pedestal width have been observed for the first time in EAST. The non-linear regressions suggest the density width scaling in type-I ELMy EAST plasma are wne∝c(νped⁎)0.27−0.33⋅(βp,ped)0.5−0.58. The density fluctuations in the bottom of the pedestal from the fluctuation reflectometry imply an enhanced density fluctuation (Pfluc) and an obvious spectral broadening in the high collisionality regime of νped⁎≥3. The experimental results suggest that the pedestal turbulence would play an important role in the evolution of the pedestal structure.

Two-stream instability with a growth rate insensitive to collisions in a dissipative plasma jet

The two-stream instability (Buneman instability) is traditionally derived as a collisionless instability with the presumption that collisions inhibit this instability. We show here via a combination of a collisional two-fluid model and associated experimental observations made in the Caltech plasma jet experiment, that in fact, a low-frequency mode of the two-stream instability is indifferent to collisions. Despite the collision frequency greatly exceeding the growth rate of the instability, the instability can still cause an exponential growth of electron velocity and a rapid depletion of particle density. Nevertheless, high collisionality has an important effect as it enables the development of a double layer when the cross section of the plasma jet is constricted by a kink-instigated Rayleigh–Taylor instability.

Micro-tearing mode dominated electron heat transport in DIII-D H-mode pedestal

A new, comprehensive set of evidence reveals that Micro-Tearing Modes (MTMs) dominate pedestal electron heat transport in an H-mode experiment in the DIII-D tokamak. The experiment investigates the role of MTMs by scanning pedestal collisionality, a main drive of MTM instability, from 0.43 to 0.84 on the pedestal top. Broadband (150–800 kHz) magnetic and density fluctuations originating from the pedestal gradient region and highly consistent with MTMs are observed, with amplitude increasing during the scan. The higher magnetic fluctuation amplitude correlates with a lower pedestal electron temperature gradient, implying MTMs may regulate the pedestal electron heat transport. The collisionality scan results in profile and transport changes consistent with predicted transport capability of MTMs: (1) experimentally-determined electron heat diffusivity increases ∼40% at the location where the broadband density fluctuations peak; (2) ion heat diffusivity has less increase (<20%); and (3) a locally flattened region in the electron temperature pedestal is observed at high collisionality. A local, linear gyrokinetic simulation finds MTMs as the most unstable mode in the pedestal gradient region. In addition, local, nonlinear simulations suggest MTMs can dominate and drive experimentally-relevant, megawatt-level electron heat flux. This result establishes MTMs as an effective transport mechanism in the H-mode pedestal, in particular at high collisionality.

Analytical model for the combined effects of rotation and collisionality on neoclassical impurity transport

The influence of rotation, collisionality and trapped particle fraction on the magnitude and direction of neoclassical impurity transport in tokamaks is analyzed using an extensive database of drift-kinetic simulations with the NEO code. It is shown that an operational window opens at sufficiently high Mach number and low collisionality, where the magnitude of the temperature screening of impurities increases with higher rotation. If the collisionality increases, this effect is quickly lost and the temperature gradient then drives an inward impurity flux when rotation is present. The boundary between these two regimes is calculated as a function of the trapped particle fraction, and it is shown that plasma parameters achieved in recent JET experiments allow them to access the new beneficial regime, in accordance with observations of reduced tungsten accumulation. Applications to ASDEX Upgrade experiments where these effects become relevant are also presented, and the implications for ITER are discussed. A method for extracting the physically distinct Pfirsch–Schlüter (PS) and banana-plateau (BP) neoclassical flux components from the NEO output is introduced and employed to construct a model that describes them analytically at arbitrary rotation and collisionality. The beneficial behavior of the screening with rotation is found to be a BP effect, in contrast to the known detrimental role of rotation in the PS component. The new analytical model is able to reproduce the results of NEO when modeling radial profiles of transport coefficients from experimental kinetic profiles, with the added feature of isolating the BP and PS components for additional physical analysis, while remaining well suited for fast applications.

The broadening of SOL profiles in JET tritium plasma and its impact on machine operation

Unusually high power loads on the beryllium limiter caused by neutral beam re-ionisation, and much cooler divertor target surfaces were observed during the recent JET tokamak tritium campaign. As both phenomena are driven by scrape-off layer (SOL) physics, the SOL features of 72 tritium H-mode discharges and their deuterium references have been studied. The majority (70) of tritium H-mode discharges had exponentially decaying SOL profiles. The tritium plasmas are observed to have increased separatrix density and collisionality compared to their deuterium references. This is associated with times broader SOL width for both density and temperature profiles. This is consistent with previous observations in highly collisional deuterium H-mode plasma on the ASDEX Upgrade tokamak (Sun et al 2015 Plasma Phys. Control. Fusion 57 125011) and interpreted as high collisionality enhancing cross-field transport across the separatrix and resulting in the broadening of near SOL above a critical value. The other two tritium H-mode discharges had near flat SOL density profiles, similar to the so-called ‘density shoulder formation’ observed in L-mode plasma. The SOL collisionality of these two pulses lies within the range of T pulses without density shoulder formation. This supports the conclusion of previous studies (Vianello et al 2017 Nucl. Fusion 57 116014; Wynn et al 2018 Nucl. Fusion 58 056001) that increased collisionality is not sufficient for the formation of a ‘density shoulder’ and additional factors, likely divertor condition or interaction with neutrals, are required. JET tritium plasma provides evidence of favourable and unfavourable effects of enhanced cross-field SOL transport on machine operation. The larger limiter power loads due to re-ionisation of neutral beam injection observed in the T pulses relative to their D references has been shown to be consistent with the combined effects of the broadening of the SOL profile and larger beam ion Larmor radius. The enhanced cross-field particle transport and the resulting broader SOL width provides more particles to ionize the fast Beam neutrals, causing the unfavourable power load issue on the beryllium limiter. The broader near SOL profiles of the T plasma spreads the heat load over a larger area and, together with the increased separatrix density, results in a favourably cooler divertor target surface.

Electron power absorption in capacitively coupled neon–oxygen plasmas: a comparison of experimental and computational results

Phase resolved optical emission spectroscopy (PROES) measurements combined with 1d3v particle-in-cell/Monte Carlo collisions (PIC/MCC) simulations are used to study the electron power absorption and excitation/ionization dynamics in capacitively coupled plasmas (CCPs) in mixtures of neon and oxygen gases. The study is performed for a geometrically symmetric CCP reactor with a gap length of 2.5 cm at a driving frequency of 10 MHz and a peak-to-peak voltage of 350 V. The pressure of the gas mixture is varied between 15 Pa and 500 Pa, while the neon/oxygen concentration is tuned between 10% and 90%. For all discharge conditions, the spatio-temporal distributions of the electron-impact excitation rate from the Ne ground state into the Ne 2p53p0 state measured by PROES and obtained from PIC/MCC simulations show good qualitative agreement. Based on the emission/excitation patterns, multiple operation regimes are identified. Localized bright emission features at the bulk boundaries, caused by local maxima in the electronegativity are found at high pressures and high O2 concentrations. The relative contributions of the ambipolar and the Ohmic electron power absorption are found to vary strongly with the discharge parameters: the Ohmic power absorption is enhanced by both the high collisionality at high pressures and the high electronegativity at low pressures. In the wide parameter regime covered in this study, the PROES measurements are found to accurately represent the ionization dynamics, i.e. the discharge operation mode. This work represents also a successful experimental validation of the discharge model developed for neon–oxygen CCPs.

Kinetic interpretation of the classical Rayleigh-Taylor instability.

Rayleigh-Taylor (RT) instabilities are prevalent in many physical regimes ranging from astrophysical to laboratory plasmas and have primarily been studied using fluid models, the majority of which have been ideal fluid models. This work presents a five-dimensional (two spatial dimensions, three velocity space dimensions) simulation using the continuum-kinetic model to study the effect of the collisional mean free path and transport on the instability growth. The continuum-kinetic model provides noise-free access to the full particle distribution function permitting a detailed investigation of the role of kinetic physics in hydrodynamic phenomena such as the RT instability. For long mean free path, there is no RT instability growth, but as collisionality increases, particles relax towards the Maxwellian velocity distribution, and the kinetic simulations reproduce the fluid simulation results. An important and novel contribution of this work is in the intermediate collisional cases that are not accessible with traditional fluid models and require kinetic modeling. Simulations of intermediate collisional cases show that the RT instability evolution is significantly altered compared to the highly collisional fluidlike cases. Specifically, the growth rate of the intermediate collisionality RT instability is lower than the high collisionality case while also producing a significantly more diffused interface. The higher moments of the distribution function play a more significant role relative to inertial terms for intermediate collisionality during the evolution of the RT instability interface. Particle energy flux is calculated from moments of the distribution and shows that transport is significantly altered in the intermediate collisional case and deviates much more so from the high collisionality limit of the fluid regime.

Local gyrokinetic collisional theory of the ion-temperature gradient mode

We present a study of the linear properties of the ion-temperature gradient (ITG) modes with collisions modelled for the first time by the linearized gyrokinetic (GK) Coulomb collision operator (Freiet al.,J. Plasma Phys., vol. 87, issue 5, 2021, 905870501) in the local limit. The study is based on a Hermite–Laguerre polynomial expansion of the perturbed ion distribution function applied to the linearized GK Boltzmann equation, yielding a hierarchy of coupled equations for the expansion coefficients, referred to as gyromoments. We explore the collisionless and high-collisional limits of the gyromoment hierarchy analytically. Parameter scans revealing the dependence of the ITG growth rate on the collisionality modelled using the GK Coulomb operator are reported, showing strong damping at small scales as the collisionality increases and, therefore, the need for a steeper gradient for the ITG onset at high collisionality to overcome the finite Larmor radius (FLR) collisional stabilization. The predictions on the ITG growth rate by the GK Coulomb operator are compared with other collision operator models, such as the Sugama, the Dougherty, as well as the momentum-conserving pitch-angle scattering and the Hirshman–Sigmar–Clarke collision operators derived for the first time in terms of gyromoments. The importance of FLR terms in the collision operators is pointed out by the appearance of a short wavelength ITG branch when collisional FLR terms are neglected, this branch being completely suppressed by FLR collisional effects. Energy diffusion is shown to be important at high collisionality and at small scale lengths. Among the GK collision operators considered in this work, the GK Sugama collision operator yields, in general, the smallest deviation compared with the GK Coulomb collision operator, while the largest deviations are found with the GK Dougherty operator. Convergence studies of the gyromoment method are reported and show that the drifts associated with the gradient and curvature of the magnetic field increase the required number of gyromoments at low collisionality. Nevertheless, the low number of gyromoments necessary for convergence at high collisionality constitutes an attractive numerical and analytical feature of the gyromoment approach to study the plasma dynamics in the boundary of fusion devices.

Role of the edge stochastic layer in density pump-out by resonant magnetic perturbations

The role of the edge stochastic layer on particle transport is addressed in DIII-D plasmas with applied resonant magnetic perturbations (RMPs) causing density pump-out (a term used to denote the density reduction at the top of the pedestal due to the applied RMPs). Using an analytical model that adds the stochastic parallel transport of electrons (Harvey et al 1981 Phys. Rev. Lett. 47 102) to the fluid equations, the ambipolar radial electric field and particle flux are calculated simultaneously. In this model the nonambipolar electron particle flux, driven by the stochastic magnetic field, is predominantly balanced by the nonambipolar perpendicular ion flux, driven by toroidal viscosity, across a narrow stochastic layer of order two percent of the plasma radius (0.98 < ψ n < 1). The model reproduces the level of density pump-out and its dependence on RMP amplitude near the separatrix for three plasma discharges for which the pedestal foot is at medium to high collisionality . The experimentally observed and numerically tested inverse density dependence of density pump-out (Hu et al 2020 Nucl. Fusion 60 076001) is accurately captured by the model: an increase in collisionality with density in the pedestal foot results in a decrease in stochastic diffusivity, and hence a decrease in the level of pump-out.

On the mitigation of cancellation errors in hybrid fluid‐kinetic methods for solving kinetic equations describing neutrals in the plasma edge

AbstractOne of the key aspects when simulating the plasma edge is the treatment of the neutral particles. Neutral particles can be described by a kinetic equation, which is difficult to solve due to the high dimensionality of the phase space and the high collisionality between the neutral particles and the plasma background, especially in the (partially) detached regimes anticipated for future reactors. We consider a recently proposed hybrid fluid‐kinetic method that is based on a micro–macro decomposition of the kinetic equation and mitigates the problems related to both the high dimensionality and the high collisionality. However, this method is prone to cancellation errors due to the introduction of particles with both positive and negative weights. In each iteration of the method, the particles undergo a weight projection step, which we identify as the main source of cancellation errors. We use techniques from numerical linear algebra for solving ill‐conditioned linear systems to improve the numerical stability of the weight projection step and reduce the cancellation errors. The reduction of cancellation errors allows for further speedup in the hybrid fluid‐kinetic method.

Edge tokamak transport in regimes with high collisionality

AbstractIn the strongly detached regimes, especially in future tokamak reactors, plasma in the divertor and in some special regions like vicinity of highly radiating X‐point is strongly collisional. Ion gyrofrequency becomes less than Coulomb collision frequency and might be of the order of ion‐neutral collision frequency. For such parameters, parallel and perpendicular ion diffusion and mobility caused by ion‐neutral collision becomes important and can to large extent determine density profiles and currents distribution in the divertor. In the present article, plasma profiles in the vicinity of divertor plates were analysed. It is demonstrated that density profiles are determined by combination of parallel and perpendicular ambipolar diffusion. Results of analytic calculations are compared with Particle‐In‐Cell Monte‐Carlo Collisions (PIC MCC) simulations of magnetized plasma and collisional transport of magnetized ions from quasi‐neutral region to the material surface. Analytic expressions are compared with the results of particle in cell simulations done for different angles between magnetic field and material surface and different plasma parameters. Impact of velocity of neutral particles on ion fluxes and currents is also investigated. Consequences for divertor plasma typical for ITER and other future tokamak‐reactors are discussed.

Implementation and verification of a conservative,multi‐species,gyro‐averaged, full‐f,Lenard‐Bernstein/Dougherty collision operator in the gyrokinetic codeGENE‐X

AbstractGyrokinetic simulations are among the main tools to predict turbulent transport in the core of fusion devices. Unlike the core, the plasma edge and scrape‐off layer are characterized by lower temperature and higher collisionality. To allow for realistic gyrokinetic modelling of edge and scrape‐off layer turbulence, it is crucial to include collisional effects into the simulations. In this work, we present a full‐f, gyro‐averaged, multi‐species, Lenard‐Bernstein/Dougherty (LBD) collision operator, for the use in the gyrokinetic turbulence codeGENE‐X. The operator accounts for exact particle density, momentum, and energy conservation, with collision frequencies chosen such that the momentum or temperature relaxation rates of the Boltzmann collision operator are recovered. We provide a conservative second‐order finite‐volume implementation of the operator and present a thorough verification. Due to the excellent conservation properties of the finite‐volume implementation, it is possible to use a coarser velocity space grid, save computational resources and, as a consequence, perform simulations of larger fusion devices.

Design and physics basis for the upcoming DIII-D SAS-VW campaign to quantify tungsten leakage and transport in a new slot divertor geometry

A set of experiments are planned to exploit the high SOL collisionality enabled by a tightly baffled slot divertor geometry to suppress tungsten leakage in DIII-D. A toroidal row of graphite tiles from the Small Angle Slot (SAS) divertor is being coated with 10–15 μm of tungsten. New spectroscopic viewing chords with in-vacuo optics will measure the W gross erosion source from the divertor surface with high spatial and temporal resolution. In parallel, the bottom of the SAS divertor is changed from a flat to a ‘V’ shape. New SOLPS-ITER/DIVIMP simulations conducted with drifts using the planned ‘V’ shape predict a substantial reduction in W sourcing and SOL accumulation in either B × ∇B direction relative to either the old SAS divertor shape or the open, lower divertor. Dedicated studies are planned to carefully characterize the level of W sourcing, leakage, and scrape-off-layer (SOL) accumulation in DIII-D over a wide range of plasma scenarios. Various actuators will be assessed for their efficacy in further reducing high-Z impurity sources and leakage from the slot divertor geometry. This coupled code-experiment validation effort will be used to stress-test physics models and build confidence in extrapolations to advanced, high-Z divertor geometries for next-step devices.

Development of advanced linearized gyrokinetic collision operators using a moment approach

The derivation and numerical implementation of a linearized version of the gyrokinetic (GK) Coulomb collision operator (Jorge et al., J. Plasma Phys., vol. 85, 2019, 905850604) and of the widely used linearized GK Sugama collision operator (Sugama et al., Phys. Plasmas, vol. 16, 2009, 112503) is reported. An approach based on a Hermite–Laguerre moment expansion of the perturbed gyrocentre distribution function is used, referred to as gyromoment expansion. This approach allows the considering of arbitrary perpendicular wavenumber and expressing the two linearized GK operators as a linear combination of gyromoments where the expansion coefficients are given by closed analytical expressions that depend on the perpendicular wavenumber and on the temperature and mass ratios of the colliding species. The drift-kinetic (DK) limits of the GK linearized Coulomb and Sugama operators are also obtained. Comparisons between the gyromoment approach and the DK Coulomb and GK Sugama operators in the continuum GK code GENE are reported, focusing on the ion-temperature-gradient instability and zonal flow damping, finding an excellent agreement. It is confirmed that stronger collisional damping of the zonal flow residual by the Sugama GK model compared with the GK linearized Coulomb (Pan et al., Phys. Plasmas, vol. 27, 2020, 042307) persists at higher collisionality. Finally, we show that the numerical efficiency of the gyromoment approach increases with collisionality, a desired property for boundary plasma applications.

Study of stability and rotation of a chain of saturated, freely-rotating magnetic islands in tokamaks

The non-linear dynamics of a chain of stationary, saturated magnetic islands is studied by solving a four-field system of equations that include non-ideal effects, lowest order finite Larmor radius corrections and neoclassical terms. The magnetic island rotation velocity is calculated self-consistently with the fields profiles. The solutions for the island rotation velocity and for the ion polarization current are determined as a function of the characteristic parameters of the system and the results are discussed. The results of the calculations show that island rotation velocity and the ion polarization current depend in a non-trivial way on the parameters characterizing the system, and some clear patterns emerge only in particular cases. An analysis of magnetic island rotation velocity is performed on experiments in COMPASS tokamak. Measured island rotation velocity is compared with the calculated ion and electron flow velocities, for different hypotheses on the toroidal rotation of the plasma. The comparison shows that the island rotation velocity is consistent with the ion flow velocity, under the hypothesis of slow toroidal rotation and low collisionality. Theoretical calculation of the island rotation velocity according to the model here developed suggests that the islands rotate weakly in the ion direction, in the hypothesis of slow toroidal rotation and high collisionality. The impossibility of directly measuring the plasma rotation velocity makes it difficult to distinguish between these different regimes.