High Collisionality Regime Research Articles

Full-F turbulent simulation in a linear plasma device using a gyro-moment approach

Simulations of plasma turbulence in a linear plasma device configuration are presented. These simulations are based on a simplified version of the gyrokinetic (GK) model proposed by Frei et al. [J. Plasma Phys. 86, 905860205 (2020)], where the full-F distribution function is expanded on a velocity-space polynomial basis allowing us to reduce its evolution to the solution of an arbitrary number of fluid-like equations for the expansion coefficients, denoted as the gyro-moments (GM). By focusing on the electrostatic and neglecting finite Larmor radius effects, a full-F GM hierarchy equation is derived to evolve the ion dynamics, which includes a nonlinear Dougherty collision operator, localized sources, and Bohm sheath boundary conditions. An electron fluid Braginskii model is used to evolve the electron dynamics, coupled to the full-F ion GM hierarchy equation via a vorticity equation where the Boussinesq approximation is used. A set of full-F turbulent simulations are then performed using the parameters of the LArge Plasma Device (LAPD) experiments with different numbers of ion GMs and different values of collisionality. The ion distribution function is analyzed illustrating the convergence properties of the GM approach. In particular, we show that higher-order GMs are damped by collisions in the high-collisional regime relevant to LAPD experiments. The GM results are then compared with those from two-fluid Braginskii simulations, finding qualitative agreement in the time-averaged profiles and statistical turbulent properties.

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.

Multilevel asymptotic-preserving Monte Carlo for kinetic-diffusive particle simulations of the Boltzmann-BGK equation

We develop a novel multilevel asymptotic-preserving Monte Carlo method, called Multilevel Kinetic-Diffusion Monte Carlo (ML-KDMC), for simulating the kinetic Boltzmann transport equation with a Bhatnagar–Gross–Krook (BGK) collision operator. This equation occurs, for instance, in mathematical models of the neutral particles in the plasma edge of nuclear fusion reactors. In this context, the Kinetic-Diffusion Monte Carlo method is known to maintain accuracy both in the low-collisional and the high-collisional limit, without an exploding simulation cost in the latter. We show that, by situating this method within a Multilevel Monte Carlo (MLMC) framework, using a hierarchy of larger time step sizes, the simulation cost is reduced even further. The different levels in our ML-KDMC method are connected via a new and improved recipe for correlating particle trajectories with different time step sizes. Furthermore, a new and more general level selection strategy is presented. We illustrate the efficiency of our ML-KDMC method by applying it to a one-dimensional test case with non-homogeneous and anisotropic plasma background. Our method yields significant speedups compared to the single-level KDMC scheme, both in the low- and high-collisional regime. In the high-collisional case, our ML-KDMC outperforms the single-level KDMC method by several orders of magnitude.

Extended investigations of isotope effects on ECRH plasma in LHD

Isotope effects of ECRH plasma in LHD were investigated in detail. A clear difference of transport and turbulence characteristics in H and D plasmas was found in the core region, with normalized radius ρ < 0.8 in high collisionality regime. On the other hand, differences of transport and turbulence were relatively small in low collisionality regime. Power balance analysis and neoclassical calculation showed a reduction of the anomalous contribution to electron and ion transport in D plasma compared with H plasma in the high collisionality regime. In core region, density modulation experiments also showed more reduced particle diffusion in D plasma than in H plasma, in the high collisionality regime. Ion scale turbulence was clearly reduced at ρ < 0.8 in high collisionality regime in D plasma compared with H plasma. The gyrokinetic linear analyses showed that the dominant instability ρ = 0.5 and 0.8 were ion temperature gradient mode (ITG). The linear growth rate of ITG was reduced in D plasma than in H plasma in high collisionality regime. This is due to the lower normalized ITG and density gradient. More hollowed density profile in D plasma is likely to be the key control parameter. Present analyses suggest that anomalous process play a role to make hollower density profiles in D plasma rather than neoclassical process. Electron scale turbulence were also investigated from the measurements and linear gyrokinetic simulations.

The plasma-wall transition with collisions and an oblique magnetic field: Reversal of potential drops at grazing incidences

The plasma-wall transition is studied by using 1d3V particle-in-cell simulations in the case of a one dimensional plasma bounded by two absorbing walls separated by 200 Debye lengths (λd). A constant and oblique magnetic field is applied to the system, with an amplitude such that r &amp;lt; λd &amp;lt; R, where r and R are the electron and ion Larmor radii, respectively. Collisions with neutrals are taken into account and modelled by an energy conservative operator, which randomly reorients ion and electron velocities. The plasma-wall transition (PWT) is shown to depend on both the angle of incidence of the magnetic field with respect to the wall, θ, and on the ion mean-free-path to Larmor radius ratio, λci/R. In the very low collisionality regime (λci≫R) and for a large angle of incidence, the PWT consists of the classical tri-layer structure (Debye sheath/Chodura sheath/pre-sheath) from the wall towards the center of the plasma. The drops of potential within different regions are well consistent with already published models. However, when sin θ≤R/λci or with the ordering λci&amp;lt;R, collisions cannot be neglected, leading to the disappearance of the Chodura sheath. In this case, a collisional model yields analytic expressions for the potential drop in the quasi-neutral region and explains, in qualitative and quantitative agreement with the simulation results, its reversal below a critical angle derived in this paper, a regime possibly met in the scrape-off layers of tokamaks. It is further shown that the potential drop in the Debye sheath slightly varies with the collisionality for λci≫R. However, it tends to decrease with λci in the high collisionality regime, until the Debye sheath finally vanishes.

Plasma expansion synthesis of tungsten nanopowder

This article reports the synthesis of tungsten nanoparticles predominantly in α-W phase by a single step plasma expansion technique. The oxidation of the metal and contribution from the β-W phase in the nanomaterial samples was observed to decrease with the increase of both the pressure in the sample collection chamber and the plasma power. We had observed production of faceted, lightly sintered particles with up to 300 nm individual sizes during high plasma current/high pressure synthesis conditions, which were measured to have the highest specific surface area of 35 m2/g. Condensation of this high temperature material at low saturation ratio and the high collisional regime had led to the synthesis of relatively bigger particle sizes in this experiment. Cauliflower like particle morphologies was observed during low pressure synthesis conditions, which is considered to have formed through spherulitic growth processes. Transmission Electron Microscopy (TEM) micrographs show very small crystallites remaining dispersed in an amorphous moss like the background, which was confirmed to be a mixture of tungsten and its oxides.

Hydrodynamic versus collisionless dynamics of a one-dimensional harmonically trapped Bose gas

By using a sum rule approach we investigate the transition between the hydrodynamic and the collisionless regime of the collective modes in a 1D harmonically trapped Bose gas. Both the weakly interacting gas and the Tonks-Girardeau limits are considered. We predict that the excitation of the dipole compression mode is characterized, in the high temperature collisionless regime, by a beating signal of two different frequencies ($\omega_z$ and $3\omega_z$) while, in the high temperature collisional regime, the excitation consists of a single frequency ($\sqrt{7}\omega_z$). This behaviour differs from the case of the lowest breathing mode whose excitation consists of a single frequency ($2\omega_z$) in both regimes. Our predictions for the dipole compression mode open promising perspectives for the experimental investigation of collisional effects in 1D configurations.

Dynamics of heavy impurities in non-linear MHD simulations of sawtoothing tokamak plasmas

The effect of sawteeth on impurity dynamics is studied with the XTOR-2F code. Non-linear full 3D MHD simulations including appropriate fluid equations for impurities in the high collisional regime show that the presence of regular sawtooth crashes affects the impurity behaviour. A spatial non-uniformity of in post-crash impurity density profiles persists due to 2D structures of impurity density which appear during sawtooth crashes. They are shown to be mainly driven by the velocity, and are responsible for the sudden impurity transport in the core plasmas.

Dependence of pedestal structure on collisionality at fixed beta in JT-60U

The dependence of pedestal structure on collisionality at fixed beta has been investigated in JT-60U. In the ITER-relevant low collisionality regime, the pedestal width does not change with edge collisionality. In the high collisionality regime, the pedestal width broadens with increased edge collisionality. The pedestal pressure gradient and width are not significantly changed when the pedestal is close to an intermediate n peeling-ballooning mode boundary at low collisionality. The experimental result indicates that conventional pedestal models where the pedestal width is independent of collisionality and is determined by at the pedestal is not a bad assumption in the ITER-relevant low collisionality regime. On the other hand, the pressure gradient decreases and the pedestal width increases at high collisionality. The pedestal broadening becomes significant when the pedestal is marginal to be unstable at the high n ballooning mode in the high collisionality regime.

Inward particle transport at high collisionality in the Experimental Advanced Superconducting Tokamak

We have made the first drift wave study of particle transport in the Experimental Advanced Superconducting Tokamak (Wan et al., Nucl. Fusion 49, 104011 (2009)). The results reveal that collisions make the particle flux more inward in the high collisionality regime. This can be traced back to effects that are quadratic in the collision frequency. The particle pinch is due to electron trapping which is not very efficient in the high collisionality regime so the approach to equilibrium is slow. We have included also the electron temperature gradient (ETG) mode to give the right electron temperature gradient, since the Trapped Electron Mode (TE mode) is weak in this regime. However, at the ETG mode number ions are Boltzmann distributed so the ETG mode does not give particle transport.

High-density H-mode operation by pellet injection and ELM mitigation with the new active in-vessel saddle coils in ASDEX Upgrade

Recent experiments at ASDEX Upgrade demonstrate the compatibility of ELM mitigation by magnetic perturbations with efficient particle fuelling by inboard pellet injection. ELM mitigation persists in a high-density, high-collisionality regime even with the strongest applied pellet perturbations. Pellets injected into mitigation phases trigger no type-I ELM-like events unlike when launched into unmitigated type-I ELMy plasmas. Furthermore, the absence of ELMs results in improved fuelling efficiency and persistent density build-up. Pellet injection is helpful to access the ELM-mitigation regime by raising the edge density beyond the required threshold level, mostly eliminating the need for strong gas puff. Finally, strong pellet fuelling can be applied to access high densities beyond the density limit encountered with pure gas puffing. Core densities of up to 1.6 times the Greenwald density have been reached while maintaining ELM mitigation. No upper density limit for the ELM-mitigated regime has been encountered so far; limitations were set solely by technical restrictions of the pellet launcher. Reliable and reproducible operation at line-averaged densities from 0.75 up to 1.5 times the Greenwald density is demonstrated using pellets. However, in this density range there is no indication of the positive confinement dependence on density implied by the ITERH98P(y,2) scaling.

Ion Temperature Measurements in the Tore Supra Scrape‐Off Layer Using a Retarding Field Analyzer

AbstractThe retarding field analyzer (RFA) is one of the only widely accepted diagnostics for measuring the ion tem‐perature Ti in the tokamak scrape‐off layer. An overview of the outstanding RFA performance over ten years of operation in Tore Supra tokamak is given and the validation of Ti measurements is addressed. The RFA measurements in Tore Supra are found to be well reproducible. The ion‐to‐electron temperature ratio is higher than one at low‐to‐moderate ion‐electron collisionality regime and converges to unity at high collisionality regime (© 2010 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Theoretical Modeling of Transport Barriers in Helical Plasmas

A unified transport model is proposed to study the physical mechanism for the formation of electron internal transport barriers (e-ITB) in helical plasmas and internal diffusion barriers (IDB) observed in the Large Helical Device (LHD). An e-ITB can be predicted with the effect of zonal flows (ZFs) in the low collisional regime when the radial variation in particle turbulent diffusivity is included. The transport analysis in this article shows that particle fueling induces IDB formation when the unified transport model is used in the high collisional regime. After particle fueling, a steep density gradient forms. To examine the density limit for the IDB in helical toroidal plasmas, the effect of radiation loss is included in a set of transport equations.

Stability and dynamics of the edge pedestal in the low collisionality regime: physics mechanisms for steady-state ELM-free operation

Understanding the physics of the edge pedestal and edge localized modes (ELMs) is of great importance for ITER and the optimization of the tokamak concept. The peeling–ballooning model has quantitatively explained many observations, including ELM onset and pedestal constraints, in the standard H-mode regime. The ELITE code has been developed to efficiently evaluate peeling–ballooning stability for comparison with observation and predictions for future devices. We briefly review recent progress in the peeling–ballooning model, including experimental validation of ELM onset and pedestal height predictions, and nonlinear 3D simulations of ELM dynamics, which together lead to an emerging understanding of the physics of the onset and dynamics of ELMs in the standard intermediate to high collisionality regime. We also discuss new studies of the apparent power dependence of the pedestal, and studies of the impact of sheared toroidal flow. Recently, highly promising low collisionality regimes without ELMs have been discovered, including the quiescent H-mode (QH) and resonant magnetic perturbation (RMP) regimes. We present recent observations from the DIII-D tokamak of the density, shape and rotation dependence of QH discharges, and studies of the peeling–ballooning stability in this regime. We propose a model of the QH-mode in which the observed edge harmonic oscillation (EHO) is a saturated kink/peeling mode which is destabilized by current and rotation, and drives significant transport, allowing a near steady-state edge plasma. The model quantitatively predicts the observed density dependence and qualitatively predicts observed mode structure, rotation dependence and outer gap dependence. Low density RMP discharges are found to operate in a similar regime, but with the EHO replaced by an applied magnetic perturbation.

Experimental observation of strong coupling effects on the dispersion of dust acoustic waves in a plasma

The dispersion properties of low frequency dust acoustic waves in the strong coupling regime are investigated experimentally in an argon plasma embedded with a mixture of kaolin and $MnO_2$ dust particles. The neutral pressure is varied over a wide range to change the collisional properties of the dusty plasma. In the low collisional regime the turnover of the dispersion curve at higher wave numbers and the resultant region of $\partial\omega/\partial k < 0$ are identified as signatures of dust-dust correlations. In the high collisional regime dust neutral collisions produce a similar effect and prevent an unambiguous identification of strong coupling effects.

Role of Kinetic Effects on the Polarization Current around a Magnetic Island

The polarization current due to a magnetic island rotating in a tokamak plasma is believed to play a central role in the initial evolution of the neoclassical tearing mode. Monte Carlo delta f simulations are performed which also cover a parameter range that is not amenable to analytic treatment but is relevant to experiments. It is shown that the polarization current can change sign when the island rotation frequency is of the order of the ion parallel streaming around the island. Moreover, the current is reduced when the island width is of the order of the ion banana width. Finally, the transition to the enhanced high-collisionality regime is shown to occur for collision frequencies higher than those typical of today's experiments.

Temperature dependence of the thermal diffusivity in high-collisionality regimes in the large helical device

The positive density dependence of energy confinement times, τE, as expressed in the international stellarator scaling 95 (ISS95), where ( is the line-averaged density and P is the heating power), declines in high-collisionality regimes in the large helical device experiments. In the low-collisionality regime, where parameter dependences in ISS95 agree well with the experiment, the temperature dependence of thermal diffusivity is as strong as predicted by the gyro-Bohm model and/or the neoclassical theory. As the collisionality increases to the plateau regime, the temperature dependence becomes moderate, where the thermal diffusivity is proportional to the square root of the electron temperature. Furthermore, the thermal diffusivity is inversely proportional to the magnetic field strength and the electron temperature gradient is proportional to the electron temperature in the high-collisionality regime. Compared with ISS95, the energy confinement time expected from these observations has a weaker density dependence together with mitigated power degradation: .

Electron Pressure Profiles in High-Density Neutral Beam Heated Plasmas in the Large Helical Device

In the Large Helical Device (LHD), electron pressure profiles in gas-fueled high-density discharges tend to have a similar shape, as if these were frozen. This frozen profile is insensitive to variations in the magnetic field strength and moderate changes in the neutral beam heat deposition profile. At the same time, however, the absolute value of the electron pressure itself increases with the heating power, the electron density, and the magnetic field strength. In this study, a reference model for the electron pressure is proposed which consists of the frozen profile and parametric dependences derived from experimental observations. It is possible to define an operational regime where this typical profile appears by comparing the electron pressure profiles with this model. In the standard configuration, at which the maximum plasma stored energy in LHD has been obtained, the frozen profile appears in the plateau to the Pfirsh-Schluter regimes. As the collisionality decreases to the collisionless regime, the electron pressure becomes smaller than the prediction of the model and the deterioration is significant in the plasma core region. This tendency is enhanced in the configuration with the outward-shifted magnetic axis. The global energy confinement time, τE, in the high-collisionality regime has a weaker density dependence together with the mitigated power degradation, scaling as τE∝nebar0.28P-0.43 (nebar and P are the line-averaged density and the heating power, respectively), compared with the International Stellarator Scaling 95, where τE∝nebar0.51P-0.59.

Theoretical interpretation of the toroidal rotation velocityobserved in Alcator C-Mod Ohmic H-mode discharges

It is shown that neoclassical theory explains quite well the origin of the co-current toroidal rotation velocity measured in the core of stationary Alcator C-Mod edge localized mode (ELM)-free Ohmic high confinement (H)-mode discharges. Both edge and core toroidal rotation velocity profiles are determined to a good approximation by the edge ion temperature and density pedestals, where the gradients are large and the plasma is in the high collisionality regime. Under these conditions, the predicted radial electric field profile is similar to those measured in the DIII-D tokamak whereas the usual expression for the poloidal velocity is modified by finite Larmor radius (FLR) effects. Over the entire plasma cross section, the expression of the toroidal velocity can approximately be cast as the product of a dimensionless non-local functional of the pedestal normalized profiles Ti(r)/Ti(rinf) and Ni(r)/Ni(rinf) with powers of the plasma density, temperature, safety factor and magnetic field at the pedestal inflexion point rinf provided the FLR related corrections are independent of the latter parameters. The collapse of the core toroidal rotation velocity when either an internal transport barrier forms (that leads to impurity accumulation), or the plasma experiences a transition from the H- to the low confinement (L)-mode, or ELMs appear, and the spin up at the L-H transition are also explained. In the edge region, power balance is consistent with the prediction from sub-neoclassical ion energy transport theory at high collisionality. The role of charge exchange neutrals is discussed and the critical density above which they are expected to noticeably slow down the rotation is estimated. The toroidal velocity gradient predicted by theory at the edge of the ELM-free Ohmic H-mode discharge mainly under study (qs = 3.4) is near the onset value for the Kelvin-Helmholtz (K-H) parallel velocity shear (PVS) instability; this result is very interesting since a transition from ELM-free to enhanced Dα (EDA) H-modes occurs at q≅3.5-4; the PVS K-H instability appears to have the characteristics of the `quasi-coherent' mode that is present in all EDA plasmas, but not in ELM-free H-modes.

Characteristics of radio frequency wave propagation in bounded plasma under the various magnetic field configurations

Detailed characteristics of radio frequency (rf) waves with pulsed modes in the whistler wave range were studied in a cylindrical rf-produced plasma, where the plasma boundary lay in the intermediate regime between infinite whistler wave propagation and bounded geometry helicon wave propagation. Excited magnetic field amplitudes and phases with three components in two-dimensional space were measured for different experimental conditions. Three magnetic field configurations were used and the diameter of the excitation loop antenna was also varied. Numerical calculation by the finite element method, which has been demonstrated to be a powerful means for this analysis, showed good agreement with the observed results, satisfying the dispersion relation and wave structures of helicons in the semisteady state and also satisfying the dispersion of whistlers with a short pulsed mode. The excited waves propagated nearly along the magnetic field lines within a small angle of less than 10°. Furthermore, in the low (high) collisionality regime, domination of standing (propagating) waves was found from the wave analysis.