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A systematic theoretical investigation has been carried out in order to explore the propagation of both linear and nonlinear dust acoustic waves (DAWs) in a collisional magnetized warm dusty plasma in the presence of nonextensive electrons and ions. A linear dispersion relation is analyzed to show that the wave frequencies of both parallel and perpendicular modes are modified by the relevant plasma parameters. The standard reductive perturbative technique leads to a Korteweg–de Vries equation with a linear damping term for the propagation dynamics of the finite amplitude waves in warm dusty plasma. It is found that the dust-neutral collision induced dissipation is responsible for the linear damping. The analysis reveals that DAW propagates in the form of a weakly dissipative compressive/rarefactive solitons and the nonlinear excitations are significantly influenced by different plasma parameters, such as dust concentration, nonextensivity, external magnetic field strength, and dust-neutral collisionality. The present results can be relevant to the DAWs in some astrophysical plasma environments, such as Saturn’s rings, interstellar dusty clouds, etc.

We demonstrate that testing for self-similarity in scale-free simulations provides an excellent tool to quantify the resolution at small scales of cosmological N-body simulations. Analysing two-point correlation functions measured in simulations using ABACUS, we show how observed deviations from self-similarity reveal the range of time and distance scales in which convergence is obtained. While the well-converged scales show accuracy below 1 percent, our results show that, with a small force softening length, the spatial resolution is essentially determined by the mass resolution. At later times the lower cut-off scale on convergence evolves in comoving units as $a^{-1/2}$ ($a$ being the scale factor), consistent with a hypothesis that it is set by two-body collisionality. A corollary of our results is that N-body simulations, particularly at high red-shift, contain a significant spatial range in which clustering appears converged with respect to the time-stepping and force softening but has not actually converged to the physical continuum result. The method developed can be applied to determine the resolution of any clustering statistic and extended to infer resolution limits for non-scale-free simulations., 15 pages, 9 figures, version published in MNRAS, small changes (more discussion of time-stepping)

openaire: EC/H2020/633053/EU//EUROfusion The bootstrap current profile in the tokamak pedestal is studied numerically using the plasma code ELMFIRE in neoclassical simulations with Joint European Torus-like parameters. The effect of a poloidally localized atom source on the bootstrap current is investigated while assuming that the ionization takes place in the pedestal region. A clear effect of poloidal source location is found within one poloidal Larmor radius for thermal particles. For cold particles, this poloidal dependence largely disappears. Without source, the simulated bootstrap current is compared to two different analytical estimates and their accuracy is tested in terms of gradient scale lengths and collisionality.

Using the 1D kinetic electron code SOL-KiT, simulations of the divertor tokamak scrape-off layer were carried out to explore the presence of kinetic effects in energy transfer between the ions and electrons. During steady-state conditions, it was found that the ion–electron energy transfer is well described by a fluid model, with only minimal differences seen when electrons are treated kinetically. During transient regimes (featuring a burst of energy into the scrape-off layer), we see evidence of enhanced energy exchange when calculated kinetically as compared to a fluid model. The kinetic correction represents an additional 8–55% ion–electron energy transfer across the domain, depending on the pre-transient plasma collisionality. Compared to the total energy going into the plasma during the transient, the correction is less than 1%, so its impact on plasma profiles may be small. The effect is seen to increase in strength along the domain, peaking in front of the divertor target. The overall discrepancy (integrated along the domain) increases during the transient energy burst and disappears on a similar timescale. However, at the target the effect peaks later and takes several multiples of the transient duration to relax. This effect may be only partially explained by an additional population of cold electrons arising from neutral ionization.

An optical diagnostic based on resonant absorption of laser light in a plasma is introduced and is used for the determination of density scale lengths in the range of 10 nm to >1 μm at the critical surface of an overdense plasma. This diagnostic is also used to extract the plasma collisional frequency, allowing inference of the temporally evolving plasma composition on the tens of femtosecond timescale. This is found to be characterized by two eras: the early time and short scale length expansion (L 0.1λ); this is consistent with a hydrogen plasma decoupling from the bulk target material. Density gradients and plasma parameters on this scale are of importance to plasma mirror optical performance and comment is made on this theme.

A new experiment, called the PHAse Space MApping (PHASMA) experiment, features laser induced fluorescence diagnostics for ion measurements, Thomson scattering diagnostics for electron velocity distribution function measurements, and a microwave scattering system for turbulence measurements. PHASMA is designed to enable the direct measurement of ion and electron vdfs in space-relevant plasma phenomena including reconnection, shocks, and turbulence. To create the conditions necessary for different experimental regimes, PHASMA employs a 2 kW, steady-state helicon source capable of generating variable-density background hydrogen, helium, argon, krypton, and xenon plasmas with controllable plasma pressure (relative to the magnetic pressure), collisionality, and azimuthal flow shear. Reconnecting flux ropes arise through the merging of discharges from two pulsed plasma guns.

In the outskirts of the intracluster medium (ICM) in galaxy clusters, the temperature decreases with radius. Due to the weakly collisional nature of the plasma, these regions are susceptible to the magneto-thermal instability (MTI), which can sustain turbulence and provide turbulent pressure support in the ICM. This instability arises due to heat conduction directed along the magnetic field, with a heat conductivity which is normally assumed to be given by the Spitzer value. Recent numerical studies of the ion mirror and the electron whistler instability using particle-in-cell codes have shown that microscale instabilities can lead to a reduced value for the heat conductivity in the ICM. This could in turn influence the efficiency with which the MTI drives turbulence. In this paper we investigate the influence of reduced heat transport on the nonlinear evolution of the MTI. We study plane-parallel, initially static atmospheres and employ a subgrid model that mimics the influence of the mirror instability on the heat conductivity. We use this subgrid model to assess the effect of microscales on the large scale dynamics of the ICM. We find that the nonlinear saturation of the MTI is surprisingly robust in our simulations. Over a factor of $\sim 10^3$ in the thermal-to-magnetic pressure ratio and collisionality we find at most modest changes to the saturation of the MTI with respect to reference simulations where heat transport is unsuppressed., Comment: 20 pages, 18 figures, accepted for publication in MNRAS

We generalize the low-gas-puff Heuristic Drift (HD) model of the power scrape-off layer width to take into account both the enhanced parallel confinement time in the SOL at high collisionality, due to enhanced thermal resistivity, and the increase of the upstream temperature at very low collisionality, due to finite target temperature. We find a wide range of separatrix densities over which the original HD model is applicable. However, at the region of high separatrix density and collisionality accessible with strong gas puffs the SOL widens, in reasonable agreement with experimental data from ASDEX-Upgrade and JET. We further find that for typical low-gas-puff H-mode conditions, the projected E × B flow shearing rate in the SOL dominates over the interchange growth rate, while at the high separatrix densities at which H-Modes return to L-Mode, the interchange growth rate approximately equals the shearing rate. The result is related to that of Halpern and Ricci with respect to the steep gradient region of the SOL of inner-wall-limiter discharges, which also show HD-like scale lengths. It is also consistent with calculations of shear-flow stabilization of interchange modes by Zhang and Krasheninnikov. Taking ω s > γ int as the criterion for retaining H-Mode performance, we use the generalized HD (GHD) model to predict the scaling for the H → L back transition. The power requirements to sustain H-Mode for existing machines and for ITER are in the range of a factor of 2 below the predictions for the L → H transition, consistent with the limited available studies of H-Mode hysteresis. We find reasonable agreement with the scaling of the density at the H → L back transition found by Bernert on ASDEX-Upgrade. Finally, we speculate that the shearing rate in the SOL of H-Mode plasmas contributes to the reduced core turbulence that supports the formation of the H-Mode pedestal and comment on the implications for ITER.

In this article, a comprehensive investigation of the linear and nonlinear waves’ structure in an unmagnetized plasma consisting of nonextensive electrons, considering collisionality and kinematic viscosity effects, is studied. Using a reductive perturbation technique, we have derived a hybrid Korteweg–de Vries–Burgers equation for ion-acoustic (IA) waves. Analytical solutions for solitary waves and shock structures are obtained. We have also solved this equation numerically in order to investigate the basic properties of solitary/shock waves in such a plasma system. The presence of nonextensive electrons with $q$ -distribution influences significantly the solitary and shock wave structures. In other words, the compressive and rarefactive-type solitons or shock waves can also be seen in this plasma model depending on the strength of nonextensivity. On the other hand, the effects of ion-neutral collision and ion kinematic viscosity on the characteristics of IA solitary/shock waves are discussed. It is found that these parameters modify the basic features of the solitonic and shock excitations.

Determination of the particle charge in aerosols and dusty plasmas requires an accurate calculation of the particle-ion collision kernel taking into account the particle-ion Coulombic coupling and ion-neutral gas molecule collisions. While the effect of Coulombic interactions of any strength is described accurately in the continuum limit and free molecular limit, an accurate physical description at intermediate collisional regimes remains elusive. Specifically, the Coulomb influenced collisions between oppositely charged particles and ions have evaded accurate theoretical description in the past. We use Langevin dynamics (LD) calculations to infer the non-dimensional collision kernel H as a function of the electrostatic potential energy to thermal energy ratio ΨE and the diffusive Knudsen number KnD, the index of ion-neutral collisionality in a finite pressure system. The LD approach yields a simple, approximate treatment of particle charging in the entire ion-neutral collision regime under the assumption that Z≡mimg→∞, where mi is the mass of an ion and mg is the mass of the background gas molecules. We show that the Gumbel distribution accurately describes the underlying distribution of H calculated using LD. The effect of high ion concentrations (at which screening of particle by free charges in space is important) on H is parameterized through a non-dimensional screening length parameter SD. Analysis of the dependence of the distribution parameters on ΨE, KnD, and SD leads to a regression for H that is valid for 0

The Lithium Tokamak eXperiment (LTX) is a spherical tokamak device designed to study lithium plasma facing components (PFCs). The lithium coated wall of LTX has been demonstrated to produce a plasma edge with high electron temperature (200 eV or greater). Plasma density in the outer scrape-off layer (SOL) is also found to be very low, around 2 × 1017m-3, as a result of the low recycling lithium boundary. The high temperature, low collisionality region of the plasma extends into the SOL. The recent upgrade to LTX-β includes installation of a neutral beam, which will provide further heating and fueling of the core plasma. Core and edge diagnostics will also be expanded. As part of this expansion, a Retarding Field Energy Analyzer (RFEA) has been developed for the SOL of LTX-β. Measurements of the ion temperature, ion energy distribution, and the local space potential will be performed in the SOL plasma using this RFEA. Upgraded high field side (HFS) and low field side (LFS) Langmuir probes will replace existing triple probes so that higher electron temperatures can be more reliably measured. The HFS probes are also positioned to give radial and vertical gradient measurements. The design of the RFEA will be presented, along with calibration data.Since a high temperature, low collisional edge is expected for LTX-β, with a high mirror ratio near the LCFS (around 4), the majority of particles in the SOL will be mirror-trapped. Trapped particle effects will therefore become significant in the physics of the SOL plasma, and warrant further theoretical investigations. Here we present a theoretical study of the ambipolar potential formed in the collisionless SOL via differential loss of the electrons and ions, known as the Pastukhov potential in the literature. Numerical results will also be presented. Keywords: Lithium PFC, Scrape off layer, Ambipolar potential, Retarding field energy analyzer

This article reports on 1D+2V heat pulse propagation studies using the COGENT guiding center kinetic code. The model uses magnetized kinetic ions and a simple Boltzmann electron model. Results agree with previous kinetic and fluid modeling benchmark studies that correspond to the parameters of edge localized modes (ELMs) observed on the JET tokamak. The plasma parameters for the edge pedestal and ensuing ELM dynamics are in the low collisionality regime. Hence, the dominant balance between the assumed Maxwellian ELM source and collisionless parallel advection causes the ion PDF to develop a significantly anisotropic velocity distribution. Adding nonlinear Coulomb ion-ion collisions to the model acts to smooth the sharp features of the ion distribution function, but the anisotropy remains robust due to the low collisionality. 2010 MSC: 00-01, 99-00, Kinetic theory, Vlasov equation, Magnetic fusion energy, Tokamak, Edge localized mode

Non-adiabatic electron response leads to significant changes in ion temperature gradient (ITG) eigenmodes, leading, in particular, to fine-structures that are significantly extended along the magnetic field lines at corresponding mode rational surfaces (MRSs). These eigenmodes can nonlinearly interact with themselves to drive zonal flows via the so-called self-interaction mechanism. In this paper, the effect of collisions on these processes are studied. In the presence of non-adiabatic electrons, the linear growth rate of ITG eigenmodes decreases with the increasing collisionality. Detailed velocity space analysis of the distribution function shows that this results from collisions leading to a more adiabatic-like response of electrons away from MRSs. In linear simulations, collisions are furthermore found to broaden the radial width of the fine-structures, which translates to narrower tails of the eigenmode in extended ballooning space. The characteristic parallel scale length associated with these tails is shown to scale with the mean free path of electrons. In nonlinear turbulence simulations accounting for physically relevant values of collisionality, the fine-structures located at MRSs, together with the associated drive of zonal flows via self-interaction, are shown to persist and play a significant role. Published under an exclusive license by AIP Publishing.

Studies have shown that in sheared $\mathbf{E}\times\mathbf{B}$ flows in an inhomogeneous ionospheric plasma, the gradient drift (GDI) or the Kelvin-Helmholtz (KHI) instability may grow. This work examines the conditions that cause one of these instabilities to dominate over the other using a novel model to study localized ionospheric instabilities. The effect of collisions with neutral particles plays an important role in the instability development. It is found that the KHI is dominant in low collisionality regimes, the GDI is dominant in high collisionality regimes, and there exists an intermediate region in which both instabilities exist in tandem. For low collisionality cases in which the velocity shear is sufficiently far from the density gradient, the GDI is found to grow as a secondary instability extending from the KHI vortices. The inclusion of a neutral wind driven electric field in the direction of the velocity shear does not impact the dominance of either instability. Using data from empirical ionospheric models, two altitude limits are found. For altitudes above the higher limit, the KHI is dominant. For altitudes below the lower limit, the GDI is dominant. In the intermediate region, both instabilities grow together. Increasing the velocity shear causes both limits to be lower in altitude. This implies that for ionospheric phenomena whose density and velocity gradients span large altitude ranges, such as subauroral polarization streams, the instabilities observed by space-based and ground-based observation instruments could be significantly different., 14 pages, 8 figures

The velocity dependent resonant interaction of particles with applied radiofrequency (rf) waves during heating and current drive in the presence of pitch angle scattering collisions gives rise to narrow collisional velocity space boundary layers that dramatically enhance the role of collisions as recently shown by Catto (J. Plasma Phys., vol. 86, 2020, 815860302). The behaviour is a generalization of the narrow collisional boundary layer that forms during Landau damping as found by Johnston (Phys. Fluids, vol. 14, 1971, pp. 2719–2726) and Auerbach (Phys. Fluids, vol. 20, 1977, pp. 1836–1844). For a wave of parallel wave number ${k_{||}}$ interacting with weakly collisional plasma species of collision frequency $\nu$ and thermal speed ${v_{\textrm{th}}}$ , the effective collision frequency becomes of order $\nu {({k_{||}}{v_{th}}/\nu )^{2/3}} \gg \nu $ . The narrow boundary layers that arise because of the diffusive nature of the collisions allow a physically meaningful wave–particle interaction time to be defined that is the inverse of this effective collision frequency. The collisionality implied by the narrow boundary layer results in changes in the standard quasilinear treatment of applied rf fields in tokamaks while remaining consistent with causality. These changes occur because successive poloidal interactions with the rf are correlated in tokamak geometry and because the resonant velocity space dependent interactions are controlled by the spatial and temporal behaviour of the perturbed full wave fields rather than just the spatially local Landau and Doppler shifted cyclotron wave–particle resonance condition associated with unperturbed motion of the particles. The correlation of successive poloidal circuits of the tokamak leads to the appearance in the quasilinear operator of transit averaged resonance conditions localized in velocity space boundary layers that maintain negative definite entropy production.

An encoder–decoder neural network has been used to examine the possibility for acceleration of a partial integro-differential equation, the Fokker–Planck–Landau collision operator. This is part of the governing equation in the massively parallel particle-in-cell code XGC, which is used to study turbulence in fusion energy devices. The neural network emphasizes physics-inspired learning, where it is taught to respect physical conservation constraints of the collision operator by including them in the training loss, along with the $\ell _2$ loss. In particular, network architectures used for the computer vision task of semantic segmentation have been used for training. A penalization method is used to enforce the ‘soft’ constraints of the system and integrate error in the conservation properties into the loss function. During training, quantities representing the particle density, momentum and energy for all species of the system are calculated at each configuration vertex, mirroring the procedure in XGC. This simple training has produced a median relative loss, across configuration space, of the order of $10^{-4}$ , which is low enough if the error is of random nature, but not if it is of drift nature in time steps. The run time for the current Picard iterative solver of the operator is $O(n^2)$ , where $n$ is the number of plasma species. As the XGC1 code begins to attack problems including a larger number of species, the collision operator will become expensive computationally, making the neural network solver even more important, especially since its training only scales as $O(n)$ . A wide enough range of collisionality has been considered in the training data to ensure the full domain of collision physics is captured. An advanced technique to decrease the losses further will be subject of a subsequent report. Eventual work will include expansion of the network to include multiple plasma species.

Secondary low frequency mode generation by energetic particle induced geodesic acoustic mode (EGAM) observed in LHD experiment is studied using nonlinear gyrokinetic theory. It is found that the EGAM frequency can be significantly higher than local geodesic acoustic mode (GAM) frequency in low collisionality plasmas, and it can decay into two GAMs as its frequency approaches twice GAM frequency, in a process analogous to the well-known two plasmon decay instability. The condition for this process to occur is also discussed., 14 pages, 2 figs

A model of ion temperature anisotropy for 2D plasma transport in the scrape-off layer (SOL) of tokamaks is described and implemented in the UEDGE fluid transport code. Two ion energy equations are used to describe the evolution of the separate parallel and perpendicular ion temperatures. The temperature anisotropy generates viscous forces in both parallel and perpendicular directions that modify the parallel force balance equation and add an additional cross-magnetic-field drift velocity. Using the full set of UEDGE plasma and neutral equations (particle continuity, momentum, and energy), simulations are performed for both a 1D poloidal case and a 2D (radial and poloidal) single-null tokamak geometry case to highlight the 2D effects. The results show that ion parallel flows near the magnetic X-point in a comparatively low collisionality regime can be overestimated by the standard isotropic Braginskii model. The 2D ion temperature anisotropy varies substantially near the X-point and also near the divertor target plates, due to ionization sources. Moving radially outwards at the outer midplane, the anisotropy decreases between the core boundary and the magnetic separatrix and then it increases while moving across the SOL to the chamber wall.

The saturation physics of ion-temperature-gradient-driven turbulence is examined in relation to the temperature-gradient variation of the heat flux, which can exhibit an upshift of the critical gradient for significant flux relative to the linear instability threshold. Gyrokinetic measurements of saturation properties and spectral energy transfer, which will be defined in Sec. , are presented, indicating that the physics of saturation is fundamentally unchanged on either side of the upshifted gradient. To analyze heat transport below and above the upshifted critical gradient, a fluid model for toroidal ion-temperature-gradient turbulence is modified to include the kinetic instability threshold. The model and the heat flux are rendered in the eigenmode decomposition to track the dominant mode-coupling channel of zonal-flow-catalyzed transfer to a conjugate stable mode. Given linear and nonlinear symmetries, the stable mode level and the cross-correlation of the unstable and stable mode amplitudes are related to the unstable mode level via linear physics. The heat flux can then be written in terms of the unstable-mode level, which through a nonlinear balance depends on the eigenmode-dependent coupling coefficients and the triplet correlation time of the dominant coupled modes. Resonance in these quantities leads to suppressed heat flux above the linear threshold, with a nonlinear upshift of the critical gradient set by the resonance broadening of a finite perpendicular wavenumber and collisionality.

The optimized stellarator Wendelstein 7-X (W7-X) is designed to have an approximately quasi-isodynamic magnetic configuration with reduced neoclassical transport in comparison to a classical stellarator, and turbulent transport is expected to be a significant source of anomalous heat transport across the plasma minor radius. The ion temperature gradient driven mode and the trapped electron mode (TEM) are thought to be responsible for the ion-scale turbulence in W7-X plasmas with volume averaged pressure below 1%. In this work, the electron temperature gradient driven turbulence is shown to be a good candidate for the explanation of the observed electron heat flux, in the inner plasma region where the density gradient is weak (in the outer region, a relatively stronger density gradient would drive additional TEM turbulence). The experimental electron heat transport measured during electron cyclotron resonant heating power and plasma density scans is compared to neoclassical predictions, and the stiffness in the electron heat transport measured during transient transport experiments is presented in three common magnetic configurations of W7-X. In low-⟨β⟩ plasma discharges, the stiffness in the electron heat flux, quantified by the ratio of the heat pulse to power balance diffusivity, χ e H P / χ e P B , is measured to be less than 2, and trend downwards with increasing collisionality.

This work presents a fast and robust method for optimizing the stationary radial distribution of temperature, density and parallel current density in a tokamak plasma and its application to first-principle-based modeling of the ITER hybrid scenario. A new solver is implemented in the RAPTOR transport code, enabling direct evaluation of the stationary solution to which the radial plasma profiles evolve. Coupled to a neural network emulation of the quasi-linear gyrokinetic QuaLiKiz transport model (QLKNN-hyper-10D), a first-principle-based estimate of the stationary state of the core plasma can be found at unprecedented computational speed (typically a few seconds on standard hardware). The stationary state solver is then embedded in a numerical optimization scheme, allowing the optimization of tokamak plasma scenarios in only a few minutes. The proposed method is applied to investigate the performance of ITER hybrid scenarios at different values of total plasma current, plasma density and pedestal height and for different power contributions in a heating mix consisting of electron cyclotron and neutral beam heating. Optimizing the radial distribution of electron cyclotron current drive (ECCD) deposition, the q profile is tailored to maximize the fusion gain Q, by maximizing the energy confinement predicted through the first-principles-based transport model, while satisfying q > 1, avoiding sawtooth oscillations. It is found that optimal use of ECCD in ITER hybrid scenarios is to deposit power as close to the core as possible, while maintaining sufficient off-axis current drive to keep q above 1. Upper limits for the fusion gain Q are shown to be constrained either by minimum power requirements for the separatrix power flow to maintain H-mode or by minimum current drive requirements for q profile tailoring. Finally, it is shown that the ITER hybrid scenario operating window is significantly extended by an upgrade of the electron cyclotron power to 40 MW.

Ion attachment and ion drag to dust particles near the edge of a nonthermal plasma sheath are of interest to better understand how particles become trapped in such sheath regions. While electron-particle collisions in plasmas and sheaths can often be described by orbital motion limited theory, quantification of ion transport about dust particles in collisional sheath regions requires a distinct modeling approach. In this work, the dimensionless ion attachment coefficients and dimensionless collection forces on negatively charged particles are calculated using ion trajectory models accounting for an external electric field in a collisional sheath, ion inertia, and finite ion mobility. By considering both ion inertia and finite ion mobility, results apply for ion transport from the fully collisional regime into a regime of intermediate collisionality. Ion collection forces are calculated in two related limits; first, the nondissipative limit, wherein the dimensionless collection force function coincides with the dimensionless attachment coefficient (anticipated in the collisionless regime), and second, a dissipative limit, wherein neutral gas collisions dissipate ion momentum, which strongly affects the resulting collection force (anticipated in the fully collisional regime). We show that ion motion about a charged particle can be parametrized by the ion Stokes number, which is the ratio of ion inertia to gas resistance to motion and dimensionless electric field strength (the external field strength normalized by the electric field at the particle surface). At intermediate Stokes numbers (${10}^{1}--{10}^{2}$), ions adopt trajectories that are extremely sensitive to the initial ion-particle impact parameter. Plots of the resulting collision angle at fixed Stokes number and dimensionless field strength as a function of impact parameter contain multiple discontinuities. Nonetheless, we obtain smooth curves for the ion attachment rates and collection forces in both the nondissipative and fully dissipative limits. Increasing the ion Stokes number is found to significantly decrease the dimensionless ion attachment coefficients and ion collection forces in comparison to coefficients evaluated with expressions derived in the fully collisional limit. In all instances, including the dissipative limit, we find the ion collection force acts in the direction of ion migration. Neural network fits are utilized to parametrize the resulting attachment coefficients and ion collection forces, and we apply these fits to examine the charge levels on 1-\ensuremath{\mu}m radius particles in external fields in the $3\ifmmode\times\else\texttimes\fi{}{10}^{2}--3\ifmmode\times\else\texttimes\fi{}{10}^{3}\phantom{\rule{0.16em}{0ex}}\mathrm{V}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{\ensuremath{-}1}$ range and pressures in the $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}1}--5\ifmmode\times\else\texttimes\fi{}{10}^{1}$ Torr (66.7--6667 Pa) range. We find the charge level is strongly sensitive to both field strength and pressure in the plasma sheath, ranging from 6 \ifmmode\times\else\texttimes\fi{} ${10}^{3}$ to 1.8 \ifmmode\times\else\texttimes\fi{} ${10}^{4}$ over the conditions examined. Calculations are also used to demonstrate that the ion collection force can be sufficiently strong to trap particles not only close to the bottom electrode of a parallel-plate reactor, but also close to the top electrode, with a critical ion density required for trapping.

The excitation of low frequency dust acoustic (or dust density) waves in a dusty plasma can be driven by the flow of ions relative to dust. We consider the nonlinear development of the ion–dust streaming instability in a highly collisional plasma, where the ion and dust collision frequencies are a significant fraction of their corresponding plasma frequencies. This collisional parameter regime may be relevant to dusty plasma experiments under microgravity or ground-based conditions with high gas pressure. One-dimensional particle-in-cell simulations are presented, which take into account collisions of ions and dust with neutrals, and a background electric field that drives the ion flow. Ion flow speeds of the order of a few times thermal are considered. Waveforms of the dust density are found to have broad troughs and sharp crests in the nonlinear phase. The results are compared with the nonlinear development of the ion–dust streaming instability in a plasma with low collisionality.

A method of Parity-Time (PT)-symmetry analysis is introduced to study the high dimensional, complicated parameter space of drift wave instabilities. We show that spontaneous PT-symmetry breaking leads to the Ion Temperature Gradient (ITG) 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.

The isotope dependence of plasma transport will have a significant impact on the performance of future D-T experiments in JET and ITER and eventually on the fusion gain and economics of future reactors. In preparation for future D-T operation on JET, dedicated experiments and comprehensive transport analyses were performed in H, D and H-D mixed plasmas. The analysis of the data has demonstrated an unexpectedly strong and favourable dependence of the global confinement of energy, momentum and particles in ELMy H-mode plasmas on the atomic mass of the main ion species, the energy confinement time scaling as ${\tau _E}\sim {A^{0.5}}$ (Maggi et al., Plasma Phys. Control. Fusion, vol. 60, 2018, 014045; JET Team, Nucl. Fusion, vol. 39, 1999, pp. 1227–1244), i.e. opposite to the expectations based only on local gyro-Bohm (GB) scaling, ${\tau _E}\sim {A^{ - 0.5}}$ , and stronger than in the commonly used H-mode scaling for the energy confinement (Saibene et al., Nucl. Fusion, vol. 39, 1999, 1133; ITER Physics Basis, Nucl. Fusion, vol. 39, 1999, 2175). The scaling of momentum transport and particle confinement with isotope mass is very similar to that of energy transport. Nonlinear local GENE gyrokinetic analysis shows that the observed anti-GB heat flux is accounted for if collisions, E × B shear and plasma dilution with low-Z impurities (9Be) are included in the analysis (E and B are, respectively the electric and magnetic fields). For L-mode plasmas a weaker positive isotope scaling ${\tau _E}\sim {A^{0.14}}$ has been found in JET (Maggi et al., Plasma Phys. Control. Fusion, vol. 60, 2018, 014045), similar to ITER97-L scaling (Kaye et al., Nucl. Fusion, vol. 37, 1997, 1303). Flux-driven quasi-linear gyrofluid calculations using JETTO-TGLF in L-mode show that local GB scaling is not followed when stiff transport (as is generally the case for ion temperature gradient modes) is combined with an imposed boundary condition taken from the experiment, in this case predicting no isotope dependence. A dimensionless identity plasma pair in hydrogen and deuterium L-mode plasmas has demonstrated scale invariance, confirming that core transport physics is governed, as expected, by the 4 dimensionless parameters ρ*, ν*, β, q (normalised ion Larmor radius, collisionality, plasma pressure and safety factor) consistently with global quasi-linear gyrokinetic TGLF calculations (Maggi et al., Nucl. Fusion, vol. 59, 2019, 076028). We compare findings in JET with those in different devices and discuss the possible reasons for the different isotope scalings reported from different devices. The diversity of observations suggests that the differences may result not only from differences affecting the core, e.g. heating schemes, but are to a large part due to differences in device-specific edge and wall conditions, pointing to the importance of better understanding and controlling pedestal and edge processes.

Absorbance of normally incident electromagnetic wave on a cold, weakly collisional, and inhomogeneous magnetoplasma slab is investigated. The plasma density is Budden-like sinusoidal profile, where the inhomogeniety is treated as a multilayered system of homogeneous sub-cells within the transfer matrix technique. For incident wave frequencies much above the ion cyclotron frequency, only right hand circularly polarized waves are relevant for wave propagation parallel to a static magnetic field. Calculations are performed in normalized parameters, that make the results suitable for many applications including atmospheric and laboratory plasmas. The presence of the dc-magnetic field leads to the formation of two absorption bands explained by plasma collisional dissipation and electron cyclotron resonance in the low frequency branch of the $R$-wave below the electron cyclotron frequency. The transmittance shows the emergence of the low frequency electron cyclotron wave, which becomes a Whistler mode at very low frequency. More detailed discussion on the effect of plasma collisionality, inhomogeneity, and dc-magnetic field on the propagation characteristics is given at the relevant place within the body of the manuscript.

We report on a detailed study of magnetic fluctuations in the JET pedestal, employing basic theoretical considerations, gyrokinetic simulations, and experimental fluctuation data to establish the physical basis for their origin, role, and distinctive characteristics. We demonstrate quantitative agreement between gyrokinetic simulations of microtearing modes (MTMs) and two magnetic frequency bands with corresponding toroidal mode numbers n = 4 and 8. Such disparate fluctuation scales, with substantial gaps between toroidal mode numbers, are commonly observed in pedestal fluctuations. Here we provide a clear explanation, namely the alignment of the relevant rational surfaces (and not others) with the peak in the ω * profile, which is localized in the steep gradient region of the pedestal. We demonstrate that a global treatment is required to capture this effect. Nonlinear simulations suggest that the MTM fluctuations produce experimentally-relevant transport levels and saturate by relaxing the background electron temperature gradient, slightly downshifting the fluctuation frequencies from the linear predictions. Scans in collisionality are compared with a simple MTM dispersion relation. At the experimental points considered, MTM growth rates can either increase or decrease with collision frequency depending on the parameters thus defying any simple characterization of collisionality dependence.

The turbulence-induced quasi-linear particle flux of a highly-charged, collisional impurity species is calculated from the electrostatic gyrokinetic equation including collisions with the bulk ions and the impurities themselves. The equation is solved by an expansion in powers of the impurity charge number $Z$. In this formalism, the collision operator only affects the impurity flux through the dynamics of the impurities in the direction parallel to the magnetic field. At reactor-relevant collisionality, the parallel dynamics is dominated by the parallel electric field, and collisions have a minor effect on the turbulent particle flux of highly-charged, collisional impurities., Comment: 10 pages

The structure of the edge plasma in a magnetic confinement system has a strong impact on the overall plasma performance. We uncover for the first time a magnetic-field-direction dependent density shelf, i.e., local flattening of the density radial profile near the magnetic separatrix, in high confinement plasmas with low edge collisionality in the DIII-D tokamak. The density shelf is correlated with a doubly peaked density profile near the divertor target plate, which tends to occur for operation with the ion $B\ifmmode\times\else\texttimes\fi{}\ensuremath{\nabla}B$ drift direction away from the $X$-point, as currently employed for DIII-D advanced tokamak scenarios. This double-peaked divertor plasma profile is connected via the $E\ifmmode\times\else\texttimes\fi{}B$ drifts, arising from a strong radial electric field induced by the radial electron temperature gradient near the divertor target. The drifts lead to the reversal of the poloidal flow above the divertor target, resulting in the formation of the density shelf. The edge density shelf can be further enhanced at higher heating power, preventing large, periodic bursts of the plasma, i.e., edge-localized modes, in the edge region, consistent with ideal magnetohydrodynamics calculations.

The expansion of plasma with non-parallel temperature and density gradients, and the generation of magnetic field via the Biermann battery is modeled using particle-in-cell simulations that include collisional effects via Monte Carlo methods. A scaling of the degree of collisionality shows that an anisotropy can be produced, and drive the Weibel instability, for gradient scales shorter than the mean free path. For larger collision rates, the Biermann battery dominates as the cause of magnetic field generation. When the most energetic particles remain collisionless, the Nernst effect causes the Biermann field to be dragged with the heat flux, piled up, and enhanced., 6 pages, 4 figures

The results of flux-driven, two-fluid simulations in single-null configurations are used to investigate the processes determining the turbulent transport in the tokamak edge. Three turbulent transport regimes are identified: (i) a developed transport regime with turbulence driven by an interchange instability, which shares a number of features with the standard L-mode of tokamak operation; (ii) a suppressed transport regime, characterized by a higher value of the energy confinement time, low-amplitude relative fluctuations driven by a Kelvin–Helmholtz instability, a strong $\boldsymbol {E}\times \boldsymbol {B}$ sheared flow and the formation of a transport barrier, which recalls the H-mode; and (iii) a degraded confinement regime, characterized by a catastrophically large interchange-driven turbulent transport, which recalls the crossing of the Greenwald density limit. We derive an analytical expression of the pressure gradient length in the three regimes. The transition from the developed transport regime to the suppressed transport regime is obtained by increasing the heat source or decreasing the collisionality and vice versa for the transition from the developed transport regime to the degraded confinement regime. An analytical expression of the power threshold to access the suppressed transport regime, linked to the power threshold for H-mode access, as well as the maximum density achievable before entering the degraded confinement regime, related to the Greenwald density, are also derived. The experimental dependencies of the power threshold for H-mode access on density, tokamak major radius and isotope mass are retrieved. The analytical estimate of the density limit contains the correct dependence on the plasma current and on the tokamak minor radius.

The saturated state of turbulence driven by the ion-temperature-gradient instability is investigated using a two-dimensional long-wavelength fluid model that describes the perturbed electrostatic potential and perturbed ion temperature in a magnetic field with constant curvature (a $Z$-pinch) and an equilibrium temperature gradient. Numerical simulations reveal a well-defined transition between a finite-amplitude saturated state dominated by strong zonal-flow and zonal-temperature perturbations, and a blow-up state that fails to saturate on a box-independent scale. We argue that this transition is equivalent to the Dimits transition from a low-transport to a high-transport state seen in gyrokinetic numerical simulations. A quasi-static staircase-like structure of the temperature gradient intertwined with zonal flows, which have patch-wise constant shear, emerges near the Dimits threshold. The turbulent heat flux in the low-collisionality near-marginal state is dominated by turbulent bursts, triggered by coherent long-lived structures closely resembling those found in gyrokinetic simulations with imposed equilibrium flow shear. The break up of the low-transport Dimits regime is linked to a competition between the two different sources of poloidal momentum in the system -- the Reynolds stress and the advection of the diamagnetic flow by the $\boldsymbol{E}\times\boldsymbol{B}$ flow. By analysing the linear ITG modes, we obtain a semi-analytic model for the Dimits threshold at large collisionality., 63 pages, 30 figures, to be submitted to J. Plasma Phys

openaire: EC/H2020/633053/EU//EUROfusion Most auxiliary heating methods provide heating to more than one particle species (electrons, ions, impurities) in a fusion plasma. This can lead to substantial temperature differences between species, depending on conditions such as heating power to the different species and collisionality, with temperature differences between species limited by inter-species thermal equipartition and transport. The analysis of the steady-state electron-ion and impurity-ion power balances presented in this paper are used for consistency-checking experimental ion and electron temperature measurements and for inferring the main ion temperature from measured impurity temperatures. As ion temperature measurements by charge exchange spectroscopy (CXS) based on impurity ions have become more difficult and time-consuming since the installation of the ITER-like wall (ILW) with Be and W PFC's, knowing the maximum sustainable temperature difference between ions and electrons, |T i - T e| allows rejecting erroneous measurements. It alsoobviates the need for an ion temperature measurement, if an electron temperature measurement is available and |T i - T e| cannot be larger than the combined errors of the underlying measurements. A power balance analysis is also required for estimating the errors of the ion and electron heat fluxes prior to any species-resolved transport analysis. The ion-impurity temperature differences are usually found to be small due to strong thermal equipartition between ion species. However, they can approach 10% in JET-ILW low density, high power discharges, such the ones under development for a future JET deuterium-tritium campaign (Joffrin et al 2019 Nucl. Fusion). This has a generally small, but not always negligible effect on the calculation of fusion reaction rates, which depend on main ion temperatures. An important outcome of this analysis is that temperature differences between impurity species are always much smaller than between the impurities and hydrogenic species and can usually be neglected. The paper presents two methods for calculating the impurity-to-main ion temperature ratio. Finally, this analysis leads to a method for the reconstruction ion temperature profiles from ion temperature data available at only one or a small number of spatial locations.

Currently there is considerable interest in creating scalable laboratory plasmas to study the mechanisms behind the formation and evolution of astrophysical phenomena such as Herbig-Haro objects and supernova remnants. Laboratory-scaled experiments can provide a well diagnosed and repeatable supplement to direct observations of these extraterrestrial objects if they meet similarity criteria demonstrating that the same physics govern both systems. Here, we present a study on the role of collision and cooling rates on shock formation using colliding jets from opposed conical wire arrays on a compact pulsed-power driver. These diverse conditions were achieved by changing the wire material feeding the jets, since the ion-ion mean free path (λ_{mfp-ii}) and radiative cooling rates (P_{rad}) increase with atomic number. Low Z carbon flows produced smooth, temporally stable shocks. Weakly collisional, moderately cooled aluminum flows produced strong shocks that developed signs of thermal condensation instabilities and turbulence. Weakly collisional, strongly cooled copper flows collided to form thin shocks that developed inconsistently and fragmented. Effectively collisionless, strongly cooled tungsten flows interpenetrated, producing long axial density perturbations.

We show that, under Braginskii magneto-hydrodynamics, anti-parallel gradients in average ion charge state and electron temperature can be unstable to the growth of self-generated magnetic fields. The instability is analogous to the field-generating thermomagnetic instability, although it is driven by the collisional thermal force magnetic source term rather than the Biermann battery term. The gradient in ion charge state causes a gradient in collisionality, which couples with temperature perturbations to create a self-generated magnetic field. This magnetic field deflects the electron heat flux in a way that reinforces the temperature perturbation. The derived linearized growth rate, typically on hydrodynamic timescales, includes the resistive and thermal smoothing. It increases with large ion composition gradients and electron heat flux, conditions typical of the hohlraum walls or contaminant mix jets in inertial confinement fusion implosions. However, extended magneto-hydrodynamic simulations indicate that the instability is usually dominated and stabilized by the nonlinear Nernst advection, in a similar manner to the standard thermomagnetic instability.

We report experimental results on merging of hypersonic plasma jets, which is the fundamental building block for forming spherically imploding plasma liners as a potential standoff compression driver for mangeto-inertial fusion. Jets are formed and launched by contoured-gap coaxial plasma guns mounted at the six spherical chamber. First, from experiments with two and three merging jets of four different species (N, Ar, Kr, Xe), we show that (1) density spatial non-uniformities can be large (with electron-density jumps ranging from 2.9 for N to 6.6 for Xe) when shocks form upon jet merging, but smaller (density jumps 10), as required for plasma liners to be an effective compression driver. Second, from experiments with six and seven merging jets using Ar, we present results with improved jet-to-jet balance of, 17 pages, 19 figures, submitted to Physics of plasma

We combine different measurements of the polytropic index of the proton plasma in the heliosphere: i) near-adiabatic index in the inner heliosphere ~1AU, ii) subadiabatic indices in the outer heliosphere ~20-40AU, and iii) near-zero indices in the inner heliosheath. These observations are unified by a single theoretical model of the polytropic index throughout its radial extent in the heliosphere; the corresponding fitting reveals the decreasing trend of the polytropic index with increasing heliocentric distance R. We anticipate that with increasing R, (i) the Debye length and mean-free-path decreases; (ii) the Landau damping is less effective, transferring thus less wave energy to particles; and (iii) the collisionality degree increases, indicating that the proton plasma in the inner heliosheath might be collisionless., Comment: 5 pages, 1 figure; to appear in RNAAS

The accompanying files contain digital data for the figures in the article "Comparison of edge turbulence characteristics between DIII-D and C-Mod simulations with XGC1", submitted for publication to the Physics of Plasmas journal. The files are in txt format, organized in columns where the first row corresponds to column headers with self-explanatory titles. The filenames contain in parentheses the figure number. Most figures are of the x vs. y format. Some figures (2a,2b,3a,3b,5b,5d,6a,6b,7a,7b,9) are drawn using data from two separate files. In these cases the x axis is common. Figures 4a,4c,5a,5c are vector field plots therefore, the x and y components of the vector fields (in these cases, the equilibrium and turbulent ExB fluxes) need to be added vectorially to obtain the arrows' length. Figures 4b,4d are contour plots. Figures 11a,11b,12a,12b are plots of distributions and the data provided in the text file are the actual distribution samples from which the distributions are calculated. Data for figures 1a,1c, 10 and 13 are not provided. Figure 10 is used only to pictorially display an example of the blob detection algorithm and is not used for any results or conclusions. It is constructed directly with simulation data. Figure 13 is drawn, not calculated, as a cartoon for explaining the blob size calculation method. Figures 1a, 1c are plots from the EFIT files used for the simulations. The shot numbers for those simulations are provided in the paper. Abstract: The physical processes taking place at the separatrix and scrape-off layer regions are crucial for the operation of tokamaks as they govern the interaction of hot plasma with the vessel walls. Numerical modeling of the edge with state-of-the-art codes attempts to elucidate the complex interactions between neoclassical drifts, turbulence, poloidal and parallel flows that control the physical set-up of the SOL region. Here, we present post-processing analysis of simulation results from the gyrokinetic code XGC1, comparing and contrasting edge turbulence characteristics from a simulation of the DIII-D tokamak against a simulation of the Alcator C-Mod tokamak. We find that the equilibrium $E \times B$ flux across the separatrix has a similar poloidal pattern in both discharges which can be explained by $\nabla B$-drifts and trapped ion excursions. However, collisionality is noted to play a major role in the way that it prevents local charge accumulations from having more global effects in the C-Mod case. In both cases, turbulent electron heat flux is observed to be higher than the ion one. This seems to be a universal characteristic of the tokamak edge, possibly related to the need of electrons to maintain quasineutrality through the only channel available to them for exiting the confinement. By Fourier analysis, we identify turbulent frequencies and growth rates of the dominant mode in both simulations. In the case of C-Mod, these numbers point to the presence of a drift wave. In the DIII-D case, further linear simulations with the {\scshape Gene} code reveal a trapped electron mode. Furthermore, using a blob detection and tracking tool, we present the amplitude and size distributions of the blobs from both simulations. The amplitude distributions are in qualitative agreement with experimental observations while the size distributions are consistent with the fact that most of the blobs are not connecting to the divertor plates and suggest that they are generated by the shearing of the turbulent modes., This work was supported by the U.S. Department of Energy Office of Science, Office of Fusion Energy Sciences under grant DE-FG02-08ER54954 and DE-SC000801 and by subcontract SO15882-C with PPPL under the U.S. Department of Energy HBPS SciDAC project DE-AC02-09CH11466. The DIII-D US DOE Grant number for the particular shot that was used as a basis for the analysis was DE-FC02-04ER54698 and for the C-Mod one, DE-FC02-99ER54512. The original XGC1 runs used computing resources on Titan at OLCF through the 2015 Innovative and Novel Computational Impact on Theory and Experiment (INCITE) program and the 2016 ALCC (ASCR Leadership Computer Challenge) award.

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.

We propose an asymptotic-preserving (AP), uniformly convergent numerical scheme for the relativistic collisional Drift-Kinetic Equation (rDKE) to simulate runaway electrons in axisymmetric toroidal magnetic field geometries typical of tokamak devices. The approach is derived from an exact Green's function solution with numerical approximations of quantifiable impact, and results in a simple, two-step operator-split algorithm, consisting of a collisional Eulerian step, and a Lagrangian orbit-integration step with analytically prescribed kernels. The AP character of the approach is demonstrated by analysis of the dominant numerical errors, as well as by numerical experiments. We demonstrate the ability of the algorithm to provide accurate answers regardless of plasma collisionality on a circular axisymmetric tokamak geometry.

The conditions and dynamics of neon gas puff Z-pinch plasmas at pinch time are studied on a pulsed power generator with a current rise time of approximately 200-ns and 0.9-mA peak current. Radial tailoring of the gas puff mass-density profile using a triple-nozzle coaxial valve (two annular gas liners and a central jet) allows production of both more stable and less stable (with regard to the magneto-Rayleigh–Taylor instability) Z-pinch implosions. A 526.5-nm, 10-J Thomson scattering diagnostic laser enables probing of the flow dynamics and plasma conditions of these implosions with both spatial and temporal resolutions. The 2.2-ns laser pulse scatters from the plasma electrons and is carried by one optical fiber to a visible light streak camera, and by a bundle of optical fibers to a time-gated camera, both after spectral dispersion by 750-mm spectrometers. The streak camera, with a 10-ns full streak time, provides subnanosecond resolution of the evolution of the pinch plasma parameters through stagnation. The time-gated camera provides spatially resolved spectra (across a field of view of 6.1 mm) at the same time as the streak. Scattering spectra suggest that temperatures are high at stagnation, with the ion temperature as much as three times higher than the electron temperature. However, we consider the possibility of nonthermal explanations for the broad scattering spectra and high effective ion temperature, including collisionality, implosion velocity distributions (velocity gradients), and small-scale hydrodynamic motion.

The authors study the bump-on tail instability using molecular dynamics to explore the roles of collisionality, correlations and the effective interparticle force law across wide ranges of plasma temperatures, densities and charge states, and show that, even with a small number of point particles, the results are robust.