Regions Of Strong Gradients Research Articles

Generalized kinetic equation for tokamak plasma equilibrium distribution function

A generalized kinetic equation for the equilibrium distribution function in a finite beta, arbitrary tokamak plasma is derived. The equation is correct to second order in ρ/L (ρ is the particle Larmor radius and L is the system size). Resolving the finite Larmor radius length scales with no restriction on the ratio of poloidal to total equilibrium magnetic field, Bϑ/B, it generalizes the drift kinetic theory of Hazeltine [Phys. Plasmas 15, 77 (1973)] to the limit of Bϑ/B∼1 (e.g., to ensure validity for spherical tokamaks). Two cases are considered. The first provides the equilibrium distribution function, consistent with the generalized gyrokinetic formalism of Dudkovskaia et al. [Plasma Phys. Controlled Fusion 65, 045010 (2023)], derived specifically to capture neoclassical equilibrium currents in the gyrokinetic stability analyses in strong gradient regions. The second assumes short length scales in the direction perpendicular to the magnetic field, which can occur as a result of small coherent magnetic structures in the plasma, such as neoclassical tearing mode magnetic islands close to threshold. This then extends the drift island equations of Dudkovskaia et al. [Nucl. Fusion 63, 016020 (2023)] for the plasma response to magnetic islands to a spherical tokamak plasma configuration. Resolving ρ∼ρϑ (or Bϑ∼B), where ρϑ is the particle poloidal Larmor radius, is also expected to influence calculations of the magnetic island propagation frequency and the associated contributions to the island onset conditions.

Neoclassical transport in strong gradient regions of large aspect ratio tokamaks

We present a new neoclassical transport model for large aspect ratio tokamaks where the gradient scale lengths are of the size of the ion poloidal gyroradius. Previous work on neoclassical transport across transport barriers assumed large density and potential gradients but a small temperature gradient, or neglected the gradient of the mean parallel flow. Using large aspect ratio and low collisionality expansions, we relax these restrictive assumptions. We define a new set of variables based on conserved quantities, which simplifies the drift kinetic equation whilst keeping strong gradients, and derive equations describing the transport of particles, parallel momentum and energy by ions in the banana regime. The poloidally varying parts of density and electric potential are included. Studying contributions from both passing and trapped particles, we show that the resulting transport is dominated by trapped particles. We find that a non-zero neoclassical particle flux requires parallel momentum input which could be provided through interaction with turbulence or impurities. We derive upper and lower bounds for the energy flux across a transport barrier in both temperature and density and present example profiles and fluxes.

Gyrokinetic simulations of turbulence and zonal flows driven by steep profile gradients using a delta-f approach with an evolving background Maxwellian

Long global gyrokinetic turbulence simulations are particularly challenging in situations where the system deviates strongly from its initial state and when fluctuation levels are high, for example, in strong gradient regions. For particle-in-cell simulations, statistical sampling noise accumulation from large marker weights due to large deviations from the control variate of a delta-f scheme makes such simulations often impractical. An adaptive control variate in the form of a flux-surface-averaged Maxwellian with a time-dependent temperature profile is introduced in an attempt to alleviate the former problem. Under simplified collisionless physics, this adaptive delta-f scheme is shown to reduce noise accumulation in the zonal flows and the simulated heat flux in a quasi-steady turbulent state. The method also avoids the collapse of the signal-to-noise ratio, which occurs in the standard non-adaptive scheme, and, therefore, allows one to reach numerically converged results even with lower marker numbers.

Phase synchronization versus modulational instability for zonal flow generation and pattern formation

From global gyrokinetic simulations of toroidal ion temperature gradient-driven (ITG) turbulence, we identify two distinguished regimes where zonal flow generation and its radial pattern formation is governed by either phases or amplitudes of the turbulence spectrum. When the unstable region is wider than the correlation length of ITG modes, the zonal flow structure changes in a turbulence time scale. We newly uncover that the radial phases of ITG modes determine the evolution of the zonal flow structure. Synchronization of mode phases induced by the global zonal flow drives a fine-scale zonal flow pattern. With a narrow unstable region comparable to the mode correlation length, the phase effect almost vanishes. In this regime, we recover that the modulational instability promptly amplifies a coherent zonal flow, leading to a lower turbulence saturation level. This finding explains the reduction of turbulent transport at a narrow width of the strong gradient region, which has been attributed to the system size effects in ion-scale gyrokinetic turbulence.

Nonrigid registration of medical image based on adaptive local structure tensor and normalized mutual information.

Nonrigid registration of medical images is especially critical in clinical treatment. Mutual information is a popular similarity measure for medical image registration; however, only the intensity statistical characteristics of the global consistency of image are considered in MI, and the spatial information is ignored. In this paper, a novel intensity‐based similarity measure combining normalized mutual information with spatial information for nonrigid medical image registration is proposed. The different parameters of Gaussian filtering are defined according to the regional variance, the adaptive Gaussian filtering is introduced into the local structure tensor. Then, the obtained adaptive local structure tensor is used to extract the spatial information and define the weighting function. Finally, normalized mutual information is distributed to each pixel, and the discrete normalized mutual information is multiplied with a weighting term to obtain a new measure. The novel measure fully considers the spatial information of the image neighborhood, gives the location of the strong spatial information a larger weight, and the registration of the strong gradient regions has a priority over the small gradient regions. The simulated brain image with single‐modality and multimodality are used for registration validation experiments. The results show that the new similarity measure improves the registration accuracy and robustness compared with the classical registration algorithm, reduces the risk of falling into local extremes during the registration process.

Global IWV trends and variability in atmospheric reanalyses and GPS observations

Abstract. This study investigates the means, variability, and trends in integrated water vapour (IWV) from two modern reanalyses (ERA-Interim and MERRA-2) from 1980 to 2016 and ground-based GPS data from 1995 to 2010. It is found that the mean distributions and inter-annual variability in IWV in the reanalyses and GPS are consistent, even in regions of strong gradients. ERA-Interim is shown to exhibit a slight moist bias in the extra-tropics and a slight dry bias in the tropics (both on the order of 0.5 to 1 kg m−2) compared to GPS. ERA-Interim is also generally drier than MERRA-2 over the ocean and within the tropics. Differences in variability and trends are pointed out at a few GPS sites. These differences can be due to representativeness errors (for sites located in coastal regions and regions of complex topography), gaps and inhomogeneities in the GPS series (due to equipment changes), or potential inhomogeneities in the reanalyses (due to changes in the observing system). Trends in IWV and surface temperature in ERA-Interim and MERRA-2 are shown to be consistent, with positive IWV trends generally correlated with surface warming, but MERRA-2 presents a more general global moistening trend compared to ERA-Interim. Inconsistent trends are found between the two reanalyses over Antarctica and most of the Southern Hemisphere, and over central and northern Africa. The uncertainty in current reanalyses remains quite high in these regions, where few in situ observations are available, and the spread between models is generally important. Inter-annual and decadal variations in IWV are also shown to be strongly linked with variations in the atmospheric circulation, especially in arid regions, such as northern Africa and Western Australia, which add uncertainty in the trend estimates, especially over the shorter period. In these regions, the Clausius–Clapeyron scaling ratio is found not to be a good humidity proxy for inter-annual variability and decadal trends.

Interpretations of the impact of cross-field drifts on divertor flows in DIII-D with UEDGE

Simulations using the multi-fluid code UEDGE indicates that, in low confinement (L-mode) plasmas in DIII-D, poloidal projection of the ionization driven flows dominate poloidal particle flows in the divertor near the divertor plates, whereas E ×B drift flows dominate the radial particle flows. In contrast, in high confinement (H-mode) conditions E ×B drift flows dominate both poloidal and radial particle flows in the divertor in the vicinity of the strong gradient region near the separatrix. UEDGE indicates that the toroidal C2+ flow velocities in the divertor plasmas are mainly entrained within 30% to the background deuterium flow in both L- and H-mode plasmas in the plasma region where the CIII 465nm emission is measured. Therefore, UEDGE indicates that the Doppler Coherence Imaging Spectroscopy (CIS), measuring the toroidal velocity of the C2+ ions, can provide insight to the deuterium flows in the divertor. Parallel-to-B velocity dominates the toroidal divertor flow; direct drift impact being less than 1%. Toroidal divertor flow is predicted to reverse when the magnetic field is reversed. This is explained by the parallel-B flow towards the nearest divertor plate corresponding to opposite toroidal directions in opposite toroidal field configurations.

Toroidal mode number determination of ELM associated phenomena on ASDEX Upgrade

In highly confined tokamak plasmas periodically appearing edge localized modes (ELMs) are accompanied by mode-like magnetohydrodynamic (MHD) activities with defined toroidal mode numbers.Here the method of determining toroidal mode numbers n on the ASDEX Upgrade tokamak with a toroidally spread magnetic pick-up coil array is reviewed and improved by taking into account intrinsic coil phases. ELM synchronization is used to characterize inter-ELM MHD activity and their development during the ELM cycle in terms of their mode numbers. The mode number development is correlated with the development of the pedestal parameters which shows that the inter-ELM modes cause transport across the pedestal. An estimation of the position of the modes is done via a comparison between the mode velocities and the plasma rotation profile at the edge.Results show that during the ELM cycle MHD modes appear at several positions in the strong gradient region with clearly defined toroidal structures in the range of n = 1–10. These structures of inter-ELM modes are preserved during the ELM crash where also a strong n = 0 phenomenon occurs.

Intermittency, nonlinear dynamics and dissipation in the solar wind and astrophysical plasmas.

An overview is given of important properties of spatial and temporal intermittency, including evidence of its appearance in fluids, magnetofluids and plasmas, and its implications for understanding of heliospheric plasmas. Spatial intermittency is generally associated with formation of sharp gradients and coherent structures. The basic physics of structure generation is ideal, but when dissipation is present it is usually concentrated in regions of strong gradients. This essential feature of spatial intermittency in fluids has been shown recently to carry over to the realm of kinetic plasma, where the dissipation function is not known from first principles. Spatial structures produced in intermittent plasma influence dissipation, heating, and transport and acceleration of charged particles. Temporal intermittency can give rise to very long time correlations or a delayed approach to steady-state conditions, and has been associated with inverse cascade or quasi-inverse cascade systems, with possible implications for heliospheric prediction.

Radiosonde observational evidence of the impact of an extremely cold SST spot on a mesoscale anticyclone

AbstractRadiosondes were launched in August 2006 from a research vessel above a spot around the Kuril Islands between the North Pacific and the Okhotsk Sea characterized by an extremely cold sea surface temperature (SST) and a large horizontal temperature gradient caused by strong tidal mixing. Because this cold SST was caused solely by this oceanic process, the observed data chiefly reflect the oceanic influence on the atmosphere. In this area, where the summertime SST is typically lower than in other seas in the same latitude belt, a minimum SST of 2°C and a horizontal gradient of 7°C/10 km were observed in August 2006. During the cruise, the area was covered by a layer of fog up to about 1000 m thick. The following observations reveal the presence of an atmospheric mesoscale anticyclone and a cold dome caused by ocean cooling of the atmosphere. The wind direction over the cold spot and the strong gradient region was northeasterly below the altitude of about 500 m, in contrast to the southwesterly geostrophic wind, and the area of northeasterly wind was characterized by a cold air mass and a high‐pressure anomaly. This ageostrophic wind distribution indicates mesoscale anticyclonic circulation below 500 m. The fog layer was also thinner in the northeasterly wind area than in other areas, suggesting vertical dry air advection (i.e., a subsidence) associated with the mesoscale anticyclone. In addition, our observational results suggest that the pressure adjustment mechanism can explain this mesoscale circulation.

The Alfvén resonance in pair plasmas

Waves propagating obliquely in a magnetized cold pair plasma experience an approximate resonance in the wavevector component perpendicular to the magnetic field, which is the analogue of the Alfvén resonance in normal electron-ion plasmas. Wave absorption at the resonance can take place via mode conversion to the analogue of the short wavelength inertial Alfvén wave. The Alfvén resonance could play a role in wave propagation in the pulsar magnetosphere leading to pulsar radio emission. Ducting of waves in strong plasma gradients may occur in the pulsar magnetosphere, which leads to the consideration of Alfvén surface waves, whose energy is concentrated in the region of strong gradients.

Experimental investigation of current free double layers in helicon plasmas

The paper presents investigations of current free double layer (CFDL) that forms in helicon plasmas. In contrast to the other work reporting on the same subject, in the present investigations the double layer (DL) forms in a mirror-like magnetic field topology. The RF compensated Langmuir probe measurements show multiple DLs, which are in connection with, the abrupt fall of densities along with potential drop of about 24 V and 18 V. The DLs strengths e ΔVpk Te are about 9.5 and 6, and the corresponding widths are about 6 and 5 D lengths. The potential drop is nearly equal to the thermal anisotropies between the two plasma regions forming the DL, which is present in the plateau region of mirror, unlike the earlier studies on the DL formation in the region of strong gradients in the magnetic field. Also, it presents a qualitative discussion on the mechanism of DL formation.

Basic investigations of electrostatic turbulence and its interaction with plasma and suprathermal ions in a simple magnetized toroidal plasma

Progress in basic understanding of turbulence and its influence on the transport both of the plasma bulk and of suprathermal components is achieved in the TORPEX simple magnetized torus. This configuration combines a microwave plasma production scheme with a quasi-equilibrium generated by a toroidal magnetic field, onto which a small vertical component is superimposed, simulating a simplified form of tokamak scrape-off layers. After having clarified the formation of blobs in ideal interchange turbulence, TORPEX experiments elucidated the mechanisms behind the blob motion, with a general scaling law relating their size and speed. The parallel currents associated with the blobs, responsible for the damping of the charge separation that develops inside them, hence determining their cross-field velocity, have been measured. The blob dynamics is influenced by creating convective cells with biased electrodes, arranged in an array on a metal limiter. Depending on the biasing scheme, radial and vertical blob velocities can be varied. Suprathermal ion transport in small-scale turbulence is also investigated on TORPEX. Suprathermal ions are generated by a miniaturized lithium source, and are detected using a movable double-gridded energy analyser. We characterize vertical and radial spreading of the ion beam, associated with the ideal interchange-dominated plasma turbulence, as a function of the suprathermal ion energy and the plasma temperature. Experimental results are in good agreement with global fluid simulations, including in cases of non-diffusive behaviour. To investigate the interaction of plasma and suprathermal particles with instabilities and turbulence in magnetic configurations of increasing complexity, a closed field line configuration has recently been implemented on TORPEX, based on a current-carrying wire suspended in the vacuum chamber. First measurements indicate the creation of circular symmetric profiles centred on the magnetic axis, and instabilities driven in the region of strong gradients, with a strong ballooning character.

Evidence of current free double layer in high density helicon discharge

This paper investigates the formation of double layer (DL) in helicon plasmas. In the experiment, argon plasma production is using the excitation of m = −1 helicon mode with magnetic mirror field with high mirror ratio of ∼1:1.7. We have specifically used the radio frequency compensated Langmuir probe (LP) to measure the relevant plasma parameters simultaneously so as to investigate the details about the plasma production. The DL, which consists of both warm and bulk populations towards higher potential region and only dense bulk plasmas towards the lower potential region downstream the antenna, is present in the transition region. LP measurements also show an abrupt fall of density along with a potential drop of about 20 V and e ΔVpk Te≈12 within a few cm. The potential drop is equal to the difference of the electron temperatures between the two plasma regions forming the DL, which is present in the plateau region of mirror, unlike in several prior studies on the DL formation in the region of strong gradients in the magnetic field. The DL is strong, current-free, electric double-layer with estimated thickness of about 10 Debye lengths.

Gyrokinetic equations for strong-gradient regions

A gyrokinetic theory is developed under a set of orderings applicable to the edge region of tokamaks and other magnetic confinement devices, as well as to internal transport barriers. The result is a practical set equations that is valid for large perturbation amplitudes [qδψ/T=O(1), where δψ=δφ-ν∥δA∥/c], which is straightforward to implement numerically, and which has straightforward expressions for its conservation properties. Here, δφ and δA∥ are the perturbed electrostatic and parallel magnetic potentials, ν∥ is the particle velocity, c is the speed of light, and T is the temperature. The derivation is based on the quantity ɛ≡(ρ/λ⊥)qδψ/T≪1 as the small expansion parameter, where ρ is the gyroradius and λ⊥ is the perpendicular wavelength. Physically, this ordering requires that the E×B velocity and the component of the parallel velocity perpendicular to the equilibrium magnetic field are small compared to the thermal velocity. For nonlinear fluctuations saturated at “mixing-length” levels (i.e., at a level such that driving gradients in profile quantities are locally flattened), ɛ is of the order ρ/Lp, where Lp is the equilibrium profile scale length, for all scales λ⊥ ranging from ρ to Lp. This is true even though qδψ/T=O(1) for λ⊥∼Lp. Significant additional simplifications result from ordering Lp/LB=O(ɛ), where LB is the spatial scale of variation of the magnetic field. We argue that these orderings are well satisfied in strong-gradient regions, such as edge and scrapeoff layer regions and internal transport barriers in tokamaks, and anticipate that our equations will be useful as a basis for simulation models for these regions.

System Size Effects on Gyrokinetic Turbulence

The scaling of turbulence-driven heat transport with system size in magnetically confined plasmas is reexamined using first-principles based numerical simulations. Two very different numerical methods are applied to this problem, in order to resolve a long-standing quantitative disagreement, which may have arisen due to inconsistencies in the geometrical approximation. System size effects are further explored by modifying the width of the strong gradient region at fixed system size. The finite width of the strong gradient region in gyroradius units, rather than the finite overall system size, is found to induce the diffusivity reduction seen in global gyrokinetic simulations.

Alfvén resonance absorption in electron-positron plasmas

AbstractWaves propagating obliquely in a magnetized cold pair plasma experience an approximate resonance in the wavevector component perpendicular to the magnetic field, which is the analogue of the Alfvén resonance in normal electron-ion plasmas. Wave absorption at the resonance can take place via mode conversion to the analogue of the short wavelength inertial Alfvén wave. The Alfvén resonance could play a role in wave propagation in the pulsar magnetosphere leading to pulsar radio emission. Ducting of waves in strong plasma gradients may occur in the pulsar magnetosphere, which leads to the consideration of Alfvén surface waves, whose energy is concentrated in the region of strong gradients.

Deconvolution of u channel magnetometer data: Experimental study of accuracy, resolution, and stability of different inversion methods

We explore the effects of sampling density, signal/noise ratios, and position‐dependent measurement errors on deconvolution calculations for u channel magnetometer data, using a combination of experimental and numerical approaches. Experiments involve a synthetic sample set made by setting hydraulic cement in a 30‐cm u channel and slicing the hardened material into ∼2‐cm lengths, and a natural lake sediment u channel sample. The cement segments can be magnetized and measured individually, and reassembled for continuous u channel measurement and deconvolution; the lake sediment channel was first measured continuously and then sliced into discrete samples for individual measurement. Each continuous data set was deconvolved using the ABIC minimization code of Oda and Shibuya (1996) and two new approaches that we have developed, using singular‐value decomposition and regularized least squares. These involve somewhat different methods to stabilize the inverse calculations and different criteria for identifying the optimum solution, but we find in all of our experiments that the three methods converge to essentially identical solutions. Repeat scans in several experiments show that measurement errors are not distributed with position‐independent variance; errors in setting/determining the u channel position (standard deviation ∼0.2 mm) translate in regions of strong gradients into measurement uncertainties much larger than those due to instrument noise and drift. When we incorporate these depth‐dependent measurement uncertainties into the deconvolution calculations, the resulting models show decreased stability and accuracy compared to inversions assuming depth‐independent measurement errors. The cement experiments involved varying directions and uniform intensities downcore, and very good accuracy was obtained using all of the methods when the signal/noise ratio was greater than a few hundred and the sampling interval no larger than half the length scale of magnetization changes. Addition of synthetic noise or reduction of sampling density decreased the resolution and accuracy of all the methods equally. The sediment‐core experiment involved uniform (axial) magnetization direction and strongly varying intensities downcore. Intensity variations are well resolved and directions are accurate to within about 5 degrees, with errors attributable to omission and/or inaccurate calibration of cross terms in the instrument response function.

Structure and dynamics of a new class of thin current sheets

New results on a steady state Vlasov theory of current sheets, which generalizes the Harris (1962) model by assuming anisotropic and nongyrotropic plasmas and using the invariant of particle motion in regions of strong gradients, are presented with the aim to explain multiprobe observations of thin current sheets in the geomagnetotail and laboratory experiments, including the effects of current sheet embedding and bifurcation. The dynamics of these sheets is explored using a full particle code with more realistic mass ratio and anisotropy parameters than those used in our earlier works. The results relevant to 2001 CLUSTER observations, with the sheet thickness appreciably exceeding the thermal ion gyroradius, include ion distributions and pressure tensor components, which reveal the important role of nongyrotropic effects on the structure of these sheets. Their flapping motions are distinguished by north‐south asymmetry of current profiles, quasi‐rectangular shape of the flapping waves, and their small propagation speed, suggesting an explanation of their propagation toward the flanks of the tail sheet. The main effect of the ion anisotropy on the sheets with thickness less than the thermal ion gyroradius, relevant to 2003 CLUSTER observations and laboratory experiments, is their charging, which may limit their minimum thickness, while their structure can be modified by electron anisotropy. Other distinctive features of these sheets are three‐peaked current density profiles, found both in simulations and in the steady state theory, the north‐south asymmetry of flapping sheets, and the shape of flapping waves, which is drastically different from the case of thicker sheets.

Sea surface temperature fronts in the midlatitude South Atlantic revealed by using microwave satellite data

The Subtropical Convergence or Frontal Zone has been little studied in the central South Atlantic Ocean. Despite limited data, some work has suggested that this feature exists continuously across the South Atlantic. Here, satellite microwave sensed sea surface temperature (SST) data, available from June 2002, are analysed for the existence of frontal gradients in the subtropical to subpolar South Atlantic with focus on the central to eastern region. The frontal locations and SST gradients in the southwest South Atlantic and in the Agulhas Current retroflection region obtained from this satellite data are consistent with those estimated previously from hydrographic observations. Evident in the satellite data is pronounced mesoscale variability in subtropical frontal features, particularly south of Africa, and extending west from the Agulhas Current retroflection to at least the Greenwich meridian, and in the southwest South Atlantic. Over the central to eastern part of the basin, the analysis suggests that there is substantial interannual variability in the strength and latitudinal location of the Northern and Southern Subtropical Front, as defined by Belkin and Gordon (1996). Some of this variability may be related to shifts in the winds, including that in the latitude of the strongest wind stress curl. On seasonal scales, this central to eastern region is also characterised by variations in the frontal intensity but shifts in the position of regions of strong gradients are less obvious. Thus the data indicate that there is no continuous subtropical frontal feature across the basin in terms of surface temperature.