Parallel Velocity Research Articles

Estimating the fate of oxygen ion outflow from the high-altitude cusp

Abstract. We have investigated the oxygen escape-to-capture ratio from the high-altitude cusp regions for various geomagnetic activity levels by combining EDI and CODIF measurements from the Cluster spacecraft. Using a magnetic field model, we traced the observed oxygen ions to one of three regions: plasma sheet, solar wind beyond a distant X-line or dayside magnetosheath. Our results indicate that 69 % of high-altitude oxygen escapes the magnetosphere, from which most escapes beyond the distant X-line (50 % of total oxygen flux). Convection of oxygen to the plasma sheet shows a strong dependence on geomagnetic activity. We used the Dst index as a proxy for geomagnetic storms and separated data into quiet conditions (Dst>0 nT), moderate conditions (0>Dst>-20 nT), and active conditions (Dst<-20 nT). For quiet magnetospheric conditions we found increased escape due to low convection. For active magnetospheric conditions we found an increase in both parallel velocities and convection velocities, but the increase in convection velocities is higher, and thus most of the oxygen gets convected into the plasma sheet (73 %). The convected oxygen ions reach the plasma sheet in the distant tail, mostly beyond 50 RE.

Effects of the non-perturbative mode structure on energetic particle transport

Energetic particles (EPs) are known to change the properties of shear Alfvén waves in tokamaks, and for this reason non-perturbative models have to be used to describe their linear and non-linear evolution. In this work, mode structures distortion with symmetry breaking properties featured by a finite radial wave phase velocity due to EP effects are considered. A mode structure of the form with complex parameters σ and s0 is used, to describe not only the width () and the mean location (Re{s0}) of the bell-shaped radial structure, but also the radial phase variations (Im{σ}, Im{s0}), where s is the normalized radial coordinate. The values of (σ, s0) are fitted from the results given by the gyrokinetic eigenvalue code LIGKA. The impact on EP transport is investigated using the drift-kinetic code HAGIS. The effects of the mode structure symmetry breaking on the mode saturation level and the EP transport are analysed. In the presence of mode structure symmetry breaking which is relevant to the simulation and experimental observations, the growth rate as well as the particle and energy transport level can vary by ∼10%. The velocity-space averaged parallel velocity of EPs in the inner region s = 0.2 ∼ 0.5 can change its sign for different mode structures, demonstrating the importance of the mode structure symmetry breaking on EP toroidal velocity reversal. This large effect (∼100%) on the mean parallel flow could have implications for EP current drive and the transport in the burning plasmas.

A study of the propagation of a solitary wave along the magnetic field in a cold collision-free plasma

A detailed study has been carried out on the propagation of a solitary wave along the magnetic field in a cold collision-free plasma. With the quasi-neutral approximation and the conservation of momentum flux and energy flux in the wave-frame, the exact analytical solutions of the stationary solitary pulse in terms of particle densities, parallel and transverse velocities, and transverse magnetic fields are presented without performing numerical integration. Graphical representations of the solutions and in particular the 3D structures of the transverse magnetic and velocity field lines are presented.

Anomalous neutralization characteristics in Na+ neutralization on Al(111) surfaces

The jellium model of free electron gas and its extended version have been widely used to understand the neutralization of alkali-metal ions on metal surfaces. We report an unexpected deviation from its prediction that we observed in the neutralization of $\mathrm{N}{\mathrm{a}}^{+}$ ions scattering from an Al(111) surface. We find that the neutralization probability decreases monotonically with increasing ion velocity for the specular scattering condition, which is consistent with the well-known parallel velocity effect. However, the neutralization probability exhibits an unexpected bell shape with the variation of outgoing angle for a given incident energy. Calculations based on the jellium model using the rate equation and including the dynamic parallel velocity effect are presented. Their results agree with the velocity dependence of the neutral fraction, but completely fail in reproducing the angle dependence. This anomalous angle dependence could be due to the appearance of inelastic processes, corresponding to inner $2p$ electron promotion in hard encounters with Al atoms for large incidence angles, when the interatomic distances become small. This can lead to the formation of autoionizing Na states that result in the formation of extra $\mathrm{N}{\mathrm{a}}^{+}$ ions, not accounted for in the jellium model.

Numerical simulation of MHD flow and heat transfer inside T-shaped cavity by the parallel walls motion

In this paper, the heat and mass transfer due to the steady, laminar, and incompressible MHD flow inside T-shaped cavity is numerically calculated. The fluid moves under an external magnetic field applied to the vertical axis of the cavity, and the cavity is driven by the parallel horizontal velocities from the upper and lower parts of the cavity. The governing equations of continuity, momentum, and the energy are solved simultaneously by using the finite difference method. The effect of Reynolds and Hartmann numbers on the streamlines, vorticity, temperature distribution, and velocity vectors in x–y directions is simulated. According to the motion of the fluid inside the cavity, some vertices vorticity will appear. It observes of their positions and the change in its positions under changing the Reynolds and Hartmann numbers. The results are presented in graphs and tables.

Nonlinear Scattering of 90° Pitch Angle Electrons in the Outer Radiation Belt by Large‐Amplitude EMIC Waves

AbstractElectromagnetic ion cyclotron (EMIC) waves can cause relativistic electron scattering and atmospheric precipitation, primarily via cyclotron resonant interactions in the Earth's radiation belts. However, the conventional quasilinear resonance theory suggests that the cyclotron resonance condition is not satisfied for 90° pitch angle (PA) electrons, which constitute the majority of electrons in the outer radiation belt, such that scattering mainly affects low‐PA electrons. In contrast to this theory, using test particle calculations, we demonstrate that even exactly 90° PA electrons can be significantly scattered by large‐amplitude EMIC waves. The finite wave force results in the parallel transport of 90° PA electrons away from the equator, corresponding to intrinsically nonresonant scattering. This can lead to parallel velocity that meets cyclotron resonance conditions as local PA deviates from 90°. Different types of resonance are identified depending on the wave normal angle, that is, first‐ and second‐order resonances for parallel and oblique waves, respectively.

A filtered Boris algorithm for charged-particle dynamics in a strong magnetic field

A modification of the standard Boris algorithm, called filtered Boris algorithm, is proposed for the numerical integration of the equations of motion of charged particles in a strong non-uniform magnetic field in the asymptotic scaling known as maximal ordering. With an appropriate choice of filters, second-order error bounds in the position and in the parallel velocity, and first-order error bounds in the normal velocity are obtained with respect to the scaling parameter. This also yields a second-order approximation to the guiding center motion. The proof compares the modulated Fourier expansions of the exact and the numerical solutions. Numerical experiments illustrate the error behaviour of the filtered Boris algorithm.

Image mapping the temporal evolution of edge characteristics in tokamaks using neural networks

We propose a method for data-driven modelling of the temporal evolution of the plasma and neutral characteristics at the edge of a tokamak using neural networks. Our method proposes a novel fully convolutional network to serve as function approximators in modelling complex nonlinear phenomenon observed in the multi-physics representations of high energy physics. More specifically, we target the evolution of the temperatures, densities and parallel velocities of the electrons, ions and neutral particles at the edge. The central challenge in this context is in modelling together the different physics principles encapsulated in the evolution of plasma and the neutrals. We demonstrate that the inherent differences in nonlinear behaviour can be addressed by forking the network to process the plasma and neutral information individually before integrating as a holistic system. Our approach takes into account the spatial dependencies of the physics parameters across the grid while performing the temporal mappings, ensuring that the underlying physics is factored in and not lost to the black-box. Having used the conventional edge plasma-neutral solver code SOLPS to build the synthetic dataset, our method demonstrates a computational gain of over 5 orders of magnitude over it without a considerable compromise on accuracy.

A variational formulation for steady surface water waves on a Beltrami flow

This paper considers steady surface waves ‘riding’ a Beltrami flow (a three-dimensional flow with parallel velocity and vorticity fields). It is demonstrated that the hydrodynamic problem can be formulated as two equations for two scalar functions of the horizontal spatial coordinates, namely the elevation η of the free surface and the potential Φ defining the gradient part (in the sense of the Hodge–Weyl decomposition) of the horizontal component of the tangential fluid velocity there. These equations are written in terms of a non-local operator H ( η ) mapping Φ to the normal fluid velocity at the free surface, and are shown to arise from a variational principle. In the irrotational limit, the equations reduce to the Zakharov–Craig–Sulem formulation of the classical three-dimensional steady water-wave problem, while H ( η ) reduces to the familiar Dirichlet–Neumann operator.

Flow helicity of wavy plasma turbulence

The helicity of flow field is an important quantity for describing the topological feature of turbulent fluids and plasmas. In this work, we discuss how helicity is determined in turbulent plasmas, by considering the drift wave turbulence and the parallel velocity gradient driven turbulence as concrete examples. Helicity evolution for each turbulence is derived and compared against the simulation data. Links between the plasma helicity and the transport channels, such as particle transport and momentum transport, are demonstrated. Several applications including the excitation of the 3D flow patterns in fusion plasmas and dynamo action in astrophysical plasmas are discussed.

Effect of the tangential NBI current drive on the stability of pressure and energetic particle driven MHD modes in LHD plasma

The aim of the present study is to analyze the stability of the pressure gradient driven modes (PM) and Alfvén eigenmodes (AE) in the large helical device (LHD) plasma if the rotational transform profile is modified by the current drive of the tangential neutral beam injectors (NBI). This study forms a basic search for optimized operation scenarios with reduced mode activity. The analysis is performed using the code FAR3d which solves the reduced MHD equations describing the linear evolution of the poloidal flux and the toroidal component of the vorticity in a full 3D system, coupled with equations for density and parallel velocity moments of the energetic particle (EP) species, including the effect of the acoustic modes. The Landau damping and resonant destabilization effects are added via the closure relation. On-axis and off-axis NBI current drive modifies the rotational transform which becomes strongly distorted as the intensity of the neutral beam current drive (NBCD) increases, leading to wider continuum gaps and modifying the magnetic shear. The simulations with on-axis NBI injection show that a counter (ctr-) NBCD in inward shifted and default configurations leads to a lower growth rate of the PM, although strong n = 1 and 2 AEs can be destabilized. For the outward shifted configurations, a co-NBCD improves the AEs stability but the PM are further destabilized if the co-NBCD intensity is 30 kA T−1. If the NBI injection is off-axis, the plasma stability is not significantly improved due to the further destabilization of the AE and energetic particle modes (EPM) in the middle and outer plasma region.

Bootstrap current and parallel ion velocity in imperfectly optimized stellarators

A novel derivation of the parallel ion velocity, and the bootstrap and Pfirsch–Schlüter currents in an imperfectly optimized (that is, almost omnigenous) stellarator magnetic field, $\boldsymbol{B}$ , is presented that somewhat more generally recovers expressions completely consistent with previous analytic results. However, it is also shown that, when the conventional radially local form of the drift kinetic equation is employed, the flow velocity and the bootstrap current acquire a spurious contribution proportional to $\unicode[STIX]{x1D714}/\unicode[STIX]{x1D708}$ , where $\unicode[STIX]{x1D714}$ denotes the $\boldsymbol{E}\times \boldsymbol{B}$ rotation frequency (due to the radial electric field $\boldsymbol{E}$ ) and $\unicode[STIX]{x1D708}$ the collision frequency. This contribution is particularly large in the $\sqrt{\unicode[STIX]{x1D708}}$ regime and at smaller collisionalities, where $\unicode[STIX]{x1D714}/\unicode[STIX]{x1D708}\gtrsim 1$ , and is presumably present in most numerical calculations, but it disappears if a more accurate drift kinetic equation is used.

Repeatability of growth characteristics and wood properties for solid wood production from Eucalyptus camaldulensis half-sib families growing in Thailand

Abstract To promote solid wood production, the diameter at breast height, height, stress-wave velocity, surface-released strain, basic density and compressive strength parallel to the grain were measured for 10 half-sib families of 12-year-old Eucalyptus camaldulensis Dehnh. trees growing in Thailand. Based on the results, growth rates, correlations among measured properties, radial and among-family variations of wood properties, and their repeatability were evaluated. Diameter at breast height, height, and wood volume were exponentially increased at initial stage, and then gradually increased toward to 12 years after planting. The maximum current annual increment and mean annual increment in wood volume showed at age of 8 and 11years old, suggesting that rotation period for optimum productivity may be ranged from 8 to 11 years old. Wood with stable properties was found greater than 6 cm from the pith. These results indicate that 12-year-old E. camaldulensis trees had already reached the maturation stage. No significant correlations were found between growth characteristics and wood properties. Significant variances in the height, stress-wave velocity, and basic density were found among the 10 families. The F-values and repeatability of the wood properties in the outer wood were higher than those in the inner wood. These results indicate that the properties of the outer wood are closely related to genetic factors. Thus, to obtain superior E. camaldulensis trees for solid wood production, the family selection should be conducted using the outer wood of aged trees.

Капиллярная неустойчивость цилиндрической струи феррожидкости, находящейся в однородном продольном магнитном поле

In this article a ferrofluid jet located inside a solenoid is considered. The jet is modeled by a cylindrical volume of incompressible inviscid fluid moving at a constant velocity parallel to the axis of the cylinder. The axes of the jet and the solenoid coincide. The variation of the strength of the magnetic field generated by the solenoid is allowed from very small to experimentally achievable maximal values. We investigate the influence of the magnetic forces on the growth rate and the wavelength of the most rapidly growing perturbations of the jet surface shape.

Study on flow structure transition in thermocapillary convection under parallel gas flow

In this paper, the influence of direction, velocity and temperature of parallel gas flow on the flow structure of non-isothermal liquid bridge is studied using PIV technique with 10 cSt silicone oil as the working fluid. Experimental results show that thermocapillary convection can be weakened by entering the parallel gas flow at a lower velocity (Vg = 0–2 m/s) from the upper disc of liquid bridge, which makes the shape of the vortices in the liquid bridge to transit from a semilune to a sickle-shaped form. Vortices approach toward the free surface gradually because the farthest radial position that the vortex can reach becomes from 2.99 mm to 2.24 mm. The velocity of particle near the free surface is also inhibited from 1.89 mm/s to 1.36 mm/s. When the velocity of parallel gas flow is increased to Vg = 3 m/s, the thermocapillary convection is enhanced. The farthest radial position that the vortex can reach is increased to 2.66 mm, and the velocity of particle is also increased from 1.36 mm/s to 2.30 mm/s. Then experiments are conducted with the velocity of parallel gas flow keeping at Vg = 2 m/s, and the temperature of parallel gas flow is set at the upper disc temperature, the lower disc temperature and the average temperature of upper and lower discs, respectively. It is found that the thermocapillary convection becomes weak obviously when the temperature of parallel gas flow is set at the average temperature of upper and lower discs. Under this condition, the farthest radial position that vortex can reach is decreased to 2.04 mm, and the velocity of particle is also the smallest (vE0 = 1.18 mm/s). When the parallel gas flow enters from the lower disc, the thermocapillary convection weakens gradually. The farthest radial position that vortex can reach decreases from 2.99 mm to 1.98 mm, and the velocity of particle near the free surface is inhibited from 1.89 mm/s to 0.32 mm/s with the increasing parallel gas velocity. Keeping the velocity of parallel gas flow at Vg = 2 m/s and changing the temperature of parallel gas flow, it is found that reducing the temperature difference between the parallel gas flow and the free surface of the liquid bridge can inhibit the thermocapillary convection.

Impact of main ion pressure anisotropy on stellarator impurity transport

Main ions influence impurity dynamics through a variety of mechanisms; in particular, via impurity-ion collisions. To lowest order in an expansion in the main ion mass over the impurity mass, the impurity-ion collision operator only depends on the component of the main ion distribution that is odd in the parallel velocity. These lowest order terms give the parallel friction of the impurities with the main ions, which is typically assumed to be the main cause of collisional impurity transport. Next-order terms in the mass ratio expansion of the impurity-ion collision operator, proportional to the component of the main ion distribution that is even in the parallel velocity, are usually neglected. However, in stellarators, the even component of the main ion distribution can be very large. In this article, such next-order terms in the mass ratio expansion of the impurity-ion collision operator are retained, and analytical expressions for the neoclassical radial flux of trace impurities are calculated in the Pfirsch–Schlüter, plateau and regimes. The new terms provide a drive for impurity transport that is physically very different from parallel friction: they are associated to anisotropy in the pressure of the main ions, which translates into impurity pressure anisotropy. It is argued that main ion pressure anisotropy must be taken into account for a correct description of impurity transport in certain realistic stellarator plasmas. Examples are given by numerically evaluating the analytical expressions for the impurity flux.

A Novel Obstacle Localization Method for an Underwater Robot Based on the Flow Field

Because the underwater environment is complex, autonomous underwater vehicles (AUVs) have difficulty locating their surroundings autonomously. In order to improve the adaptive ability of AUVs, this paper presents a novel obstacle localization strategy based on the flow features. Like fish, the strategy uses the flow field information directly to locate the object obstacles. Two different localization methods are provided and compared. The first method, which is named the Method of Spatial Distribution (MSD), is based on the spatial distribution of the flow field. The second method, which is named the Method of Amplitude Variation (MAV), is provided by the amplitude variation of the flow field. The flow field around spherical targets is obtained by a numerical method, and both methods use the parallel velocity component on the virtual lateral line. During the study, different target numbers, detective ratios, spacing ratios, and flow velocities are taken into account. It is demonstrated that both methods are able to locate object obstacles. However, the prediction accuracy of MAV is higher than that of MSD. That implies that MAV is more robust than MSD. These new findings indicate that the object obstacles can be directly located based on the flow field information and robust flow sensing is perhaps not based on the spatial distribution of the flow field but rather, on its fluctuation range.

Subglacial roughness of the Greenland Ice Sheet: relationship with contemporary ice velocity and geology

Abstract. The subglacial environment of the Greenland Ice Sheet (GrIS) is poorly constrained both in its bulk properties, for example geology, the presence of sediment, and the presence of water, and interfacial conditions, such as roughness and bed rheology. There is, therefore, limited understanding of how spatially heterogeneous subglacial properties relate to ice-sheet motion. Here, via analysis of 2 decades of radio-echo sounding data, we present a new systematic analysis of subglacial roughness beneath the GrIS. We use two independent methods to quantify subglacial roughness: first, the variability in along-track topography – enabling an assessment of roughness anisotropy from pairs of orthogonal transects aligned perpendicular and parallel to ice flow and, second, from bed-echo scattering – enabling assessment of fine-scale bed characteristics. We establish the spatial distribution of subglacial roughness and quantify its relationship with ice flow speed and direction. Overall, the beds of fast-flowing regions are observed to be rougher than the slow-flowing interior. Topographic roughness exhibits an exponential scaling relationship with ice surface velocity parallel, but not perpendicular, to flow direction in fast-flowing regions, and the degree of anisotropy is correlated with ice surface speed. In many slow-flowing regions both roughness methods indicate spatially coherent regions of smooth beds, which, through combination with analyses of underlying geology, we conclude is likely due to the presence of a hard flat bed. Consequently, the study provides scope for a spatially variable hard- or soft-bed boundary constraint for ice-sheet models.

A Look at Phase Space Intermittency in Magnetized Plasma Turbulence

Abstract In a proton–electron magnetized plasma, we analyze turbulence at kinetic scales captured by a gyrokinetic formalism. The interval of scales spans the range between the proton and the electron gyroradii, while the use of the proper mass ratio between the two species ensures a realistic scale separation for the nonlinear couplings. The simulation is pertinent to astrophysical conditions, employing a straight field line magnetic geometry for the guide field, a plasma β of one, and a temperature ratio between the two species of unity. We investigate the intermittency of the distribution functions in the perpendicular direction, measured over the phase space as a way to account for the velocity space structures generated via Landau damping as well as for the nonlinear spatial mixing (i.e., the turbulent cascade). The analysis makes use of a Hermite decomposition in the parallel velocity. Electron structures are found to be strongly intermittent compared to weakly intermittent protons. Moreover, we find evidence linking intermittency with phase mixing and electron Landau damping, as intermittent electron structures also exhibit strong parallel velocity structures.

Triple decomposition of velocity gradient tensor in homogeneous isotropic turbulence

The triple decomposition of a velocity gradient tensor is studied with direct numerical simulations of homogeneous isotropic turbulence, where the velocity gradient tensor ∇u is decomposed into three components representing an irrotational straining motion (∇u)EL, a rigid-body rotation (∇u)RR, and a shearing motion (∇u)SH. Strength of these motions can be quantified with the decomposed components. A procedure of the triple decomposition is proposed for three-dimensional flows, where the decomposition is applied in a basic reference frame identified by examining a finite number of reference frames obtained by three sequential rotational transformations of a Cartesian coordinate. Even though more than one basic reference frame may be available for the triple decomposition, the results of the decomposition depend little on the choice of basic reference frame. In homogeneous isotropic turbulence, regions with strong rigid-body rotations or straining motions are highly intermittent in space, while most flow regions exhibit moderately strong shearing motions in the absence of straining motions and rigid-body rotations. In the classical double decomposition, the velocity gradient tensor is decomposed into a rate-of-rotation tensor Ωij and a rate-of-strain tensor Sij. Regions with large ω2=2ΩijΩij can be associated with rigid-body rotations and shearing motions while those with large s2=2SijSij can be associated with irrotational straining motions and shearing motions. Therefore, vortices with rigid-body rotations and shear layers in turbulence cannot be detected solely by thresholding ω or s while they can be identified simply with (∇u)RR and (∇u)SH in the triple decomposition, respectively. The thickness of the shear layer detected in the triple decomposition is about 8 times of Kolmogorov scale, while the velocity parallel to the layer changes rapidly across the layer, in which the velocity difference across the shear layer is of the order of the root-mean-squared velocity fluctuation.