Perturbed Distribution Function Research Articles

Radial and azimuthal gradients of the moving groups in Gaia DR3: The slow and fast bar degeneracy problem

The structure and dynamics of the central bar of the Milky Way (MW) are still under debate whilst being fundamental ingredients for the evolution of our Galaxy. The recent Gaia DR3 offers an unprecedented detailed view of the 6D phase space of the MW, allowing for a better understanding of the complex imprints of the bar on the phase space. We aim to identify and characterise the dynamical moving groups across the MW disc, and use their large-scale distribution to help constrain the properties of the Galactic bar. We used 1D wavelet transforms of the azimuthal velocity ($V_ distribution in bins of radial velocity to robustly detect the kinematic substructure in the Gaia DR3 catalogue. We then connected these structures across the disc to measure the azimuthal (phi ) and radial ($R$) gradients of $V_ of the moving groups. We simulated thousands of perturbed distribution functions using backward integration, sweeping a large portion of parameter space of feasible Galaxy models that include a bar, in order to compare them with the data and to explore and quantify the degeneracies. The radial gradient of the Hercules moving group ($ V_ R$ = 28.1pm 2.8 $) cannot be reproduced by our simple models of the Galaxy that show much larger slopes both for a fast and a slow bar. This suggests the need for more complex dynamics (e.g. a different bar potential, spiral arms, a slowing bar, a complex circular velocity curve, external perturbations, etc.). We measured an azimuthal gradient for Hercules of $ V_ = -0.63pm $deg$^ $ and find that it is compatible with both the slow and fast bar models. Our analysis points out that in using this type of analysis, at least two moving groups are needed to start breaking the degeneracies. We conclude that it is not sufficient for a model to replicate the local velocity distribution; it must also capture its larger-scale variations. The accurate quantification of the gradients, especially in the azimuthal direction, will be key for the understanding of the dynamics governing the disc.

Cosmic-Eν: An- emulator for the non-linear neutrino power spectrum

ABSTRACT Cosmology is poised to measure the neutrino mass sum Mν and has identified several smaller-scale observables sensitive to neutrinos, necessitating accurate predictions of neutrino clustering over a wide range of length scales. The FlowsForTheMasses non-linear perturbation theory for the the massive neutrino power spectrum, $\Delta ^2_\nu (k)$, agrees with its companion N-body simulation at the $10~{{\ \rm per\ cent}}-15~{{\ \rm per\ cent}}$ level for k ≤ 1 h Mpc−1. Building upon the Mira-Titan IV emulator for the cold matter, we use FlowsForTheMasses to construct an emulator for $\Delta ^2_\nu (k)$, Cosmic-Eν, which covers a large range of cosmological parameters and neutrino fractions Ων, 0h2 ≤ 0.01 (Mν ≤ 0.93 eV). Consistent with FlowsForTheMasses at the 3.5 per cent level, it returns a power spectrum in milliseconds. Ranking the neutrinos by initial momenta, we also emulate the power spectra of momentum deciles, providing information about their perturbed distribution function. Comparing a Mν = 0.15 eV model to a wide range of N-body simulation methods, we find agreement to 3 per cent for k ≤ 3kFS = 0.17 h Mpc−1 and to 19 per cent for k ≤ 0.4 h Mpc−1. We find that the enhancement factor, the ratio of $\Delta ^2_\nu (k)$ to its linear-response equivalent, is most strongly correlated with Ων, 0h2, and also with the clustering amplitude σ8. Furthermore, non-linearities enhance the free-streaming-limit scaling $\partial \log (\Delta ^2_\nu /\Delta ^2_{\rm m}) / \partial \log (M_\nu)$ beyond its linear value of 4, increasing the Mν-sensitivity of the small-scale neutrino density.

Plasma Ion Velocity Distribution Function Perturbed by Ion-Acoustic Solitons: Analytical Calculations Based on KDV Equation

Using the Korteweg–De Vries equation, for background plasma, the distribution functions perturbed by ion-acoustic solitons are calculated. For describing the perturbed distribution functions, the explicit formula is obtained, which is suitable for practical applications. The results are compared with the analytical calculations and simulation results obtained previously.

DRIFT-KINETIC EQUATIONS IN MAGNETIZED CURRENT-CARRYING PLASMAS

Kinetic models of magnetized current-carrying plasma have been developed to study the influence of magnetic drift effects on the wave-particle interactions in tokamaks and cylindrical plasma columns. The drift-kinetic equations are derived for the perturbed distribution functions of trapped and untrapped particles in a two-dimensional axisymmetric toroidal plasma, taking into account their bounce oscillations and the finite orbit-widths of their banana trajectories.

Moment-based approach to the flux-tube linear gyrokinetic model

This work reports on the development and numerical implementation of the linear electromagnetic gyrokinetic (GK) model in a tokamak flux-tube geometry using a moment approach based on the expansion of the perturbed distribution function on a velocity-space Hermite–Laguerre polynomials basis. A hierarchy of equations of the expansion coefficients, referred to as the gyro-moments (GMs), is derived. We verify the numerical implementation of the GM hierarchy in the collisionless limit by performing a comparison with the continuum GK code GENE, recovering the linear properties of the ion temperature gradient, trapped electron, kinetic ballooning and microtearing modes, as well as the collisionless damping of zonal flows. An analysis of the distribution functions and ballooning eigenmode structures is performed. The present investigation reveals the ability of the GM approach to describe fine velocity-space-scale structures appearing near the trapped and passing boundary and kinetic effects associated with parallel and perpendicular particle drifts. In addition, the effects of collisions are studied using advanced collision operators, including the GK Coulomb collision operator. The main findings are that the number of GMs necessary for convergence decreases with plasma collisionality and is lower for pressure gradient-driven modes, such as in H-mode pedestal regions, compared with instabilities driven by trapped particles and magnetic gradient drifts often found in the core. The accuracy of approximations often used to model collisions (relative to the GK Coulomb operator) is studied in the case of trapped electron modes, showing differences between collision operator models that increase with collisionality and electron temperature gradient, consistent with the results of Pan et al. (Phys. Rev. E, vol. 103, 2021, L051202). Such differences are not observed in other edge microinstabilities, such as microtearing modes. The importance of a proper collision operator model is also confirmed by analysing the collisional damping of geodesic acoustic modes and zonal flows.

Low frequency twisted waves in a self-gravitating nonextensive complex plasma

Abstract The effects of dust–dust self-gravitational force and nonextensive characteristics of plasma species on the low frequency twisted waves owing to the helical wave structure in complex (dusty) plasmas are analyzed. The electrons and ions of the plasma are modelled by nonextensive q-distribution function while massive dust particles are Maxwellian distributed. The self-gravitational effects are incorporated in the Vlasov equation of kinetic theory where perturbed distribution function, electrostatic and gravitational potentials are expressed with Laguerre–Gauss functions. The governing equations of kinetic theory are solved together under paraxial approximations. The dispersion relations and damping rates of twisted dust-acoustic waves (TDAWs) are obtained for two situations; (a) super-extensivity (q < 1) and (b) sub-extensivity (q > 1). The effects of self-gravity, nonextensivity and twist parameter significantly modified the basic features of dust-acoustic waves. This study contributes to our understanding of the complex dynamics of TDAWs in interstellar dust clouds, considering the interplay of self-gravity, nonextensivity, and helical phase structures. The obtained theoretical and numerical results provide valuable insights into the behavior of these waves and offer a foundation for further investigations in this field. However, understanding of the topic can be enhanced through a combination of theoretical models, numerical simulations and observational data.

Twisted dust-acoustic waves in a self-gravitating dusty plasma with nonextensive q-distributed electrons and ions

We have investigated the twisted dust-acoustic waves (TDAWs) in an electrostatic self-gravitating dusty plasma whose electrons and ions are modelled by nonextensive q-distribution function while massive dust particles are Maxwellian distributed. A well-known kinetic theory is employed for this purpose where perturbed distribution function, electrostatic and gravitational potentials are expressed with Laguerre–Gauss functions. The governing equations of kinetic theory are solved together under paraxial approximations. The dispersion relations and instability growth rates are obtained for two situations; a) super-extensivity (q < 1) and b) sub-extensivity (q > 1). Significant modifications concerning the wave frequencies and growth rates are presented with respect to self-gravitation parameter, twist parameter, nonextensive parameter and streaming speed. It is observed that wave frequency and growth rate of TDAWs reduces in the presence of self-gravitating effects. Furthermore, the growth rates exhibit a significant enhancement in amplitude with the increase in twist parameter, q-parameter and streaming speed. Our present results may have applications in interstellar dust clouds and in the dusty plasma environments of Halley’s Comet.

Robust single frequency index-patterned laser design using a Fourier design method.

We use a Fourier-transform based method to investigate the magnitude and robustness of mode selectivity in as-cleaved discrete-mode semiconductor lasers, where a small number of refractive index perturbations are introduced into a Fabry-Pérot laser cavity. Three exemplar index perturbation patterns are considered. Our results demonstrate the capability to significantly improve modal selectivity by choosing a perturbation distribution function that avoids placing perturbations near to the cavity centre. Our analysis also highlights the ability to select functions that can increase the yield despite facet phase errors introduced during device fabrication.

On the collisional damping of plasma velocity space instabilities

For plasma velocity space instabilities driven by particle distributions significantly deviated from a Maxwellian, weak collisions can damp the instabilities by an amount that is significantly beyond the collisional rate itself. This is attributed to the dual role of collisions that tend to relax the plasma distribution toward a Maxwellian and to suppress the linearly perturbed distribution function. The former effect can dominate in cases where the unstable non-Maxwellian distribution is driven by collisionless transport on a timescale much shorter than that of collisions, and the growth rate of the ideal instability has a sensitive dependence on the distribution function. The whistler instability driven by electrostatically trapped electrons is used as an example to elucidate such a strong collisional damping effect of plasma velocity space instabilities, which is confirmed by first-principles kinetic simulations.

Validation of the current and pressure coupling schemes with nonlinear simulations of TAE and analysis on the linear stability of tearing mode in the presence of energetic particles

Both current and pressure coupling schemes have been adopted in the hybrid kinetic–magnetohydrodynamic code CLT-K recently. Numerical equivalences between these two coupling schemes are strictly verified under different approximations. First, when considering only the perturbed distribution function of energetic particles (EPs), the equivalence can be proved analytically. Second, when both the variations of the magnetic field and the EP distribution function are included, the current and pressure coupling schemes numerically produce the same result in the nonlinear simulations. On this basis, the influences of co-/counter-passing and trapped EPs on the linear stabilities of the m/n = 2/1 tearing mode (TM) have been investigated (where m and n represent the poloidal and toroidal mode numbers, respectively). The results of scanning of EPs show that the co-passing and trapped EPs are found to stabilize the TM, while the counter-passing EPs tend to destabilize the TM. The behind (de)stabilization mechanisms of the TM by EPs are carefully analyzed. Furthermore, after exceeding critical EP betas, the same branch of the high-frequency mode is excited by co-/counter-passing and trapped EPs, which is identified as the m/n = 2/1 energetic particle mode.

A Simplified Linearized Lattice Boltzmann Method for Acoustic Propagation Simulation.

A simplified linearized lattice Boltzmann method (SLLBM) suitable for the simulation of acoustic waves propagation in fluids was proposed herein. Through Chapman-Enskog expansion analysis, the linearized lattice Boltzmann equation (LLBE) was first recovered to linearized macroscopic equations. Then, using the fractional-step calculation technique, the solution of these linearized equations was divided into two steps: a predictor step and corrector step. Next, the evolution of the perturbation distribution function was transformed into the evolution of the perturbation equilibrium distribution function using second-order interpolation approximation of the latter at other positions and times to represent the nonequilibrium part of the former; additionally, the calculation formulas of SLLBM were deduced. SLLBM inherits the advantages of the linearized lattice Boltzmann method (LLBM), calculating acoustic disturbance and the mean flow separately so that macroscopic variables of the mean flow do not affect the calculation of acoustic disturbance. At the same time, it has other advantages: the calculation process is simpler, and the cost of computing memory is reduced. In addition, to simulate the acoustic scattering problem caused by the acoustic waves encountering objects, the immersed boundary method (IBM) and SLLBM were further combined so that the method can simulate the influence of complex geometries. Several cases were used to validate the feasibility of SLLBM for simulation of acoustic wave propagation under the mean flow.

Toward efficient runs of nonlinear gyrokinetic simulations assisted by a convolutional neural network model recognizing wavenumber-space images

A neural-network based innovative model recognizing the wavenumber space images has been developed to accurately forecast when the saturation of turbulent heat fluxes commences, i.e., the saturation time, in nonlinear gyrokinetic simulations. The wavenumber space images of the perturbed distribution function are focused on, which better represent the characteristics of turbulence. The model exploiting the state-of-the-art convolutional neural network model is capable of detecting minuscule differences between the images. Once the wavenumber space image is fed into the developed model, it can quickly and almost perfectly classify which phase of the turbulence evolution in nonlinear gyrokinetic simulations the image is in: the linearly and nonlinearly growing phases and the saturation phase. It can also predict the simulation time at which the image was processed with significantly high accuracy. The model enables us to forecast the saturation time of the gyrokinetic simulation in question by feeding an image at an early stage of the simulation and receiving the degree of progress toward the saturation. The ability of the model makes it possible to easily search out a desirable initial condition that rapidly conducts the simulation to a saturation phase. Such a pre-prediction model is important for running long time simulations on a large scale supercomputer like Fugaku in view of the efficient use of computational resources. In order to improve the predictive capability for the simulation that is going to be performed, several prediction models are trained by data with different major instabilities. The best predictor is selected to be in use based on the result of the pre-performed linear stability calculation with low computational cost.

Linearized Kinetic Theory of Plasma Waves

A striking illustration of the shortcomings of the simple fluid description appeared in the dispersion relation obtained in the presence of thermal effects. In this work, it is shown that the substitution of the fluid description with the tools of the kinetic theory leads to solving these limitations. The distribution function f_α is linearized and the Vlasov–Poisson kinetic system is described. The three terms that control the evolution of the perturbed distribution function and their physical effects are discussed.

Interaction of Ion Cyclotron Electromagnetic Wave with Energetic Particles in the Existence of Alternating Electric Field Using Ring Distribution

The elements that impact the dynamics and collaborations of waves and particles in the magnetosphere of planets have been considered here. Saturn’s internal magnetosphere is determined by substantiated instabilities and discovered to be an exceptional zone of wave activity. Interchanged instability is found to be one of the responsible events in view of temperature anisotropy and energization processes of magnetospheric species. The generated active ions alongside electrons that constitute the populations of highly magnetized planets like Saturn’s ring electron current are taken into consideration in the current framework. The previous and similar method of characteristics and the perturbed distribution function have been used to derive dispersion relation. In incorporating this investigation, the characteristics of electromagnetic ion cyclotron wave (EMIC) waves are determined by the composition of ions in plasmas through which the waves propagate. The effect of ring distribution illustrates non-monotonous description on growth rate (GR) depending upon plasma parameters picked out. Observations made by Cassini found appropriate for modern study, have been applied to the Kronian magnetosphere. Using Maxwellian ring distribution function of ions and detailed mathematical formulation, an expression for dispersion relation as well as GR and real frequency (RF) are evaluated. Analysis of plasma parameters shows that, proliferating EMIC waves are not developed much when propagation is parallelly aligned with magnetosphere as compared to waves propagating in oblique direction. GR for the oblique case, is influenced by temperature anisotropy as well as by alternating current (AC) frequency, whereas it is much affected only by AC frequency for parallel propagating waves.

Effect of the Relativistic Electron Beam on Propagating Whistler-Mode Wave for Ring Distribution in the Saturn Magnetosphere

Cassini and many investigators reported whistler chorus near Saturn equatorial plane moving outwards. Whistler can propagate when going to high latitude and can alter its characteristics while interacting resonantly with available energetic electrons. Here investigating wave for a relativistic beam of the electron. It is observed and reported by Cassini Magnetospheric Imaging Instrument (MIMI) that inward radial injection of highly energetic particles is most dominant in Saturn intrinsic magnetosphere. Within this paradigm, an empirical energy dispersion relation for propagated whistler-mode oscillations in quasi Saturn magnetospheric plasma from such a non-monotonous ringed distribution function has been established. The kinetic approach and method of characteristics methodologies were used in the computations, which have been shown to be the best for building perturbed plasma states. The perturbed distribution function was estimated using the unperturbed particle routes. The ring distribution function was used to construct an unexpected growth rate expression for relativistic plasma in the inner magnetosphere. The results from the Saturn magnetosphere have been calculated and interpreted using a range of parameters. Temperature heterogeneity was shown to be a significant source of free energy that aided the propagation of a whistler-mode wave. By raising the peak value, the bulk injection of energetic hot electron injection impacts the growth rate. Growth was also demonstrated to be accelerated when the propagation angle increased. The research contributes to a better understanding of the relationship between wave and particle emissions and VLF emissions on a large scale.

Perturbed distribution functions with accurate action estimates for the Galactic disc

In the Gaia era, understanding the effects of the perturbations of the Galactic disc is of major importance in the context of dynamical modelling. In this theoretical paper we extend previous work in which, making use of the epicyclic approximation, the linearized Boltzmann equation had been used to explicitly compute, away from resonances, the perturbed distribution function of a Galactic thin-disc population in the presence of a non-axisymmetric perturbation of constant amplitude. Here we improve this theoretical framework in two distinct ways in the new code that we present. First, we use better estimates for the action-angle variables away from quasi-circular orbits, computed from the AGAMA software, and we present an efficient routine to numerically re-express any perturbing potential in these coordinates with a typical accuracy at the per cent level. The use of more accurate action estimates allows us to identify resonances such as the outer 1:1 bar resonance at higher azimuthal velocities than the outer Lindblad resonance, and to extend our previous theoretical results well above the Galactic plane, where we explicitly show how they differ from the epicyclic approximation. In particular, the displacement of resonances in velocity space as a function of height can in principle constrain the 3D structure of the Galactic potential. Second, we allow the perturbation to be time dependent, thereby allowing us to model the effect of transient spiral arms or a growing bar. The theoretical framework and tools presented here will be useful for a thorough analytical dynamical modelling of the complex velocity distribution of disc stars as measured by past and upcoming Gaia data releases.

Impact of hot injected beam on whistler mode with alternating electric field (AC) in the magnetosphere of Saturn

Whistlers are believed to be generated by its own and responsible to evolve dynamical properties of magnetized planetary environment. Growing whistler instability can cause other uncertainties in the magnetosphere and evident to be generated by mean of injection events and temperature variance in plasma environment. In this paper the empirical dispersion relation has developed for parallel propagating whistler mode instability in an infinite saturnian magneto plasma in the presence of perpendicular electric field for ring distribution function having non-monotonous nature. Method of characteristics solutions alongside kinetic approach found to be most suitable in order to achieve perturbed plasma states. The perturbed and unperturbed particle trajectories have taken into consideration to determine perturbed distribution function. A remarkable growth rate expression with added hot plasma injection has been calculated in inner magnetosphere near 6.18 Rs. The results obtained using demonstrative value of the parameters suited to the Saturnian magnetosphere have been computed and discussed. Pressure (Temperature) anisotropy is found to be a peculiar source of free energy for whistler mode instability. The AC frequency irrespective of its magnitude, affects the growth rate significantly. The bulk of energetic hot electrons injection influences the growth rate by increasing its peak value. The result obtained provide the important view of wave particle interaction and useful to analyze the VLF emissions observed over a wide frequency range.

Twisted waves in symmetric and asymmetric bi-ion kappa-distributed plasmas

Waves in bi-ion plasmas are affected by asymmetry. The kinetic theory of the Maxwellian and Lorentzian/kappa-distributed bi-ion plasma is ameliorated to incorporate the transfer of orbital angular momentum from the helical electric field to the plasma modes. By operating the Laguerre–Gaussian function, the perturbed distribution function and helical electric field are decomposed into characteristic axial and azimuthal components. In symmetric bi-ion plasmas, the conventional ion modes/waves are only present if both ions have similar masses and the concentration of the electrons is negligible. An imbalance of the symmetry is considered by the contamination of a small fraction of the heavy immobile ions, which urges the negative ions to become heavier than the positive ions in the bi-ion plasma system. The distinct masses of the positive and negative ions provoke mass-asymmetry in the kappa-distributed bi-ion plasmas. The signature of the unique acoustic-laden twisted modes in non-Maxwellian asymmetric bi-ion plasma is perceived by the temperature of the lighter positive ions and the dynamics of the heavier negative ion. The deliberated results of Landau damping are displayed for distinct values of the azimuthal wave-number and spectral index, temperature-variation, and mass-asymmetry.

Thermoelectric transport properties in 3D Dirac semimetal Cd3As2

Thermoelectric transport properties, namely, electrical conductivity, electronic thermal conductivity, and diffusion thermopower are theoretically investigated in 3D Dirac semimetal Cd3As2. We employ Boltzmann transport formalism and consider the electron scattering by charged impurities, short-range disorder, acoustic phonons, and optical phonons. The Boltzmann transport equation is solved using the Ritz iteration technique to obtain the first-order perturbation distribution function for the interaction of electrons with inelastic polar optical phonons scattering. The numerical results are presented in the temperature range 2–300 K with the electron concentration in the range (0.1–10) × 1018 cm−3. It is found that, at low temperature < ~70 K transport coefficients are dominated by charged impurity scattering and at higher temperature the phonon scattering is found to be dominant. The validity of Wiedemann–Franz law is examined. Recently observed experimental results are explained by our theory.

Unsteady Plasma Flow Near an Oscillating Rigid Plane Plate Under the Influence of an Unsteady Nonlinear External Magnetic Field

In an irreversible thermodynamics framework, Stokes’ second problem was examined for unsteady oscillating flow. The objective was to apply that for a plasma near an illimitable oscillating rigid plane plate under the influence of an unsteady nonlinear applied magnetic field. The Bhatnagar-Gross-Krook (BGK) pattern of the Boltzmann kinetic equation supplemented by Maxwell’s equations was investigated. The method of moments was applied with a two-sided distribution function. The exact traveling wave solution was obtained for a system consisting of four non-homogeneous partial differential equations. The velocity, shear stress, viscosity coefficient, generated electric field, applied nonlinear magnetic field, polarization, gyro-radius, and gyro-frequency were calculated. Furthermore, the distinction between the equilibrium velocity distribution function and the perturbed distribution functions was theoretically clarified at distinct time values. The advantage of the Boltzmann equation permitted us to consider irreversible non-equilibrium thermodynamics principles. For that purpose, the calculated distribution functions should be used in the formulae of entropy, entropy flux, thermodynamic forces, and kinetic coefficient. From the analysis of the results, it is found that Boltzmann’s H-theorem, thermodynamics laws, and Le Chatelier’s principle were consistent with our model for the whole system. The distinct contributions of the forces exerted on the system modified its internal energies; they were expressed via the Gibbs formula. The results demonstrated that the proposed model is capable of describing the behavior of plasma helium gas in the upper atmosphere ionic belts. Based on the analytical calculations, 3D-Graphics illustrating the physical quantities were drawn to predict their conduct, and the results are deeply discussed.