Arbitrary Density Profile Research Articles

Techniques for solving static Klein-Gordon equation with self-interaction λϕ4 and arbitrary spherical source terms

The Klein-Gordon equation for a scalar field sourced by a static spherically symmetric background is an interesting second-order differential equation with applications in particle physics, astrophysics, and elsewhere. Here we present static solutions for generic source density profiles in the case where the scalar field has no interactions or a mass term. For a λϕ4 self-interaction term, we develop the techniques that are necessary numerical computation. We also provide code to perform the numerical calculations that can be adapted for arbitrary density profiles. ▪.

Numerical model for linear stimulated Raman scattering in inhomogeneous plasmas

Numerical model for calculating convective gains and absolute thresholds of stimulated Raman scattering (SRS) in inhomogeneous plasmas is constructed based on the Fourier-space method. The model is valid for arbitrary density profiles and scattering geometries, including both backscattering and side scattering. It is shown that 90 deg side scatter has a lower absolute threshold than other scattering geometries. Backscatter, on the other hand, has a relatively large absolute threshold under conventional direct-drive ignition conditions. For a parabolic density profile, the absolute threshold of backscatter decreases dramatically at the peak of parabola, but is still much larger than that of side scatter. We also discuss the absolute thresholds of side scatter under different density profiles, showing not big differences with the linear density profile as well as the analytic formulas. Convective gains, however, are sensitive to the density profiles and collisional damping. The k-space numerical model is verified via analytic formulas and real-space envelope model, and it offers us new perspective on the scattering angles compared with previous models for SRS.

From ray to spray: augmenting amplitudes and taming fast oscillations in fully numerical neutrino codes

In this note we describe how to complement the neutrino evolution matrix calculated at a given energy and trajectory with additional information which allows to reliably extrapolate it to nearby energies or trajectories without repeating the full computation. Our method works for arbitrary matter density profiles, can be applied to any propagation model described by an Hamiltonian, and exactly guarantees the unitarity of the evolution matrix. As a straightforward application, we show how to enhance the calculation of the theoretical predictions for experimentally measured quantities, so that they remain accurate even in the presence of fast neutrino oscillations. Furthermore, the ability to “move around” a given energy and trajectory opens the door to precise interpolation of the oscillation amplitudes within a grid of tabulated values, with potential benefits for the computation speed of Monte-Carlo codes. We also provide a set of examples to illustrate the most prominent features of our approach.

Parametric study of 1D plasma photonic crystals with smooth and discontinuous density profiles

Plasma photonic crystals (PPCs) have the potential to significantly expand the capabilities of current millimeter wave technologies by providing high speed (microsecond time scale) control of energy transmission characteristics in the GHz through low THz range. Furthermore, plasma-based devices can be used in higher power applications than their solid-state counterparts without experiencing significant changes in function or incurring damage. Plasmas with periodic variations in density can be created externally, or result naturally from instabilities or self-organization. Due to plasma's diffuse nature, PPCs cannot support rapid changes in density. Despite this fact, most theoretical work in PPCs is based on solid-state photonic crystal methods and assumes constant material properties with abrupt changes at material interfaces. In this work, a linear model is derived for a one-dimensional cold-plasma photonic crystal with an arbitrary density profile. The model is validated against a discontinuous Galerkin method numerical solution of the same device configuration. Bandgap maps are then created from derived group velocity data to elucidate the operating regime of a theoretical PPC device. The bandgap maps are compared for one-dimensional PPCs with both smooth and discontinuous density profiles. This study finds that bandgap behavior is strongly correlated with the density profile Fourier content and that density profile shapes can be engineered to produce specific transmission characteristics.

ITER Toroidal Interferometer and Polarimeter (TIP) beam refraction in 3D density profiles

Calculations of the expected refraction of the five ITER Toroidal Interferometer and Polarimeter (TIP) chords are presented for a range of conditions including high-density axisymmetric, ELMing H-mode cases and shattered pellet disruption mitigation cases. The calculations are carried out with a newly developed ray tracing code capable of following TIP’s 10.59μm laser beams through arbitrary 3D electron density profiles. Using JOREK simulations of ELM density perturbations in a 15MA ITER baseline plasma, it is shown that refraction from ELMs is expected to be negligible. It is found, however, that TIP interferometers will be able to clearly resolve the line-integrated density perturbation from ELMs and contribute to the ITER measurement requirement “14. H-mode, ELMs and L-H mode transition indicator”. Calculations of the expected refraction in a NIMROD simulated shattered pellet disruption mitigation scenario with peak local electron densities of ne=3.7×1021 m−3 (max line-averaged densities of navg=1.3×1021 m−3) also show tolerable refraction and it is likely that most, if not all chords, would avoid signal loss. For both axisymmetric and structured plasmas with line-averaged densities in the mid to upper 1021 m−3 range, values likely present only during disruption mitigation, refraction becomes significant and could limit the ability of TIP to make reliable density measurements.

Towards 1% accurate galaxy cluster masses: including baryons in weak-lensing mass inference

Galaxy clusters are a promising probe of late-time structure growth, but constraints on cosmology from cluster abundances are currently limited by systematics in their inferred masses. One unmitigated systematic effect in weak-lensing mass inference is ignoring the presence of baryons and treating the entire cluster as a dark matter halo. In this work we present a new flexible model for cluster densities that captures both the baryonic and dark matter profiles, a new general technique for calculating the lensing signal of an arbitrary density profile, and a methodology for stacking those lensing signal to appropriately model stacked weak-lensing measurements of galaxy cluster catalogues. We test this model on 1400 simulated clusters. Similarly to previous studies, we find that a dark matter-only model overestimates the average mass by 7.5%, but including our baryonic term reduces that to 0.7%. Since two more variables are marginalized over when we include our baryonic term the posteriors on the cluster mass calibration are larger than the dark matter-only model. Additionally, to mitigate the computational complexity of our model, we construct an emulator (surrogate model) which accurately interpolates our model for parameter inference, while being much faster to use than the raw model. We also provide an open-source software framework for our model and emulator, called maszcal, which will serve as a platform for continued efforts to improve these mass-calibration techniques. In this work, we detail our model, the construction of the emulator, and the tests which we used to validate that our model does mitigate bias. Lastly, we describe tests of the emulator's accuracy.

Time-resolved study of holeboring in realistic experimental conditions

The evolution of dense plasmas prior to the arrival of the peak of the laser irradiation is critical to understanding relativistic laser plasma interactions. The spectral properties of a reflected laser pulse after the interaction with a plasma can be used to gain insights about the interaction itself, whereas the effect of holeboring has a predominant role. Here we developed an analytical model, describing the non-relativistic temporal evolution of the holeboring velocity in the presence of an arbitrary overdense plasma density and laser intensity profile. We verify this using two-dimensional particle-in-cell simulations, showing a major influence on the holeboring dynamic depending on the density profile. The influence on the reflected laser pulse has been verified during an experiment at the PHELIX laser. We show that this enables the possibility to determine the sub-micrometer scale length of the preplasma by measuring the maximum holeboring velocity and acceleration during the laser-plasma interaction.

Modeling femtosecond pulse propagation and high harmonics generation in hollow core fibers

One way to increase the well known low efficiency of high order harmonics generation is to place the gas medium in a hollow core waveguide. The numerical model used to obtain driving and harmonics field configuration along and across the waveguide was developed for an arbitrary gas density profile and arbitrary fiber diameter modulation. The model was tested against experimental measurements and excellent agreement was obtained for the fluorescence emission along the waveguide. We analyse the influence of the diameter modulation which result from the fabrication process on both pulse propagation and on harmonic generation.

Surface wave characteristics of a volume source horizontally translating in a stratified fluid

The present work aims to investigate the free surface wave system of a volume source translating in a stratified fluid. In this paper, a modified model is established with linearized governing equations and the free surface condition. This modified model can describe both the internal and surface waves excited by a volume source with arbitrary density profiles. The wave characteristics that are analyzed include the half-wedge angle, crestlines, the maximum amplitude, and the apparent angle. The results show that the entire wave system is complex and composed by an infinite number of single wave modes. The different modes can be divided into surface modes (mode number n = 0) and internal modes (n ≥ 1). It is found that internal modes have many similarities to each other but are quite different from surface modes. In the subcritical area [Fr<Frn, where the Froude number is Fr=U/gL and the critical Froude number of mode n is Frn=cpn(0)/gL], the wave structure of the nth mode contains divergent and transverse waves, and the half-wedge angle of surface mode waves increases from the Kelvin-wave angle of 19°28′ to 90°, while the half-wedge angle of internal mode waves increases from 0° to 90°. In the supercritical domain (Fr ≥ Frn), there are only divergent waves, and the half-wedge angle of all mode waves decays as sin−1(Frn/Fr). The amplitude of waves is related to the velocity of the source, the location of the source, the depth of the fluid, the Brunt–Väisälä frequency, the thickness of the pycnocline, and the center location of the pycnocline. The effects of these factors have been discussed in this paper. The apparent angle, which indicates the highest peak of waves, is also discussed. The results show that the apparent angle of all mode waves scales like Fr−1 at large Froude numbers.

Secular resonance sweeping and orbital excitation in decaying disks

We revisit the problem of secular resonance sweeping during the dissipation of a protoplanetary disk and its possible role in exciting the orbits of primordial asteroids, in the light of recent models of solar system evolution. We develop an integrator that incorporates the gravitational effect of a uniformly (or not) depleting, axisymmetric disk with arbitrary surface density profile; its performance is verified by analytical calculations. The secular response of fictitious asteroids, under perturbations from Jupiter, Saturn and a decaying disk, is thoroughly studied. Note that the existence of a symmetry plane induced by the disk, lifts the inherent degeneracy of the two-planet system, such that the '$s_5$' nodal frequency can also play a major role. We examine different resonant configurations for the planets (2:1, 3:2, 5:3), disk models and depletion scenarios. For every case we compute the corresponding time paths of secular resonances, which show when and where resonance crossing occurs. The excitation of asteroids, particularly in inclination, is studied in the various models and compared to analytical estimates. We find that inclination excitation in excess of $\sim 10^{\circ}$ is possible in the asteroid belt, but the nearly uniform spread of $\Delta i\sim 20^{\circ}$ observed calls for the combined action of secular resonance sweeping with other mechanisms (e.g. scattering by Mars-sized embryos) that would be operating during terrestrial planet formation. Our results are also applicable to extrasolar planetary systems.

Hydrostatic Interfaces in Bodies With Nonhydrostatic Lithospheres

AbstractBelow the lithospheres of the terrestrial planets, dwarf planets, and moons, density interfaces adjust over geologic time to align with surfaces of constant gravitational potential. It is well known that the shape of such hydrostatic surfaces is controlled by the pseudo‐rotational potential, tidal potential, and the induced potential of nonspherical density interfaces in the body. When a lithosphere is present, however, additional gravitational terms must be considered that arise from, for example, surface relief and crustal thickness variations. A first‐order formalism is presented for calculating the shape of hydrostatic density interfaces beneath the lithosphere when the gravity field and surface shape of the body are known. Using an arbitrary discretized density profile, the shapes are obtained by solving a simple matrix equation. As examples, lithospheric gravity anomalies account for about 10% of the relief along hydrostatic interfaces in Mars, whereas for the Moon, the lithospheric gravity is the dominant contributor to the core shape. Spherical harmonic degree‐1 mass anomalies in the lithosphere generate degree‐1 relief along the core‐mantle boundary, and for Mars and the Moon, the core is offset from the center of mass of the body by about 90 m. The moments of inertia of the core of these bodies are also misaligned with respect to the principal moments of the entire body. An improved crustal thickness map of Mars is constructed that accounts for gravity anomalies beneath the lithosphere, and the consequences of core relief on the Martian free core nutation are quantified.

AGAMA: action-based galaxy modelling architecture

Agama is a publicly available software library for a broad range of applications in the field of stellar dynamics. It provides methods for computing the gravitational potential of arbitrary analytic density profiles or N-body models; orbit integration and analysis; transformations between position/velocity and action/angle variables; distribution functions expressed in terms of actions and their moments; iterative construction of self-consistent multicomponent galaxy models. Applications include the inference about the structure of Milky Way or other galaxies from observations of stellar kinematics; preparation of equilibrium initial conditions for N-body simulations; analysis of snapshots from simulations. The library is written in C++, provides a Python interface, and can be coupled to other stellar-dynamical software: Amuse, Galpy and Nemo.

Secular Evolution Driven by Massive Eccentric Disks/Rings: An Apsidally Aligned Case

Abstract Massive eccentric disks (gaseous or particulate) orbiting a dominant central mass appear in many astrophysical systems, including planetary rings, protoplanetary and accretion disks in binaries, and nuclear stellar disks around supermassive black holes in galactic centers. We present an analytical framework for treating the nearly Keplerian secular dynamics of test particles driven by the gravity of an eccentric, apsidally aligned, zero-thickness disk with arbitrary surface density and eccentricity profiles. We derive a disturbing function describing the secular evolution of coplanar objects, which is explicitly related (via one-dimensional, convergent integrals) to the disk surface density and eccentricity profiles without using any ad hoc softening of the potential. Our analytical framework is verified via direct orbit integrations, which show it to be accurate in the low-eccentricity limit for a variety of disk models (for disk eccentricity ≲0.1–0.2). We find that free precession in the potential of a disk with a smooth surface density distribution can naturally change from prograde to retrograde within the disk. Sharp disk features—edges and gaps—are the locations where this tendency is naturally enhanced, while the precession becomes very fast. Radii where free precession changes sign are the locations where substantial (formally singular) growth of the forced eccentricity of the orbiting objects occurs. Based on our results, we formulate a self-consistent analytical framework for computing an eccentricity profile for an aligned, eccentric disk (with a prescribed surface density profile) capable of precessing as a solid body under its own self-gravity.

Numerical computation of gravitational field of infinitely-thin axisymmetric disc with arbitrary surface mass density profile and its application to preliminary study of rotation curve of M33

AbstractWe developed a numerical method[-70pt] to compute the gravitational field of an infinitely-thin axisymmetric disc with an arbitrary surface mass density profile. We evaluate the gravitational potential by a split quadrature using the double exponential rule and obtain the acceleration vector by numerically differentiating the potential by Ridders’ algorithm. By using the new method, we show the rotation curves of some non-trivial discs: (i) truncated power-law discs, (ii) discs with a non-negligible center hole, (iii) truncated Mestel discs with edge-softening, (iv) double power-law discs, (v) exponentially-damped power-law discs, and (vi) an exponential disc with a sinusoidal modulation of the density profile. Also, we present a couple of model fittings to the observed rotation curve of M33: (i) the standard deconvolution by assuming a spherical distributin of the dark matter and (ii) a direct fit of infinitely-thin disc mass with a double power-law distribution of the surface mass density.

Precision bounds for gradient magnetometry with atomic ensembles

We study gradient magnetometry with an ensemble of atoms with arbitrary spin. We calculate precision bounds for estimating the gradient of the magnetic field based on the quantum Fisher information. For quantum states that are invariant under homogeneous magnetic fields, we need to measure a single observable to estimate the gradient. On the other hand, for states that are sensitive to homogeneous fields, a simultaneous measurement is needed, as the homogeneous field must also be estimated. We prove that for the cases studied in this paper, such a measurement is feasible. We present a method to calculate precision bounds for gradient estimation with a chain of atoms or with two spatially separated atomic ensembles. We also consider a single atomic ensemble with an arbitrary density profile, where the atoms cannot be addressed individually, and which is a very relevant case for experiments. Our model can take into account even correlations between particle positions. While in most of the discussion we consider an ensemble of localized particles that are classical with respect to their spatial degree of freedom, we also discuss the case of gradient metrology with a single Bose-Einstein condensate.

Numerically calibrated model for propagation of a relativistic unmagnetized jet in dense media

Relativistic jets reside in high-energy astrophysical systems of all scales. Their interaction with the surrounding media is critical as it determines the jet evolution, observable signature, and feedback on the environment. During its motion the interaction of the jet with the ambient media inflates a highly pressurized cocoon, which under certain conditions collimates the jet and strongly affects its propagation. Recently, Bromberg et al. (2011) derived a general simplified (semi)analytic solution for the evolution of the jet and the cocoon in case of an unmagnetized jet that propagates in a medium with a range of density profiles. In this work we use a large suite of 2D and 3D relativistic hydrodynamic simulations in order to test the validity and accuracy of this model. We discuss the similarities and differences between the analytic model and numerical simulations and also, to some extent, between 2D and 3D simulations. Our main finding is that although the analytic model is highly simplified, it properly predicts the evolution of the main ingredients of the jet-cocoon system, including its temporal evolution and the transition between various regimes (e.g., collimated to uncollimated). The analytic solution predicts a jet head velocity that is faster by a factor of about 3 compared to the simulations, as long as the head velocity is Newtonian. We use the results of the simulations to calibrate the analytic model which significantly increases its accuracy. We provide an applet that calculates semi-analytically the propagation of a jet in an arbitrary density profile defined by the user at http://www.astro.tau.ac.il/~ore/propagation.html.

Theory of relativistic radiation reflection from plasmas

We consider the reflection of relativistically strong radiation from plasma and identify the physical origin of the electrons' tendency to form a thin sheet, which maintains its localisation throughout its motion. Thereby, we justify the principle of relativistic electronic spring (RES) proposed in [Gonoskov et al., Phys. Rev. E 84, 046403 (2011)]. Using the RES principle, we derive a closed set of differential equations that describe the reflection of radiation with arbitrary variation of polarization and intensity from plasma with an arbitrary density profile for an arbitrary angle of incidence. We confirm with ab initio PIC simulations that the developed theory accurately describes laser-plasma interactions in the regime where the reflection of relativistically strong radiation is accompanied by significant, repeated relocation of plasma electrons. In particular, the theory can be applied for the studies of plasma heating and coherent and incoherent emissions in the RES regime of high-intensity laser-plasma interaction.

General kinetic solution for the Biermann battery with an associated pressure anisotropy generation

Fully kinetic analytic calculations of an initially Maxwellian distribution with arbitrary density and temperature gradients exhibit the development of temperature anisotropies and magnetic field growth associated with the Biermann battery. The calculation, performed by taking a small order expansion of the ratio of the Debye length to the gradient scale, predicts anisotropies and magnetic fields as a function of space given an arbitrary temperature and density profile. These predictions are shown to qualitatively match the values measured from particle-in-cell simulations, where the development of the Weibel instability occurs at the same location and with a wavenumber aligned with the predicted temperature anisotropy.

Generalized skew-symmetric interfacial probability distribution in reflectivity and small-angle scattering analysis

Generalized skew-symmetric probability density functions are proposed to model asymmetric interfacial density distributions for the parameterization of any arbitrary density profiles in the `effective-density model'. The penetration of the densities into adjacent layers can be selectively controlled and parameterized. A continuous density profile is generated and discretized into many independent slices of very thin thickness with constant density values and sharp interfaces. The discretized profile can be used to calculate reflectivities via Parratt's recursive formula, or small-angle scattering via the concentric onion model that is also developed in this work.

Dynamics of straight vortex filaments in a Bose–Einstein condensate with the Gaussian density profile

The dynamics of interacting quantized vortex filaments in a rotating trapped Bose-Einstein condensate, which is in the Thomas-Fermi regime at zero temperature and described by the Gross-Pitaevskii equation, is considered in the hydrodynamic "anelastic" approximation. In the presence of a smoothly inhomogeneous array of filaments (vortex lattice), a non-canonical Hamiltonian equation of motion is derived for the macroscopically averaged vorticity, with taking into account the spatial non-uniformity of the equilibrium condensate density determined by the trap potential. A minimum of the corresponding Hamiltonian describes a static configuration of deformed vortex lattice against a given density background. The minimum condition is reduced to a vector nonlinear partial differential equation of the second order, for which some approximate and exact solutions are found. It is shown that if the condensate density has an anisotropic Gaussian profile then equation of motion for the averaged vorticity admits solutions in the form of a spatially uniform vector with a nontrivial time dependence. An integral representation is obtained for the matrix Green function determining the non-local Hamiltonian of a system of arbitrary shaped vortex filaments in a condensate with Gaussian density. ... A simple approximate expression for the two-dimensional Green function is suggested at rather arbitrary density profile, and its successful comparison to the exact result in the Gaussian case is done. Approximate equations of motion are derived which describe a long-wave dynamics of interacting vortex filaments in condensates with the density depending on the transverse coordinates only.