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At least 253 records · Page 14
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DOE OSTI2015

Analysis of linear and nonlinear conductivity of plasma-like systems on the basis of the Fokker-Planck equation

The problems of high linear conductivity in an electric field, as well as nonlinear conductivity, are considered for plasma-like systems. First, we recall several observations of nonlinear fast charge transport in dusty plasma, molecular chains, lattices, conducting polymers, and semiconductor layers. Exploring the role of noise we introduce the generalized Fokker-Planck equation. Second, one-dimensional models are considered on the basis of the Fokker-Planck equation with active and passive velocity-dependent friction including an external electrical field. On this basis, it is possible to find the linear and nonlinear conductivities for electrons and other charged particles in a homogeneous external field. It is shown that the velocity dependence of the friction coefficient can lead to an essential increase of the electron average velocity and the corresponding conductivity in comparison with the usual model of constant friction, which is described by the Drude-type conductivity. Applications including novel forms of controlled charge transfer and non-Ohmic conductance are discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Fokker Planck and Krook theory of energetic electron transport in a laser produced plasma

Various laser plasma instabilities, such as the two plasma decay instability and the stimulated Raman scatter instability, produce large quantities of energetic electrons. How these electrons are transported and heat the plasma are crucial questions for laser fusion. This paper works out a Fokker Planck and Krook theory for such transport and heating. The result is a set of equations, for which one can find a simple asymptotic approximation for the solution, for the Fokker Planck case, and an exact solution for the Krook case. These solutions are evaluated and compared with one another. They give rise to expressions for the spatially dependent heating of the background plasma, as a function of the instantaneous laser and plasma parameters, in either planar or spherical geometry. These formulas are simple, universal (depending weakly only on the single parameter Z, the charge state), and can be easily be incorporated into a fluid simulation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Fokker-Planck equation in the presence of a uniform magnetic field

The Fokker-Planck equation in the presence of a uniform magnetic field is derived which has the same form as the case of no magnetic field but with different Fokker-Planck coefficients. The coefficients are calculated explicitly within the binary collision model, which are free from infinite sums of Bessel functions. They can be used to investigate relaxation and transport phenomena conveniently. The kinetic equation is also manipulated into the Landau form from which it is straightforward to compare with previous results and prove the conservation laws.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

NUMERICAL ANALYSIS OF THE FOKKER-PLANCK EQUATION WITH ADIABATIC FOCUSING: ISOTROPIC PITCH-ANGLE SCATTERING

We present numerical solutions to both the standard and modified two-dimensional Fokker-Planck equations with adiabatic focusing and isotropic pitch-angle scattering. With the numerical solution of the particle distribution function, we then discuss the related numerical issues, calculate the parallel diffusion coefficient using several different methods, and compare our numerical solutions for the parallel diffusion coefficient to the analytical forms derived earlier. We find the numerical solution to the diffusion coefficient for both the standard and modified Fokker-Planck equations agrees with that of Shalchi for the mean squared displacement method of computing the diffusion coefficient. However, we also show the numerical solution agrees with that of Litvinenko and Shalchi and Danos when calculating the diffusion coefficient via the velocity correlation function.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Sensitivity analysis for dose deposition in radiotherapy via a Fokker–Planck model

In this paper, we study the sensitivities of electron dose calculations with respect to stopping power and transport coefficients. We focus on the application to radiotherapy simulations. We use a Fokker–Planck approximation to the Boltzmann transport equation. Equations for the sensitivities are derived by the adjoint method. The Fokker–Planck equation and its adjoint are solved numerically in slab geometry using the spherical harmonics expansion (P N ) and an Harten-Lax-van Leer finite volume method. Our method is verified by comparison to finite difference approximations of the sensitivities. Finally, we present numerical results of the sensitivities for the normalized average dose deposition depth with respect to the stopping power and the transport coefficients, demonstrating the increase in relative sensitivities as beam energy decreases. In conclusion, this in turn gives estimates on the uncertainty in the normalized average deposition depth, which we present.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2015

SU-E-T-22: A Deterministic Solver of the Boltzmann-Fokker-Planck Equation for Dose Calculation

Purpose: The Boltzmann-Fokker-Planck equation (BFPE) accurately models the migration of photons/charged particles in tissues. While the Monte Carlo (MC) method is popular for solving BFPE in a statistical manner, we aim to develop a deterministic BFPE solver based on various state-of-art numerical acceleration techniques for rapid and accurate dose calculation. Methods: Our BFPE solver is based on the structured grid that is maximally parallelizable, with the discretization in energy, angle and space, and its cross section coefficients are derived or directly imported from the Geant4 database. The physical processes that are taken into account are Compton scattering, photoelectric effect, pair production for photons, and elastic scattering, ionization and bremsstrahlung for charged particles.While the spatial discretization is based on the diamond scheme, the angular discretization synergizes finite element method (FEM) and spherical harmonics (SH). Thus, SH is used to globally expand the scattering kernel and FFM is used to locally discretize the angular sphere. As a Result, this hybrid method (FEM-SH) is both accurate in dealing with forward-peaking scattering via FEM, and efficient for multi-energy-group computation via SH. In addition, FEM-SH enables the analytical integration in energy variable of delta scattering kernel for elastic scattering with reduced truncation error from the numerical integration based on the classic SH-based multi-energy-group method. Results: The accuracy of the proposed BFPE solver was benchmarked against Geant4 for photon dose calculation. In particular, FEM-SH had improved accuracy compared to FEM, while both were within 2% of the results obtained with Geant4. Conclusion: A deterministic solver of the Boltzmann-Fokker-Planck equation is developed for dose calculation, and benchmarked against Geant4. Xiang Hong and Hao Gao were partially supported by the NSFC (#11405105), the 973 Program (#2015CB856000) and the Shanghai Pujiang Talent Program (#14PJ1404500)

60 APPLIED LIFE SCIENCES↗
DOE OSTI2017

FOKKER-PLANCK ANALYSIS OF TRANSVERSE COLLECTIVE INSTABILITIES IN ELECTRON STORAGE RINGS

We analyze single bunch transverse instabilities due to wakefields using a Fokker-Planck model. We expand on the work of Suzuki [1], writing out the linear matrix equation including chromaticity, both dipolar and quadrupolar transverse wakefields, and the effects of damping and diffusion due to the synchrotron radiation. The eigenvalues and eigenvectors determine the collective stability of the beam, and we show that the predicted threshold current for transverse instability and the profile of the unstable agree well with tracking simulations. In particular, we find that predicting collective stability for high energy electron beams at moderate to large values of chromaticity requires the full Fokker-Planck analysis to properly account for the effects of damping and diffusion due to synchrotron radiation.

FOKKER-PLANCK ANALYSIS↗
DOE OSTI2012

Moment-Preserving SN Discretizations for the One-Dimensional Fokker-Planck Equation

The Fokker-Planck equation: (1) Describes the transport and interactions of charged particles, (2) Many small-angle scattering collisions, (3) Asymptotic limit of the Boltzmann equation (Pomraning, 1992), and (4) The Boltzmann collision operator becomes the angular Laplacian. SN angular discretization: (1) Angular flux is collocated at the SN quadrature points, (2) The second-order derivatives in the Laplacian term must be discretized, and (3) Weighted finite-difference method preserves zeroth and first moments (Morel, 1985). Moment-preserving methods: (1) Collocate the Fokker-Planck operator at the SN quadrature points, (2) Develop several related and/or equivalent methods, and (3) Motivated by discretizations for the angular derivative appearing in the transport equation in one-dimensional spherical coordinates.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Cosmological constraints from the Planck cluster catalogue with DES shear profiles and Chandra observations

We present cosmological constraints from the Planck PSZ2 cosmological cluster sample, using weak-lensing shear profiles from Dark Energy Survey (DES) data and X-ray observations from the Chandra telescope for the mass calibration. We compute hydrostatic mass estimates for all clusters in the PSZ2 sample with a scaling relation between their Sunyaev-Zeldovich signal and X-ray derived hydrostatic mass, calibrated with the Chandra data. We introduce a method to correct these masses with a hydrostatic mass bias using shear profiles from wide-field galaxy surveys. We simultaneously fit the number counts of the PSZ2 sample and the mass calibration with the DES data, finding $Ω_\text{m}=0.312^{+0.018}_{-0.024}$, $σ_8=0.777\pm 0.024$, $S_8\equiv σ_8 \sqrt{Ω_\text{m} / 0.3}=0.791^{+0.023}_{-0.021}$, and $(1-b)=0.844^{+0.055}_{-0.062}$ for our baseline analysis when combined with BAO data. When considering a hydrostatic mass bias evolving with mass, we find $Ω_\text{m}=0.353^{+0.025}_{-0.031}$, $σ_8=0.751\pm 0.023$, and $S_8=0.814^{+0.019}_{-0.020}$. We verify the robustness of our results by exploring a variety of analysis settings, with a particular focus on the definition of the halo centre used for the extraction of shear profiles. We compare our results with a number of other analyses, in particular two recent analyses of cluster samples obtained from SPT and eROSITA data that share the same mass calibration data set. We find that our results are in overall agreement with most late-time probes, in very mild tension with CMB results (1.6$σ$), and in significant tension with results from eROSITA clusters (2.9$σ$). We confirm that our mass calibration is consistent with the eROSITA analysis by comparing masses for clusters present in both Planck and eROSITA samples, eliminating it as a potential cause of tension.

Aymerich, G. [Orsay, IAS; AIM, Saclay] (ORCID:0009↗
DOE OSTI2025

End–to–End Metasurface Design for Temperature Imaging via Broadband Planck‐Radiation Regression

A theoretical framework is presented for temperature imaging from long-wavelength infrared (LWIR) thermal radiation (e.g., 8–12 µm) through the end-to-end design of a metasurface-optics frontend and a computational-reconstruction backend. A new nonlinear reconstruction algorithm, “Planck regression”, is introduced to reconstruct the temperature map from a gray scale sensor image, even in the presence of severe chromatic aberration, by exploiting black body and optical physics particular to thermal imaging. This algorithm is combined with an end-to-end approach that optimizes manufacturable, single-layer metasurfaces to yield the most accurate reconstruction. The designs demonstrate high-quality, noise-robust reconstructions of arbitrary temperature maps (including completely random images) in simulations of an ultra-compact thermal-imaging device. Here, it is also shown that Planck regression is much more generalizable to arbitrary images than a straightforward neural-network reconstruction, which requires a large training set of domain-specific images.

36 MATERIALS SCIENCE↗
DOE OSTI2017

The quantum Fokker-Planck equation of stochastic inflation

We derive the stochastic description of a massless, interacting scalar field in de Sitter space directly from the quantum theory. This is done by showing that the density matrix for the effective theory of the long wavelength fluctuations of the field obeys a quantum version of the Fokker-Planck equation. This equation has a simple connection with the standard Fokker-Planck equation of the classical stochastic theory, which can be generalised to any order in perturbation theory. We illustrate this formalism in detail for the theory of a massless scalar field with a quartic interaction.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

Planck 2015 constraints on spatially-flat dynamical dark energy models

We determine constraints on spatially-flat tilted dynamical dark energy XCDM and ΦCDM inflation models by analyzing Planck 2015 cosmic microwave background (CMB) anisotropy data and baryon acoustic oscillation (BAO) distance measurements. XCDM is a simple and widely used but physically inconsistent parameterization of dynamical dark energy, while the ΦCDM model is a physically consistent one in which a scalar field Φ with an inverse power-law potential energy density powers the currently accelerating cosmological expansion. Both these models have one additional parameter compared to standard ΛCDM and both better fit the TT + lowP + lensing + BAO data than does the standard tilted flat-ΛCDM model, with Δχ 2 = –1.26 (–1.60) for the XCDM (ΦCDM) model relative to the ΛCDM model. Here, while this is a 1.1σ (1.3σ) improvement over standard ΛCDM and so not significant, dynamical dark energy models cannot be ruled out. In addition, both dynamical dark energy models reduce the tension between the Planck 2015 CMB anisotropy and the weak lensing σ8 constraints.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Limit on graviton mass using stacked galaxy cluster catalogs from SPT-SZ, Planck-SZ and SDSS-redMaPPer

In the last few years, there has been a resurgence of interest in obtaining observational bounds on the graviton mass, following the detection of gravitational waves, because of the versatility of massive graviton theories in resolving multiple problems in cosmology and fundamental physics. In this work, we apply the method proposed in Rana et al., (2018), which consists of looking for Yukawa-like fall off in the gravitational potential, to stacked galaxy cluster catalogs from three disparate surveys. These include catalogs from 2500 sq. degree SPT-SZ survey, the Planck all-sky SZ catalog, and a redMaPPer selected catalog from 10,000 sq. degree of SDSS-DR8 data. The 90% c.l. limits which we obtained on the graviton mass using SPT, Planck and SDSS are: m{sub g}<4.73×10{sup −30} eV, 3.0×10{sup −30} eV, and 1.27×10{sup −30} eV respectively; or in terms of Compton wavelength are λ{sub g}>2.62×10{sup 20} km, 4.12×10{sup 20} km, 9.76×10{sup 20} km. These limits are about five times more stringent than the previous best bound from galaxy clusters.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

Planck intermediate results (Corrigendum) : V. Pressure profiles of galaxy clusters from the Sunyaev-Zeldovich effect

Figure 7 of our original publication (Planck Collaboration 2013) is flawed. The correct figure is presented here and we stress that our original conclusion on the radial distribution of the gas fraction remains unchanged. There was an error in the reconstruction of the temperature profiles used to derive the gas mass distribution from the joint Planck and XMM-Newton pressure profile, and thereby a prediction for the gas fraction profiles. The error in the temperature profile reconstruction applies to this paper only. The predicted gas fraction profiles for both hypothesis on the temperature profiles, i.e., from hypothesis H1 and H2, were affected similarly. Now corrected, they are in better agreement at R 500 with the measurement by Pratt et al. (2009) on the REXCESS sample and with the expectations from the CMB. The Perseus profile (Simionescu et al. 2011) is still marginally compatible with our prediction within our large dispersion (shaded blue and red area on the figure).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

Planck intermediate results. XII: Diffuse Galactic components in the Gould Belt system

We perform here an analysis of the diffuse low-frequency Galactic components in the southern part of the Gould Belt system (130° ≤ l ≤ 230° and -50° ≤ b ≤ -10°). Strong ultra-violet flux coming from the Gould Belt super-association is responsible for bright diffuse foregrounds that we observe from our position inside the system and that can help us improve our knowledge of the Galactic emission. Free-free emission and anomalous microwave emission (AME) are the dominant components at low frequencies (ν < 40 GHz), while synchrotron emission is very smooth and faint. We separated diffuse free-free emission and AME from synchrotron emission and thermal dust emission by using Planck data, complemented by ancillary data, using the correlated component analysis (CCA) component-separation method and we compared our results with the results of cross-correlation of foreground templates with the frequency maps. We estimated the electron temperature T e from Hα and free-free emission using two methods (temperature-temperature plot and cross-correlation) and obtained T e ranging from 3100 to 5200K for an effective fraction of absorbing dust along the line of sight of 30% (f d = 0.3). We estimated the frequency spectrum of the diffuse AME and recovered a peak frequency (in flux density units) of 25.5 ± 1.5 GHz. We verified the reliability of this result with realistic simulations that include biases in the spectral model for the AME and in the free-free template. By combining physical models for vibrational and rotational dust emission and adding the constraints from the thermal dust spectrum from Planck and IRAS, we are able to present a good description of the AME frequency spectrum for plausible values of the local density and radiation field.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Planck 2013 results. XX. Cosmology from Sunyaev–Zeldovich cluster counts

We present constraints on cosmological parameters using number counts as a function of redshift for a sub-sample of 189 galaxy clusters from the Planck SZ (PSZ) catalogue. The PSZ is selected through the signature of the Sunyaev-Zeldovich (SZ) effect, and the sub-sample used here has a signal-to-noise threshold of seven, with each object confirmed as a cluster and all but one with a redshift estimate. We discuss the completeness of the sample and our construction of a likelihood analysis. Using a relation between mass M and SZ signal Y calibrated to X-ray measurements, we derive constraints on the power spectrum amplitude σ8 and matter density parameter Ω m in a flat ΛCDM model. We test the robustness of our estimates and find that possible biases in the Y&ndash;M relation and the halo mass function are larger than the statistical uncertainties from the cluster sample. Assuming the X-ray determined mass to be biased low relative to the true mass by between zero and 30%, motivated by comparison of the observed mass scaling relations to those from a set of numerical simulations, we find that σ 8 = 0.75 ± 0.03, Ω m = 0.29 ± 0.02, and σ 8 (Ω m /0.27) 0.3 = 0.764 ± 0.025. The value of σ 8 is degenerate with the mass bias; if the latter is fixed to a value of 20% (the central value from numerical simulations) we find σ 8 (Ω m /0.27) 0.3 = 0.78 ± 0.01 and a tighter one-dimensional range σ 8 = 0.77 ± 0.02. We find that the larger values of σ 8 and Ω m preferred by Planck's measurements of the primary CMB anisotropies can be accommodated by a mass bias of about 40%. Alternatively, consistency with the primary CMB constraints can be achieved by inclusion of processes that suppress power on small scales relative to the ΛCDM model, such as a component of massive neutrinos. We place our results in the context of other determinations of cosmological parameters, and discuss issues that need to be resolved in order to make further progress in this field.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Planck 2013 results. V. LFI calibration

We discuss the methods employed to photometrically calibrate the data acquired by the Low Frequency Instrument on Planck. Our calibration is based on a combination of the orbital dipole plus the solar dipole, caused respectively by the motion of the Planck spacecraft with respect to the Sun and by motion of the solar system with respect to the cosmic microwave background (CMB) rest frame. The latter provides a signal of a few mK with the same spectrum as the CMB anisotropies and is visible throughout the mission. In this data releasewe rely on the characterization of the solar dipole as measured by WMAP. We also present preliminary results (at 44 GHz only) on the study of the Orbital Dipole, which agree with the WMAP value of the solar system speed within our uncertainties. We compute the calibration constant for each radiometer roughly once per hour, in order to keep track of changes in the detectors’ gain. Since non-idealities in the optical response of the beams proved to be important, we implemented a fast convolution algorithm which considers the full beam response in estimating the signal generated by the dipole. Moreover, in order to further reduce the impact of residual systematics due to sidelobes, we estimated time variations in the calibration constant of the 30 GHz radiometers (the ones with the largest sidelobes) using the signal of an internal reference load at 4 K instead of the CMB dipole. We have estimated the accuracy of the LFI calibration following two strategies: (1) we have run a set of simulations to assess the impact of statistical errors and systematic effects in the instrument and in the calibration procedure; and (2) we have performed a number of internal consistency checks on the data and on the brightness temperature of Jupiter. Errors in the calibration of this Planck/LFI data release are expected to be about 0.6% at 44 and 70 GHz, and 0.8% at 30 GHz. Both these preliminary results at low and high ℓ are consistent with WMAP results within uncertainties and comparison of power spectra indicates good consistency in the absolute calibration with HFI (0.3%) and a 1.4σ discrepancy with WMAP (0.9%).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Planck 2013 results. XXIII. Isotropy and statistics of the CMB

The two fundamental assumptions of the standard cosmological model-that the initial fluctuations are statistically isotropic and Gaussian-are rigorously tested using maps of the cosmic microwave background (CMB) anisotropy from the Planck satellite. The detailed results are based on studies of four independent estimates of the CMB that are compared to simulations using a fiducial ΛCDM model and incorporating essential aspects of the Planck measurement process. Deviations from isotropy have been found and demonstrated to be robust against component separation algorithm, mask choice, and frequency dependence. Many of these anomalies were previously observed in the WMAP data, and are now confirmed at similar levels of significance (about 3σ). However, we find little evidence of non-Gaussianity, with the exception of a few statistical signatures that seem to be associated with specific anomalies. In particular, we find that the quadrupole-octopole alignment is also connected to a low observed variance in the CMB signal. A power asymmetry is now found to persist on scales corresponding to about &ell; = 600 and can be described in the low-&ell; regime by a phenomenological dipole modulation model. However, any primordial power asymmetry is strongly scale-dependent and does not extend to arbitrarily small angular scales. Finally, it is plausible that some of these features may be reflected in the angular power spectrum of the data, which shows a deficit of power on similar scales. Indeed, when the power spectra of two hemispheres defined by a preferred direction are considered separately, one shows evidence of a deficit in power, while its opposite contains oscillations between odd and even modes that may be related to the parity violation and phase correlations also detected in the data. Although these analyses represent a step forward in building an understanding of the anomalies, a satisfactory explanation based on physically motivated models is still lacking.

79 ASTRONOMY AND ASTROPHYSICS↗