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C. Vocks - One of the best experts on this subject based on the ideXlab platform.
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a kinetic model for ions in the solar corona including wave particle interactions and Coulomb Collisions
The Astrophysical Journal, 2002Co-Authors: C. VocksAbstract:A model for the kinetics of ions in the solar corona is presented. The model includes wave-particle interactions within the framework of quasi-linear theory and Coulomb Collisions calculated by using the Landau collision integral. The integration of the ion velocity distribution functions (VDFs) over the velocity components perpendicular to the background magnetic field yields so-called reduced VDFs. Coupled Vlasov equations for these reduced VDFs are derived. Since they depend only on the coordinate s, speed v∥, and time t, they can be solved numerically with reasonable effort. The model equations guarantee conservation of energy between waves and particles. The Vlasov equations are solved using a temporal relaxation scheme. Tests of the numerical method concerning conservation of momentum and energy, relaxation into thermal equilibrium, and the reproduction of the shape of the known VDF in the case of a temperature gradient have been performed successfully. Kinetic results for ions in a coronal funnel are presented. They show a preferred heating of the heavy ions in agreement with solar observations and strong deviations of their reduced VDFs from a Maxwellian distribution function. An extensive discussion of the model results for the solar corona is presented in a companion paper.
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Kinetic Results for Ions in the Solar Corona with Wave-Particle Interactions and Coulomb Collisions
The Astrophysical Journal, 2002Co-Authors: C. VocksAbstract:In a companion paper, a kinetic model for ions in the solar corona has been described. The model is based on reduced velocity distribution functions (VDFs) that depend only on one spatial coordinate s and one velocity component v ∥ along the background magnetic field, and includes wave-particle interactions and Coulomb Collisions. In this paper, numerical solutions of the kinetic equations for various ions in a coronal funnel and a coronal hole are presented. It is found that heavy ions are heated preferentially and that sizable temperature anisotropies form, results that are in accord with Solar and Heliospheric Observatory observations. The reduced VDFs of the heavy ions are found to develop pronounced deviations from a Maxwellian, which increase with height because of the decrease of the density, and thus of the efficiency of Coulomb Collisions. Calculations of the wave damping/growth rate γ show that the VDFs can reach the limit of marginal stability over a wide range of resonance speeds, at which wave absorption ceases. The consequences for the spectral evolution of the waves in the corona are discussed. The way in which the heavy ion mass and charge influence the kinetic model results is also studied.
Russell M Kulsrud - One of the best experts on this subject based on the ideXlab platform.
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effect of Coulomb Collisions on time variations of the solar neutrino flux
Monthly Notices of the Royal Astronomical Society, 2000Co-Authors: Leonid Malyshkin, Russell M KulsrudAbstract:We consider the processes that might suppress the time variations in the solar neutrino flux produced by the radial motion of the Earth through the neutrino interference pattern. We calculate these time variations and the extent to which they are suppressed by Coulomb Collisions of the neutrino-emitting nuclei. This is done for both the 0.862-MeV 7Be neutrino line and the continuous neutrino spectrum, assuming a Gaussian energy response function of the neutrino detector. We find that the collisional decoherence averages out the time variations for neutrino masses A simple and clear physical picture of the time-dependent solar neutrino problem is presented and qualitative coherence criteria are discussed.
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effect of Coulomb Collisions on time variations of the solar neutrino flux
arXiv: Astrophysics, 1999Co-Authors: Leonid Malyshkin, Russell M KulsrudAbstract:We consider the possibility of time variations of the solar neutrino flux due to the radial motion of the Earth and neutrino interference effects. We calculate the time variations of the detected neutrino flux and the extent to which they are suppressed by Coulomb Collisions of the neutrino emitting nuclei. To properly treat the Collisions, it is necessary to simultaneously include in our analysis all other significant physical decoherence effects: the energy averaging and the averaging over the position of neutrino emission. A simple and clear physical picture of the time dependent solar neutrino problem is presented and qualitative coherence criteria are discussed. Exact results for the detected neutrino flux and its time variations are obtained for both the case of a solar neutrino line, and the case of the continuous neutrino spectrum with a Gaussian shape of the energy response function of the neutrino detector. We give accurate constraints on the vacuum mixing angle and the neutrino masses required for flux time variations to not be suppressed. Pac(s): 26.65.+t, 14.60.Pq, 96.60.Jw
Bernie D. Shizgal - One of the best experts on this subject based on the ideXlab platform.
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Fokker-Planck equation for Coulomb relaxation and wave-particle diffusion: Spectral solution and the stability of the Kappa distribution to Coulomb Collisions.
Physical Review E, 2020Co-Authors: Wucheng Zhang, Bernie D. ShizgalAbstract:The present paper considers the time evolution of a charged test particle of mass $m$ in a constant temperature heat bath of a second charged particle of mass $M$. The time dependence of the distribution function of the test particles is given by a Fokker-Planck equation with a diffusion coefficient for Coulomb Collisions as well as a diffusion coefficient for wave-particle interactions. For the mass ratio $m/M\ensuremath{\rightarrow}0$, the steady distribution is a Kappa distribution which has been employed in space physics to fit observed particle energy spectra. The time dependence of the distribution functions with some initial value is expressed in terms of the eigenvalues and eigenfunctions of the linear Fokker-Planck operator and also interpreted with the transformation to a Schr\"odinger equation. We also consider the explicit time dependence of the distribution function with a discretization of the Fokker-Planck equation. We study the stability of the Kappa distribution to Coulomb Collisions.
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Fokker-Planck equation for Coulomb relaxation and wave-particle diffusion: Spectral solution and the stability of the Kappa distribution to Coulomb Collisions.
Physical review. E, 2020Co-Authors: Wucheng Zhang, Bernie D. ShizgalAbstract:The present paper considers the time evolution of a charged test particle of mass m in a constant temperature heat bath of a second charged particle of mass M. The time dependence of the distribution function of the test particles is given by a Fokker-Planck equation with a diffusion coefficient for Coulomb Collisions as well as a diffusion coefficient for wave-particle interactions. For the mass ratio m/M→0, the steady distribution is a Kappa distribution which has been employed in space physics to fit observed particle energy spectra. The time dependence of the distribution functions with some initial value is expressed in terms of the eigenvalues and eigenfunctions of the linear Fokker-Planck operator and also interpreted with the transformation to a Schrödinger equation. We also consider the explicit time dependence of the distribution function with a discretization of the Fokker-Planck equation. We study the stability of the Kappa distribution to Coulomb Collisions.
S A Gonzalez - One of the best experts on this subject based on the ideXlab platform.
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corection of the jicamarca electron ion temperature ratio problem verifying the effect of electron Coulomb Collisions on the incoherent scatter spectrum
Journal of Geophysical Research, 2001Co-Authors: Nestor Aponte, M P Sulzer, S A GonzalezAbstract:Ever since the first attempts to fit Jicamarca autocorrelation function (ACF) measurements in the 1970s using a full nonlinear least squares analysis, an apparent electron-ion temperature ratio below unity has been deduced for a large portion of the F region data. The cause of this unexpected and geophysically unreasonable result has been a mystery until recently, when Sulzer and Gonzalez [1999] (herein SG) explained how electron Coulomb Collisions can distort, or narrow, the incoherent backscatter spectrum, and that for this narrowing to be observable two conditions must be met. First, the radar k vector must lie in a small range near perpendicular to the magnetic field, and second, the radar wavelength must be sufficiently long. Both of these conditions are true at Jicamarca. The accurate calculations from the SG theory are now available in a compact library, which we have incorporated into an incoherent scatter least squares fitting code. Using this code, we have reduced Jicamarca ACF data taken with the Faraday double-pulse mode, and find that the SG theory correctly interprets the ACF data from Jicamarca, thereby solving the longstanding Te/Ti ratio problem and thus allowing accurate electron and ion temperature measurements.
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the effect of electron Coulomb Collisions on the incoherent scatter spectrum in the f region at jicamarca
Journal of Geophysical Research, 1999Co-Authors: M P Sulzer, S A GonzalezAbstract:The fact that the incoherent backscatter spectrum narrows when the radar beam is nearly perpendicular to the magnetic field is well known and has been used at Jicamarca for more than 30 years to measure very accurate line-of-sight velocities. Recently it has become clear that these spectra are narrower than expected. We have explained this effect and also the small change to the spectral shape required at somewhat larger angles to correct the ratio of electron to ion temperature seen in some studies. Coulomb Collisions affecting the motion of the electrons are responsible for the additional spectral narrowing. We have carried out very accurate simulations of electron motion resulting in incoherent scatter spectra which are qualitatively similar to spectra resulting from other types of Collisions, and to those predicted in an analytic solution for the Coulomb case [Woodman, 1967]. However, we found that the spectrum of the velocity time series in the radar line of sight departs significantly from the nearly Lorentzian form expected with simple collisional models. This causes the collisional effects to extend to somewhat shorter scale lengths, or further from perpendicular to the magnetic field than expected. In order to investigate the collisional process more closely, we performed another simulation combining the effects of electron-ion Collisions and a simple friction model (Langevin equation) in an adjustable combination. This one showed that the effect of electron-ion Collisions alone would result in collisional effects extending several degrees farther from perpendicular to the field than when both kinds of Collisions are included. Collisions affecting the speed of the electrons tend to limit the size of the effect at larger angles from perpendicular. Thus the effect of these Collisions on the incoherent scatter spectrum cannot be accurately predicted from simple models but depends on the detailed physics of the Collisions.
Russel E. Caflisch - One of the best experts on this subject based on the ideXlab platform.
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A Monte Carlo method with negative particles for Coulomb Collisions
Journal of Computational Physics, 2015Co-Authors: Bokai Yan, Russel E. CaflischAbstract:In this work we propose a novel negative particle method for the general bilinear collision operators in the spatial homogeneous case and apply it to Coulomb Collisions. This new method successfully reduces the growth of particle numbers from the numerical time scale to the physical time scale for Coulomb Collisions. We also propose a particle resampling method which reduces the particle number to further improve the efficiency. Various numerical simulations are performed to demonstrate the accuracy and efficiency of the method.
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Multilevel Monte Carlo simulation of Coulomb Collisions
Journal of Computational Physics, 2014Co-Authors: M. S. Rosin, Russel E. Caflisch, Andris M. Dimits, Lee Ricketson, Bruce I. CohenAbstract:We present a new, for plasma physics, highly efficient multilevel Monte Carlo numerical method for simulating Coulomb Collisions. The method separates and optimally minimizes the finite-timestep and finite-sampling errors inherent in the Langevin representation of the Landau-Fokker-Planck equation. It does so by combining multiple solutions to the underlying equations with varying numbers of timesteps. For a desired level of accuracy @e, the computational cost of the method is O(@e^-^2) or O(@e^-^2([email protected])^2), depending on the underlying discretization, Milstein or Euler-Maruyama respectively. This is to be contrasted with a cost of O(@e^-^3) for direct simulation Monte Carlo or binary collision methods. We successfully demonstrate the method with a classic beam diffusion test case in 2D, making use of the Levy area approximation for the correlated Milstein cross terms, and generating a computational saving of a factor of 100 for @e=10^-^5. We discuss the importance of the method for problems in which Collisions constitute the computational rate limiting step, and its limitations.
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higher order time integration of Coulomb Collisions in a plasma using langevin equations
Journal of Computational Physics, 2013Co-Authors: A M Dimits, Russel E. Caflisch, M. S. Rosin, B I Cohen, Lee RicketsonAbstract:The extension of Langevin-equation Monte-Carlo algorithms for Coulomb Collisions from the conventional Euler-Maruyama time integration to the next higher order of accuracy, the Milstein scheme, has been developed, implemented, and tested. This extension proceeds via a formulation of the angular scattering directly as stochastic differential equations in the fixed-frame spherical-coordinate velocity variables. Results from the numerical implementation show the expected improvement [O(@Dt) vs. O(@Dt^1^/^2)] in the strong convergence rate both for the speed |v| and angular components of the scattering. An important result is that this improved convergence is achieved for the angular component of the scattering if and only if the ''area-integral'' terms in the Milstein scheme are included. The resulting Milstein scheme is of value as a step towards algorithms with both improved accuracy and efficiency. These include both algorithms with improved convergence in the averages (weak convergence) and multi-time-level schemes. The latter have been shown to give a greatly reduced cost for a given overall error level when compared with conventional Monte-Carlo schemes, and their performance is improved considerably when the Milstein algorithm is used for the underlying time advance versus the Euler-Maruyama algorithm. A new method for sampling the area integrals is given which is a simplification of an earlier direct method and which retains high accuracy. This method, while being useful in its own right because of its relative simplicity, is also expected to considerably reduce the computational requirements for the direct conditional sampling of the area integrals that is needed for adaptive strong integration.
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Calculation of the Nanbu-Trubnikov Kernel: Implications for Numerical Modeling of Coulomb Collisions*
Bulletin of the American Physical Society, 2008Co-Authors: Andris M. Dimits, Russel E. Caflisch, Chiaming Wang, Bruce I. Cohen, Yanghong HuangAbstract:We investigate the accuracy of and assumptions underlying the numerical binary Monte-Carlo collision operator due to Nanbu [K. Nanbu, Phys. Rev. E 55 (1997)]. The numerical experiments that resulted in Nanbu's parameterized collision kernel are approximate realizations of the Coulomb-Lorentz pitch-angle scattering process, for which an analytical solution is available. It is demonstrated empirically that Nanbu's collision operator quite accurately recovers the effects of Coulomb-Lorentz pitch-angle Collisions, or processes that approximate these even for very large values of the collisional time step. An investigation of the analytical solution shows that Nanbu's parameterized kernel is highly accurate for small values of the normalized collision time step, but loses some of its accuracy for larger values of the time step. Finally, a practical collision algorithm is proposed that for small-mass-ratio Coulomb Collisions improves on the accuracy of Nanbu's algorithm.
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Calculation of the Trubnikov and Nanbu Collision Kernels: Implications for Numerical Modeling of Coulomb Collisions
2008Co-Authors: A M Dimits, Russel E. Caflisch, Chiaming Wang, B I Cohen, Yanghong HuangAbstract:We investigate the accuracy of and assumptions underlying the numerical binary Monte-Carlo collision operator due to Nanbu [K. Nanbu, Phys. Rev. E 55 (1997)]. The numerical experiments that resulted in the parameterization of the collision kernel used in Nanbu's operator are argued to be an approximate realization of the Coulomb-Lorentz pitch-angle scattering process, for which an analytical solution for the collision kernel is available. It is demonstrated empirically that Nanbu's collision operator quite accurately recovers the effects of Coulomb-Lorentz pitch-angle Collisions, or processes that approximate these (such interspecies Coulomb Collisions with very small mass ratio) even for very large values of the collisional time step. An investigation of the analytical solution shows that Nanbu's parameterized kernel is highly accurate for small values of the normalized collision time step, but loses some of its accuracy for larger values of the time step. Careful numerical and analytical investigations are presented, which show that the time dependence of the relaxation of a temperature anisotropy by Coulomb-Lorentz Collisions has a richer structure than previously thought, and is not accurately represented by an exponential decay with a single decay rate. Finally, a practical collision algorithm is proposed that for small-mass-ratio interspecies Coulomb Collisions improves onmore » the accuracy of Nanbu's algorithm.« less
