Coupling of charged particles via Coulombic interactions: Numerical simulations and resultant kappa-like velocity space distribution functions

2016 ◽  
Vol 121 (3) ◽  
pp. 1907-1919 ◽  
Author(s):  
Brent M. Randol ◽  
Eric R. Christian
Keyword(s):  
Numerical Simulations ◽  
Charged Particles ◽  
Distribution Functions ◽  
Velocity Space ◽  
Space Distribution ◽  
Coulombic Interactions

Orbit Tomography of energetic particle distribution functions

2021 ◽  
Author(s):  
Luke Stagner ◽  
William W Heidbrink ◽  
Mirko Salewski ◽  
Asger Schou Jacobsen ◽  
Benedikt Geiger
Keyword(s):  
Distribution Function ◽  
Phase Space ◽  
Energetic Particle ◽  
Particle Distribution ◽  
Distribution Functions ◽  
Velocity Space ◽  
Space Distribution ◽  
Weight Functions ◽  
Ion Distribution ◽  
Fast Ions

Abstract Both fast ions and runaway electrons are described by distribution functions, the understanding of which are of critical importance for the success of future fusion devices such as ITER. Typically, energetic particle diagnostics are only sensitive to a limited subsection of the energetic particle phase-space which is often insufficient for model validation. However, previous publications show that multiple measurements of a single spatially localized volume can be used to reconstruct a distribution function of the energetic particle velocity-space by using the diagnostics' velocity-space weight functions, i.e. Velocity-space Tomography. In this work we use the recently formulated orbit weight functions to remove the restriction of spatially localized measurements and present Orbit Tomography, which is used to reconstruct the 3D phase-space distribution of all energetic particle orbits in the plasma. Through a transformation of the orbit distribution, the full energetic particle distribution function can be determined in the standard {energy,pitch,r,z}-space. We benchmark the technique by reconstructing the fast-ion distribution function of an MHD-quiescent DIII-D discharge using synthetic and experimental FIDA measurements. We also use the method to study the redistribution of fast ions during a sawtooth crash at ASDEX Upgrade using FIDA measurements. Finally, a comparison between the Orbit Tomography and Velocity-space Tomography is shown.

scholarly journals Non-Linear Langevin and Fractional Fokker–Planck Equations for Anomalous Diffusion by Lévy Stable Processes

Entropy ◽  
2018 ◽  
Vol 20 (10) ◽  
pp. 760 ◽  
Author(s):  
Johan Anderson ◽  
Sara Moradi ◽  
Tariq Rafiq
Keyword(s):  
Anomalous Diffusion ◽  
Transport Coefficient ◽  
Numerical Solutions ◽  
Distribution Functions ◽  
Space Distribution ◽  
Non Linear ◽  
Non Local ◽  
Local Transport ◽  
Fokker Planck Equations ◽  
Fokker Planck

The numerical solutions to a non-linear Fractional Fokker–Planck (FFP) equation are studied estimating the generalized diffusion coefficients. The aim is to model anomalous diffusion using an FFP description with fractional velocity derivatives and Langevin dynamics where Lévy fluctuations are introduced to model the effect of non-local transport due to fractional diffusion in velocity space. Distribution functions are found using numerical means for varying degrees of fractionality of the stable Lévy distribution as solutions to the FFP equation. The statistical properties of the distribution functions are assessed by a generalized normalized expectation measure and entropy and modified transport coefficient. The transport coefficient significantly increases with decreasing fractality which is corroborated by analysis of experimental data.

Subgrid modelling of ion pitch-angle scattering for magnetosheath waves in a global hybrid-Vlasov simulation

2021 ◽  
Author(s):  
Maxime Dubart ◽  
Urs Ganse ◽  
Adnane Osmane ◽  
Andreas Johlander ◽  
Markus Battarbee ◽  
...  
Keyword(s):  
Velocity Distribution ◽  
Numerical Simulations ◽  
Spatial Resolution ◽  
Pitch Angle ◽  
Space Physics ◽  
Distribution Functions ◽  
Cyclotron Instability ◽  
Angle Scattering ◽  
Velocity Distribution Functions ◽  
Proton Cyclotron

<p>Numerical simulations are widely used in modern space physics and are an essential tool to understand or discover new phenomena which cannot be observed using spacecraft measurements. However, numerical simulations are limited by the space grid resolution of the system and the computational costs of having a high spatial resolution. Therefore, some physics may be unresolved in part of the system due to its low spatial resolution. We have previously identified, using Vlasiator, that the proton cyclotron instability is not resolved for grid cell sizes larger than four times the inertial length in the solar wind, for waves in the downstream of the quasi-perpendicular shock in the magnetosheath of a global hybrid-Vlasov simulation. This leads to unphysically high perpendicular temperature and a dominance of the mirror mode waves. In this study, we use high-resolution simulations to measure and quantify how the proton cyclotron instability diffuses and isotropizes the velocity distribution functions. We investigate the process of pitch-angle scattering during the development of the instability and propose a method for the sub-grid modelling of the diffusion process of the instability at low resolution. This allows us to model the isotropization of the velocity distribution functions and to reduce the temperature anisotropy in the plasma while saving computational resources.</p>

Die kinetische Energie ionisierter Molekülfragmente I. Methodik

1964 ◽  
Vol 19 (4) ◽  
pp. 484-493 ◽  
Author(s):  
Rolf Taubert
Keyword(s):  
Probability Function ◽  
Solid Angle ◽  
Initial Energy ◽  
Ion Source ◽  
Distribution Functions ◽  
Velocity Space ◽  
Ion Current ◽  
Molecular Fragments ◽  
Fragment Ions ◽  
Energy Distribution Functions

Methods of measuring initial energies of ionized molecular fragments are discussed in terms of the velocity space. An ion source together with the collector arrangement define a certain part of the velocity space from where ions are collected. If this part is not equivalent to a fixed solid angle in velocity space, discrimination due to initial energy takes place. Well defined discrimination effects can be used to measure the initial energy probability function WE of an ion ensemble. Emphasis is laid especially upon the deflection method. Using this method one obtaines the probability function WE simply by differentiating the primarily measured ion current distribution. The necessary working conditions which have to be fulfilled are discussed in some detail and an experimental arrangement is described, which has been used to measure the initial energy distribution functions of fragment ions from the lower paraffins.

scholarly journals Wigner Distributions of Quark

2016 ◽  
Vol 40 ◽  
pp. 1660055
Author(s):  
Asmita Mukherjee ◽  
Sreeraj Nair ◽  
Vikash Kumar Ojha
Keyword(s):  
Phase Space ◽  
Wigner Distribution ◽  
Distribution Functions ◽  
Space Distribution ◽  
Parton Distributions ◽  
Transverse Momentum Dependent ◽  
Phase Space Distribution ◽  
Generalized Parton Distributions ◽  
Wigner Distributions ◽  
Classical Phase Space

Wigner distribution functions are the quantum analogue of the classical phase space distribution and being quantum implies that they are not genuine phase space distribution and thus lack any probabilistic interpretation. Nevertheless, Wigner distributions are still interesting since they can be related to both generalized parton distributions (GPDs) and transverse momentum dependent parton distributions (TMDs) under some limit. We study the Wigner distribution of quarks and also the orbital angular momentum (OAM) of quarks in the dressed quark model.

Sign in / Sign up

Export Citation Format

Share Document