scholarly journals On the Determination of Kappa Distribution Functions from Space Plasma Observations

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 212 ◽  
Author(s):  
Georgios Nicolaou ◽  
George Livadiotis ◽  
Robert T. Wicks
Keyword(s):  
Distribution Function ◽  
Velocity Distribution ◽  
Space Plasma ◽  
Distribution Functions ◽  
Specific Method ◽  
Kappa Distribution ◽  
Kappa Index ◽  
Velocity Distribution Functions ◽  
Bulk Parameters ◽  
Plasma Bulk

The velocities of space plasma particles, often follow kappa distribution functions. The kappa index, which labels and governs these distributions, is an important parameter in understanding the plasma dynamics. Space science missions often carry plasma instruments on board which observe the plasma particles and construct their velocity distribution functions. A proper analysis of the velocity distribution functions derives the plasma bulk parameters, such as the plasma density, speed, temperature, and kappa index. Commonly, the plasma bulk density, velocity, and temperature are determined from the velocity moments of the observed distribution function. Interestingly, recent studies demonstrated the calculation of the kappa index from the speed (kinetic energy) moments of the distribution function. Such a novel calculation could be very useful in future analyses and applications. This study examines the accuracy of the specific method using synthetic plasma proton observations by a typical electrostatic analyzer. We analyze the modeled observations in order to derive the plasma bulk parameters, which we compare with the parameters we used to model the observations in the first place. Through this comparison, we quantify the systematic and statistical errors in the derived moments, and we discuss their possible sources.

scholarly journals Statistical Uncertainties of Space Plasma Properties Described by Kappa Distributions

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 541
Author(s):  
Georgios Nicolaou ◽  
George Livadiotis
Keyword(s):  
Accurate Determination ◽  
Space Plasma ◽  
High Energy ◽  
Distribution Functions ◽  
Kappa Distribution ◽  
Plasma Properties ◽  
Electrostatic Analyzer ◽  
Bulk Parameters ◽  
Plasma Bulk

The velocities of space plasma particles often follow kappa distribution functions, which have characteristic high energy tails. The tails of these distributions are associated with low particle flux and, therefore, it is challenging to precisely resolve them in plasma measurements. On the other hand, the accurate determination of kappa distribution functions within a broad range of energies is crucial for the understanding of physical mechanisms. Standard analyses of the plasma observations determine the plasma bulk parameters from the statistical moments of the underlined distribution. It is important, however, to also quantify the uncertainties of the derived plasma bulk parameters, which determine the confidence level of scientific conclusions. We investigate the determination of the plasma bulk parameters from observations by an ideal electrostatic analyzer. We derive simple formulas to estimate the statistical uncertainties of the calculated bulk parameters. We then use the forward modelling method to simulate plasma observations by a typical top-hat electrostatic analyzer. We analyze the simulated observations in order to derive the plasma bulk parameters and their uncertainties. Our simulations validate our simplified formulas. We further examine the statistical errors of the plasma bulk parameters for several shapes of the plasma velocity distribution function.

Statistical Inferences of Lift-Off Velocity Distribution Function Form for Saltating Particles

2010 ◽  
Vol 108-111 ◽  
pp. 783-788
Author(s):  
Jian Jun Wu ◽  
Li Hong He
Keyword(s):  
Distribution Function ◽  
Weibull Distribution ◽  
Velocity Distribution ◽  
Goodness Of Fit ◽  
Velocity Distribution Function ◽  
Forward Direction ◽  
Distribution Functions ◽  
Velocity Distribution Functions ◽  
Lift Off ◽  
Log Normal

The lift-off velocity distribution of saltating particles, which have been proposed to characterize the dislodgement state of saltating particles, is one of the key issues in the theoretical study of windblown sand transportation. But there were various statistical relations in the early researches. In this paper, the Kolmogorov-Smirnov test for goodness-of-fit is adopted to make an inference of the most probable form of lift-off velocity distribution functions for saltating particles on the basis of the experimental data. The statistical results show that the distribution function of vertical lift-off velocities conforms better to Weibull distribution function than to the normal, log-normal, gamma and exponential ones; while, the distribution function of the absolute values of horizontal lift-off velocities is best described by log-normal distribution in forward direction and Weibull distribution in backward direction, respectively. Finally, two more examples prove to support the above conclusions.

Flowing Granular Materials and the Maxwell-Boltzmann Velocity Distribution

2000 ◽  
Author(s):  
Edward J. Boyle
Keyword(s):  
Distribution Function ◽  
Velocity Distribution ◽  
Hard Sphere ◽  
Body Force ◽  
Canonical Ensemble ◽  
Granular Flows ◽  
Velocity Distribution Function ◽  
Distribution Functions ◽  
Velocity Distribution Functions ◽  
Single Granule

Abstract The single-granule velocity distribution function is shown to be Maxwell-Boltzmann for hard-sphere granular flows at steady-state exhibiting no gradients and absent a body-force. This is accomplished by approximating the two-granule velocity distribution function as the product of two single-granule velocity distribution functions and a correlating function and by applying to a canonical ensemble a function analogous to Boltzmann’s H-function.

scholarly journals Velocity Distribution Functions and Transport Coefficients of Electron Swarms in Gases in the Presence of Crossed Electric and Magnetic Fields

1995 ◽  
Vol 48 (3) ◽  
pp. 557 ◽  
Author(s):  
KF Ness
Keyword(s):  
Distribution Function ◽  
Magnetic Fields ◽  
Velocity Distribution ◽  
Transport Coefficients ◽  
Velocity Distribution Function ◽  
Distribution Functions ◽  
Electron Motion ◽  
Electric And Magnetic Fields ◽  
Velocity Distribution Functions ◽  
Spatially Homogeneous

A multi-term solution of the Boltzmann equation is used to calculate the spatially homogeneous velocity distribution function of a dilute swarm of electrons moving through a background of denser neutral molecules in the presence of crossed electric and magnetic fields. As an example, electron motion in methane is considered.

Neoclassical transport processes in weakly collisional plasmas with fractured velocity distribution functions

2014 ◽  
Vol 81 (1) ◽  
Author(s):  
A. A. Kabantsev ◽  
C. F. Driscoll ◽  
D. H. E. Dubin ◽  
Yu. A. Tsidulko
Keyword(s):  
Distribution Function ◽  
Velocity Distribution ◽  
Transport Theory ◽  
Particle Energy ◽  
Distribution Functions ◽  
Transport Processes ◽  
Electrostatic Confinement ◽  
Neoclassical Transport ◽  
Novel Theory ◽  
Velocity Distribution Functions

Ripples in magnetic or electrostatic confinement fields give rise to trapping separatrices, and conventional neoclassical transport theory describes the collisional trapping/detrapping of particles with fractured distribution function. Our experiments and novel theory have now characterized a new kind of neoclassical transport processes arising from chaotic (nominally collisionless) separatrix crossings, which occur due to E × B plasma rotation along θ−ruffled or wave-perturbed separatrices. This chaotic neoclassical transport becomes dominant at low collisionality when the collisional spreading of particle energy during the dynamical period is less than the separatrix energy ruffle.

Electromagnetic ion-cyclotron wave growth rates and their variation with velocity distribution function shape

1977 ◽  
Vol 17 (1) ◽  
pp. 123-131 ◽  
Author(s):  
Abraham Shrauner ◽  
W. C. Feldman
Keyword(s):  
Distribution Function ◽  
Velocity Distribution ◽  
Growth Rates ◽  
Velocity Distribution Function ◽  
Distribution Functions ◽  
Wave Growth ◽  
Ion Cyclotron ◽  
Velocity Distribution Functions ◽  
Velocity Moments ◽  
Function Shape

The sensitivity of electromagnetic ion-cyclotron wave growth rates to the details of the shape of proton velocity distribution functions is explored. For this purpose two different forms of bi-Lorentzian for the proton distribution functions were adopted. The growth rates for the two types of bi-Lorentzians and the biMaxwellians for the beam (hot) protons are compared. Although the growth rates for the three shapes depend on the velocity moments of the different velocity distributions in a similar way, their magnitudes were found to vary considerably.

scholarly journals The auroral O<sup>+</sup> non-Maxwellian velocity distribution function revisited

1997 ◽  
Vol 15 (2) ◽  
pp. 249-254 ◽  
Author(s):  
D. Hubert ◽  
F. Leblanc
Keyword(s):  
Magnetic Field ◽  
Distribution Function ◽  
Velocity Distribution ◽  
Polar Angle ◽  
Velocity Distribution Function ◽  
Distribution Functions ◽  
Field Direction ◽  
Magnetic Field Direction ◽  
Velocity Distribution Functions ◽  
The Magnetic Field

Abstract. New characteristics of O+ ion velocity distribution functions in a background of atomic oxygen neutrals subjected to intense external electromagnetic forces are presented. The one dimensional (1-D) distribution function along the magnetic field displays a core-halo shape which can be accurately fitted by a two Maxwellian model. The Maxwellian shape of the 1-D distribution function around a polar angle of 21 ± 1° from the magnetic field direction is confirmed, taking into account the accuracy of the Monte Carlo simulations. For the first time, the transition of the O+ 1-D distribution function from a core halo shape along the magnetic field direction to the well-known toroidal shape at large polar angles, through the Maxwellian shape at polar angle of 21 ± 1° is properly explained from a generic functional of the velocity moments at order 2 and 4.

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