Suprathermal plasma distribution functions with relativistic cut-offs

ABSTRACT In typical plasma physics scenarios, when treated on kinetic levels, distribution functions with suprathermal wings are obtained. This raises the question of how the associated typical velocity moments, which are needed to arrive at magnetohydrodynamic plasma descriptions, may appear. It has become evident that the higher velocity moments in particular, for example the pressure or heat transport, which are constructed as integrations of the distribution function, contain unphysical contributions from particles with velocities greater than the velocity of light. In what follows, we discuss two possibilities to overcome this problem. One is to calculate a maximal, physically permitted, upper velocity, which can be realized in view of the underlying energization processes, and to stop the integration there. The other is to modify the distribution function relativistically so that no particles with superluminal (v ≥ c) velocities appear. On the basis of a typical collision-free plasma scenario, like the plasma in the heliosheath, we obtain the corresponding expressions for electron and proton pressures and can show that in both cases the pressures are reduced compared with their classical values; however, electrons experience a stronger reduction than protons. When calculating pressure ratios, it turns out that these are of the same order of magnitude regardless of which of the two methods is used. The electron, as the low-mass particle, undergoes the more pronounced pressure reduction. It may turn out that electrons and protons constitute about equal pressures in the heliosheath, implying that no pressure deficit need be claimed here.

Download Full-text

The κ-cookbook: a novel generalizing approach to unify κ-like distributions for plasma particle modelling

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa1969 ◽

2020 ◽

Vol 497 (2) ◽

pp. 1738-1756 ◽

Cited By ~ 1

Author(s):

K Scherer ◽

E Husidic ◽

M Lazar ◽

H Fichtner

Keyword(s):

Debye Length ◽

Distribution Functions ◽

Energy Distributions ◽

Pickup Ions ◽

Plasma Distribution ◽

Special Cases ◽

Power Law Exponent ◽

Velocity Moments ◽

Analytical Expressions ◽

Generalized Distribution

ABSTRACT In the literature different so-called κ-distribution functions are discussed to fit and model the velocity (or energy) distributions of solar wind species, pickup ions, or magnetospheric particles. Here, we introduce a generalized (isotropic) κ-distribution as a ‘cookbook’, which admits as special cases, or ‘recipes’, all the other known versions of κ-models. A detailed analysis of the generalized distribution function is performed, providing general analytical expressions for the velocity moments, Debye length, and entropy, and pointing out a series of general requirements that plasma distribution functions should satisfy. From a contrasting analysis of the recipes found in the literature, we show that all of them lead to almost the same macroscopic parameters with a small standard deviation between them. However, one of these recipes called the regularized κ-distribution provides a functional alternative for macroscopic parametrization without any constraint for the power-law exponent κ.

Download Full-text

Kinetic entropy-based measures of distribution function non-Maxwellianity: theory and simulations

Journal of Plasma Physics ◽

10.1017/s0022377820001270 ◽

2020 ◽

Vol 86 (5) ◽

Author(s):

Haoming Liang ◽

M. Hasan Barbhuiya ◽

P. A. Cassak ◽

O. Pezzi ◽

S. Servidio ◽

...

Keyword(s):

Distribution Function ◽

Magnetic Reconnection ◽

Entropy Density ◽

Distribution Functions ◽

Local Distribution ◽

Particle In Cell ◽

Maxwellian Plasma ◽

Plasma Distribution ◽

Maxwellian Distribution Function ◽

Quantitative Understanding

We investigate kinetic entropy-based measures of the non-Maxwellianity of distribution functions in plasmas, i.e. entropy-based measures of the departure of a local distribution function from an associated Maxwellian distribution function with the same density, bulk flow and temperature as the local distribution. First, we consider a form previously employed by Kaufmann & Paterson (J. Geophys. Res., vol. 114, 2009, A00D04), assessing its properties and deriving equivalent forms. To provide a quantitative understanding of it, we derive analytical expressions for three common non-Maxwellian plasma distribution functions. We show that there are undesirable features of this non-Maxwellianity measure including that it can diverge in various physical limits and elucidate the reason for the divergence. We then introduce a new kinetic entropy-based non-Maxwellianity measure based on the velocity-space kinetic entropy density, which has a meaningful physical interpretation and does not diverge. We use collisionless particle-in-cell simulations of two-dimensional anti-parallel magnetic reconnection to assess the kinetic entropy-based non-Maxwellianity measures. We show that regions of non-zero non-Maxwellianity are linked to kinetic processes occurring during magnetic reconnection. We also show the simulated non-Maxwellianity agrees reasonably well with predictions for distributions resembling those calculated analytically. These results can be important for applications, as non-Maxwellianity can be used to identify regions of kinetic-scale physics or increased dissipation in plasmas.

Download Full-text

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

Journal of Plasma Physics ◽

10.1017/s002237780002047x ◽

1977 ◽

Vol 17 (1) ◽

pp. 123-131 ◽

Cited By ~ 59

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.

Download Full-text

Comparison of the Potency of 8-L-Arginine, 8-D-Arginine and 8-D-Homoarginine Vasopressin Analogs with Substituted Phenylalanine in Position 2

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19941439 ◽

1994 ◽

Vol 59 (6) ◽

pp. 1439-1450 ◽

Cited By ~ 2

Author(s):

Miroslava Žertová ◽

Jiřina Slaninová ◽

Zdenko Procházka

Keyword(s):

Amino Acid ◽

Solid Phase Synthesis ◽

Solid Phase ◽

Basic Amino Acid ◽

The Other ◽

Side Chain ◽

Inhibitory Potency ◽

Phase Synthesis ◽

Other Hand ◽

Order Of Magnitude

An analysis of the uterotonic potencies of all analogs having substituted L- or D-tyrosine or -phenylalanine in position 2 and L-arginine, D-arginine or D-homoarginine in position 8 was made. The series of analogs already published was completed by the solid phase synthesis of ten new analogs having L- or D-Phe, L- or D-Phe(2-Et), L- or D-Phe(2,4,6-triMe) or D-Tyr(Me) in position 2 and either L- or D-arginine in position 8. All newly synthesized analogs were found to be uterotonic inhibitors. Deamination increases both the agonistic and antagonistic potency. In the case of phenylalanine analogs the change of configuration from L to D in position 2 enhances the uterotonic inhibition for more than 1 order of magnitude. The L to D change in position 8 enhances the inhibitory potency negligibly. Prolongation of the side chain of the D-basic amino acid in position 8 seems to decrease slightly the inhibitory potency if there is L-substituted amino acid in position 2. On the other hand there is a tendency to the increase of the inhibitory potency if there is D-substituted amino acid in position 2.

Download Full-text

Scaling

10.1093/oso/9780198821939.003.0003 ◽

2018 ◽

Author(s):

Stefan Thurner ◽

Rudolf Hanel ◽

Peter Klimekl

Keyword(s):

Distribution Function ◽

Dynamical Systems ◽

Complex Systems ◽

Power Law ◽

Scaling Laws ◽

Power Laws ◽

Distribution Functions ◽

Temporal Process ◽

Approximate Power

Scaling appears practically everywhere in science; it basically quantifies how the properties or shapes of an object change with the scale of the object. Scaling laws are always associated with power laws. The scaling object can be a function, a structure, a physical law, or a distribution function that describes the statistics of a system or a temporal process. We focus on scaling laws that appear in the statistical description of stochastic complex systems, where scaling appears in the distribution functions of observable quantities of dynamical systems or processes. The distribution functions exhibit power laws, approximate power laws, or fat-tailed distributions. Understanding their origin and how power law exponents can be related to the particular nature of a system, is one of the aims of the book.We comment on fitting power laws.

Download Full-text

On N-body simulations of globular cluster streams

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stab886 ◽

2021 ◽

Vol 504 (1) ◽

pp. 648-653

Author(s):

Nilanjan Banik ◽

Jo Bovy

Keyword(s):

Dark Matter ◽

Cold Dark Matter ◽

Analytical Models ◽

Numerical Density ◽

Stellar Streams ◽

Small Scales ◽

Order Of Magnitude ◽

Low Mass ◽

Stream Density ◽

Tidal Streams

ABSTRACT Stellar tidal streams are sensitive tracers of the properties of the gravitational potential in which they orbit and detailed observations of their density structure can be used to place stringent constraints on fluctuations in the potential caused by, e.g. the expected populations of dark matter subhaloes in the standard cold dark matter (CDM) paradigm. Simulations of the evolution of stellar streams in live N-body haloes without low-mass dark matter subhaloes, however, indicate that streams exhibit significant perturbations on small scales even in the absence of substructure. Here, we demonstrate, using high-resolution N-body simulations combined with sophisticated semi-analytical and simple analytical models, that the mass resolutions of 104–$10^5\, \rm {M}_{\odot }$ commonly used to perform such simulations cause spurious stream density variations with a similar magnitude on large scales as those expected from a CDM-like subhalo population and an order of magnitude larger on small, yet observable, scales. We estimate that mass resolutions of ${\approx}100\, \rm {M}_{\odot }$ (${\approx}1\, \rm {M}_{\odot }$) are necessary for spurious, numerical density variations to be well below the CDM subhalo expectation on large (small) scales. That streams are sensitive to a simulation’s particle mass down to such small masses indicates that streams are sensitive to dark matter clustering down to these low masses if a significant fraction of the dark matter is clustered or concentrated in this way, for example, in MACHO models with masses of 10–$100\, \rm {M}_{\odot }$.

Download Full-text

EVOLUTION OF SHELL STRUCTURE IN NUCLEI

International Journal of Modern Physics E ◽

10.1142/s0218301311019581 ◽

2011 ◽

Vol 20 (08) ◽

pp. 1663-1675 ◽

Cited By ~ 4

Author(s):

A. BHAGWAT ◽

Y. K. GAMBHIR

Keyword(s):

Shell Structure ◽

Crucial Role ◽

Field Model ◽

Mean Field ◽

Mass Region ◽

The Other ◽

Mean Field Model ◽

Relativistic Mean Field ◽

Shell Closures ◽

Low Mass

Systematic investigations of the pairing and two-neutron separation energies which play a crucial role in the evolution of shell structure in nuclei, are carried out within the framework of relativistic mean-field model. The shell closures are found to be robust, as expected, up to the lead region. New shell closures appear in low mass region. In the superheavy region, on the other hand, it is found that the shell closures are not as robust, and they depend on the particular combinations of neutron and proton numbers. Effect of deformation on the shell structure is found to be marginal.

Download Full-text