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

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.

Suprathermal plasma distribution functions with relativistic cut-offs

2019 ◽  
Vol 491 (3) ◽  
pp. 3967-3973
Author(s):  
H-J Fahr ◽  
M Heyl
Keyword(s):  
Distribution Function ◽  
Heat Transport ◽  
Distribution Functions ◽  
The Other ◽  
Pressure Reduction ◽  
Plasma Distribution ◽  
Order Of Magnitude ◽  
Low Mass ◽  
Velocity Moments ◽  
Free Plasma

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.

Physical interpretation of the Padé approximation of the plasma dispersion function

2000 ◽  
Vol 64 (3) ◽  
pp. 287-296 ◽  
Author(s):  
ANDERS TJULIN ◽  
ANDERS I. ERIKSSON ◽  
MATS ANDRÉ
Keyword(s):  
Distribution Function ◽  
Physical Interpretation ◽  
Distribution Functions ◽  
Padé Approximant ◽  
General Distribution ◽  
Dispersion Function ◽  
Complex Velocity ◽  
Pade Approximant ◽  
Maxwellian Plasma ◽  
Plasma Dispersion

It is shown that using Padé approximants in the evaluation of the plasma dispersion function Z for a Maxwellian plasma is equivalent to the exact treatment for a plasma described by a ‘simple-pole distribution’, i.e. a distribution function that is a sum of simple poles in the complex velocity plane (v plane). In general, such a distribution function will have several zeros on the real v axis, and negative values in some ranges of v. This is shown to be true for the Padé approximant of Z commonly used in numerical packages such as WHAMP. The realization that an approximation of Z is equivalent to an approximation of f(v) leads the way to the study of more general distribution functions, and we compare the distribution corresponding to the Padé approximant used in WHAMP with a strictly positive and monotonically decreasing approximation of a Maxwellian.

scholarly journals Full particle-in-cell simulations of kinetic equilibria and the role of the initial current sheet on steady asymmetric magnetic reconnection

2016 ◽  
Vol 82 (3) ◽  
Author(s):  
J. Dargent ◽  
N. Aunai ◽  
G. Belmont ◽  
N. Dorville ◽  
B. Lavraud ◽  
...  
Keyword(s):  
Distribution Function ◽  
Magnetic Reconnection ◽  
Current Sheet ◽  
Initial Conditions ◽  
Electron Flow ◽  
Electron Distribution Function ◽  
Ion Distribution ◽  
Initial Current ◽  
Particle In Cell ◽  
Kinetic Equilibrium

Tangential current sheets are ubiquitous in space plasmas and yet hard to describe with a kinetic equilibrium. In this paper, we use a semi-analytical model, the BAS model, which provides a steady ion distribution function for a tangential asymmetric current sheet and we prove that an ion kinetic equilibrium produced by this model remains steady in a fully kinetic particle-in-cell simulation even if the electron distribution function does not satisfy the time independent Vlasov equation. We then apply this equilibrium to look at the dependence of magnetic reconnection simulations on their initial conditions. We show that, as the current sheet evolves from a symmetric to an asymmetric upstream plasma, the reconnection rate is impacted and the X line and the electron flow stagnation point separate from one another and start to drift. For the simulated systems, we investigate the overall evolution of the reconnection process via the classical signatures discussed in the literature and searched in the Magnetospheric MultiScale data. We show that they seem robust and do not depend on the specific details of the internal structure of the initial current sheet.

Scaling

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.

scholarly journals PIC methods in astrophysics: simulations of relativistic jets and kinetic physics in astrophysical systems

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Kenichi Nishikawa ◽  
Ioana Duţan ◽  
Christoph Köhn ◽  
Yosuke Mizuno
Keyword(s):  
Plasma Physics ◽  
Magnetic Reconnection ◽  
Laser Plasma ◽  
High Performance ◽  
Relativistic Jets ◽  
Astrophysical Plasmas ◽  
Computing Power ◽  
Particle In Cell ◽  
The Future ◽  
Pic Method

AbstractThe Particle-In-Cell (PIC) method has been developed by Oscar Buneman, Charles Birdsall, Roger W. Hockney, and John Dawson in the 1950s and, with the advances of computing power, has been further developed for several fields such as astrophysical, magnetospheric as well as solar plasmas and recently also for atmospheric and laser-plasma physics. Currently more than 15 semi-public PIC codes are available which we discuss in this review. Its applications have grown extensively with increasing computing power available on high performance computing facilities around the world. These systems allow the study of various topics of astrophysical plasmas, such as magnetic reconnection, pulsars and black hole magnetosphere, non-relativistic and relativistic shocks, relativistic jets, and laser-plasma physics. We review a plethora of astrophysical phenomena such as relativistic jets, instabilities, magnetic reconnection, pulsars, as well as PIC simulations of laser-plasma physics (until 2021) emphasizing the physics involved in the simulations. Finally, we give an outlook of the future simulations of jets associated to neutron stars, black holes and their merging and discuss the future of PIC simulations in the light of petascale and exascale computing.

scholarly journals The effects of density inhomogeneities on the radio wave emission in electron beam plasmas

2021 ◽  
Vol 87 (2) ◽  
Author(s):  
Xin Yao ◽  
Patricio A. Muñoz ◽  
Jörg Büchner ◽  
Xiaowei Zhou ◽  
Siming Liu
Keyword(s):  
Magnetic Reconnection ◽  
Radio Wave ◽  
Solar Flares ◽  
Electron Beams ◽  
Distribution Functions ◽  
Plasma Emission ◽  
Langmuir Waves ◽  
Radio Emissions ◽  
Density Inhomogeneities ◽  
Effects Of Density

Type III radio bursts are radio emissions associated with solar flares. They are considered to be caused by electron beams travelling from the solar corona to the solar wind. Magnetic reconnection is a possible accelerator of electron beams in the course of solar flares since it causes unstable distribution functions and density inhomogeneities (cavities). The properties of radio emission by electron beams in an inhomogeneous environment are still poorly understood. We capture the nonlinear kinetic plasma processes of the generation of beam-related radio emissions in inhomogeneous plasmas by utilizing fully kinetic particle-in-cell code numerical simulations. Our model takes into account initial electron velocity distribution functions (EVDFs) as they are supposed to be created by magnetic reconnection. We focus our analysis on low-density regions with strong magnetic fields. The assumed EVDFs allow two distinct mechanisms of radio wave emissions: plasma emission due to wave–wave interactions and so-called electron cyclotron maser emission (ECME) due to direct wave–particle interactions. We investigate the effects of density inhomogeneities on the conversion of free energy from the electron beams into the energy of electrostatic and electromagnetic waves via plasma emission and ECME, as well as the frequency shift of electron resonances caused by perpendicular gradients in the beam EVDFs. Our most important finding is that the number of harmonics of Langmuir waves increases due to the presence of density inhomogeneities. The additional harmonics of Langmuir waves are generated by a coalescence of beam-generated Langmuir waves and their harmonics.

scholarly journals Brief Communication: The double layer in the separatrix region during magnetic reconnection

2015 ◽  
Vol 22 (2) ◽  
pp. 167-171
Author(s):  
J. Guo ◽  
B. Yu
Keyword(s):  
Electron Beam ◽  
Magnetic Reconnection ◽  
Double Layer ◽  
Particle In Cell ◽  
Acoustic Instability ◽  
Ion Acoustic ◽  
Evolution Stage ◽  
Spatial Size ◽  
Electron Holes ◽  
Observation Results

Abstract. With two-dimensional (2-D) particle-in-cell (PIC) simulations we investigate the evolution of the double layer (DL) driven by magnetic reconnection. Our results show that an electron beam can be generated in the separatrix region as magnetic reconnection proceeds. This electron beam could trigger the ion-acoustic instability; as a result, a DL accompanied with electron holes (EHs) can be found during the nonlinear evolution stage of this instability. The spatial size of the DL is about 10 Debye lengths. This DL propagates along the magnetic field at a velocity of about the ion-acoustic speed, which is consistent with the observation results.

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