Modeling anisotropic Maxwell–Jüttner distributions: derivation and properties

Livadiotis, G.

doi:10.5194/angeo-34-1145-2016

Cited by 13 publications

(13 citation statements)

References 30 publications

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“…Second, the particle temperature is assumed for simplicity to be isotropic, whereas observations indicate that electron temperature in the magnetosphere in general is anisotropic and electron distribution functions can be more complex than simple anisotropic distributions (Li et al, 2010). The transition to an anisotropic Maxwell-Jüttner distribution is outlined in Livadiotis (2016) and Treumann and Baumjohann (2016).…”

Section: Discussionmentioning

confidence: 99%

Non-diffusive pitch-angle scattering of a distribution of energetic particles by coherent whistler waves

Yoon

Bellan

2021

Preprint

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A recent study and a companion talk [1] showed that an exact rearrangement of the relativistic particle equation of motion under a coherent circularly-polarized electromagnetic wave leads to an equation describing the motion of the &#8220;frequency mismatch&#8221; parameter &#958; under a pseudo-potential &#968;(&#958;). When the particle undergoes a so-called &#8220;two-valley motion&#8221; in &#958;-space, it experiences large changes in &#958; and thus its pitch-angle because &#958; is a function of the particle&#8217;s velocity parallel to the background magnetic field. This single-particle analysis is extended [2] to a distribution of relativistic particles. First, the condition for two-valley motion is derived with parameters relevant to magnetospheric contexts. Single-particle simulations verify that particles which satisfy this condition indeed undergo large pitch-angle fluctuations. Second, assuming a relativistic Maxwellian particle distribution, the fraction of particles that undergo two-valley motion is analytically derived and is numerically verified by Monte-Carlo simulations. A significant fraction (1% - 5%) of the distribution undergoes two-valley motion for typical magnetospheric parameters. For sufficiently fast interactions where a uniform background magnetic field and a constant wave frequency can be assumed, the widely-used second-order trapping theory [3] is shown to be an erroneous approximation of the present theory.&#160;[1] P. M. Bellan, Phys. Plasmas, 20 (4), Art. No. 042117 (2013)[2] Y. D. Yoon and P. M. Bellan, JGR Space Physics, 125 (6), Art. No. e2020JA027796 (2020)[3] D. Nunn, Planet. and Space Sci., 22 (3), 349-378 (1974)&#160;

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Section: Discussionmentioning

confidence: 99%

Non-diffusive pitch-angle scattering of a distribution of energetic particles by coherent whistler waves

Yoon

Bellan

2021

Preprint

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“…instead of MB distribution ( f MB ) [56][57][58][59][60][61]. Jüttner distribution is indeed the relativistic extension of generalized isotropic MB distribution when E(p) = mγ(p)c 2 .…”

Section: Relativistic Gasmentioning

confidence: 99%

“…in which Z JE and Z JV are new normalization constants [57]. These constants can be evaluated using the normalization condition…”

Section: Relativistic Gasmentioning

confidence: 99%

A Note on Effects of Generalized and Extended Uncertainty Principles on Jüttner Gas

2021

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In recent years, the implications of the generalized (GUP) and extended (EUP) uncertainty principles on Maxwell–Boltzmann distribution have been widely investigated. However, at high energy regimes, the validity of Maxwell–Boltzmann statistics is under debate and instead, the Jüttner distribution is proposed as the distribution function in relativistic limit. Motivated by these considerations, in the present work, our aim is to study the effects of GUP and EUP on a system that obeys the Jüttner distribution. To achieve this goal, we address a method to get the distribution function by starting from the partition function and its relation with thermal energy which finally helps us in finding the corresponding energy density states.

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“…(Equations (37a-d) constitute the basic formulae connecting statistical mechanics with thermodynamics; e.g., see other similar cases in [108,109].) Next, we define an alternative entropic formula.…”

Section: Connection To Thermodynamicsmentioning

confidence: 99%

On the Simplification of Statistical Mechanics for Space Plasmas

Livadiotis

2017

Entropy

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Space plasmas are frequently described by kappa distributions. Non-extensive statistical mechanics involves the maximization of the Tsallis entropic form under the constraints of canonical ensemble, considering also a dyadic formalism between the ordinary and escort probability distributions. This paper addresses the statistical origin of kappa distributions, and shows that they can be connected with non-extensive statistical mechanics without considering the dyadic formalism of ordinary/escort distributions. While this concept does significantly simplify the usage of the theory, it costs the definition of a dyadic entropic formulation, in order to preserve the consistency between statistical mechanics and thermodynamics. Therefore, the simplification of the theory by means of avoiding dyadic formalism is impossible within the framework of non-extensive statistical mechanics.

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Modeling anisotropic Maxwell–Jüttner distributions: derivation and properties

Cited by 13 publications

References 30 publications

Non-diffusive pitch-angle scattering of a distribution of energetic particles by coherent whistler waves

Non-diffusive pitch-angle scattering of a distribution of energetic particles by coherent whistler waves

A Note on Effects of Generalized and Extended Uncertainty Principles on Jüttner Gas

On the Simplification of Statistical Mechanics for Space Plasmas

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