Kappa distribution from particle correlations in nonequilibrium, steady-state plasmas

Davis, Sergio; Avaria, Gonzalo; Bora, Biswajit; Jain, Jalaj; Moreno, José; Pavez, Cristian; Soto, Leopoldo

doi:10.1103/physreve.108.065207

Cited by 3 publications

(2 citation statements)

References 73 publications

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“…This treatment follows the parameterization of the kappa distribution in terms of (u, β S ) introduced in [53], in which (58) is obtained using superstatistics as…”

Section: An Example: Velocities In a Collisionless Plasmamentioning

confidence: 99%

A superstatistical measure of distance from canonical equilibrium

Davis

2024

J. Phys. A: Math. Theor.

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Non-equilibrium systems in steady states are commonly described by generalized statistical mechanical frameworks such as superstatistics, which assumes that the inverse temperature β = 1 / ( k B T ) is an unknown quantity having some pre-established statistical distribution. The uncertainty in β is usually understood as the fluctuation of a physical observable, however, it has been previously proved (Davis and Gutiérrez 2018 Physica A 505 864–70) that β in a superstatistical model cannot be associated to an observable function B ( Γ ) of the microstates Γ. In this work, we provide an information-theoretical interpretation of this theorem by introducing a new quantity D , the mutual information between β and Γ. Our results show that D is also a measure of departure from canonical equilibrium, and reveal a minimum, non-zero uncertainty about β given Γ for every non-canonical superstatistical ensemble. The behavior of D is illustrated in the case of a collisionless plasma described by kappa distributions, revealing the precise sense in which the spectral index κ can be understood as a measure of distance from equilibrium.

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“…This treatment follows the parameterization of the kappa distribution in terms of (u, β S ) introduced in [53], in which (58) is obtained using superstatistics as…”

Section: An Example: Velocities In a Collisionless Plasmamentioning

confidence: 99%

A superstatistical measure of distance from canonical equilibrium

Davis

2024

J. Phys. A: Math. Theor.

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“…Then, starting from this fact, Ourabah (2020) showed that kappa distributions and other non-Maxwellian distributions can be understood as one type of several superstatistics fundamental classes, demystifying kappa distributions as a fundamental model. Furthermore, Davis et al (2023) used superstatistics to show that an assumption about the temperature is not required to correctly describe the velocity distribution of a given system, suggesting that kappa distributions can be explained in terms of the properties of the superstatistical inverse temperature distribution and not necessarily in terms of the κ parameter. In summary, the correct definition of temperature in an out-of-equilibrium system (if any) is a fundamental question in nonequilibrium statistical mechanics that does not have a simple answer, and it is not in the scope of this work to provide one.…”

Section: Introductionmentioning

confidence: 99%

Magnetic Spectra Comparison for Kappa-distributed Whistler Electron Fluctuations

H. P.,

Moya,

Zenteno-Quinteros

et al. 2024

ApJ

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In the inner heliosphere, space measurements have revealed that plasma is well described by the kappa distributions, which are characterized by the value of the κ parameter. This parameter indicates how far plasma is from the ideal Maxwell–Boltzmann equilibrium distribution and gives the distribution a typical high-energy power-law tail. In these quasi-equilibrium conditions, the plasma spontaneously emits electromagnetic fluctuations. When suprathermal electrons are involved, these spontaneous emissions get enhanced, and the kappa distributions improve the description of the related nonthermal effects by taking into account the contribution of these high-energy electrons. Nevertheless, the kappa distributions describe different scenarios in which the velocity distribution may obey a power-law decay. Here, we present a systematic and quantitative comparison of kappa-distributed magnetized plasma through a comparison of magnetic spectra for electron cyclotron whistler mode fluctuations. Our results show that for a kappa distribution with a thermal speed equal to the one obtained in thermal equilibrium, the magnetic field fluctuations exhibit higher energy levels that scale with increasing values of β and decreasing values of κ, even though the same thermal speed is considered for all studied cases. Conversely, for a kappa distribution with a kappa-dependent thermal speed, the magnetic field fluctuations tend to exhibit less total energy with lower kappa values, even when compared to the Maxwellian distribution equilibrium results in the same range of parameters.

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Kappa-tail Technique: Modeling and Application to Solar Energetic Particles Observed by Parker Solar Probe

Livadiotis,

Cummings,

Cuesta

et al. 2024

ApJ

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We develop the kappa-tail fitting technique, which analyzes observations of power-law tails of distributions and energy flux spectra, and connects them to theoretical modeling of kappa distributions, to determine the thermodynamics of the examined space plasma. In particular, we (i) construct the associated mathematical formulation; (ii) prove its decisive lead for determining whether the observed power-law is associated with kappa distributions; and (iii) provide a validation of the technique using pseudo-observations of typical input plasma parameters. Then, we apply this technique to a case study by determining the thermodynamics of solar energetic particle (SEP) protons, for an SEP event observed on 2021 April 17, by the Parker Solar Probe (PSP)/Integrated Science Investigation of the Sun instrument suite on board PSP. The results show SEP temperatures and densities of the order of ∼1 MeV and ∼5 × 10−7 cm−3, respectively.

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Kappa distribution from particle correlations in nonequilibrium, steady-state plasmas

Cited by 3 publications

References 73 publications

A superstatistical measure of distance from canonical equilibrium

A superstatistical measure of distance from canonical equilibrium

Magnetic Spectra Comparison for Kappa-distributed Whistler Electron Fluctuations

Kappa-tail Technique: Modeling and Application to Solar Energetic Particles Observed by Parker Solar Probe

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