Relaxation of Relativistic Plasmas Under the Effect of Wave‐Particle Interactions

Lapenta, Giovanni; Markidis, Stefano; Marocchino, A.; Kaniadakis, Giorgio

doi:10.1086/520326

Cited by 60 publications

(52 citation statements)

References 20 publications

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“…If the beam density ratio is 3, which gives a larger relative growth rate for the mixed mode, the heated electron distribution can be approximated by a power-law E −2.7 , where E is the relativistic electron energy . The power-law decrease is similar to that observed for relativistic electrostatic two-stream instabilities Lapenta et al, 2007). This power-law decrease corresponds to a turbulent, marginally stable state (Treumann and Jaroschek, 2008).…”

Section: Magnetic Field Generationsupporting

confidence: 79%

“…PIC simulations have modelled colliding plasmas in one dimension (1-D) (Chapman et al, 2005;Matsukiyo and Scholer, 2006;Schmitz et al, 2002;Hoshino and Shimada, 2002;Dawson, 1987, 1989;Sorasio et al, 2006;Ohsawa, 1999, 2000) or in 2-D or 3-D (Lembege et al, 2004;Dieckmann et al, 2006bFrederiksen et al, 2004;Hededal et al, 2004;Hededal and Nishikawa, 2005;Jaroschek et al, 2004;Hellinger et al, 2007;Spitkovsky, 2008a;Chang et al, 2008;Kato, 2007;Kazimura et al, 1998;Langdon et al, 1988). Interpenetrating plasmas are considered by Shimada and Hoshino (2002); Silva et al (2003); Fonseca et al (2003); Lapenta et al (2007). The shock physics is three-dimensional.…”

Section: Initial Conditionsmentioning

confidence: 99%

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The formation of relativistic plasma structures and their potential role in the generation of cosmic ray electrons

Dieckmann¹

2008

Nonlin. Processes Geophys.

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Abstract. Recent particle-in-cell (PIC) simulation studies have addressed particle acceleration and magnetic field generation in relativistic astrophysical flows by plasma phase space structures. We discuss the astrophysical environments such as the jets of compact objects, and we give an overview of the global PIC simulations of shocks. These reveal several types of phase space structures, which are relevant for the energy dissipation. These structures are typically coupled in shocks, but we choose to consider them here in an isolated form. Three structures are reviewed. (1) Simulations of interpenetrating or colliding plasma clouds can trigger filamentation instabilities, while simulations of thermally anisotropic plasmas observe the Weibel instability. Both transform a spatially uniform plasma into current filaments. These filament structures cause the growth of the magnetic fields. (2) The development of a modified two-stream instability is discussed. It saturates first by the formation of electron phase space holes. The relativistic electron clouds modulate the ion beam and a secondary, spatially localized electrostatic instability grows, which saturates by forming a relativistic ion phase space hole. It accelerates electrons to ultra-relativistic speeds. (3) A simulation is also revised, in which two clouds of an electron-ion plasma collide at the speed 0.9c. The inequal densities of both clouds and a magnetic field that is oblique to the collision velocity vector result in waves with a mixed electrostatic and electromagnetic polarity. The waves give rise to growing corkscrew distributions in the electrons and ions that establish an equipartition between the electron, the ion and the magnetic energy. The filament-, phase space hole-and corkscrew structures are discussed with respect to electron acceleration and magnetic field generation.Correspondence to: M. E. Dieckmann

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Section: Magnetic Field Generationsupporting

confidence: 79%

Section: Initial Conditionsmentioning

confidence: 99%

The formation of relativistic plasma structures and their potential role in the generation of cosmic ray electrons

Dieckmann¹

2008

Nonlin. Processes Geophys.

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“…Kaniadakis statistics has been applied in astrophysics, e.g., relativistic plasmas [19] and stellar rotational velocities [20].…”

Section: Introductionmentioning

confidence: 99%

Third law of thermodynamics as a key test of generalized entropies

et al. 2015

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The laws of thermodynamics constrain the formulation of statistical mechanics at the microscopic level. The third law of thermodynamics states that the entropy must vanish at absolute zero temperature for systems with nondegenerate ground states in equilibrium. Conversely, the entropy can vanish only at absolute zero temperature. Here we ask whether or not generalized entropies satisfy this fundamental property. We propose a direct analytical procedure to test if a generalized entropy satisfies the third law, assuming only very general assumptions for the entropy S and energy U of an arbitrary N-level classical system. Mathematically, the method relies on exact calculation of β=dS/dU in terms of the microstate probabilities p(i). To illustrate this approach, we present exact results for the two best known generalizations of statistical mechanics. Specifically, we study the Kaniadakis entropy S(κ), which is additive, and the Tsallis entropy S(q), which is nonadditive. We show that the Kaniadakis entropy correctly satisfies the third law only for -1<κ<+1, thereby shedding light on why κ is conventionally restricted to this interval. Surprisingly, however, the Tsallis entropy violates the third law for q<1. Finally, we give a concrete example of the power of our proposed method by applying it to a paradigmatic system: the one-dimensional ferromagnetic Ising model with nearest-neighbor interactions.

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“…3 In the astrophysical domain, the first applications of this power-law statistics studied stellar polytropes (Plastino & Plastino 1993) and the peculiar velocity function of galaxy clusters (Lavagno et al 1998). More recently, Kaniadakis statistics has also been studied in the theoretical and experimental context, however the first application with a possible connection with astrophysical system has been the simulation in relativistic plasmas (Lapenta et al 2007). More recently, by considering the distribution of stellar rotational velocity for low-mass stars in the Pleiades open cluster, Carvalho et al (2008) showed that κ and q distributions give a good fit for the observed distribution.…”

Section: Non-gaussian Statistics and Stellar Systems L49mentioning

confidence: 99%

Non-Gaussian Statistics and Stellar Rotational Velocities of Main-Sequence Field Stars

Carvalho

Nascimento

Silva

et al. 2009

ApJ

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In this Letter, we study the observed distributions of rotational velocity in a sample of more than 16,000 nearby F and G dwarf stars, magnitude complete, and presenting high-precision V sin i measurements. We show that the velocity distributions cannot be fitted by a Maxwellian. In addition, an analysis based on both Tsallis and Kaniadakis power-law statistics is by far the most appropriate statistics and gives a very good fit. It is also shown that single and binary stars have similar rotational distributions. This is the first time, to our knowledge, that these two new statistics have been tested for the rotation of such a large sample of stars, pointing solidly to a solution of the puzzling problem of the function governing the distribution of stellar rotational velocity.

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Relaxation of Relativistic Plasmas Under the Effect of Wave‐Particle Interactions

Cited by 60 publications

References 20 publications

The formation of relativistic plasma structures and their potential role in the generation of cosmic ray electrons

The formation of relativistic plasma structures and their potential role in the generation of cosmic ray electrons

Third law of thermodynamics as a key test of generalized entropies

Non-Gaussian Statistics and Stellar Rotational Velocities of Main-Sequence Field Stars

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