Collisional cross sections and momentum distributions in astrophysical plasmas: Dynamics and statistical mechanics link

Ferro, F.; Quarati, Piero

doi:10.1103/physreve.71.026408

Cited by 14 publications

(15 citation statements)

References 29 publications

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“…In particular, if we impose that superextensivity and quantum uncertainty give the same modifications on the actual distribution function, we obtain that the underlying cross section must be [4] …”

Section: Pos(nic-ix)094mentioning

confidence: 99%

“…In the presence of the field F , different types of interactions among the ions modify the tail of the ion momentum distribution in characteristic energy ranges with respect to a pure MaxwellBoltzmann distribution (MB) [4]. These corrections to the MB distribution may be interpreted within the framework of the nonextensive statistical mechanics [5] where, as we shall show, the entropic parameter can be expressed in terms of the collision cross sections of the various nonnegligible interactions.…”

Section: Introductionmentioning

confidence: 99%

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Microdynamical effects on momentum distribution in stellar plasmas

Ferro¹,

Bachari²,

Maero³

et al. 2010

Proceedings of International Symposium on Nuclear Astrophysics - Nuclei in the Cosmos - IX — PoS(NIC-IX)

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We show that, if a random force is present, the microscopic dynamics of ion elastic collisions and quantum effects may sensibly modify the momentum distribution of ions and electrons in stellar plasmas. We also show that a few microscopic interactions among the particles, that are significant in very specific energy intervals, lead to peculiar slight corrections to the usual MaxwellBoltzmann distribution. All these modifications can be easily taken into account by using the nonextensive statistical mechanics. Consequences on the resonant and non-resonant fusion rates are remarkable and may affect strongly some astrophysical processes. A few examples are reported.

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Section: Pos(nic-ix)094mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Microdynamical effects on momentum distribution in stellar plasmas

Ferro¹,

Bachari²,

Maero³

et al. 2010

Proceedings of International Symposium on Nuclear Astrophysics - Nuclei in the Cosmos - IX — PoS(NIC-IX)

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“…In this work we introduce a new expression of the plasma DR rate as a function of the temperature, derived assuming a small deformation of the Maxwell distribution and containing factors that modify the usual, well known exponential behaviour. Deviations are caused by presence of correlations among particles in non ideal plasmas, of random electric microfields distribution and of random forces whose effects are non linear [10,11]. All these effects are taken into account by means of an appropriate parameter q, which is the entropic parameter of the nonextensive Tsallis thermostatistics [12,13].…”

Section: Introductionmentioning

confidence: 99%

Dielectronic recombination rates in astrophysical plasmas

Bachari¹,

Ferro²,

Maero³

et al. 2010

Proceedings of International Symposium on Nuclear Astrophysics - Nuclei in the Cosmos - IX — PoS(NIC-IX)

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In this work we introduce a new expression of the plasma Dielecronic Recombination (DR) rate as a function of the temperature, derived assuming a small deformation of the Maxwell-Boltzmann distribution and containing corrective factors, in addition to the usual exponential behaviour, caused by non-linear effects in slightly non ideal plasmas. We then compare the calculated DR rates with the experimental DR fits in the low temperature region.

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“…The presence of higher powers of p, i.e., higher derivative terms, can be interpreted as a signal of non-locality in the Fokker-Planck equation. We stress that these distributions are stationary (stable or metastable) and what counts to decide the distribution is the type of collisions between ions and the dependence on momentum of the elastic collision cross sections (Coulomb, screened Coulomb, enforced Coulomb, among others), or the presence of ion-ion correlations [9].…”

Section: Deviations From Maxwellian Distributionmentioning

confidence: 99%

Nuclear astrophysical plasmas: ion distribution functions and fusion rates

Lissia

Quarati

2005

Europhysics News

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T his article illustrates how very small deviations from the Maxwellian exponential tail, while leaving unchanged bulk quantities, can yield dramatic effects on fusion reaction rates and discusses several mechanisms that can cause such deviations.Fusion reactions are the fundamental energy source of stars and play important roles in most astrophysical contexts. Since the beginning of quantum mechanics, basic questions were addressed such as how nuclear reactions occur in stellar plasmas at temperatures of few keV (1 keV ≈ 11.6 x 10 6 K) against Coulomb barriers of several MeV and what reactions or reaction networks dominate the energy production. It was soon realized that detailed answers to such questions involved not only good measurements or quantum mechanical understanding of the relevant fusion cross sections, but also the use of statistical physics to describe the energy and momentum distributions of the ions and their screening [1].Gamow understood that reacting nuclei penetrate Coulomb barriers by means of the quantum tunnel effect and Bethe successfully proposed the CNO and then the pp cycle as candidates for the stellar energy production: this description has been directly confirmed by several terrestrial experiments that have detected neutrinos produced by pp and CNO reactions in the solar core [2].In the past only a few authors (e.g., d'E. Atkinson, Kacharov, Clayton, Haubold) have examined critically the energy distribution and proposed that such a distribution could deviate from the Maxwellian form. In fact, it is commonly accepted that main-sequence stars like the Sun have a core, i.e. an electron nuclear plasma, where the ion velocity distribution is Maxwellian. In the following, we first discuss why even tiny deviations from the Maxwellian distribution can have important consequences and then what can be the origin of such deviations. Thermonuclear reaction in plasmas and distribution tailsIn a gas with n1 (n2) particles of type 1 (2) per cubic centimeter and relative velocity v, the reaction rate r (the number of reactions per unit volume and unit time) is given by (1)where σ = σ(v) is the nuclear cross section of the reaction. The reaction rate per particle pair is defined as the thermal average Therefore, the reaction rate per particle pair < σv > is determined by the specific cross section and by the velocity distribution function of the reacting particles. When no energy barrier is present and far from resonances, cross sections do not depend strongly on the energy. Most of the contribution to < σv > comes from particles with energy of the order of kT, and the dependence on the specific form of f (v) is weak. The same is true for bulk properties that receive comparable contributions from all particles: e.g., the equation of state.The (EG = 45.09 MeV, blue). Correspondingly, the peaks become (much) lower; note that the three curves have been multiplied times 10 5 , 10 17 , and 10 26 , respectively, to make them visible on the same scale.

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Collisional cross sections and momentum distributions in astrophysical plasmas: Dynamics and statistical mechanics link

Cited by 14 publications

References 29 publications

Microdynamical effects on momentum distribution in stellar plasmas

Microdynamical effects on momentum distribution in stellar plasmas

Dielectronic recombination rates in astrophysical plasmas

Nuclear astrophysical plasmas: ion distribution functions and fusion rates

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