Analysis of non-Maxwellian fusion reaction rates with electron screening

Lapenta, Giovanni; Quarati, Piero

doi:10.1007/bf01306085

Cited by 7 publications

(4 citation statements)

References 21 publications

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“…The Maxwell-Boltzmann (MB) distribution is believed to be highly correct and the many-body physics involved does not determine sensible deviations from the standard statistics used [6]. However, non-Maxewellian (flattened) distributions in plasmas heated by inverse bremsstrahlung (collisional) absorption of sufficiently strong electromagnetic fields have been predicted and recently measured [7][8][9]; in D -3 He fusion plasma experiments, a nonthermal component of the ion distribution and the possible consequences on the nuclear rates have been investigated [10,11].…”

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“…The distribution f is also the solution of a Boltzmann equation without collisions (at equilibrium the distributions obtained with and without the collision term coincide). Non-Maxwellian distribution can give thermonuclear reaction rates r =< σv > smaller than the standard ones [11], allowing a reduced flux of neutrinos from the sun interior, particularly at energies above few k B T .…”

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“…Infact, B does not have any effect and can be ignored because we maintain the solar luminosity at its known value and the increase of the central temperature T to counteract the effect of B on the power of the sun raises the 8 B neutrino flux back to the value it had at B = 0. The special condition (11) or α = β(Ψ − Φ 0 ), which is a constraint characteristic of the solar core, shows that α is a function of Ψ or (E + E), therefore the comparison between two different but equivalent expressions of f done to derive a relation between n and q in Ref.s [3,17] is not allowed in this case. Finally, we find that the parameters β 0 , β 1 , β 2 are:…”

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Generalized statistics and solar neutrinos

1996

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In this paper we will show that, because of the long-range microscopic memory of the random force, acting in the solar core, mainly on the electrons and the protons than on the light and heavy ions (or, equally, because of anomalous diffusion of solar core constituents of light mass and of normal diffusion of heavy ions), the equilibrium statistical distribution that these particles must obey, is that of generalized Boltzmann-Gibbs statistics (or the Tsallis non-extensive statistics), the distribution differing very slightly from the usual Maxwellian distribution. Due to the high-energy depleted tail of the distribution, the nuclear rates are reduced and, using earlier results on the standard solar model neutrino fluxes, calculated by Clayton and collaborators, we can evaluate fluxes in good agreement with the experimental data. While proton distribution is only very slightly different from Maxwellian there is a little more difference with electron distribution. We can define one central electron temperature as a few percent higher than the ion central temperature nearly equal to the standard solar model temperature. The difference is related to the different reductions with respect to the standard solar model values needed for B and CN O neutrinos and for Be neutrinos.PACS number(s): 73.40.Hm, 71.30.+h, 96.60.K

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Generalized statistics and solar neutrinos

1996

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“…Primarily, the interaction of the energetic charged particles produced in exothermic nuclear reactions with the fuel plasma enhances the tail part of the Maxwellian spectrum [4,5]. Previously, enhanced tail of ion speed distribution has been modeled mathematically using either the tail-enhanced variants of the generalized Maxwellian distribution [4,6], or the Lorentzian (Kappa) speed distribution [4,7] that reasonably describes a power-law suprathermal tail comprising of accelerated hot ion population. Effect of anisotropy on the fusion reactivity arising from the ion drifts have been discussed previously using drifting tri-Maxwellian ion velocity distribution [8].…”

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Estimation of total fusion reactivity and contribution from supra-thermal tail using 3-parameter Dagum ion speed distribution

Majumdar

Das

2016

Annals of Nuclear Energy

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Abstract. Thermonuclear fusion reactivity is a pivotal quantity in the studies pertaining to fusion energy production, fusion ignition and energy break-even analysis in both inertially and magnetically confined systems. Although nuclear fusion reactivity and thereafter the power density of a magnetic confinement fusion reactor and the fulfillment of the ignition criterion are quantitatively determined by assuming the ion speed distribution to be Maxwellian, a significant population of suprathermal ions, with energy greater than the quasi-Maxwellian background plasma temperature, is generated by the fusion reactions and auxiliary heating in the fusion devices. In the current work 3-parameter Dagum speed distribution has been introduced to include the effect of suprathermal ion population in the calculation of total fusion reactivity. The extent of enhancement in the fusion reactivity, at different back-ground temperatures of the fusion fuel plasma, due to the suprathermal ion population has also been discussed.

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