Effect of the magnetic field on fusion reaction rates

Jarvis, O.N.; Imazu, Shingo

doi:10.1088/0741-3335/29/7/012

Cited by 3 publications

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“…It was claimed that relatively weak magnetic fields reduce collision rates of nuclear reactions by a factor of two through alignments of directions in which charged nuclei can move [87,88]. The claim is, however, wrong [89,90] since it was based on a completelymistaken treatment of 2D space perpendicular to the field direction, and cases of B = 0 and B = 0 are not treated consistently.…”

Section: Appendix B: Effect On Nuclear Reaction Ratesmentioning

confidence: 99%

Updated constraint on a primordial magnetic field during big bang nucleosynthesis and a formulation of field effects

Kawasaki

Kusakabe

2012

Phys. Rev. D

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A new upper limit on the amplitude of primordial magnetic field (PMF) is derived by a comparison between a calculation of elemental abundances in big bang nucleosynthesis (BBN) model and the latest observational constraints on the abundances. Updated nuclear reaction rates are adopted in the calculation. Effects of PMF on the abundances are consistently taken into account in the numerical calculation with the precise formulation of changes in physical variables. We find that abundances of 3 He and 6 Li increase while that of 7 Li decreases when the PMF amplitude increases, in the case of the baryon-to-photon ratio determined from the measurement of cosmic microwave background radiation. We derive a constraint on the present amplitude of PMF, i.e., B(0) < 1.5 µG [corresponding to the amplitude less than 2.0 × 10 11 G at BBN temperature of T = 10 9 K] based on the rigorous calculation. PACS numbers: 26.35.+c, 98.62.En, 98.80.Es, 98.80.Ft * kusakabe@icrr.u-tokyo.ac.jp 1 I. INTRODUCTIONPrimordial nucleosynthesis, or big bang nucleosynthesis (BBN), has been assumed [1] to occur through complicated nonequilibrium processes. It involves many reactions including radiative neutron capture reactions [1-3] and weak interactions converting protons and neutrons to each others [4] as well as relativistic quantum statistics [5]. In BBN, only D, 3 He, 4 He and 7 Li can be produced in significant amounts [6], and yields of heavier elements are generally expected to be small [7,8]. The BBN model predicts the relic of a dense hot radiation [3,9] to be observed as cosmic microwave background radiation (CMBR) today [10].The BBN has been studied over a long period, and the theory is now precisely structured (e.g., [6,). The simplest, standard BBN (SBBN) model is characterized by one parameter, i.e, baryon-to-photon number ratio η with the fixed number of light neutrino species of N = 3. The η value is constrained precisely with data of the Wilkinson Microwave Anisotropy Probe (WMAP) [39-41]. The SBBN model prediction of light element abundances for the WMAP η value is rather consistent with primordial abundances inferred from observations. There is, however, a discrepancy between the predicted and observed primordial abundances of 7 Li. The SBBN predicts a 7 Li abundance which is a factor of 2.4 − 4.3 times higher [42] than the observationally deduced abundance. Possible solutions to this discrepancy have been proposed (e.g. [43] and references therein).O'Connel and Matese [44] have estimated the neutron β-decay rate in the presence of a strong magnetic field, and suggested that an increase in the rate due to primordial magnetic fields (PMFs) decreases 4 He abundance. Greenstein [45] subsequently suggested that the energy of PMFs enhances the expansion rate of the universe, and it tends to increase the 4 He abundance rather than decrease it as suggested in Ref. [44]. Matese & O'Connel [46] then performed a detailed investigation on the PMF effects on BBN, and concluded that the effect through the expansion rate is predominant over ...

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Section: Appendix B: Effect On Nuclear Reaction Ratesmentioning

confidence: 99%

Updated constraint on a primordial magnetic field during big bang nucleosynthesis and a formulation of field effects

Kawasaki

Kusakabe

2012

Phys. Rev. D

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'Effect of the magnetic field on fusion reaction rates'

Haines¹

1987

Plasma Phys. Control. Fusion

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IMAZU (1986) claims that a moderate magnetic field can halve the nuclear reaction rate in a high temperature plasma. In a comment JARVIS (1987) points out that this must be incorrect because a magnetic field has no effect on the velocity distribution of particles in thermodynamic equilibrium, and assigned the error to a misinterpretation of a geometrical model in equation ( 7).Jarvis' criticism can be further strengthened by considering the tensor expansion of the Fokker-Planck equation (JOHNSTON, 1960). Here it is clear that the magnetic field only affectsf, (giving the usual magnetic effects on current and heat flux) and higher order terms. Indeed Imazu specifically assumes (assumption 5 ) thatfis onlyf, =,f, (a Maxwellian) and allf, = 0, n 2 1. It follows that the fusion collision rate will be unaffected by the magnetic field.Imazu further claims (p. 863) that the Coulomb collision rate is not affected in the same way as fusion reactions because in this case a 90" collision is the sum of many simultaneous glancing collisions. This is a correct result but for the wrong reason.The assumed ordering throughout Imazu's paper is that the Larmor radius of the ion rL is much greater than the Debye length i.,. Readers will recall that then the Coulomb interaction between particles occurs as if the magnetic field were zero, since in this range of impact parameters, limited by i,, the V x B force is negligible compared to the Coulomb electric field.The error in Imazu is in the limitation of the volume V , in his Fig. 4 to ~~~2 n r , -. This figure is the projection into the plane (perpendicular to B) of a spiral or helical motion. and there is no such limit to V ,

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Response to the Comment "Effect of the Magnetic Field on Fusion Reaction Rates"

Imazu

1987

Plasma Phys. Control. Fusion

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Effect of the magnetic field on fusion reaction rates

Cited by 3 publications

References 1 publication

Updated constraint on a primordial magnetic field during big bang nucleosynthesis and a formulation of field effects

Updated constraint on a primordial magnetic field during big bang nucleosynthesis and a formulation of field effects

'Effect of the magnetic field on fusion reaction rates'

Response to the Comment "Effect of the Magnetic Field on Fusion Reaction Rates"

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