On the Magnetic Field Spectrum and Its Fluctuations in a Primeval Cold Plasma in Thermal Equilibrium

Main Article Content

Francisco Caruso
Vitor Oguri
Felipe Silveira


This work reassesses previous results and generalizes the expression for the low-frequency spectrum of magnetic fields fluctuations in a thermal plasma, that was previously obtained within the framework of the fluctuation-dissipation theorem. The new approach presented here is able to avoid any approximation yielding a unique expression that covers both the low- and high-frequency spectrum, without the need of procedures to smooth the junction between the two limit frequency regions formerly used. Also, the simultaneous dependence of this intensity on the plasma and on the collisional frequencies is discussed. Finally, the total emitted plasma energy is compared to the Stefan-Boltzmann law of a pure black-body.

Magnetic field, plasma physics, primordial plasma.

Article Details

How to Cite
Caruso, F., Oguri, V., & Silveira, F. (2020). On the Magnetic Field Spectrum and Its Fluctuations in a Primeval Cold Plasma in Thermal Equilibrium. Asian Journal of Research and Reviews in Physics, 3(2), 10-21. https://doi.org/10.9734/ajr2p/2020/v3i230116
Original Research Article


Parker EN. Cosmical magnetic fields: Their origin and their activity, first ed. Oxford University Press, Oxford; 1979.

Rees MJ. The origin and cosmogonic implications of seed magnetic fields. Q. Jl R. Astr. Soc. 1987;28:197-206.

RÜdigger G, Hollerbach R. The magnetic Universe. Geophysical and astrophysical dynamo theory, first ed. Wiley VCH, Weinheim; 2004.

Kulsrud RM, Zweibel EG. On the origin of cosmic magnetic fields. Rep. Prog. Phys. 2008;71(4):04690-046934.

Biermann L. On the origin of magnetic fields on stars and in interstellar space. Z. Naturforsch. A. 1950;5:65-71.

Miranda OD, Opher R. The creation of largescale voids by explosions of primordialsupernovae. MNRAS. 1996;283(3):912- 918.

Miranda, Oswaldo D, Opher Reuven. Comparing single-cycle and multicycle explosive scenarios for the formation of voids. APJ. 1997;482:(2):573-576.

Miranda, Oswaldo D, Opher, Merav, Opher, Reuven. Seed magnetic fields generated by primordial supernova explosions. MNRAS. 1996;301(2):547-550.

Rostoker N, Aamodt R, Eldridge, O. Kinetic theory of plasma and electromagnetic fields. Annals of Physics. 1965;31(2):243-291.

Schlickeiser R, Yoon PH. Spontaneous electromagnetic fluctuations in unmagnetized plasmas I: General theory and nonrelativistic limit. Phys. of Plasmas. 2012;19(2):022105-1-022105-9.

Simes FJR, et al. Particle-in-cell simulations on spontaneous thermal magnetic field fluctuations. Phys. of Plasmas. 2013;19(2):100702-1-100702-3.

Tajima T, Cable S, Shibata K, Kulrsrud RM. On the origin of cosmological magnetic fields. APJ. 1992;390(2):309-321.

Johnson JB. Thermal agitation of electricity in conductors. Phys. Rev. 1928;32(1):97-109.

Nyquist H. Thermal agitation of electric charge in conductors. Phys. Rev. 1928;32(1):110-113.

Kubo R. Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems. J. Phys. Soc. Jpn. 1957;12(6):570-586.

Tajima T, Cable S, Kulrsrud RM. On zerofrequency magnetic fluctuations in plasmas. Phys. Fluids B. 1992;4(7):2338-2345.

Opher, Merav, Opher, Reuven. Was the electromagnetic spectrum a blackbody spectrum in the early universe? Phys. Rev. Lett. 1997;79(14): 2628-2631.

Opher, Merav, Opher, Reuven. Magnetic field spectrum in a plasma in thermal equilibrium in the epoch of primordial nucleosynthesis. Phys. Rev. D. 1997;56(6):3296–3306.

Bellan PM. Fundamentals of plasma physics, first ed. Cambridge University Press, Cambridge; 2006.

J¨Üttner F. Das Maxwellsche Gesetz der Geschwindig keitsverteilung in der relativtheorie. Ann. Phys. (Berl.). 1911;339(5)856-882.

Livadiotis G. Modeling anisotropic Maxwell- JÜttner distributions: Derivation and propeties. Ann. Geophys. 2016;34:1145-1158.

Gradshteyn IS, Ryzhik IM. Table of integrals, series and products, seventh ed. Elsevier, Amsterdam; 2007.