Statistics of the Multi-Component System of Quantum Particles
Authors: Gerasimov Yu.V., Maslov A.G. | Published: 08.02.2015 |
Published in issue: #1(58)/2015 | |
DOI: 10.18698/1812-3368-2015-1-69-75 | |
Category: Physics | |
Keywords: statistics, plasma, distribution function, statistical weight, method of Lagrange multipliers |
This paper contains the theoretical solution of the problem of creating statistics for multi-component quantum system ofparticles in conditions of additional restrictions. This problem appears for solving applied problems that are related to the interaction of the plasma formations with other bodies, objects andfields. For the solving problem authors suggested mathematical formulation of statistical weight for multi-component quantum system. The physical formulation of the problem has demanded introduction of additional restrictions, used in rational parameters definition with help of the method of Lagrange multipliers. In the limiting cases the generalized approach turns to the well-known Fermi-Dirac, Bosa-Einstein and Maxwell-Boltzmann statistics. In view with the additional restriction on volume occupied by the system the main thermodynamics identify in the generalized form was used for the determination of the Lagrange multipliers that allows to describe the plasma formations located in a limited volume.
References
[1] Maslov V.P. Interaction of classical fermions with bosons. Matem. Zametki [Mathematical Notes, pp. 269-272], 1998, vol. 64, iss. 2, pp. 315-317 (in Russ.). DOI: 10.4213/mzm1401
[2] Vijayan T., Venkatramani N. Heating and transport of metal plasma in a vacuum-arc rail gun. IEEE Transactions on Plasma Science, 2004, vol. 32, no. 2, pp. 770-774. DOI: 10.1109/TPS.2004.828536
[3] Landen D., Satapathy S. Eddy current effects in the laminated containment structure of railguns. IEEE Transactions on Magnetics, 2007, iss. 1, vol. 43, pp. 150-156. DOI: 10.1109/TMAG.2006.887449
[4] Lehmann P., Reck B., Vo M.D., Behrens J. Acceleration of a suborbital payload using an electromagnetic railgun. IEEE Transactions on Magnetics, 2007, vol. 43, iss. 1, pp. 480-485. DOI: 10.1109/TMAG.2006.887666
[5] Gerasimov Yu.V., Gerasimov M.Yu., Karetnikov G.K., Selivanov A.B., Fionov A.S. Assessing parameters of launching nanosatellites into near earth orbit using pulse launch and control systems. Polet [Flight], 2014, no. 3, pp. 49-54 (in Russ.).
[6] Gerasimov Yu.V., Karetnikov G.K., Selivanov A.B., Fionov A.S. Evaluation of relative final mass of a nanosatellite delivered to the near-earth space using a pulsed launcher and a pulsed correcting thruster. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Mashinostr. [Herald of the Bauman Moscow State Tech. Univ., Mech. Eng.], 2013, no. 3 (92), pp. 69-72 (in Russ.).
[7] Eynshteyn A., Tamm I.E., Smorodinskiy Ya.A., Kuznetsov B.G., eds. Sobranie nauchnykh trudov. V 4 t. [Collection of scientific works. In 4 vol.]. Moscow, Nauka Publ., 1966. 632 p. (vol. 3).
[8] Dirak P.A.M., Sukhanov A. D., eds. Sobranie nauchnykh trudov. V 4 t. [Collection of scientific works. In 4 vol.]. Moscow, Fizmatlit Publ, 2003. 846 p. (vol. 2).
[9] Fermi E., Pontekorvo B., eds. Nauchnye trudy v 2 t. [Scientific works. In 2 vol.]. Moscow, Nauka Publ, 1971. 818 p. (vol. 1).