Revista mexicana de física E
versión impresa ISSN 1870-3542
JIMENEZ-AQUINO, J.I; ROMERO-BASTIDA, M y PEREZ-GUERRERO NOYOLA, A.C. Brownian motion in a magnetic field and in the presence of additional external forces. Rev. mex. fís. E [online]. 2008, vol.54, n.1, pp. 81-86. ISSN 1870-3542.
Our purpose in this paper is to solve exactly the Fokker-Planck-Kramers equation of a charged particle (heavy-ion) embedded in a fluid and under the influence of mechanical and electromagnetic forces. In this work the magnetic field is assumed to be constant and pointing along any direction of a Cartesian reference frame; the mechanical and electrical forces are both space-independent, but in general time-dependent. Our proposal relies upon two transformations of the Langevin equation associated with the charged particle's phase-space (r, u). The first one is a fixed rotation which transforms the (r, u)-coordinates into other (r', u')-coordinates, and makes it possible to re-orientate the magnetic field along an appropriate direction (say along the z'-axis). The second one is a time-dependent rotation which transforms the (r', u')-coordinates into other (r", u")-coordinates, in which the resulting Langevin equation strongly resembles that of ordinary Brownian motion in the presence of external forces. Under these circumstances, the Fokker-Planck-Kramers equation can immediately be solved in the (r", u") phase-space, following our methodology developed in Ref. [Phys. Rev. E 76 (2007) 021106]
Palabras llave : (FP) Fokker-Planck; (FPK) Fokker-Planck-Kramers.