In the presence of only uniform magnetic field B, the motion of a charge= d particle can be described with gyration about the guiding center and moti= on along the field line. This motion gets more complicated when we add, in = the first place, uniform external forces like electric fields or gravitatio= nal forces. Even more complicated situations arise with nonuniform magnetic= field configuration, or time varying electric fields. We talk about the dr= ift of the particle (guiding center motion).

=20In the presence of both magnetic and electric fields, the equation of mo=
tion for charged particle (mass m, charge q) is m dv/dt =3D q (E + v x B). =
This leads to plasma drift (or E x B drift, as it is also called) with velo=
city v =3D E x B / B^2 (see ionospheric convection). Because v is independent of the mass an=
d sign of the charge, it is the same for negatively and positively charged =
particles, and does not create electric current. However, in a plasma where=
collisions between charged and neutral particles are important, an importa=
nt current called the **Hall current** is created because ions=
move slower (ion - neutral collision frequency is greater than electron - =
neutral collision frequency). To give an example, the pulsating auroral patches are often seen to =
drift under the E x B influence.

The situation is not much different in the case of gravitational force, = for which we get v =3D (m/q) g x B / B^2. However, this drift is opposite f= or particles of opposite charge, and a current is created even in a collisi= onless plasma.

=20The gradient and curvature of the magnetic field B create drifts that ad= d up and are in opposite directions for particles of opposite signs (formin= g currents). Both drifts are perpendicular to B, and in addition the gradie= nt drift is perpendicular to the field gradient, and the curvature drift to= the plane in which the magnetic field is curved. Also, the gradient and cu= rvature drifts are proportional to the perpendicular and parallel energies = of the particle, respectively. The east to west directed ring current in the Earth 's magne= tosphere is created by the combined curvature and gradient drift.

= =20Closely related to the gradient drift is the fact that, when magnetic fi=
eld has longitudinal variation (i.e., convergence or divergence of the fiel=
d lines), both positively and negatively charged particles are accelerated =
in the direction of decreasing magnetic field. This results to what is call=
ed the **magnetic mirror effect**, where particles are reflect=
ed from the region of converging magnetic field lines. This relates also to=
the first adiabatic invariance, i.e., that the orbital magnetic moment is =
constant.

See Sibeck et al. (1987) for discussion on drift shell splitting.

=20The effect of a slowly varying electric field on a charged particle drif= t is the addition of polarization drift velocity, v =3D m (dE(perp)/dt) / (= qB^2). Since this drift is in opposite direction for charges of opposite si= gn, a net polarization current is produced. When the frequency of the chang= ing electric field is the same as the particle's cyclotron frequency , a cy= clotron resonance is created. This leads to increase in the particle speed = and, due to collisions between particles, to radio frequency heating of the plasma.

=20- =20
- Sibeck, D. G., R. W. McEntire, A. T. Y. Lui, R. E. Lopez, and S. M. Kri= migis, Magnetic field drift shell splitting: Cause of unusual dayside parti= cle pitch angle distributions during storms and substorms, J. Geophys. Res.= , 92, 13485-13497, 1987. =20