# Drift mechanisms

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

### Uniform external forces

In the precence of both magnetic and electric fields, the equation of motion for charged particle (mass m,
charge q) is m d**v**/dt = q (**E** + **v** x **B**). This leads to **plasma
drift** (or **E** x **B** drift, as it is also called) with velocity **v** = **E** x
**B** / B^2. Because v is independent of the mass and 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 important 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** = (m/q)
**g** x **B** / B^2. However, this drift is opposite for particles of opposite charge, and a
current is created even in a collisionless plasma.

### Nonuniform magnetic fields

The gradient and curvature of the magnetic field **B** create drifts that add up and are in opposite
directions for particles of opposite signs (forming currents). Both drifts are perpendicular to **B**,
and in addition the **gradient 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 curvature drifts are
proportional to the perpendicular and parallel energies of the particle, respectively. The east to west
directed **ring current** in the Earth 's magnetosphere is created by the combined curvature and gradient drift.
Closely related to the gradient drift is the fact that, when magnetic field has longitudinal variation (i.e.,
convergence or divergence of the field lines), both positively and negatively charged particles are
accelerated in the direction of decreasing magnetic field. This results to what is called the **magnetic
mirror** effect, where particles are reflected from the region of converging magnetic field lines. This
relates also to the **first adiabatic invariancy**, i.e., that the orbital magnetic moment is
constant.

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

### Time-varying electric fields

The effect of a slowly varying electric field on a charged particle drift is the addition of **polarization
drift** velocity, **v** = m (d**E**(perp)/dt) / (qB^2). Since this drift is in opposite
direction for charges of opposite sign, a net polarization current is produced. When the frequency of the
changing electric field is the same as the particle's cyclotron
frequency , a **cyclotron resonance** is created. This leads to increase in the particle speed
and, due to collisions between particles, to **radio frequency heating** of the plasma.

### References

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

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