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Equations (70) and (86) can be combined to give

(87) 
The three terms on the righthand side of the above expression are conventionally
called the magnetic, or gradB, drift, the inertial
drift, and the polarization drift, respectively.
The magnetic drift,

(88) 
is caused by the slight variation of the gyroradius with gyrophase as a
charged particle
rotates in a nonuniform magnetic field. The gyroradius is reduced
on the highfield side of the Larmor orbit, whereas it is increased on the
lowfield side. The net result is that the orbit does not quite
close. In fact, the motion consists of the conventional gyration around the magnetic
field combined with a slow drift which is perpendicular to both the
local direction of the magnetic field and the local gradient of the
fieldstrength.
Given that

(89) 
the inertial drift can be written

(90) 
In the important limit of stationary magnetic fields and weak electric fields, the
above expression is dominated by the final term,

(91) 
which is called the curvature drift.
As is easily demonstrated, the quantity
is a vector whose direction is towards the centre of the circle which
most closely approximates the magnetic fieldline at a given point, and whose
magnitude is the inverse of the radius of this circle. Thus, the
centripetal acceleration imposed by the curvature of the magnetic field
on a charged particle following a fieldline gives rise to a slow drift which is
perpendicular to both the local direction of the magnetic field and the
direction to the local centre of curvature of the field.
The polarization drift,

(92) 
reduces to

(93) 
in the limit in which the magnetic field is stationary but the electric
field varies in time. This expression can be understood as a polarization drift
by considering what happens when we suddenly impose an electric field on a
particle at rest. The particle initially accelerates in the direction of
the electric field, but is then deflected by the magnetic force. Thereafter,
the particle undergoes conventional gyromotion combined with
drift. The time
between the switchon of the field and the magnetic deflection is approximately
. Note that there is no deflection if
the electric field is directed parallel to the magnetic field,
so this argument only applies to perpendicular electric fields. The initial
displacement of the particle in the direction of the field is of order

(94) 
Note that, because
, the displacement of the
ions greatly exceeds that of the electrons.
Thus, when an electric field
is suddenly switched on in a plasma, there is an initial polarization of
the plasma medium caused, predominately, by a displacement of the ions in the direction of the
field. If the electric field, in fact, varies continuously
in time, then there is a slow drift due to the constantly changing polarization of the
plasma medium. This drift is essentially the time derivative of Eq. (94) [i.e.,
Eq. (93)].
Next: Invariance of Magnetic Moment
Up: Charged Particle Motion
Previous: Guiding Centre Motion
Richard Fitzpatrick
20110331