Let us now consider how we might construct a device to confine a
collisionless (i.e., very hot) plasma. Obviously, we cannot use conventional
solid walls, because they would melt. However, it is possible to confine a
hot plasma using a magnetic field (fortunately, magnetic fields do not melt!): this
called magnetic confinement.
The electric field in confined plasmas is
usually weak (i.e., ), so that the
is similar in magnitude to the magnetic and curvature drifts. In this
case, the bounce point condition,
, reduces to
It is clear from Fig. 1 that the magnetic field-strength
on a magnetic field-line situated close to the axis of the device attains a
local minimum at , increases symmetrically
as increases until
reaching a maximum value at about the location of the two
field-coils, and then decreases as is further increased. According to
Eq. (117), any particle which satisfies the inequality
Now, on the mid-plane
(n.b. From now on, we shall write
, for ease of notation.) Thus, the trapping
condition (118) reduces to
It is clear that if plasma is placed inside a magnetic mirror machine then all
of the particles whose velocities lie in the loss cone promptly escape, but the
remaining particles are confined. Unfortunately, that is not
the end of the story. There is no such thing as an absolutely collisionless
plasma. Collisions take place at a low rate even in very hot plasmas.
effect of collisions is to cause diffusion of particles in velocity space.
Thus, in a mirror machine collisions continuously scatter trapped particles into
the loss cone, giving rise to a slow leakage of plasma out of the device.
Even worse, plasmas whose distribution functions deviate strongly from an isotropic
Maxwellian (e.g., a plasma confined
in a mirror machine) are prone to velocity space instabilities, which tend to
relax the distribution function back to a Maxwellian. Clearly, such instabilities
are likely to have a disastrous effect on plasma confinement in a mirror machine.
For these reasons, magnetic mirror machines are not particularly successful
plasma confinement devices, and attempts to achieve nuclear fusion using
this type of device have mostly been abandoned.
Next: Van Allen Radiation Belts Up: Charged Particle Motion Previous: Adiabatic Invariants Richard Fitzpatrick 2011-03-31