Robert Clark writes:
On Oct 14, 4:35 pm, "Paul F. Dietz" wrote:
"Confinement. Nonneutral plasmas can be confined for long periods of
time using only static electric and magnetic fields. One such
configuration is called a Penning Trap, after the inventor F. M.
Penning. The trap consists of a several cylindrically symmetric
electrodes and a uniform magnetic field applied along the axis of the
trap (see diagram below).

A Penning trap is limited in the number of ions it can store
due to the self-repulsion of the ions. If one does the analysis,
it turns out the energy stored in the magnetic field of the
trap must be at least as large as the rest energy of the stored
ions.

So, if you are storing highly charged ordinary ions, the
ionization energy of those ions is a small fraction of the energy
of the trap's magnets, and adds little to the stored energy
of the system.

Electrostatic quadrupole (Paul) traps may be able to evade
this limit; I'm not clear on that.

Paul

Yes, by the Brillouin limit the total rest energy of the particles
must be less than the magnetic field energy, *under the specialized
conditions for which the Brillouin limit holds*. Such traps operating
under this limit are still useful for fusion research since you can
inject more particles to continually get more fusion energy out while
the magnetic field remains the same.
....

The magnetic field only confines the ions in one direction. You
should probably estimate the magnitude of the *electric* field
required. How does the energy in that field compare to the ionization
energy?

CM