Gradient Equilibria

Non-neutral plasmas are normally confined in constant axial magnetic field. Sometimes, however the plasma is subjected to a field with an axial gradient. The theory of plasmas in a gradient predicts several interesting features: In cold, dense plasmas the density must scale with the magnetic field strength; the electrostatic potential varies along the field lines to make this density variation possible. Further, the plasma profile does not follow the magnetic field lines; the plasma radius in the high-field region of the magnetic mirror is smaller than would be obtained by simply following the field lines from the plasma's low-field radial edge into the high-field region. Also, electrons are trapped both in the high-field region and low-field region. Our experimental observations confirm several aspects of our theory. The density scaling with magnetic field is linear for cold plasmas; for hot, low-density plasmas the density is nearly independent of the magnetic field strength, as one expects in the case of a neutral plasma in a magnetic mirror. As predicted, the plasma profile does not follow the field lines. All of this has implications for the stability of the m=1 diocotron mode in traps with an axial gradient in the magnetic field. We find that this mode is surprisingly long-lived despite the gradient, surviving through over 1000 cycles.

For dense, cold non-neutral plasmas:

For tenuous, hot non-neutral plasmas:
(Similar to a neutral plasmas) For example, for a plasma held in a magnetic field that decrease linearly as shown below:

The dense, cold equilibria looks like this:

While the hot, tenuous equilibria looks like this:

More information can be found in this poster