Bohm-diffusion

The diffusion of plasma across a magnetic field was conjectured to follow the Bohm diffusion scaling as indicated from the early plasma experiments of very lossy machines.

Bohm diffusion is characterized with a diffusion coefficient equal to

where B is the magnetic field strength, T is the temperature, and e is the elementary charge.

It was first observed in 1949 by David Bohm, E. H. S. Burhop, and Harrie Massey while studying magnetic arcs for use in isotope separation. It has since been observed that many other plasmas follow this law. Fortunately there are exceptions where the diffusion rate is lower, otherwise there would be no hope of achieving practical fusion energy. In Bohm's original work he notes that the fraction 1/16 is not exact; in particular "the exact value of [the diffusion coefficient] is uncertain within a factor of 2 or 3." Lyman Spitzer considered this fraction as a factor related to plasma instability.

Generally diffusion can be modelled as a random walk of steps of length ${\displaystyle \delta }$ and time ${\displaystyle \tau }$. If the diffusion is collisional, then ${\displaystyle \delta }$ is the mean free path and ${\displaystyle \tau }$ is the inverse of the collision frequency. The diffusion coefficient D can be expressed variously as

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