Bohm Diffusion
An early empirical scaling for anomalous cross-field transport, unusually fast and only weakly field-dependent.
The Bohm scaling
David Bohm observed that plasma diffused across a magnetic field far faster than collisional theory predicted, and inversely with only the first power of the field rather than the square. The empirical coefficient is:
D_Bohm = (1/16) * k_B T_e / (e B)The 1/16 is empirical. The key feature is the 1/B dependence and the linear rise with temperature, both very different from classical collisional diffusion, which goes as 1/B^2 and falls with temperature.
Why it is pessimistic
Bohm diffusion implies confinement degrades only slowly as the field is raised, which would make magnetic confinement very hard. Fortunately, real tokamak transport is usually better than Bohm and closer to the gyro-Bohm scaling, which improves with field and with smaller gyroradius.
When Bohm still appears
- In some turbulent regimes and near the plasma edge, transport can approach Bohm levels
- Bohm-like scaling emerges when turbulence eddies are the size of the machine rather than the gyroradius
- It is used as a conservative upper bound in early scoping studies
How it is used numerically
Bohm and gyro-Bohm coefficients appear in reduced transport models as multipliers on the gradient-driven fluxes. Comparing whether a device is Bohm-like or gyro-Bohm-like is a standard way to characterize the turbulence regime from experiment or gyrokinetic simulation.
The distinction matters for extrapolation: a Bohm-scaled machine gains little from being larger or higher-field, whereas a gyro-Bohm machine benefits strongly from both. Compact high-field designs like the Hyperion breeder rely on the more favorable gyro-Bohm behavior confirmed by modern turbulence simulation.