Bohm Diffusion Coefficient Calculator

Bohm diffusion is an empirical formula for how fast plasma particles diffuse across magnetic field lines, discovered by David Bohm in 1949 while studying magnetic arc discharges. It describes 'anomalous' transport, cross-field diffusion far faster than classical collisional theory alone would predict, driven by plasma turbulence and fluctuating electric fields rather than simple particle-particle collisions.

D_Bohm = Te[eV] / (16 B), where Te is the electron temperature in electronvolts and B is the magnetic field strength in tesla. The numerical coefficient 1/16 comes directly from Bohm's original empirical fit to his magnetic arc discharge data.

It is called anomalous because it is far faster (often many orders of magnitude) than 'classical' diffusion, the rate predicted by treating cross-field transport as arising purely from Coulomb collisions randomly kicking particles across field lines. Bohm-like transport instead arises from plasma turbulence and electric field fluctuations, which move particles across the field far more effectively than collisions alone.

Classical collisional diffusion scales as 1/B² because a particle's gyroradius (which sets its random-walk step size in the classical picture) shrinks as 1/B, and diffusion scales as step size squared. Bohm's turbulence-driven mechanism instead ties the diffusion rate to the E×B drift velocity, giving a different, weaker 1/B dependence, meaning strong magnetic fields suppress Bohm diffusion less effectively than they suppress classical diffusion.

If real fusion plasmas always diffused at the full Bohm rate, the confinement times needed for a practical fusion reactor would have been essentially unreachable with realistic magnetic fields and device sizes. Decades of fusion research showed that well-optimized tokamaks achieve confinement significantly better than the pessimistic Bohm scaling, though still 'anomalous' relative to purely classical collisional theory.

Yes, it remains an important conservative benchmark and appears in some plasma regimes (like certain edge and scrape-off-layer conditions) where turbulent transport genuinely approaches Bohm-like scaling. Understanding and suppressing Bohm-like turbulent transport (through techniques like improved magnetic confinement geometries and transport barriers) remains an active area of fusion research.

At typical tokamak conditions, classical (collisional) diffusion coefficients are often many orders of magnitude smaller than the Bohm estimate, real tokamak transport usually falls somewhere between the two extremes, closer to classical in well-confined 'H-mode' operation and closer to Bohm-like in more turbulent conditions.

Not in the basic formula used here, which depends only on electron temperature and magnetic field strength. This is part of what made Bohm's original 1/16 coefficient formula striking, its simplicity and lack of density dependence, in contrast to classical diffusion, which does depend on density through the collision frequency.

Bohm diffusion can be understood as particles undergoing an E×B drift across field lines driven by fluctuating electric fields with a characteristic step size comparable to the plasma's macroscopic scale, rather than the microscopic gyroradius step size of classical diffusion. This turbulence-driven random walk, empirically calibrated to the 1/16 coefficient, gives transport rates far exceeding the classical collisional estimate.

Bohm's original formula was derived from electron transport measurements in his magnetic arc experiments, so it is conventionally expressed using the electron temperature. Ion Bohm-like diffusion coefficients follow the same functional form but with the appropriate ion temperature substituted, depending on the specific transport process being modeled.