Engineering & Science
Bohm Diffusion Coefficient Formula: Turbulent Cross-Field Plasma Transport
Calculate David Bohm’s anomalous cross-field plasma diffusivity D_B = T_e_eV / (16 * B) (m^2/s) and cylindrical Bessel radial confinement time τ_B = a^2 / (5.783 * D_B) in Hall thrusters and magnetrons.
Why magnetized plasmas leak across B-fields as 1/B instead of classical 1/B² collisional transport!
Classical collisional transport theory predicts cross-magnetic-field plasma diffusion should scale as 1 / B^2—yet in 1946–1949 calutron arc experiments, David Bohm discovered electrostatic drift-wave microturbulence drives anomalous cross-field diffusion thousands of times faster, scaling inversely with the FIRST power of magnetic field: D_Bohm = k_B * T_e / (16 * e * B) = T_e_eV / (16 * B_Tesla) (m^2/s)!
Evaluate a magnetized plasma column of minor radius a = 0.50 m with electron temperature T_e = 25 eV and axial field B = 2.50 T: Bohm diffusivity D_Bohm = 25 / (16 * 2.50) = 0.6250 m^2/s, yielding fundamental J_0 Bessel radial confinement time τ_B = a^2 / (2.4048^2 * D_Bohm) = 69.17 ms (doubling to 138.33 ms and halving D_Bohm to 0.3125 m^2/s at B = 5.00 T)!
| Magnetic Field B (T_e = 25 eV, Radius a = 0.50 m) | Bohm Diffusivity D_B (m²/s) | Radial Confinement Time τ_B (ms) | Transport Scaling |
|---|---|---|---|
| B = 2.50 T (Baseline Magnetron / Thruster) | 0.6250 m²/s | 69.17 ms | Drift-Wave Turbulent Limit |
| B = 5.00 T (2× Higher Field) | 0.3125 m²/s | 138.33 ms | Linear 1/B Bohm Improvement |
| Invalid T_e <= 0, B <= 0, or a <= 0 | "Invalid Magnetic Confinement Inputs" | Error Guard | Positivity Guard |
Bohm Cross-Field Plasma Diffusion Coefficient D_Bohm (m²/s)
Evaluates T_e_eV / (16 * B_Tesla) directly in SI units (since k_B * T / e equals temperature in electron-volts B2!).
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0), "Invalid Magnetic Confinement Inputs", ROUND(B2 / (16 * B3), 4))Cylindrical Fundamental-Mode Bohm Confinement Time τ_B (ms)
Computes (a^2 / (2.4048^2 * D_Bohm)) * 1000 in milliseconds using the first Bessel root j_0,1 = 2.4048 for plasma radius a (B4, m).
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0), "Invalid Magnetic Confinement Inputs", ROUND((B4 ^ 2) / ((2.4048 ^ 2) * (B2 / (16 * B3))) * 1000, 2))Try the example
Use the original values or change them to test your understanding.