This browser-side companion to the Braginskii lecture turns the closure ordering into a working calculator. It estimates gyro radii, skin depths, Coulomb mean free paths, magnetic diffusivity, Braginskii transport scales, and the usual MHD dimensionless numbers, then summarizes whether collisional single-fluid MHD is comfortable, marginal, or clearly breaking down for the chosen regime.
Changing preset updates the sliders below. The liquid-metal entry is intentionally a conducting-fluid kludge, not a faithful weakly coupled plasma state.
Logarithmic slider for ni in m-3.
Electron temperature in eV.
Ion temperature in eV.
Magnetic-field strength in tesla.
Characteristic macroscopic scale in meters.
Used for Rm, S, and the dynamical ratio ωτi ∼ Uτi/L.
Hydrogen A = 1, deuterium A = 2, helium A = 4, carbon A = 12.
Assumes a single effective ion species.
Collision-rate estimate used in the Spitzer/Braginskii scalings.
These extra knobs feed the simple tearing and resistive-interchange time estimates below.
Used in the FKR benchmark scaling γτA ∼ S-3/5(kL)2/5(Δ′L)4/5.
Dimensionless outer-layer drive for the classical FKR estimate.
Low-β resistive-interchange proxy. The classical resistive branch is most natural for 0 < Ds < 1/4.
The transport numbers below use standard order-of-magnitude Spitzer and Braginskii estimates. They are meant to organize the lecture’s validity logic: quasi-neutrality, collisional closure, magnetization, Hall corrections, and flux freezing.
Log-scale ladder comparing the Debye length, skin depths, Larmor radii, mean free paths, and the chosen macroscopic scale L.
Matching log-scale ladder for collision, cyclotron, plasma, advection, Alfvén, and resistive rates.
Characteristic speeds, dimensionless numbers, and the most useful single-fluid checkpoints.
Order-of-magnitude Braginskii / Spitzer transport scales in SI diffusivity units where possible.
Particle and collective scales that tend to signal departures from simple one-fluid MHD.
Macroscopic propagation, diffusion, and collision times built from the chosen plasma state and scale L.
Simple later-lecture scaling estimates for classical tearing and resistive-interchange growth.
νei ∝ ne Z ln Λ / Te3/2,
νii ∝ ni Z4 ln Λ / (√A Ti3/2).
Transport estimates use
ν∥i ∼ 0.96 Tiτi/mi,
χ∥e ∼ 3.16 Teτe/me,
and
ηM = ηΩ / μ0.
The later-lecture benchmark estimates use
τA = L / VA,
τR = L2 / ηM,
S = τR / τA,
γFKRτA ∼ S-3/5(kL)2/5(Δ′L)4/5,
and
γRIτA ∼ Ds2/3S-1/3.