HBF SCIENTIFIC LAB · 7.4.6

Preparing Torus Lab

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Lab 04 · Toroidal configuration screening + 3D probe

Torus Lab

An analytic toroidal screening notebook with an orbitable 3D geometry and prescribed-field probe, plus field scales, cylindrical safety factor, beta, density, alpha orbit-width proxy, and a uniform p–¹¹B source comparison.

cylindrical q3D prescribed-field probeuniform source screennot an equilibrium solver
Correct use: compare parameter scales and identify obvious incompatibilities before using an equilibrium, orbit, transport, or MHD code. Cylindrical-q and qρ/√ε badges qualify only for a/R₀≤0.35. Passing any screen is not a confinement prediction.

Configuration diagnostics

3D torus and particle laboratory

Geometry follows R₀, a and κ. Field lines integrate the prescribed Bφ+Bθ approximation; they are not a Grad–Shafranov equilibrium.

Initializing local 3D renderer…

Orbitable input geometry, original PBR vessel, coils and industrial hall, three traced prescribed-field lines, an optional midplane probe, and an optional qρ/√ε proxy envelope. Pointer orbit is visual-only; complete numerical values are in the tables. Trajectories use a relativistic Boris pusher in this prescribed field. Purple glow is illustrative; field-line color is relative |B| within each line. Play automatically reveals the interior. Boundary crossings stop display markers; they are not material wall hits or confinement predictions.
Viewer layers — display only

Radial field scales

Uniform p–¹¹B source screen

Qualification matrix

QuantityWhat it can screenWhat it cannot prove
q(a), cylindricalField/current consistency in a circular uniform-current approximation.Real q-profile, equilibrium, kink/tearing stability.
β and βNPressure-to-field scale and empirical comparison.p–¹¹B stability limit or achievable pressure.
Greenwald fractionComparison with an empirical tokamak density scaling.Applicability to hot p–¹¹B composition.
ρ and qρ/√εFast-alpha magnetization/orbit-width order of magnitude.Prompt loss fraction, ripple, collisions, or wall load.
Uniform fusion screenSource/radiation scale under fixed density and temperature.Ignition, confinement, alpha deposition, or net power.