Field Layers

Helicity density h = 𝐀·𝐁

h cloud (color = sign)

cross term only (𝐀ᶜ·𝐁ᵐ + 𝐀ᵐ·𝐁ᶜ)

Vector fields

Presets

Device Geometry

Coil turns N 12

Base radius 1.00

Tip radius 0.22

Cone height 1.8

Coil current I₀ 1.00

Magnet moment m 0.80

Winding order — the wire itself is a helix

Micro density 30

Micro radius 0.070

Micro winding sense

RIGHT

LEFT

Audio Modulation

Frequency 0.90

Depth 0.70

I(t) = I₀ · (1 + depth · sin ωt). The time-varying 𝐀 contributes 𝐄 = −∂𝐀/∂t and pumps 𝐄·𝐁.

View & Render

Slicing

VOL

Render

Domain 2.5

Grid spacing 0.40

Arrow size 2.5

h dot size 1.5

Helicity Ledger — ∫ 𝐀·𝐁 d³x

TOTAL H

0.000

cross (odd in I)

0.000

self (even in I)

0.000

cross = 𝐀ᶜᵒⁱˡ·𝐁ᵐᵃᵍ + 𝐀ᵐᵃᵍ·𝐁ᶜᵒⁱˡ · self = 𝐀ᶜᵒⁱˡ·𝐁ᶜᵒⁱˡ + 𝐀ᵐᵃᵍ·𝐁ᵐᵃᵍ

The one-switch discriminator: flip POLARITY. The magnet-crossed term reverses sign; the coil's own term does not. With the magnet installed, the cross term dominates — the texture's handedness follows the switch.

Coil Current I(t)

ωt 0.00

Helicity Pump — dH/dt = −2 ∫ 𝐄·𝐁 d³x

−2∫𝐄·𝐁 (volume term) 0.000

Zero with modulation off: the DC texture is static — it radiates nothing and pumps nothing. Switch modulation on and the same pseudoscalar 𝐄·𝐁 that sources the chiral anomaly starts driving H.

Reading the box

The cone's spiral pitch gives the winding azimuthal and axial current — its vector potential is a twisted texture. The axial magnet supplies the reference 𝐁. Their overlap is the helicity density h = 𝐀·𝐁, a pseudoscalar: it flips sign in a mirror. The program vocabulary "right / left torsion field" maps onto the sign of the magnet-crossed helicity — one pseudoscalar, one sign, one switch. POWER off kills the texture; a bare dipole alone carries h = 0.

Winding order: switch between a plain conical spiral and the double-wound form — the wire itself a small helix laid along the cone, a spiral of spirals with its own winding sense. The double winding acts solenoid-like: part of 𝐁 stays confined along the wire tube while the outside texture is carried by 𝐀 — the Aharonov-Bohm configuration, built into the winding. All fields integrate over the true double-wound path; nothing is approximated away.