CRT deflection yoke simulator

Model. The yoke is wound toroidally on a ferrite ring core in four quadrants (top/bottom × left/right); each quadrant's turns are joined in series to its neighbors so all four are driven by the single current from one driver circuit, in directions chosen so horizontal components cancel and vertical components add. Every turn is a closed loop confined to one angular position — an inner leg along the core's bore (tracking the tube's own taper from gun end to flare end), a radial crossover over the core's screen-end face, the outer leg back along the core's outside, and a radial crossover over the gun-end face closing the loop. The field uses the screened-toroid limit of the ferrite: with μ_r » 1 the ring is a low-reluctance return path that decouples the outer legs and crossovers from the bore — their flux closes through the ferrite and never reaches the beam. The bore sees only the exact Biot–Savart field of the inner legs plus their magnetic images in the core's inner surface; since the legs lie on that surface, each image coincides with its conductor at strength $\kappa = \dfrac{\mu_r - 1}{\mu_r + 1}$, so the bore field is $(1+\kappa)\,B_\text{inner}$ — very nearly doubled for any real ferrite, with no fitted parameters. This boundary-value treatment produces the nearly uniform transverse bore field a deflection yoke is designed for. Saturation: the bore's return flux crowds into the ring cross-section (roughly r_bore/thickness denser than in the bore), and $\kappa$ is derated by a tanh knee when that estimated core flux approaches B_sat; at the WG6100 operating point the core runs near 10% of B_sat, so the response is linear. No hysteresis, gap reluctance, or eddy-current effects are modeled. The electron enters at full anode energy (relativistic γ from the accelerating voltage) and drifts through the yoke; the integrator is a relativistic Boris rotation, which conserves speed exactly in a pure magnetic field. Deflection is toward −y for the wound current sense; magnitudes are what matter here. Defaults follow the Wells-Gardner 6100 vertical coil: 46 turns per quadrant, 5.5 A full-scale, 40 mm yoke, 19.5 kV anode.