A CME is a magnetised plasma cloud. The Earth's field holds it off where the solar-wind ram pressure balances the magnetic pressure of the compressed dipole (Chapman-Ferraro):
ρv² = (2 Beq (RE/r0)³)² / 2μ0 → r0/RE = (2 Beq² / μ0ρv²)1/6, with Beq = 31 µT and ρ = n mp. Quiet wind gives about 10 RE; a Carrington-class pulse about 4-5 RE, inside the geosynchronous orbit at 6.6 RE.
The boundary shape is the Shue form r(θ) = r0 (2/(1+cosθ))0.6. Kp, aurora latitude and transit time use the same mappings as the 3D lab: Kp = 3 + 6s, latitude = 78 - 60s degrees, transit 90 h to 15 h, where s = (v-500)/2700.
Ground currents: for a plane wave over uniform ground, E = Z H = √(ωμ0ρg) · B/μ0, and the voltage along a line is V = E L. Dst is a simple illustrative scaling (-30 - 870 s nT), not a forecast model.
Simplifications: no IMF Bz coupling, a 2D meridian slice, uniform ground, simplified bow shock. Not a space-weather forecasting tool.