Key constants
v_e (effective exhaust velocity)0.034c ≈ 10 200 km/s
v_α (alpha velocity, 2.9 MeV He²⁺)0.039c ≈ 11 700 km/s
E per reaction (p + ¹¹B → 3α)8.7 MeV
η_directional (idealized R=50)0.95
η_smearing (Sec 2.5)0.85
η_capture (asymmetric mirror, R_f=50)~0.95
Reference acceleration (10-day Jupiter)0.43 g
Equations driving this sim
Δv_brachistochrone = 2·√(d·a)
v_c = √(μ/R); v_esc = √(2μ/R) — circular & escape, body radius R
Δv_orbit = v_esc − v_c = (√2 − 1)·√(μ/R) — parking ↔ ∞ each end
Δv_total = Δv_transfer + Δv_orbit(origin) + Δv_orbit(target)
Δv_surface = √(2μ/R) — optional, surface ↔ ∞ excl. atmosphere/rotation
v_e = 0.039c · √η_total
m₀/m_f = exp(Δv_total / v_e) — Tsiolkovsky
ε(z) = r_L(z) / L_B — adiabaticity, §2.4
r_L = 0.24 / B(z) — Larmor radius (m)
Open questions (paper §5–6)
- Particle-tracing simulation (§6.1) — actual three-body kinematics through a realistic field profile.
- Beam neutralization (§5) — Alfvén-Lawson limit for 17 MA alpha beam needs co-moving electrons; quantitative sufficiency unproven.
- Bremsstrahlung budget (§5) — radiation losses can approach or exceed fusion power under unfavorable conditions.
- Trapped perpendicular population (§3.3) — alphas born near π/2 to the axis bounce indefinitely; capture vs thermalization race not quantified.
- Forward mirror @ 20–50 T (§3.3) — beyond current demonstrated HTS magnet capability.
Visualization scale (mission view)
In the default Mission scale view, planet radii are inflated ×500 so worlds are visible at solar-system zoom; heliocentric orbital distances stay at real AU. The ratio of planet visual radius to orbital distance is therefore ≈500× larger than reality — Earth's disc reads as ≈1/47 of its orbital radius instead of ≈1/23 500. As a consequence, the first ~10 hours of a high-thrust trip from Earth (and the last few hours arriving at the destination) sit visually inside the inflated bounding sphere of the parent body and are clipped from the trajectory tube. The ship is at its true heliocentric position the entire time; it just happens to be inside an inflated mesh until it has traveled enough kilometers to "exit" visually. Toggle True scale to render every body at its real radius — planets become sub-pixel from system zoom and only resolve up close. All physics — Δv, propellant fraction, flight time, gravity wells, body μ — is computed in real units in either view.
Two further visualization conventions, applied only in mission view: (1) major moons are drawn at a per-parent visual offset (Luna ×12 around Earth, Phobos/Deimos ×250 around Mars, Galileans ×100 around Jupiter, Titan/Enceladus ×80 around Saturn, Triton ×60 around Neptune) so each moon system stays legible at solar-system zoom — moon orbital periods are real, but the visible parent-distance is compressed/expanded; (2) the spacecraft mesh is rendered at a fixed visual length so it doesn't disappear at zoomed-out missions. Moon mean anomaly at epoch and inclination are placeholders (axis-aligned, evenly-spaced phase) — for moon-phase-sensitive missions, consult JPL Horizons. Heliocentric planet positions and orbital speeds are J2000-grade and match Horizons within arcseconds.
What this sim is
A parametric calculator + brachistochrone visualizer. Not a particle-tracing simulation, not an engineering design study, and not a claim that any of this works. Treat all numbers as defining a target design space, not predicting performance.