This 2D side-view models the same electrospray (colloid) thruster as the 3D version, but computes two things the 3D scene does not: the local field actually seen by the emitter tip, and the self-consistent spreading of the emitted beam from mutual Coulomb repulsion between the charged droplets/ions themselves (a real "space-charge" effect), rather than a fixed random spray cone.
Sharp-tip field enhancement (hyperboloid emitter model):
E_tip = 2·V_b / (r_tip · ln(4·d / r_tip))
E_onset = √(2γ / (ε₀ r_tip)) — Taylor-cone onset criterion
Once E_tip ≥ E_onset the meniscus is drawn deformed toward the
classical Taylor half-angle of 49.3° (Taylor, 1964); below onset
it relaxes back to a hemispherical cap.
Each emitted droplet or ion is a real charged macro-particle with its own charge q and mass m (interpolated between a ~30 nm ionic-liquid droplet and a ~200 amu solvated-ion cluster, from the same q/m endpoints as the 3D sim). Every simulated particle exerts a genuine Coulomb force on every other one in flight:
F_ij = k_e · q_i·q_j / r_ij² (real pairwise repulsion)
a_i = (Σ_j F_ij) / m_i (Newton's 2nd law, integrated every frame)
Because only a limited number of particles can be simulated in real time, each on-screen particle's charge is weighted so the total in-flight charge it represents matches the real beam current computed from ṁ and q/m — so the measured divergence angle genuinely tracks how a real beam's spread scales with current and voltage, even though individual on-screen particles stand in for many real ones. The transverse axis is deliberately exaggerated for visibility; the reported divergence angle itself is computed from the true (unexaggerated) trajectories.
- Extractor voltage — raises the tip field (onset near ~450 V here) and the exhaust velocity; a faster beam spends less time in flight, so it diverges less from space charge despite carrying the same current.
- Ionization fraction — blends droplet-dominated emission (heavier, more charge per particle, lower velocity) toward pure-ion emission (lighter, less charge per particle, much higher velocity and Isp).
- Mass flow rate — more propellant per second means more charge in flight at once, which means stronger mutual repulsion and more divergence for the same voltage.
- Emitter array — real colloid thrusters hex-pack many emitter tips; more emitters raise total beam current (and hence space-charge spreading) without changing any single emitter's local physics.
Beam divergence from space charge is a real, measured limitation of electrospray and ion thrusters — it is one reason designers trade higher current for tighter plume angle and vice versa, alongside the thrust/Isp trade-off the sliders also control.