An ion or Hall-effect thruster ionizes a propellant gas and accelerates the ions electrostatically across an accelerating voltage V. Treating the acceleration as a straight conversion of electrical energy to kinetic energy of a singly-charged ion of mass m gives its exhaust velocity directly:
v_e = sqrt(2 q V / m) (exhaust velocity, m/s)
F = ṁ · v_e (thrust, N)
Isp = v_e / g0 (specific impulse, s)
P_beam = ½ ṁ v_e² (kinetic power in the beam, W)
P_elec = P_beam / η (electrical input power, W)
where q = 1.602×10⁻¹⁹ C, m is the ion mass, ṁ the propellant mass-flow rate, and η the thruster's electrical efficiency (how much of the input power ends up as directed beam kinetic energy — the rest is lost to ionization, grid impingement and divergence).
At a fixed electrical power P, increasing V raises v_e (and Isp) but forces ṁ down to hold P constant — since F = 2P/v_e = 2ηP/(g0·Isp), thrust and Isp trade off along a hyperbola F·Isp = const. That is the fundamental power-limited tradeoff of electric propulsion: high-Isp missions accept low thrust; chemical rockets instead burn propellant fast for high thrust at low Isp (typically 300–450 s), independent of any electrical power budget.
- Beam pane — ions accelerate between the emitter and grid; particle speed and spacing scale with vₑ and ṁ.
- Tradeoff curve — F vs Isp at the current electrical power, with your operating point and a chemical-rocket reference marked.
- Comparison bars — thrust and Isp of this electric thruster vs. a representative chemical thruster burning propellant at the same mass-flow rate.