Ion Thruster Child-Langmuir Calculator
Electric spacecraft propulsion: Determine ion beam exhaust velocity ($v_e$), specific impulse ($I_{sp}$), Child-Langmuir space-charge limited current density ($j$), and thruster efficiency.
Grid Voltages & Geometry
Screen-to-neutralizer potential
Screen to accelerator grid spacing
Active multi-aperture grid diameter
Screen grid transparency (~65–70%)
Propellant Gas & Beam Current
Total extracted ion beam current
Child-Langmuir Space-Charge Limit
The maximum extractable current density between two planar electrostatic electrodes is bounded by mutual electrostatic repulsion of the ion cloud:
$$j_{\text{max}} = \frac{4 \epsilon_0}{9} \sqrt{\frac{2 q}{m}} \frac{V_{\text{total}}^{3/2}}{d^2}$$
Beam exhaust velocity: $v_e = \sqrt{\frac{2 q V_{\text{net}}}{m}}$.
Specific Impulse & Thrust
Specific Impulse (I_sp)
--
Generated Thrust (T)
--
Beam Velocity & Electric Power
Exhaust Beam Velocity (v_e)
--
√(2·q·V / m)
Beam Kinetic Power (P_b)
--
V_net · I_b
Child-Langmuir Grid Extraction Limit
Max Child-Langmuir Current Density (j_max):
--
Operating Current Density (j_act):
--
Perveance Extraction Margin:
--
Mass Flow Rate (ṁ):
--
Recommended Tools & Equipment
Tested hardware and components for high reliability
100% Free Tool
Zero Sign-Up