FEEP, MEMS thrusters — micro-propulsion — Hinglish notes

3.3.43 · Physics › Rocket Propulsion

WHAT are we even trying to do?

WHY high exhaust speed matters — rocket equation ki logic yaad karo. $Δ v$ velocity change karne ke liye exhaust velocity $v_{e}$ use karte hue, propellant fraction yeh hota hai: $\frac{m _{p}}{m _{0}} = 1 - e^{- Δ v / v_{e}} .$ Ek small satellite mein propellant almost hota hi nahi, isliye hum $v_{e}$ bahut bada (tens of km/s) banate hain — tab ek chamach propellant bhi poori mission ke liye kaafi hoga. Electric thrusters yahan jeetते hain.

FEEP — Field Emission Electric Propulsion

HOW: deriving the physics from scratch

Step 1 — Liquid sharp cone kyon banata hai? Emitter ki tip pe conducting liquid ko do competing effects feel hote hain:

Surface tension $γ$ surface ko smooth rakhna chahti hai (andar pull karti hai).
Electric field ek outward electrostatic pressure $\frac{1}{2} ε_{0} E^{2}$ create karta hai.

Yeh step kyon? Jab electric pull aur surface tension balance ho jate hain, liquid apne aap ek sharp cone mein arrange ho jata hai — Taylor cone — half-angle $\approx 49. 3^{\circ}$ ke saath. Tip se ions emit hote hain.

Step 2 — Ions kitni speed tak pahunchte hain? Ek ion jiske charge $q$ aur mass $m$ hai, potential difference $V$ se guzarta hai aur kinetic energy gain karta hai: $q V = \frac{1}{2} m v_{e}^{2} .$ Yeh step kyon? Energy conservation: electric potential energy → kinetic energy. Exhaust speed ke liye solve karo: $v_{e} = \frac{2 q V}{m}$

Step 3 — Thrust kitna milta hai? Thrust momentum per second hai. Agar ion mass flow rate $\overset{m}{˙}$ hai, $F = \overset{m}{˙} v_{e} .$ Ion beam current hai $I = \frac{q}{m} \overset{m}{˙}$ (charge per second), isliye $\overset{m}{˙} = \frac{m}{q} I$ . Substitute karo: $F = \overset{m}{˙} v_{e} = \frac{m}{q} I \frac{2 q V}{m} = I \frac{2 mV}{q}$

Why FEEP is superb for precision

Thrust beam current se set hoti hai, jise hum electronically nanoamps tak tune kar sakte hain → µN thrust resolution.
Bahut high $I_{s p}$ (thousands of seconds) → almost koi propellant nahi.
Downside: kilovolt-level high voltage chahiye, thrust tiny hai (µN), aur cesium surfaces ko contaminate kar sakta hai.

MEMS Thrusters

HOW a cold-gas MEMS thruster works (derivation): Chamber pressure $p_{0}$ , temperature $T_{0}$ par gas ek micro-nozzle se expand hoti hai. Ideal expansion ke liye, gas parcel ki energy conservation exhaust speed deti hai (enthalpy → kinetic energy): $v_{e} = \frac{2 γ}{γ - 1} \frac{R T _{0}}{M} [1 - (\frac{p _{e}}{p _{0}})^{\frac{γ - 1}{γ}}] .$ Yeh step kyon? Ek hot high-pressure gas mein stored thermal (enthalpy) energy hoti hai; nozzle use directed kinetic energy mein convert karta hai. Bracket woh fraction hai jo pressure drop ke across enthalpy release hoti hai. Thrust: $F = \overset{m}{˙} v_{e} + (p_{e} - p_{a}) A_{e} .$

MEMS ka catch — Reynolds number. Micro-scale par channels tiny hote hain, isliye $R e = \frac{ρ v L}{μ}$ small hota hai → viscous (friction) losses dominate karte hain aur boundary layer flow ka zyada hissa kha jaati hai. Isliye real MEMS efficiency ideal formula se kam hoti hai.

Figure — FEEP, MEMS thrusters — micro-propulsion

Worked Examples

Common Mistakes

Flashcards

Micro-propulsion ko kaunsa thrust class define karta hai?

Roughly

μ

N to mN.

FEEP ka full form kya hai?

Field Emission Electric Propulsion.

FEEP mein emitter tip par liquid metal kaunsi shape banata hai?

Taylor cone (half-angle ≈ 49.3°).

Potential

V

se accelerate hone ke baad ion exhaust velocity ka formula?

v_{e} = 2 q V / m

Beam current

I

ke terms mein FEEP thrust ka formula?

F = I 2 mV / q

(equivalently

F = \overset{m}{˙} v_{e}

Tiny satellites ke liye high exhaust velocity kyon use karte hain?

Almost koi propellant nahi chahiye (rocket equation:

m_{p} \approx m_{0} Δ v / v_{e}

FEEP mein kaun sa parameter thrust set karta hai aur kaun sa

I_{s p}

Beam current thrust set karta hai; accelerating voltage

v_{e}

hence

I_{s p}

set karta hai.

Typical FEEP propellants kaun se hain?

Caesium ya indium (liquid metals).

MEMS ka full form kya hai?

Micro-Electro-Mechanical Systems (silicon micro-machining).

MEMS thruster efficiency ideal se kam kyon hoti hai?

Small size → low Reynolds number → dominant viscous/wall losses.

Cold-gas thrust equation (pressure term ke saath)?

F = \overset{m}{˙} v_{e} + (p_{e} - p_{a}) A_{e}

Δ v ≪ v_{e}

ke liye approximate propellant mass?

m_{p} \approx m_{0} Δ v / v_{e}

Recall Feynman: explain to a 12-year-old

Socho ek shoebox size ki spaceship space mein float kar rahi hai. Use giant fire engine nahi chahiye — use ek tiny, gentle, super-controllable poke chahiye. FEEP mein hum ek sharp needle pe liquid metal ki ek drop rakhte hain aur ek strong electric "pull" on karte hain. Pull itni strong hoti hai ki woh tip se tiny charged bits ko pluck karke unhe bahut, bahut fast shoot kar deti hai (jaise 100 km per second!). Ek taraf stuff shoot karne se ship doosri taraf push hoti hai — yahi poke hai. Kyunki bits itni fast fly karti hain, hum almost koi metal use nahi karte, isliye ek thimble bhar metal saalon tak chalta hai. MEMS wahi idea hai lekin ek tiny computer chip ki tarah built — poora rocket silicon mein carve kiya gaya taaki small satellite pe fit ho sake.

Connections

Rocket Equation — high $v_{e}$ propellant kyon bachata hai.
Specific Impulse — $I_{s p} = v_{e} / g_{0}$ , efficiency metric.
Ion Thrusters — same charge-accelerate principle, larger scale.
Electrospray & Colloid Thrusters — FEEP ka cousin, charged droplets use karta hai.
Taylor Cone — electrohydrodynamic surface shape.
Reynolds Number — micro-nozzles efficiency kyon lose karte hain.
CubeSats & Attitude Control — micro-propulsion ke customers.