Hall-effect thruster — cross-field discharge, annular channel: Foundations

3.3.42 · D1 · Physics › Rocket Propulsion › Hall-effect thruster — cross-field discharge, annular channe

Is page pe assume kiya gaya hai ki tum kuch nahi jaante. Hum parent note mein use hue har letter aur symbol ko ek ek karke build karenge, har ek apni jagah earn karega agle se pehle. Agar tum koi symbol is page par pehle dekh chuke ho, baad ki lines us par lean kar sakti hain — lekin kabhi ulta nahi.

0. Scene: machine ke andar physically kya hota hai

Kisi bhi symbol se pehle, hardware ka picture banao.

Figure dekho. Ek Hall thruster ek ring-shaped groove hai (ek annulus — socho ek doughnut jiska upar ka hissa slice kar diya, toh ek circular trench dikhti hai). Gas peeche ki wall se feed hoti hai (anode), aur fast particles ki ek jet khule front se bahar nikalti hai (exit plane). Hum neeche har symbol ko is picture ke ek spot se attach karenge.

Teen directions matter karti hain, aur unke simple names hain:

Axial = thrust direction ke along, back-to-front (pale-yellow arrow).
Radial = ring ke center se bahar ki taraf, jaise wheel ki ek spoke (chalk-blue arrow).
Azimuthal = ring ke around jaana, trench ko circle mein follow karna (chalk-pink arrow).

1. Charge, mass, aur do players

Poora device do tarah ke particles ke beech ki contest hai. Toh pehle hum batate hain ki "tarah" aur "kitna charge" ka matlab kya hai.

$q = 1.6 \times 1 0^{- 19} C$ ek electron (negative) ya ek singly-ionised ion (positive) ka charge hai.

Do players:

Symbol	Kaun	Mass
$m_{e}$	electron (tiny, negative)	$9.11 \times 1 0^{- 31}$ kg
$m_{i}$	xenon ion (heavy, positive)	$2.18 \times 1 0^{- 25}$ kg

2. "Ion" aur "plasma" ka matlab kya hai

Poori kahani ke liye dekho Plasma Quasineutrality.

3. Do fields aur jo forces woh banate hain

Ab channel mein bharne waali invisible cheezein.

Poori derivation yahan hai Lorentz Force. Yahan jo matter karta hai:

Figure teen arrows ko right angles par milte dikhata hai: $E$ axial, $B$ radial, aur sideways magnetic nudge azimuthal. "Crossed fields" ka simple matlab hai $E ⊥ B$ — woh 90° par milte hain.

4. Circular motion — kyun ek trapped particle circle mein jaata hai

Agar ek moving charge par sirf sideways force ho, toh path curl hokar ek circle ban jaata hai. Us circle ko describe karne ke liye do ideas chahiye.

Magnetic push ko needed string-pull ke barabar karo: magnetic force $q v_{⊥} B$ hi centripetal force $m v_{⊥}^{2} / r_{L}$ hai: $q v_{⊥} B = \frac{m v _{⊥}^{2}}{r _{L}} \Rightarrow r_{L} = \frac{m v _{⊥}}{q B} .$

Poora treatment: Larmor Radius and Cyclotron Motion.

Yahan $L_{channel}$ sirf trench ki width hai (ek length, metres mein), woh plain-language ruler jis se hum loops compare karte hain.

5. "Magnetized" — honest condition

Chota loop kaafi nahi; particle ko kisi cheez se bump hone se pehle bahut saare loops complete karne chahiye.

6. Drift, energy, aur thrust symbols

Prerequisite map

Upar se neeche padho: charge aur mass duniya ko do players mein split karte hain; Lorentz force aur "hamesha sideways" fact circles banata hai; circles Larmor radius deta hai; radius aur magnetized test decide karta hai kaun trap hota hai; meanwhile quasineutrality ek strong field exist karne deta hai ions ko fling karne ke liye — aur thrust neeche nikalta hai.

Ion Thruster (Gridded) — competitor jo Child–Langmuir Law se limited hai.
Plasma Quasineutrality, Lorentz Force, Larmor Radius and Cyclotron Motion, Magnetic Mirror & Guiding-Centre Drifts, Tsiolkovsky Rocket Equation.
Parent: Hall thruster (Hinglish).

Equipment checklist

Right side cover karo; parent note kholne se pehle har ek bol pana chahiye.

E

par arrow ka kya matlab hai, aur channel mein

E

kis taraf point karta hai?

Yeh ek directed quantity mark karta hai;

E

axially point karta hai (anode se exit) aur

+

ions ko bahar push karta hai.

Magnetic force kabhi kisi particle ko speed up kyun nahi karti?

Kyunki

v \times B

hamesha

v

⊥

hota hai, toh yeh sirf path turn kar sakta hai — koi kaam nahi karta.

Larmor radius formula batao aur har symbol kya hai.

r_{L} = m v_{⊥} / (q B)

: mass

m

, cross-field speed

v_{⊥}

, charge

q

, field strength

B

Ek magnet electrons ko trap karta hai lekin ions ko kyun nahi?

r_{L} \propto m

; ion

\sim 2.4 \times 1 0^{5} \times

heavy hai, toh uska loop channel se bada ho jaata hai jabki electron ka fit ho jaata hai.

"Magnetized" hone ke liye chote loop ke alawa kya chahiye?

Collision se pehle bahut saare whirls:

ω_{c} τ ≫ 1

, jahan

ω_{c} = q B / m

aur

τ

collision time hai.

Quasineutral ka matlab kya hai aur yahan kyun matter karta hai?

Equal

+

aur

-

densities ⇒ koi net space charge nahi ⇒ plasma ke andar ek strong axial

E

reh sakti hai.

v_{d}

kya hai aur crossed fields mein uski magnitude?

Loop center ki sideways glide;

∣ v_{d} ∣ = E / B

, Hall current ke roop mein azimuthally run karti hai.

Exhaust speed ke terms mein thrust likho.

F = \overset{m}{˙} v_{e}

, jahan

v_{e} = 2 q Δ V / m_{i}

Δ V

se girne par milta hai.

Recall Ek-line self-test

Agar tum bina dekhke saare aath reveals fill kar sako, toh tum parent derivations ke liye ready ho. Ready? ::: Tabhi, jab upar ka har symbol tumhare dimaag mein ek picture ki taraf point kare, sirf ek letter nahi.