Ion engine — ionization, acceleration grid, neutralizer: Foundations

3.3.41 · D1 · Physics › Rocket Propulsion › Ion engine — ionization, acceleration grid, neutralizer

Yeh page ek toolbox hai. Jab tak tum parent note aaram se nahi padh sakte, tumhe har letter aur symbol ka matlab jaanna hoga, woh kaun si picture represent karta hai, aur yeh topic uske bina kyon nahi chal sakta. Hum inhe ek aisi order mein banate hain jahan har ek cheez pehle wali pe lean karti hai.

0. Bilkul shuruat: charge aur force

Figure — Ion engine — ionization, acceleration grid, neutralizer

Figure s01 — Do amber "+" balls cyan arrows ke saath ek doosre se bhaagti hui (upar: like charges repel), aur ek "+" amber ball aur "−" cyan ball white arrows ke saath ek doosre ki taraf khichti hui (neeche: opposite charges attract). Notice karo ki arrows hamesha do charges ko milane wali line ke along point karti hain.

Letter $q$ sirf "kitna charge hai" ke liye hota hai. Iska unit hai coulomb (C). Ek electron itna charge carry karta hai: $q_{e} = 1.602 \times 1 0^{- 19} C .$ Yeh exact number parent note mein har jagah milta hai — ab tum jaante ho ki yeh sirf "ek electron (ya ek singly-charged ion) ka charge" hai.

1. Atom, electron, ion — characters ka group

Figure s02 — Left: ek neutral xenon atom (amber core "Xe") jiske around chhe cyan "−" electrons hain, perfectly balanced. Ek white "e− hits" arrow use strike karta hai. Right: result — ek amber "Xe+" core sirf paanch electrons ke saath, aur do cyan electrons udh rahe hain (bullet plus knocked-loose wala). Dekho electron count chhe se paanch ho jaata hai jaise ek charge use positive tip karta hai.

$Xe^{+}$ mein " $+$ " superscript ka literally matlab hai "is cheez mein ab charge $+ q_{e}$ hai." Jab bhi tum $q$ acceleration formulas mein dekhte ho, ek singly-charged ion ke liye yeh $+ 1.602 \times 1 0^{- 19}$ C hota hai.

2. Mass — symbol $m$

Parent page pe key masses:

Xenon ion: $m_{Xe} = 2.18 \times 1 0^{- 25}$ kg.
Electron: lagbhag $9.11 \times 1 0^{- 31}$ kg — xenon ion se lagbhag 240,000 guna halka.

3. Voltage / potential difference — symbol $V$

Definition Potential difference

$V$ (voltage) Seedhi baat: voltage do jagahon ke beech "electrical height drop" hai. Ek charge high voltage se low voltage tak "neeche girti pahaadi pe" speed gain karta hai — bilkul jaise ek ball hill se dhalta hua speed gain karta hai. Picture: ek ramp. Upar ka end = high potential, neeche ka end = low potential. Upar se release kiya gaya positive charge neeche slip karta hai, tez aur tez hote hue. Topic ko iska zaroori hona: do grids exactly aise hi $V$ size ka downhill create karti hain (jaise 1200 volts). Ion usmein "girta" hai aur tez nikalta hai. $V$ woh knob hai jo engineers exhaust speed set karne ke liye ghoomante hain. Iska unit — volt (V): ek volt matlab "har ek coulomb charge ke liye jo drop karti hai, use ek joule energy milta hai." Symbols mein, $1 V = 1 J / C$ (ek joule per coulomb). Isliye voltage literally energy-per-charge measure karta hai, yahi reason hai ki ek charge jo energy gain karta hai woh charge × voltage hai.

Figure s03 — Ek cyan ramp "high V" (amber, top-left) se "low V" (amber, bottom-right) tak slope karti hai. Teen amber "+" balls slope pe aur neeche baithti hain har ek ke saath ek longer white velocity arrow, dikhata hai positive charge neeche dhalta hua tez hota jaata hai. Cyan label padhta hai "energy gained = qV". Ek negative charge isi ramp pe upar khichti.

4. Electron-volt — symbol $eV$

5. Kinetic energy — symbol $K E$ aur $\frac{1}{2} m v^{2}$

6. Speed aur exhaust speed — symbol $v_{e}$

$q V = \frac{1}{2} m v_{e}^{2}$ rearrange karne par parent page ka boxed result milta hai: $v_{e} = \frac{2 q V}{m} .$ Isme har symbol ab define ho chuka hai: $q$ (charge, §0), $V$ (voltage, §3), $m$ (mass, §2).

7. Rates: dot notation $\overset{m}{˙}$ aur current $I$

Formula Thrust as a rate of momentum — step by step build karo

Shuru karo: thrust woh momentum hai jo per second bahar phenka jaata hai. Har ion $m v_{e}$ momentum carry karta hai, aur $N$ per second nikalte hain, isliye $F = N (m v_{e}) . (step 1: count \times momentum each)$ Kyon: yeh sirf "kitne × kitna each" hai, rate ki definition. Speed substitute karo $v_{e} = 2 q V / m$ (§6 se), kyunki hum $F$ knobs $V$ aur $q$ ke terms mein chahte hain, hidden $v_{e}$ mein nahi: $F = N m \frac{2 q V}{m} . (step 2)$ Ion count replace karo $N$ . Hum directly ions measure nahi karte, lekin hum current ammeter se measure kar sakte hain. Kyunki $I = N q$ hai, $N = I / q$ solve karo aur plug in karo — uncountable $N$ ko measurable $I$ se trade karo: $F = \frac{I}{q} m \frac{2 q V}{m} . (step 3)$ Algebra tidy karo. Loose $m$ , $1/ q$ , aur square root ko combine karo ek root ke andar pull karke (using $\frac{m}{q} \frac{2 q V}{m} = \frac{2 mV}{q}$ ): $F = I \frac{2 mV}{q} . (step 4: the parent-page form)$ Yeh final shape useful kyon hai: yeh thrust directly un cheezoon ke terms mein dikhata hai jo tum set ya measure karte ho — beam current $I$ aur grid voltage $V$ — aur dikhata hai ki yeh bhaare ions (large $m$ ) ko prefer karta hai.

8. Force / thrust — symbol $F$

Sab kuch kaise fit hota hai

Upar se neeche padho: charge + electron + ionization energy tumhe ion build karne deta hai; voltage usp par work karta hai, jo kinetic energy ban jaata hai, jo exhaust speed deta hai; speed ko mass aur phenkne ki rate ke saath combine karo, aur tumhe thrust milta hai, jo ship ko move karta hai. Yahi parent page ki teen-stage story hai — Ionize, Accelerate, phir balanced rakkho.

Engines ki overall family: Electric Propulsion Overview aur Chemical vs Electric Propulsion.
Ionization energy kaise set hoti hai: Plasma Physics — Ionization Energy.
$V$ badhane par thrust forever kyun nahi badhta: Child-Langmuir Space Charge Law.

Equipment checklist

Khud test karo — right side cover karo aur reveal karne se pehle jawab do.

Symbol

q

ka matlab kya hai aur ek electron ke liye iska value kya hai?

Electric charge;

q_{e} = 1.602 \times 1 0^{- 19}

Voltage drop mein ek positive charge kis taraf move karta hai, aur electron kis taraf?

Positive charge high→low voltage (downhill) move karta hai; electron low→high (uphill) move karta hai, opposite.

Ion kya hota hai, aur singly-ionized xenon atom kaise likhte hain?

Ek charged atom (missing/added electron); likha jaata hai

Xe^{+}

Symbol

m

kya stand karta hai aur topic bhaare ions ko kyon prefer karta hai?

Mass; bhaare ions har throw mein zyada momentum carry karte hain, isliye zyada thrust.

Voltage

V

ek charge ke saath kya karta hai, aur ek volt kya hota hai?

Yeh ek electrical "downhill" hai jis par positive charge slide karta hai;

1 V = 1 J / C

(ek joule per coulomb).

Ek electron-volt (eV) define karo.

Woh energy jo ek electron ek volt se girke gain karta hai

= 1.602 \times 1 0^{- 19}

Work–Energy Theorem ek sentence mein batao.

Kisi object pe kiya gaya total work uski kinetic energy mein change ke barabar hota hai.

Kinetic energy formula likho aur batao ½ kahan se aata hai.

K E = \frac{1}{2} m v^{2}

; ½ isliye aata hai kyunki steady acceleration ke dauran average speed final speed ki aadhi hoti hai.

v_{e}

kya hai aur

q, V, m

ke terms mein yeh kya equal hai?

Exhaust speed;

v_{e} = 2 q V / m

\overset{m}{˙}

mein dot ka kya matlab hai?

"Rate per second" — mass jo per second nikal rahi hai.

Current

I

, ion count

N

, aur charge

q

kaise related hain, aur

I

kis direction mein point karta hai?

I = N q

; current positive-charge flow ke saath chalta hai, isliye ion beam current peeche ki taraf point karta hai.

Yahan

F

kya hai aur yeh chota hone ke bawajood useful kyon hai?

Thrust (aage ki push); tiny (~0.1 N) lekin months tak chalta hai, isliye total

Δ v

bahut bada hota hai.