Fusion — solar fusion, tokamak (concept)

WHY does fusion release energy?

Derivation of energy released (from first principles)

WHAT we want: the energy $Q$ liberated when nuclei combine.

WHY it works: mass is not conserved exactly — the product is lighter than the sum of the parts. That "missing mass" $\Delta m$ became energy.

HOW — step by step for the key reaction $^2_1\text{D} + {}^3_1\text{T} \to {}^4_2\text{He} + n$ :

Total rest mass of reactants $= m_D + m_T$ . Why? Energy is locked in rest mass.
Total rest mass of products $= m_{He} + m_n$ .
Mass defect: $\Delta m = (m_D + m_T) - (m_{He} + m_n)$ . Why subtract? The decrease in mass is what got converted.
Energy released: $Q = \Delta m\, c^2$ Why $c^2$ ? Einstein's mass–energy equivalence: a tiny mass times the huge number $c^2$ = a lot of energy.

Solar fusion — the proton–proton (p–p) chain

The net result of the p–p chain: $4\,{}^1_1\text{H} \to {}^4_2\text{He} + 2e^+ + 2\nu_e + \text{energy}$

HOW the chain runs (concept-level):

$p + p \to {}^2\text{D} + e^+ + \nu_e$ — the bottleneck (weak interaction, very slow). Why slow? A proton must turn into a neutron via the weak force.
${}^2\text{D} + p \to {}^3\text{He} + \gamma$
${}^3\text{He} + {}^3\text{He} \to {}^4\text{He} + 2p$

Tokamak — fusion on Earth

Why a magnetic field confines plasma (first principles)

A charged particle in a magnetic field feels the Lorentz force $\vec F = q\vec v\times\vec B$ , which is always perpendicular to velocity → it makes the particle circle the field lines (gyration) instead of crossing them. Why this helps: particles are tied to field lines, so by bending the field into a closed loop (torus), you trap them.

Worked Examples

Worked example 1 — D–T fusion energy

$^2\text{D} + {}^3\text{T} \to {}^4\text{He} + n$ . Given $m_D=2.014102$ , $m_T=3.016049$ , $m_{He}=4.002603$ , $m_n=1.008665$ (u). Find $Q$ .

Step 1: Reactant mass $= 2.014102+3.016049 = 5.030151$ u. Why? Sum the inputs. Step 2: Product mass $= 4.002603+1.008665 = 5.011268$ u. Why? Sum the outputs. Step 3: $\Delta m = 5.030151-5.011268 = 0.018883$ u. Why subtract? That's the mass lost → energy. Step 4: $Q = 0.018883 \times 931.5 = 17.6$ MeV. Why ×931.5? Converts u· $c^2$ to MeV.

Result: $Q \approx \mathbf{17.6\ MeV}$ — the most promising reactor reaction.

Common Mistakes (Steel-manned)

Recall Feynman: explain to a 12-year-old

The Sun makes light by smooshing tiny hydrogen bits together to make helium. When they stick, a teeny bit of their weight vanishes and turns into a HUGE burst of energy — that's $E=mc^2$ . But the bits hate being close (they push apart like same-pole magnets), so you need things crazy-hot to force them together. On Earth we build a doughnut-shaped magnetic cage called a tokamak to hold super-hot gas (plasma) without it melting the walls, hoping to make our own little sun for power.

Flashcards

Why does fusion of light nuclei release energy?

The product has higher binding energy per nucleon; the lost mass

\Delta m

becomes energy via

Q=\Delta m\,c^2

What is the net solar p–p reaction and its energy?

4\,^1\text{H}\to{}^4\text{He}+2e^++2\nu_e

, releasing 26.7 MeV. Why is the Sun's core (1.5×10⁷ K) able to fuse at all despite being "too cold"? ::: Quantum tunnelling through the Coulomb barrier. What reaction do reactors like ITER use and its Q-value? ::: D–T fusion, $^2\text{D}+{}^3\text{T}\to{}^4\text{He}+n$ , $Q\approx17.6$ MeV. What shape is a tokamak and what confines the plasma? ::: A torus (doughnut); magnetic fields confine the plasma. Why doesn't the magnetic force heat the plasma? ::: $\vec F=q\vec v\times\vec B$ is perpendicular to velocity → does no work. State the Lawson (triple product) criterion conceptually. ::: $n\,T\,\tau_E$ must exceed a threshold (

3\times10^{21}

keV·s/m³ for D–T) for net energy gain.

Why must a tokamak be hotter than the Sun's core?

It lacks the Sun's gravitational compression, so higher temperature is needed to drive fusion.

What is plasma?

A hot ionised gas of free electrons and ions, responsive to magnetic fields.

Fusion vs fission: which side of the iron peak?

Fusion = light nuclei below iron; fission = heavy nuclei above iron.

Connections

Binding Energy per Nucleon Curve — explains why both fusion and fission release energy.
Mass-Energy Equivalence (E=mc^2) — source of the released energy.
Nuclear Fission — the complementary process for heavy nuclei.
Lorentz Force — the basis of magnetic confinement.
Quantum Tunnelling — why the Sun fuses despite low core temperature.
Plasma — Fourth State of Matter

Concept Map

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Dekho, fusion ka funda simple hai: do chhote nuclei (jaise hydrogen) ko aapas mein joR do, toh ek bada nucleus banta hai jo zyada tightly bound hota hai. Is process mein thoRa sa mass "gayab" ho jaata hai aur woh mass $E=mc^2$ ke hisaab se huge energy ban jaati hai. Yehi cheez Sun ko chamka rahi hai — Sun ke core mein 4 hydrogen milke ek helium banate hain aur ~26.7 MeV energy release hoti hai. Mast baat yeh hai ki Sun ka core "sirf" 1.5 crore kelvin hai, jo actually itna garam bhi nahi ki protons apni repulsion (same charge, isliye push) ko classically harayein — yeh sirf quantum tunnelling ki wajah se hota hai, isliye reaction slow hai aur Sun arbon saal jeeta hai.

Ab Earth pe yeh karna mushkil hai kyunki humare paas Sun jaisi gravity nahi jo plasma ko dabaa ke rakhe. Isliye humein aur zyada garam karna paRta hai — lagbhag $10^8$ K, Sun se bhi 10 guna! Itni heat pe koi bhi deewar pighal jaayegi, toh idea yeh hai ki plasma (ionised garam gas, jisme free electrons aur ions hote hain) ko magnetic field se ek doughnut-shape (torus) box mein pakad ke rakho. Is machine ko tokamak kehte hain. Magnetic force $F=qv\times B$ velocity ke perpendicular hoti hai, isliye particles field lines ke around ghoomte rehte hain, deewar ko touch nahi karte — aur dhyaan rakho, yeh force koi work nahi karti, sirf direction badalti hai.

Reactor ke liye sabse achha reaction D–T hai ( $^2$ D + $^3$ T → He + n, $Q=17.6$ MeV) kyunki yeh sabse kam temperature pe sabse zyada easily hota hai. Lekin net energy faayde ke liye teen cheezein ek saath badi honi chahiye: density $n$ , temperature $T$ , aur confinement time $\tau_E$ — inka product (Lawson criterion) ek threshold cross kare. Yaad rakho: fusion = halke nuclei joRna, fission = bhaari nuclei toRna, dono iron ki taraf jaate hain curve pe. Yehi exam ka aur real-world clean-energy ka core idea hai.

Fusion — solar fusion, tokamak (concept)

WHY does fusion release energy?

Derivation of energy released (from first principles)

Solar fusion — the proton–proton (p–p) chain

Tokamak — fusion on Earth

Why a magnetic field confines plasma (first principles)

Worked Examples

Common Mistakes (Steel-manned)

Flashcards

Connections

Concept Map

Hinglish (regional understanding)

Go deeper — visual, from zero

Test yourself — Modern Physics

Connections