Foundations — Fusion — solar fusion, tokamak (concept)

This page assumes you have seen none of the notation on the parent note. We build each symbol from the picture up, in an order where every symbol only uses symbols already earned.

1. The nucleus, the proton, the neutron

The picture: look at figure s01. A nucleus is a little cluster of red balls (protons) and grey balls (neutrons) packed together. The electrons live far outside — we ignore them here because fusion is about the nucleus.

Why the topic needs this: fusion means combining nuclei. You cannot talk about combining things you haven't named.

2. Nuclide notation ${}_Z^A\text{X}$

The parent note writes things like ${}_1^2\text{D}$ and ${}_2^4\text{He}$. Let us fully unpack that stack of numbers.

Why the topic needs this: the whole reaction ${}_1^2\text{D}+{}_1^3\text{T}\to {}_2^4\text{He}+n$ is bookkeeping with these labels. Notice the totals balance: protons before $=1+1=2$, after $=2+0=2$; balls before $=2+3=5$, after $=4+1=5$. Nothing is lost in count — but as we'll see, a sliver of mass is.

3. Why nuclei push apart — the Coulomb barrier

The picture: figure s02 shows the energy "hill" two protons must climb as they approach (the red curve). Far apart, the push is gentle. Very close, a different, much stronger attraction (the strong force) suddenly takes over and yanks them together — that's the deep valley on the right.

Why the topic needs this: every "insane temperature" and "compress it" statement on the parent page exists purely to defeat this hill.

4. Temperature $T$ = how fast the particles jiggle

The picture: imagine the red balls of figure s01 vibrating. Cold → gentle jiggle, they never reach the hilltop of s02. Hot → violent jiggle, some pairs ram right over the barrier.

Why the topic needs this: "heat to $10^8$ K" literally means "make them jiggle hard enough to climb the Coulomb hill." $T$ appears again inside the Lawson criterion.

5. Mass, the mass defect $\Delta m$, and $E=m{c}^2$

Now the heart of the energy release. First, mass.

$\Delta m=(\sum m_{\text{reactants}})-(\sum m_{\text{products}})$

Here $\sum$ (capital sigma) just means "add up all of these."

Why the topic needs this: the entire "Derivation of energy released" and every worked $Q$-value on the parent page is just plugging masses into $Q=\Delta m{c}^2$.

6. Binding energy per nucleon $B/A$ — the "map" that says which way is downhill

The picture: figure s03 is the famous Binding Energy per Nucleon Curve. It rises steeply from hydrogen, peaks near iron (${}^{56}\text{Fe}$, about $8.8\text{MeV}$ per nucleon), then gently falls. Higher up the curve = more tightly bound = more stable.

Why the topic needs this: this curve is the reason fusion releases energy at all, and why only light nuclei qualify.

7. Plasma — the stuff inside the reactor

Why the topic needs this: you can't magnetically grab a neutral gas. Fusion fuel must first become plasma so magnets can hold it.

8. Magnetic field $\vec{B}$, velocity $\vec{v}$, and the Lorentz force

The picture: figure s04. A charged particle moves along $\vec{v}$; the field $\vec{B}$ points into the region; the resulting force $\vec{F}=q\vec{v}\times \vec{B}$ points sideways, at a right angle to $\vec{v}$. A force forever sideways to motion doesn't speed the particle up or slow it down — it curves the path into a circle. So charged particles spiral around field lines instead of crossing them.

Why the topic needs this: this is why a magnetic doughnut can confine plasma — particles are leashed to the looped field lines. It also debunks the "magnet heats the plasma" mistake on the parent page.

9. Putting the confinement symbols together: $n$, ${\tau }_E$, and the triple product

Why the topic needs this: this single line is the scoreboard for "did the reactor produce more energy than it cost."

The prerequisite map

Equipment checklist

Test yourself — cover the right side and answer: