NEXA
NUCLEUS OF ATOMIC EXPLORATION
MODULE 3 · NEXA SERIES FOR EDUCATORS
The confinement
challenge
A reactor’s energy balance — and the yardstick that decides whether fusion pays off
High School · 15–20 minutes · nexatomic.com/educadores
Made by students, for students.
NEXA — nexatomic.com
THE BRIDGE
The physics works. Now, the engineering.
Module 2 showed where the energy comes from. But a plasma above 100 million °C has three problems at once — and solving only two is not enough.
1
Heat it
Reach — and stay at — fusion temperature.
2
Hold it
No material in the world can serve as a wall for the plasma.
3
Lose little
Energy leaks all the time. Fusion must generate more than leaks out.
NEXA · Series for Educators — Module 3 · The confinement challenge
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THE WALL PROBLEM
Nothing can touch a fusion plasma
No material survives continuous contact with 100 million °C. But the important detail is the opposite of what it seems: when the plasma touches the wall, it is the plasma that dies.
What does NOT happen
There is no explosion, no runaway reaction. The plasma holds very little matter — grams — and no chain reaction to feed.
What happens
The plasma cools on contact, gets contaminated with wall atoms and goes out in seconds. The damage is to the experiment — the wall suffers local erosion, the reactor stops.
It is the same safety argument from Module 1 — now seen from the engineering side.
NEXA · Series for Educators — Module 3 · The confinement challenge
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THE THREE CAGES
Three ways to hold a plasma
GRAVITATIONAL
Stars: the gravity of colossal masses compresses the plasma. Not replicable on Earth.
MAGNETIC
Our route: charged particles stay trapped in magnetic fields. Tokamaks and stellarators.
INERTIAL
Lasers compress a fuel capsule for instants. The NIF route, in the USA.
This module and the next ones follow the magnetic route — the most mature for continuous electricity.
NEXA · Series for Educators — Module 3 · The confinement challenge
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THE INVISIBLE CAGE
Charged particles obey the magnetic field
In a plasma, everything carries electric charge — and a charged particle does not cross magnetic field lines: it spirals around them, trapped like a bead on a wire. Well-designed fields become a bottle without walls.
magnetic field line
particle spiraling
The tokamak idea
Close the field lines into a ring and the particles circulate without ever meeting a wall. How that becomes a real machine is the subject of Module 4.
NEXA · Series for Educators — Module 3 · The confinement challenge
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THE ENERGY BALANCE
A reactor is a contest between generating and leaking
Even confined, the plasma loses energy non-stop — through radiation and transport. The characteristic time of that loss has a name: τE, the energy confinement time. It is the third character in this story.
IN
external heating
BORN
fusion power
OUT
radiation + transport
τE — energy confinement time: if the heating were switched off now, it is the characteristic time the plasma would take to lose its energy. The larger the τE, the better the bottle.
NEXA · Series for Educators — Module 3 · The confinement challenge
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1957
The Lawson criterion: the original yardstick
John Lawson asked the right question: under what conditions does a confined plasma produce more energy than it loses? The original answer has two factors — density and confinement time — evaluated at a given temperature.
n · τE
density × confinement time
Dense or patient — or both
The criterion allows trade-offs: a denser plasma can confine for less time; a more rarefied one must hold its energy longer. What it cannot do is fail at both.
Precision that matters: the Lawson criterion is n·τE. The famous triple product came later, as an extension — and it is the next slide.
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THE MODERN YARDSTICK
The triple product: n · T · τE
Adding temperature as the third factor creates the figure of merit used to this day — with a nearly single target for D-T fusion.
IGNITION (D-T)
n · T · τE ≥ 2.9 × 10²¹
m⁻³ · keV · s — with the minimum at a temperature of 14 keV (≈ 160 million °C)
For scientific breakeven (Q = 1), the target is ≈ 4.6 × 10²⁰ — about 6 times less demanding. Always state which condition you are using.
Three knobs, one target
Density, temperature and confinement trade off — and that is exactly the game NEXA’s simulator lets you play.
Source: Wurzel & Hsu, Phys. Plasmas 29, 062103 (2022)
NEXA · Series for Educators — Module 3 · The confinement challenge
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THE SCORE
Q: how much fusion gives back of what it receives
Q compares fusion power with the heating power injected into the plasma. It is a staircase — and every step has a name.
Q = 0,67
JET, 1997 — the real D-T record
Q = 1
scientific breakeven: fusion equals injected heating
Q ≈ 5
self-heating (alphas) matches the external sources
Q ≈ 10
the ITER goal — plasma Q
Q → ∞
ignition: the plasma sustains itself
Q is of the plasma, not the wall socket: no magnetic fusion reactor has ever produced net electricity — coils, cryogenics and heating still consume more than the machine gives back.
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FINAL 5 MINUTES
For classroom discussion
1
Why doesn’t “just heat it more” solve it — what does τE add to the story?
2
What is the difference between the Lawson criterion and the triple product?
3
Does Q = 1 mean the reactor “pays for itself”? Why not?
4
If the plasma touches the wall, what happens — and why is that a safety argument?
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CONTINUE FROM HERE
To learn more
nexatomic.com/simulator
Turn the three knobs of the triple product — density, temperature, confinement — and chase breakeven in the browser.
Wurzel & Hsu (2022) — arXiv:2105.10954
The open-access paper that maps the progress of every fusion concept on the triple-product yardstick.
ITER Organization — iter.org
The machine designed for Q ≈ 10 — and the subject of the next module.
Materials for educators
nexatomic.com/educadores
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Made by students, for students
NEXA was born in a high-school classroom — and exists to prove that serious science can be told by those who are learning, for those who are learning. Our goal is simple: no student should stay far from nuclear fusion for lack of good, free material in their own language.
And no one is closer to students than you. If this module made a difference in your class, pass it on to another educator, adapt it to your context — and tell us how it went. Every classroom report improves the next module, and every teacher who joins makes this community of scientific and educational growth larger.
Materials, reports and contact: nexatomic.com/educadores
Triple-product and Q-gain figures: Wurzel & Hsu, Phys. Plasmas 29, 062103 (2022), arXiv:2105.10954 · infographics: NEXA. License: CC BY-NC-SA 4.0 — copy, adapt and redistribute for non-commercial purposes, with attribution.