Lesson 6 of 6

Fusion reactors.

About 30 minutes · 6 practice questions

Read the full article: Fusion reactors

How to hold a plasma ten times hotter than the centre of the Sun. A cage of field lines, why a plain ring leaks, the twist and the safety factor, Lawson's triple product, why hotter is not always better, and what stronger magnets buy.

Step 1 of 6 · A cage of field lines

Step 1 of 6

A cage of field lines

Fusing deuterium and tritium gives about 17.6 MeV per reaction, but only in a plasma at about 150 million kelvin, where the nuclei move fast enough to overcome the electric repulsion between them. In the Unit on magnetism we saw that a magnetic force on a moving charge is at right angles to its motion. In the Scene, an ITER-sized tokamak, with a wedge cut out of its side.

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Step 2 of 6

No twist

Show field and particles is On: the field lines, and on them ions (orange) and electrons (blue), with their circles and drift greatly enlarged. Plasma temperature and Field strength are locked, and Plasma current is free.

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Step 3 of 6

Too much twist

The current in the plasma makes a field that wraps round it the short way, and together with the coils’ field it turns every field line into a spiral. The twist is measured by the safety factor $q$ ⁠: how many times a field line goes round the ring the long way for each time it goes round the short way. The bigger the current, the tighter the twist and the smaller $q$ ⁠. Plasma current is locked, and Field strength is free.

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Step 4 of 6

The triple product

Holding the plasma is not enough: it has to make more fusion power than it loses. In 1955 John Lawson showed that this depends on the product of three numbers: the density $n$ ⁠, the number of fuel nuclei in a cubic metre; the temperature $T$ ⁠; and the energy confinement time $\tau_E$ ⁠, how long the plasma would keep its heat if the heating were switched off. For deuterium and tritium, ignition needs about

$n\,T\,\tau_E \gtrsim 3 \times 10^{21}\ \mathrm{keV \cdot s/m^3}$ ⁠

with $T$ ⁠ measured in kiloelectronvolts. The chart beside the Scene is a Lawson diagram, and the dot on it is the Scene’s plasma. All the controls are locked.

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Step 5 of 6

Hotter

The gain $Q$ ⁠ is the fusion power divided by the heating power fed into the plasma. At $Q = 1$ ⁠ they are equal, and at ignition the plasma heats itself. Field strength and Plasma current are locked, and Plasma temperature is free.

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Step 6 of 6

Stronger magnets

ITER is built with niobium–tin superconducting magnets. A new generation of superconductors, which work in much stronger fields, has opened another route: not a bigger machine, but a stronger field. Plasma temperature is locked.

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Interactive scene

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Each step sets up the Scene for you, and a control marked “fixed” stays put for that step.

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Practice · Choose

The plasma inside the tokamak is ten times hotter than the centre of the Sun. What keeps it off the walls?

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Practice · Predict, then look

The field and particles are showing. Plasma current is turned down to zero, no twist: only the coils’ field is left, running round the ring and closing on itself. What will happen to the particles?

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Practice · Predict, then look

ITER’s settings: Field strength 5.3 T and Plasma current 15 MA, with an edge safety factor $q = 3$ ⁠. The field is lowered to JET’s field, 3.45 T, and the current is left alone. What will happen?

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Practice · Calculate

At ITER’s settings the plasma holds about $5.1 \times 10^{19}$ ⁠ fuel nuclei in each cubic metre, at 150 million K, and the energy confinement time is about 3.0 s. What is the triple product $nT\tau_E$ ⁠, in keV·s/m³?

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Practice · Predict, then look

ITER’s settings, with a gain $Q \approx 10$ ⁠. Plasma temperature is doubled from 150 to 300 million K, without changing Field strength. What will happen to $Q$ ⁠?

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Practice · Reach the target

The idea behind SPARC and other new machines: stronger magnets. Plasma temperature is locked at 150 million K. Change Field strength and Plasma current until the plasma reaches ignition, without kinking, and press Check.