Why nuclei resist joining
Definition
Electrostatic repulsion
Electrostatic repulsion is the force that pushes apart two objects carrying the same type of electric charge.
- Every nucleus contains protons, and protons carry positive charge, so every nucleus is positively charged.
- Two objects with the same type of charge repel each other, so two nuclei approaching one another push each other apart.
- That repulsive force gets rapidly stronger as the separation gets smaller, so the closer the nuclei get, the harder they are pushed back.
- The attractive force that would hold the two nuclei together once they merge acts only over an extremely short range, roughly the width of a nucleus itself.
- So the two nuclei have to be forced right up against each other before that attraction can take over, and the electrostatic repulsion is fighting them the whole way in.
- Getting that close means the nuclei must arrive with a great deal of kinetic energy, because that energy is used up doing work against the repulsion as they approach.
- This is why fusion needs extreme conditions and does not simply happen in a container of hydrogen gas on a laboratory bench.
Why the temperature must be high
- Temperature is a measure of the average kinetic energy of the particles in a substance.
- Raising the temperature therefore makes the nuclei move faster, and a faster nucleus arrives at a collision with more kinetic energy to spend.
- At a very high temperature, enough nuclei have enough kinetic energy to overcome the electrostatic repulsion and get close enough to fuse.
- At a low temperature the nuclei move slowly, so they run out of kinetic energy while they are still far apart and the repulsion pushes them back before they can touch.
- The temperatures involved run to tens of millions of degrees, far hotter than anything a flame or a furnace can reach.
- At those temperatures the atoms have long since lost their electrons, so the fuel is a plasma of bare nuclei and free electrons rather than a gas of atoms.
Why the pressure must be high
- High pressure squeezes the fuel into a smaller volume, so there are far more nuclei packed into each cubic metre.
- Nuclei that are packed closely together travel a much shorter distance before meeting another one, so collisions happen far more often.
- This matters because even in a very hot plasma only a small fraction of collisions actually result in fusion, so a large number of collisions per second is needed to give a useful rate of energy release.
- At low pressure the nuclei are spread thinly, so collisions are rare and almost no fusion happens even if the nuclei are moving fast enough.
- The two conditions do different jobs and neither replaces the other: temperature decides whether a collision can lead to fusion, and pressure decides how many collisions there are.
- In the core of the Sun both conditions are supplied free by gravity, because the weight of the layers above squeezes the core to an enormous pressure and keeps it enormously hot.
Key Idea
- High temperature gives the nuclei enough kinetic energy to overcome the electrostatic repulsion between their positive charges.
- High pressure packs the nuclei closer together so that collisions happen often enough for a useful amount of fusion.
Building a fusion power station
- A power station on Earth cannot reach anything like the pressure at the centre of the Sun, so it has to make up for that with an even higher temperature, above a hundred million degrees.
- Reaching that temperature takes a very large energy input before any fusion happens at all.
- No solid container can hold the plasma, because any material touching it would melt or vaporise, and the contact would also cool the plasma below the temperature fusion needs.
- The plasma is therefore held away from the walls by powerful magnetic fields inside a ring-shaped vessel, which works because a plasma is made of charged particles.
- The magnets, the heating equipment and the vacuum vessel are all complex and expensive, and running the magnets uses a great deal of electricity of its own.
- A plasma at these conditions is also difficult to hold steady, because small disturbances grow quickly and can end the reaction in a fraction of a second.
- A power station must keep the conditions going continuously, not for a few seconds at a time, because the electricity supply has to be constant.
- The fast neutrons produced by the reaction damage the inner walls over time and make them radioactive, so parts must be replaced and eventually disposed of.
- The economic test is strict: the station must generate enough electricity to pay back the energy used to heat and confine the plasma, and to cover the cost of building, running and repairing it, and still have electricity left to sell.
- Individual fusion reactions releasing energy is not enough, and no fusion reactor has yet supplied electricity to a grid, which is why fusion is still an area of research rather than a working power source.
Example
Testing the energy balance
- In one pulse of an experimental reactor, 50 MJ50\ \text{MJ}50 MJ of energy is supplied to heat and confine the plasma, and the fusion reactions release 60 MJ60\ \text{MJ}60 MJ.
- More energy comes out than goes in, since 6050=1.2\dfrac{60}{50}=1.25060=1.2, so at first sight the reactor appears to be a net source of energy.
- That energy still has to be turned into electricity through a coolant, a turbine and a generator, and only about 40%40\%40% of it survives that chain.
- The useful electrical output is therefore 0.40×60=24 MJ0.40\times60=24\ \text{MJ}0.40×60=24 MJ.
- That is less than the 50 MJ50\ \text{MJ}50 MJ that was put in, so the reactor uses more electricity than it delivers.
- To break even, the fusion energy needed is 500.40=125 MJ\dfrac{50}{0.40}=125\ \text{MJ}0.4050=125 MJ, which is more than twice the current output, and a station also has to cover its construction and repair costs on top of that.
Exam technique
Explaining the conditions for fusion
- Start from the charge: nuclei contain protons, protons are positive, so two nuclei repel each other electrostatically.
- Then attach each condition to its own consequence: high temperature gives greater kinetic energy to overcome the repulsion, high pressure gives more frequent collisions.
- Where a question asks why fusion does not happen at low temperature and pressure, answer both halves, because there is normally a mark for each.
- For the power station question, link the conditions to a practical problem and then to money, for example that containing the plasma needs powerful magnets, which are expensive to build and to run.
- Use the word because at every step, since the marks are for the causal links rather than for naming the conditions.
Common Mistake
- Do not say that high pressure gives the nuclei the energy to overcome the repulsion; that is what high temperature does.
- Do not say that nuclei repel because they are heavy or because of gravity; the repulsion is electrostatic and comes from their positive charge.
- Do not say that electrons repel the nuclei; at these temperatures the electrons have already been stripped away.
- Do not claim fusion is impossible; it happens in stars and in experimental reactors, and the difficulty is making it produce more useful energy than it consumes.
- Do not answer the economic question by saying only that fusion is expensive; say what makes it expensive and why the output has to exceed the input.
Self review
- Explain why two nuclei repel each other as they approach.
- Explain why fusion does not happen at a low temperature.
- Explain why fusion does not happen at a low pressure, even if the nuclei are hot.
- State how the conditions needed for fusion are produced in the core of the Sun.
- Explain why the plasma in a fusion reactor cannot be held in an ordinary container.
- Give two reasons why a fusion power station is difficult to make economic.