# THE ENERGY OF THE STARS - NUCLEAR FUSION

In nuclear fission a heavy nucleus is split by neutron bombardment but if two light nuclei can be joined together we have another way of releasing energy - this is known as nuclear fusion.

Many scientists in both Europe, Japan and the United States are working to achieve controlled fusion. The lure of fusion is that the fuel could be heavy hydrogen (deuterium), extracted from sea water - one part in 6700 of the hydrogen atoms in sea water is deuterium and this gives an almost unlimited energy source for the foreseeable future.

The big problem here is that both the nuclei are positive and to get them to fuse we have to somehow make them come very close together so that the strong nuclear force becomes greater than the electrostatic repulsion. The way this is done is to make them collide at very high speed by raising the temperature of the gas to over 100 million oC, several times hotter than the centre of the Sun!

At these temperatures the gas becomes a plasma, a sea of electrons and ions and is a real problem to contain.

The most likely fusion reaction is the deuterium(D) - tritium(T) one shown below:

 21D + 31T giving 42He + 10n + 17.6 MeV 2.014 102u + 3.016 049u 4.002 604u + 1.008665u

Giving a mass defect of 0.018888 and an energy of 17.6 MeV. This is less than for the fission of one nucleus of uranium but since the density of deuterium is so much less than uranium the yield per kilogram is comparable.

In 1kg of deuterium there are approximately 3 x 1026 atoms and so the energy released per kilogram would be 8.45x1014 J. The temperature at which the power generation rate exceeds the loss rate is called the critical ignition temperature. This is about 4.5 x 107 K for the D - T reaction but rises to 4 x 108 K for the apparently simpler D - D reaction.

Problems
1. Suggest why the critical ignition temperature is higher for the D - D reaction than for the D - T reaction.
2. Calculate the energy released in the following reactions:
(a) D(D,n)3H
(b) D(D,T)1H
(c) T(T,2n)4He

### schoolphysics: Nuclear fusion animation

To see an animation of nuclear fusion click on the animation link.

## THE TOKOMAK AND JET

One solution (used at JET, the Joint European Torus) is to use a magnetic field to hold the plasma in a doughnut shaped container. The magnetic field around the torus keeps the charged plasma away from the sides of the container.

The special design of magnetic field in JET called a tokomak, first developed in the Soviet Union, gives its name to this general type of fusion reactor. If the plasma touched the walls it would simply cool - there is not enough thermal energy in it to melt the container. One of the main problems with JET has been to control this plasma, it writhes and twists and eventually leaks out of the magnetic field. In JET the plasma is heated in three ways: by giving it energy using radio waves, firing a beam of atoms into the gas and passing a current of up to 7 MA through it!
You can see from the D-T reaction above that neutrons are produced and these would make the structure radioactive. However the scale of this can be limited by using suitable materials and there is no radioactive waste like the products from a fission reactor.

To provide the equivalent of the worlds annual electricity needs during the latter part of the twentieth century with 40% efficient power stations we would need to burn:
1 700 000 000 tons of coal or
85 000 tons of uranium in conventional reactors or
1000 tons of uranium in fast breeder reactors or
1000 tons of lithium in D-T fusion reactors or
135 tons of deuterium in D-D fusion reactors!

For a fusion reactor of the JET type to become operational we would need a plasma temperature in the region of 100 - 150 million degrees celsius, a central plasma density of around 10-6 kgm-3, this is 2 - 3x1020 particles m-3, and an energy confinement time of 1 - 2 seconds all at the same time.

Unfortunately tritium does not occur naturally but in a commercial fusion reactor lithium would be used as a heat absorbing blanket and this would also breed tritium to keep the reaction going. The reactions for this are:

The second reaction looks more promising until you realise that only 7.4% of natural lithium is 6Li.
On 9th November 1991 a breakthrough was achieved at JET when they first used the correct fuel, a mixture of deuterium and tritium in the torus. At 7.44 pm they produced a pulse of of power from fuison lasting about 2 seconds, peaking at almost two megawatts, with the plasma reaching a temperature of 200 million oC,. They only used 0.2 g off tritium mixed with six times as much deuterium but it was still a step towards the 50-50 mixture that the are hoping to use in the future.

The next stage of the fusion reactor story could be the building of ITER (International Thermonuclear Experimental Reactor).
This would:
be about 25 metres high
have a plasma chamber 4.3 m by 8.4 m
have a field on the axis of 4.85T
have a maximum plasma current of 22 MA and give a nominal fusion power of 1000 MW.

Getting the energy out will be a real problem because it is thought that some parts of the machine will be exposed to some 25 million watts per square metre.
The go ahead for European, Russian and United States cooperation for such a machine was given in late 1992 and it is hoped that the machine could become operational by the year 2005. Unfortunately this was not to be.
However it still seems unlikely that a commercial fusion reactor will be built before the year 2040.

FUSION WITH LASERS
In the USA at Lawrence Livermore National Laboratory high powered lasers are being used to create fusion. Ten laser beams are directed onto a small plastic sphere containing a mixture of deuterium and tritium. The power of this laser array, called NOVA is enormous. Some 124.5 kJ of radiant energy with a wavelength of 1050 nm are delivered to a 0.5 mm diameter sphere in 2.5 ns giving a power input of 5 x 1013 watts raising its temperature to over 400 MoC! Even higher powers of 1014 are planned.

Their recipe for fusion goes like this:
Take a 5mm capsule of potassium dihydrogen phosphate (KDP) filled with 5mg of deuterium-tritium fuel. Apply 200 kJ of energy, then wait for 10-9 s, result a little star!

© Keith Gibbs 2011