Physics 6 Tutorial 12 - Renewable and Non-Renewable Energy Sources

This tutorial is for students of the Welsh Board and Eduqas Syllabuses.

The last two topics are for students studying the CEA syllabus.

This is a long tutorial.  You may wish to go through it slowly in several sessions.

 

Contents

Non-Renewable Energy Sources

Power from the Sun

Intensity of Sunlight

Intensity Calculations
Photovoltaic Cells
Wind Turbines

Power from a Turbine

Hydroelectric Power

Tidal Power Stations

Pumped Storage Power Stations

Nuclear Enrichment and Breeding

Breeder Reactors

Fusion Power

Inertial Confinement

Gravitational Confinement

 

Non-Renewable Energy Sources

Non-renewable energy sources captured their energy from the Sun millions of years ago.  They have given us the lifestyle that we enjoy today.  Imagine life without electricity (think back to the last time your house lost its electricity).  Our modern way of life depends on fossil fuels:

All of these give off carbon dioxide, which is a greenhouse gas, when they are burned.  Greenhouse gases (which we discussed in the previous tutorial) are associated with global warming with all the problems that climate change is bringing.

 

Another problem that the use of fossil fuels bring is that of pollution.  Not only do fossil fuels give out carbon dioxide, but also sulphur dioxide.  All organisms have sulphur in them, coming from an amino acid called cysteine, which is an essential part of the proteins that make up living cells.  Sulphur dioxide reacts with rain water to make acid rain that has caused long term damage to trees.

 

In the Twentieth Century, coal was burned in large amounts in open fires to heat homes, as well as for firing boilers for locomotives, and steam engines to power machinery.  Mains gas was derived from coal, rather than methane that is used today.  Town gas was principally carbon monoxide, which is highly toxic.  The smoke from such activities led to smog which made for breathing difficulties for many people, sometimes fatal.  It needs to be remembered also that in those days, most adults smoked tobacco, so a large proportion of the population had smoking related health issues.  The number of fatalities led to clean air legislation which demanded smokeless fuels.

 

While smog has become less of a problem, pollution from road traffic has taken its place.  The internal combustion engine in cars, lorries, and buses produces not only carbon dioxide, but also carbon monoxide, and nitrogen dioxideCatalytic converters are now compulsory to reduce such pollutants  The diesel engine also produces tiny particles of soot.  In recent years, motorists were encouraged to buy diesel cars because they use less fuel, hence less carbon dioxide is produced.  However the cars produced more pollutants, so manufacturers were forced to add diesel particulate filtration systems in to reduce these to an acceptable level.  A number of manufacturers, not only Volkswagen, added cheat software into the engine management systems of the cars, so that when they were tested in stationary test facilities, the cars produced much less pollution than when out on the road.  Volkswagen was caught in the emissions scandal, but other manufacturers have since owned up.  The re-programming to cut down the emissions has had adverse effects on performance and reliability of affected cars.

 

Government has demanded that fossil fuel be banned as a sole fuel for cars by 2040.  Electric and hybrid cars will be the rule.  This brings another issue, how to charge the batteries of the cars.  Millions of cars will need charging points.  This brings up other questions:

 

Many countries that in the Twentieth Century had totalitarian regimes that kept their peoples poor have now embraced the technological age.  Why should their people not have all the benefits that it brings?  Why can't they drive around in the decent cars that we take for granted?  Why should they not have good computers?

 

Another pressing problem has arisen in the international public consciousness, that of plastic pollution.  Plastics are made from oil.  They don't degrade naturally.  While an increasing amount of such materials is recycled, a lot is dumped and some ends up in the sea.  Marine plastic pollution is becoming an increasing threat to marine environments and the species that live there.  The clean-ups that are being carried out are a small fraction of what is there.

 

All of these increase the demand for fossil fuels with all the attendant issues.  Some wealthy and influential individuals and corporations say that pollution and global warming is not an issue, despite the evidence to the contrary.  So there needs to be different ways of providing the energy to power the lifestyle that we take for granted. 

 

And this is what we are going on to consider now.

 

 

Power from the Sun

The Sun, like all stars, gets its power from fusion.

 

Fusion means joining nuclei together, every alchemist’s dream.  It is easier said than done.  The idea is that light nuclei are joined together, increasing the binding energy per nucleon.  This will result in lots of energy being given out. 

 

Question 1

How does fusion differ from fission?

Answer

 

The process in stars has three stages:

1. Proton + Proton ® Deuterium + positron + electron neutrino

2. Deuterium + proton ® Helium 3 + photon

3. Helium 3 + Helium 3 ® Helium 4 + proton + proton

 

Since two protons are left over, the reaction is self sustaining.

 

Question 2

Data to use:

Mass of deuterium nucleus = 3.3425 × 10-27 kg

Mass of tritium nucleus = 6.6425 × 10-27 kg

Mass of helium nucleus = 6.6465 ×10-27 kg

Mass of a neutron = 1.675 × 10-27 kg

 

What is the energy in J and eV released in this reaction above?

Answer

 

 

Intensity of Sunlight

Intensity of radiation is defined as:

Power per unit area

 

The physics code for intensity is I and the units are watt per square metre (W m-2).  The equation is:

 

 

The energy has a maximum value, often written I0, at the source.  We treat the source as a point source.  As the light waves propagate, they spread out. For each doubling of radius, the intensity goes down by 4 times:

 


 

This is called the Inverse Square Law.  The equation for the inverse square law is:


 

where k is some constant, and r is the radius from the point source.

 

This is true for all waves.  Note that intensity is sometimes called irradiance

 

 

Intensity Calculations

We often don't know the values of I0 or k, the constant.  So an equation like this:

is not very useful.

 

However if we have a second equation like this:

we can do something with the two.  We can combine these in a rearranged form to give us:

 

I1(r1)2 = kI0 = I2(r2)2

 

So we can write:

I1(r1)2 = I2(r2)2

 

 

We can rearrange this into a ratio:

 

Question 3

The Earth is 150 million km from the Sun.  The intensity of light at the equator is 1400 W m-2.   

The radius of the Sun is 6.96 × 108 m

 

Modelling the Sun as a point source, work out the intensity of the light at the surface of the Sun.

Answer

 

Using Stefan's Law and Wien's Law, the intensity of light on the Sun's surface is 7.3 × 107 W m-2.  Your answer to Question 3 is lower than this because not all the radiation is absorbed by the Earth's surface.  Some is reflected by clouds and water.

 

 

Photovoltaic Cells

This garden lamp has a rechargeable battery in it that is charged up by sunlight during the day.  At night the battery is discharged through the LED lamp.

 

 

The theory of photovoltaic effect is described briefly in Electronics Tutorial 3.  The circuit symbol for a photovoltaic cell is:

 

 

Solar cells are not very efficient, about 10 % at the most.  To get a useful amount of power, we need to have a large array.  You can see large arrays of solar cells on the roofs of houses.  They can feed batteries to store energy for later use.  More commonly they are connected to the mains through an inverter, a device that converts the direct current output of the solar cell into alternating current of the mains.  The idea is shown in the picture below:

 

Image from www.powermyhome.co.uk

 

The isolation switch allows the inverter to be isolated from the mains, in case something goes wrong.  The current then passes through an electricity meter to work out how much electricity has been generated by the photovoltaic array.  Then the credit meter is connected to the consumer unit.

 

If the output of the photovoltaic array is greater than the current being used in the house, the surplus is sold to the electricity board.

 

The output voltage of a typical photovoltaic cell is about 0.5 V.  To get a useful voltage, the cells need to be arranged in series, like this:

 

 

Question 4

How many photovoltaic cells would be needed to give out a voltage of 240 V?

Answer

 

A typical photovoltaic cell will give a current of about 2.5 A.  If we want a bigger current, we can place the solar cells in parallel like this:

 

Question 5

What is the maximum current this array could give out?

Answer

 

A single series array would give out 240 V at 2.5 A.

 

Question 6

A typical photovoltaic array gives out a power of 4.8 kW at a voltage of 240 V.  Each cell gives 2.5 A at 0.5 V.

Show that about 3500 cells are required for this array.

How should they be arranged?

Answer

 

From your answer to question 6, you can see that a very large number of solar cells is needed.  Therefore solar panels are expensive.

 

Solar cells are about 10 % efficient.  Therefore they can give out just one tenth of the solar radiation that falls on them.

 

Question 7

The average intensity of sunshine in the UK is about 500 W m-2 (Intensity (W m-2 ) = Power (W) ÷ area (m2)

The area of a solar cell is 25 cm2.  The cell is arranged so that it can give out a voltage of 1.2 V.

 

(a) What is the absolute maximum power that the cell could provide if it were 100 % efficient?

(b) In reality the cell is 10 % efficient.  What is the maximum power obtained.

(c) What is the charging current if the voltage is 1.2 V?

(d) How long does it take to charge up a 600 mAh Ni-MH battery?

Answer

 

In an array of photovoltaic cells, there are also parallel diodes:

Suppose a mess appeared on one of the cells.  Without a parallel diode, the current would flow though the cell, which would act as a (rather poor) diode, and could get hot.  The diodes by-pass the affected cells.

 

 

Wind Turbines

Wind turbines are a familiar feature on out landscape.  They convert the kinetic energy from the wind into electrical energy to feed into the local grid.   Large amounts of power can be generated by large arrays of turbines called wind farms.  Some of these are off-shore, such as the examples shown below that are just off the Belgian coast.

 

Image by Hans Hillewaert - Wikimedia Commons

 

Although wind turbines are regarded as modern technology, the use of wind to power devices is many hundreds of years old.  In the UK the technology was used to grind corn for bread flour.  Wind was also used to power pumps in the East of England and in the Netherlands.  Wind turbines to power electrical generators were built as early as 1887.

 

Wind turbines made in three different types:

Animate gif by Ssgxnh Wikimedia Commons

The most common is the modern HAWT.

 

The picture below shows how a large wind turbine is made:

 

The wind spins the rotor at a rate of about 1 revolution per second (1 Hz).  The rotational speed is increased considerably by a gearbox.  The high speed shaft turns the generator that generates the electricity.  The yaw drive motor points the assembly into the wind, as it changes direction.

 

The whole assembly is contained in a housing called a nacelle.  The nacelle is mounted on a tower that can be over 100 m high.

 

The anenometer detects wind speed.  If the wind speed gets too high, damage can be done to the machine.  In this case, the blades are feathered so that the wind passes easily without turning the rotor, and the brake is applied.

 

In calm conditions, the generator acts as a motor to turn the turbine slowly.  This process is called barring, and prevents the low speed shaft being distorted by the weight of the rotor.  It explains the seemingly absurd sight of a wind turbine turning on a calm day.

 

 

Power from a Turbine

Consider a turbine in a wind of wind speed v m s-1.  The density of the air is r kg m-3.  The rotor sweeps an area of A m2.

 

Every second a cylinder of volume V m3 of air passes the turbine.  This cylinder has a length of v m and area A m2

 

V = Av

 

The air has density r kg m-3. We know that mass = density × volume.  Therefore:

 

m = rAV

 

So every second, rAV kg of air passes.  We know that the kinetic energy of any mass is:

 

 The kinetic energy every second of this mass of air is therefore:

And this tidies up to:

 

Remember that this is kinetic energy every second, which is power.  So our final equation is:

 

 

Question 8

A wind turbine has blades of length 20.0 m.  A wind is blowing with a steady speed of 10.0 m s-1

(a) Calculate the maximum power available from the machine.  Give your answer to an appropriate number of significant figures.

(b) What assumption have you made?

Density of air is 1.2 kg m-3.

Answer

 

There is a maximum power that can be absorbed by the machine.  If the wind speed doubled from 10 m s-1 to 20 m s-1, the machine would give out 8 times the power (in this case 6  MW), which is quite sufficient to overheat the generator and set it on fire.  Wind speeds of 20 m s-1 (gale) are common on windy days.

 

Question 9

The wind turbine in Question 8 can deliver a maximum 1.0 MW in continuous operation.

What is the wind speed that will deliver this?

Answer

 

To prevent damage on windy days, the turbine is shut down and the blades are feathered so that the wind has no turning effect.  The idea is shown here:

 

Pilots of multi-engine aeroplanes do the same if one of the engines fails.  If the propeller is not feathered, it will "windmill", trying to drive the failed engine.  This will increase the drag and make the aeroplane much harder to control.  If it's a single engine aeroplane, the pilot will still feather the propeller.  This will increase the range as the pilot glides downwards to make the emergency landing.  If the propeller is fixed pitch (the blades cannot be moved), feathering cannot be done.

 

Wind turbines do NOT extract all the energy of the wind.  Theory suggests that the maximum power achieved is no more than 16/27 (59.3 %) of the wind power.  Therefore the equation above can be modified to:

 

(8/27 = 16/27 × 1/2)

 

Since wind is free, engineers don't worry too much about this.  You will not be asked about this equation in the exam.

 

 

Hydroelectric Power

When water falls from a height, potential energy is turned to kinetic energy.  Some of this kinetic energy can be extracted to generate electrical energy.  Water power has been used since ancient times, so connecting a water-wheel to a generator was an obvious thing to to do when generators were invented in the second half of the nineteenth century.  The earliest hydroelectric power station was installed in 1878 by the British engineer and businessman, William George Armstrong (1810 - 1900) at Cragside, his house in the Northumberland town of Rothbury.

 

Hydro-electric power can be used to describe tiny installations like the one below, to enormous ones with a capacity of 22500 MW in China. 

 

 

The principle is the same.  A dam stores water on a reservoir.  The water has gravitational potential energy.  Water is guided along a trough (or race) to a water turbine.  In a larger installation, the water is taken to the turbine through large pipes called penstocks.  The kinetic energy of the fast-flowing water is converted to electrical energy.  Once the water has passed through the turbine, it flows through a tailrace to the river downstream of the dam.  The picture shows the idea:

 

Image from Tennessee Valley Authority, Wikimedia Commons

 

We will look at the physics of the hydroelectric power station using the diagram below:

 

 

The height difference between the surface of the reservoir and the level of the river is h m.  Water is flowing through the penstock of area A m2 at a speed of v m s-1.  The flow rate is the volume, V m3, of water flowing per second can be written as Dv/Dt, or r.

 

So we can write:

r = Av

 

The gravitational potential energy is:

 

Ep = mgDh

 

This gets converted to kinetic energy:

 

By the Law of Conservation of Energy, we can write:

 

The m terms obligingly cancel out:

And rearranging:

Now we know from the wind turbine that:

 

And we can write this in an untidy form:

 

 

Now we can substitute for v2:

 

And this tidies up to:

P = rAvgDh

 

 

The term Av is the volume every second, so we can write:

 

The term Dv/Dt is the flow rate, r m3 s-1.  So we can now write an expression:

 

P = rrgDh

 

This assumes that the power station is 100 % efficient, which it isn't.  It may be 80 % (0.80) efficient.  We can modify the relationship to take this into account:

 

  P = rrgDhk

 

The term k is a constant with a value between 0 and 1. 

 

Question 10

A water turbine discharges into a river, the surface of which is 60 m below the surface of the reservoir that feeds it.  It is fed by a penstock (water pipe) of diameter 1.0 m and the water is regulated by a valve to flow at 10 m s-1.

(a) Calculate the water flow.  Give the correct unit.

(b) Calculate the power from the generator if the machine is 60 % efficient.

Answer

 

 

There are three main types of hydroelectric power station:

 

Tidal Power Stations

Britain's coasts have some of the highest tidal ranges in the world.  It makes sense to try to extract energy from the huge volumes of water that daily surge up and down estuaries like that of the Severn.  A causeway can be built to make a large lagoon as a reservoir.  At a certain point in the causeway, a dam can be built with a turbine hall built into it, as shown in the diagram:

 

 

Water flows into the tidal lagoon (or storage pool) on the incoming tide.  As it does so, it turns a generator to generate electricity.  The water is stored in the tidal lagoon, so that as the tide turns and the level of the sea drops, the turbines will turn the other way to produce electrical energy.

 

There is nothing new in this.  Tide mills have been used in Europe for many centuries.  The first tidal power station was built on the mouth of the Rance in France in 1966.  The main problem is that such installations are very challenging and expensive to build.

 

In some areas where there are narrow channels and strong currents, a free-standing water turbine can be set up on a suitable foundation.  In effect it's a water version of a wind-turbine.  Such a device is shown, called a sea-generator in the picture below:

Image by Fundy - Wikimedia Commons

 

These kinds of devices are clearly much less expensive to install.

 

Question 11

Give two advantages and two disadvantages of a tidal power station with a storage pool.

Answer

 

 

Pumped Storage Power Stations

In Wales there are two pumped storage power stations:

Another pumped storage power station was considered for Exmoor in Devon, but Central Electricity Generating Board did not proceed with the plans.

 

The power station installation is similar to that of a conventional hydroelectric scheme, except that the water flowing from the tail-races does not flow away down a river.  It is stored in a lower reservoir.  The idea is shown in this diagram:

 

 

The whole idea of this scheme is to soak up excess energy from the National Grid when the load is light (during the night when most people are in bed).  Power stations give out all or nothing; it is difficult to get them to reduce their output in periods of reduced demand.  Therefore pumped storage power stations are a good way of maintaining the load.

 

During quiet periods, the generators become motors, and the turbine is a pump.  So water is pumped up from the lower reservoir to the upper reservoir.  When the reservoir is full, the power station is on standby for a peak in demand.  Within seconds, valves open allowing the water to fall from the upper reservoir.  The water passes through turbine (which was the pump) and the motors become generators.

 

When demand has reduced, the generators are switched over to become motors again.

 

The efficiency of such a power station is about 70 %.  Therefore for each 100 MW h (megawatt-hours) used in pumping the water, 70 MW h are generated by the falling water.

 

Question 12

When a pumped storage is in pumping mode, each motor pumps 21 m3 s-1 against a change in level of 300 m. 

(a) If water has a density of 1000 kg m-3, calculate the power of each motor.  Assume that the value of the constant k = 1.

(b) In fact the motors each have a power of 75 MW.  What is the efficiency of the motor-pump unit?

Answer

 

 

Nuclear Enrichment and Breeding

If you need to review the process of fission, have a look at Nuclear Physics Tutorial 7.  In this section, we will look at the processing of uranium to make it useful in nuclear power station.

 

Uranium comes in a number of isotopes, the most common of which is:

The fissile isotope is:

This isotope represents 0.7 % of the total uranium.

 

Uranium is a heavy metal and decays by alpha decay.  The half-life of uranium-238 is 4500 million years, while the half life of uranium-235 is 704 million years.  The fissile nature of uranium-235 is completely separate from its radioactive decay.  All isotopes of uranium share the same chemical properties in that the metal reacts readily with other elements.  Pure uranium metal rapidly gains a coat of uranium oxide.  It is a dense and hard metal which is a poor conductor of electricity.

 

Uranium-235 is fissile when it captures a thermal neutron.  Thermal neutrons have a kinetic energy equivalent to an infra-red photon, about 1 eV (1.6 × 10-19 J).  The neutron is travelling at about  14 000 m s-1 - fast enough for us, but as far as particle movement is concerned, a slug.  The uranium nuclei are not smashed by this interaction.  They form a wobbly drop that splits into two or three fission products.  When the uranium splits, a large amount of energy is released in a chain reaction.  On average three neutrons are released, to be captured by other uranium-235 nuclei.  In this case, the energy is released very quickly and in an uncontrolled way.  The result is a powerful and destructive explosion.

 

If the chain reaction is controlled, so that one thermal neutron is captured by one nucleus, the heat can be used to heat up a coolant, which in turn boils water, to turn a steam turbine.  This turns a generator to produce electricity in the conventional way.  Please see Nuclear Physics Tutorial 8.

 

Uranium is mined as an ore.  This has a low concentration of uranium (<1.0 %) and is quite useless for energy production.  The ore is processed into more concentrated (60 %) uranium oxide called yellowcake.  In yellowcake, the concentration of uranium-235 is low.  Therefore the probability of a neutron capture event is too low for there to be energy from fission.  Therefore, further processing needs to be done to convert the uranium oxide into uranium hexafluoride for enrichment.  Uranium hexafluoride is a crystalline solid at room temperature, to it needs to be heated to turn it into a gas.  For enrichment the gas is passed into a gas centrifuge.  

 

 

In this machine, the uranium hexafluoride made with the heavier uranium-238 has a greater centripetal force, so the molecules pass towards the outside of the drum.  The lighter uranium-235 hexafluoride molecules remain closer to the centre of the machine and can be extracted.   Additionally the heat applied causes convection currents in which the lighter uranium-235 hexafluoride molecules are carried to the top by the convection currents.

 

The rate of rotation 90 000 rpm (1500 s-1) has to be very high to separate the two different hexafluorides, because the masses are very close.  This compares with 1500 rpm for a washing machine, or 30 000 rpm for a gas turbine.

 

Question 13

The formula for uranium hexafluoride is UF6.  The relative atomic mass of fluorine is 19.

Calculate the masses of the hexafluoride compounds of two isotopes of uranium.  Express it as a percentage.

(The answer is NOT 1.26 %)

Answer

 

The enriched uranium needs to be 20 % uranium-235 for reactor grade uranium, while for highly enriched uranium (weapons grade), the concentration needs to be up to 80 %.  The highly enriched uranium is also used in research reactors to produce isotopes for medical use.

 

The uranium is converted to an oxide before insertion into fuel rods.  This is because uranium metal is very reactive, and melts at 1400 K, a temperature that can be reached in a reactor core.  The oxide is compressed to form pellets which are, in turn, loaded into fuel rods.

 

The uranium-238 left over is called depleted uranium. It is stored as uranium hexafluoride (UF6).  The storage has to be done with a great deal of care as UF6 is highly toxic and potentially damaging to the environment.  It reacts readily with water vapour in the air to produce uranyl fluoride (UO2F2) and hydrogen fluoride (HF).  Hydrogen fluoride reacts readily with water to form hydrofluoric acid which is highly corrosive.  In the UK, it is estimated that there are 30 000 tonnes of stored uranium hexafluoride.

 

Metallic uranium is a dense metal, density 19.1 × 103 kg m-3, compared with 11.34 × 103 kg m-3 for lead.  It is reactive with oxygen, so the metal needs protection to separate it from the oxygen in the air.  Uses have included or include:

 

The use of depleted uranium in munitions is controversial. While uranium is only weakly radioactive, it has high toxicity.  Fragments can pollute an environment and can be ingested. 

 

 

Breeder Reactors

Plutonium is another radionuclide with fissile isotopes.  It is a dull grey metal that is highly reactive and rapidly oxidises.  It has a density of 16.63 × 103 kg m-3.  Plutonium has a number of isotopes including the following that decay with the following half-lives:

Therefore plutonium isotopes are found only in trace amounts in nature.

 

The plutonium isotope used in reactors is plutonium-239.  This isotope is produced in a reactor.  The steps in production is shown in the following steps:

1. The uranium nucleus captures a neutron from a fission event:

 

2.  The uranium-239 decays with beta decay to neptunium:

      The half life for this decay is 1410 s (23.5 min).

 

3. The neptunium decays by beta minus decay to plutonium.

 

Question 14

Write down the equation that describes this decay.

Answer

 

       The half-life of the decay to plutonium 239 is 2.35 days (2.03 × 105 s).

 

In a fast breeder reactor, there is a certain amount of uranium-235 the fission of which provides neutrons to be captured (as well as contributing to the energy of the reactor).  While we learn that each fission event gives out 3 neutrons, 2 of which are absorbed, this figure is an average.  So some neutrons are captured by plutonium nuclei:

 

 

 

As with uranium-235, the fission products are random pairs, which release on average 3 neutrons.  The fission products are the result of 73 % of the neutron capture events.  The other 27 % result in a plutonium-240 nucleus in an excited state.  It loses the excess energy by emission of a gamma photon

 

The plutonium-240 decays by alpha decay by alpha decay.

 

The plutonium fuel builds up in the reactor and doubles every 10 years.  So after 10 years, the idea is that the plutonium fuel can be removed and placed in a second reactor.  Up to 75 % of the uranium-238 is used in conversion to plutonium

 

Fast breeder transfer their energy by liquid sodium.  The sodium melts at a temperature of 98 oC.  Therefore is is liquid at reactor temperatures.  It does not slow down (moderate) the neutrons as water does.  Sodium has a high specific heat capacity, so can transfer a lot of energy to a heat exchanger where water is boiled to turn a turbine and generate electricity.    It is essential that the liquid sodium does not come in contact with the water, otherwise a violent reaction leading to an explosion will result.

 

Fusion Power

The most powerful fusion bombs used reactions that are thought to go on in the Sun.  If it could be controlled in the same way as a fission reaction can be controlled, it would be possible to get huge amounts of energy from very small amounts of hydrogen fuel.  The only waste product would be helium which is an inert gas.

 

A possible fusion reaction is:

 

 

It is not simply a case of sticking some deuterium and tritium together and shaking it up.  Each nucleus has to have sufficient energy to:

 

This means that the gases have to be heated to a very high temperature, 100 million Kelvin.  As all matter at this temperature exists as an ionised gas (plasma), it has to be confined in a very small space by powerful magnetic fields.  This is called magnetic confinement

 

A considerable amount of effort has been made to make fusion work to generate electricity.  A fusion reactor would be made to boil water to turn a turbine.  Fusion has occurred, but the energy put in to cook the gases enough to make them fuse is far greater than the energy got out by a fusion reaction.  The prize of vast amounts of energy is still being sought.  A possible plan for a fusion reactor is shown below.  It is based on a torus, a ring shaped like a doughnut.

 

 

From the side, the torus looks like this:

 

 

The plasma consists of nuclei that have been stripped of all orbiting electrons; they are bare nuclei. In the middle of the torus is a large solenoid (coil of wire) that acts as the primary of a transformer when an alternating current flows through it.  The plasma acts as a single-turn secondary, so vast currents are possible. It is heated up and confined using strong magnetic fields, generated by the electromagnets.  The temperature gets to about 100 million to 200 million Kelvin.  More deuterium and tritium nuclei are injected at very high speed, and this causes the fusion.  The plasma needs to be replenished continuously for it to be sustained. 

 

Heat is removed from the torus using a coolant like liquid lithium, or water.  This passes to a heat exchanger which boils water to steam to turn the turbines in the turbine hall to generate electricity.

 

That's the idea.  However there are problems that include:

 

Question 15

Waste materials consist of helium and neutrons.  These are referred to as "ash".  What happens to the ash?

Answer

 

Inertial Plasma Confinement

To get fusion, nuclei have to slammed together and held there by very high temperatures and pressures.  In the earliest days of fusion, such conditions could only be achieved by the detonation of a fission device.  The atoms were ionised into a plasma by the intense heat of a fission explosion, and confined by the intense pressure of the explosion.  The fusion reaction would happen in an uncontrolled manner, releasing huge amounts of energy.  The amount of hydrogen nuclei would fill a small party balloon, but release enough energy to cause immense damage to a wide area.

 

 

The third bomb from the left is one such device.  It is a genuine fusion bomb, but it's now in a museum and has been deactivated.  It would have been dropped from a high-flying bomber.

 

This would be useless for controlled fusion.  We have seen how plasma can be confined using magnetic fields and it is not easy to do.  An alternative method to holding the plasma with strong magnetic fields is to slam the hydrogen nuclei together with laser beams.  This is called inertial confinement.

 

A small capsule containing deuterium and tritium is exposed to very intense laser light.  The light has energy of 10 000 J in 1 × 10-9 s. 

 

 

The intense heating effect from the laser driver means that the temperature rises very rapidly to 1 × 108 K. The result of this is that surface explodes like this, compressing the capsule with intense pressure:

 

 

The compression arises due to Newton III (for every action, there is an equal and opposite reaction).  Since there is an outward pressure, there must be an inwards pressure.  The intense pressure forms a shockwave that is sufficient to push the nuclei together, overcoming the strong force that would normally push them apart.  This enables the fusion to occur, releasing a large amount of energy.

 

 

The shockwave compresses the material right in the centre and the fusion reaction propagates through the body of the capsule more rapidly than the capsule can expand.  This explains why the confinement is inertial.

 

 

In this case, the lasers act as direct drivers. 

 

There is another way of doing achieving the compression.  Lasers are directed onto the inner surface of a gold plated hollow capsule which contains the fuel pellet of deuterium and tritium.  The gold-plated capsule is called a hohlraum (German - hohl - hollow; raum - "space").  It bathes the fuel pellet with soft (low energy) X-rays, which causes the surface explosion.  The lasers act as indirect drivers.

 

 

Gravitational Confinement

Plasma can be confined due to the force of gravity.  However this can only occur in very large bodies of plasma, such as those found in stars.  There is a minimum size for a body of gas to compress the plasma sufficiently to allow fusion reactions to occur.  The star Proxima Centauri is a red dwarf.  It has a radius of 2.0 × 105 km, about 14 % of that of the Sun.  Its mass is 12 % of the mass of the Sun.  It is little bigger than the gas giant Jupiter. 

 

In theory, for fusion to start in a star, the mass needs to be about 7 % of the mass of the Sun.  Some astronomers think the Jupiter is a star that failed to ignite.