Nuclear Fusion Reactors

By Barrie Lawson, UK

Solar Fusion

The Sun’s immense energy is due to ongoing nuclear fusion occurring in its core where the temperature is around 15 Million degrees Celsius. It’s not a simple reaction, but a series reactions starting with the fusion of the two simplest atomic nuclei, the Hydrogen nuclei (protons), followed by fusion of the products of the initial reactions to create ever more complex atomic nuclei in a chain of reactions known as the p-p chain described on the Nuclear Theory page.

Earthly Fusion

Over the last 50 years, the promise of reaping unlimited energy from safe, low cost fuels has launched numerous attempts to mimic the thermonuclear action of the Sun and the stars in order to harness the potential energy of nuclear fusion. However, it is difficult to recreate the environment of the Sun here on Earth and the only successful project so far has been the Hydrogen Bomb. Up to now, none of the attempts to produce sustained, controlled nuclear fusion has been able to produce energy on a commercial scale, although small scale demonstration units have delivered enough power to verify that the principle works and to show that power generation by nuclear fusion should be feasible.

Attempts at achieving controlled thermonuclear fusion have followed two basic methods, magnetic confinement as pioneered by the Tokamak (Russian acronym for: "torus-shaped magnetic chamber") developed in Russia and inertial confinement as exemplified by the National Ignition Facility (NIF) reactor in the USA. Both of these methods employ gigantic, expensive machines whose principles are described here and development times are measured in decades rather than years.

The Tokamak was first on the scene, conducting the first ever controlled fusion reaction in 1968. Since then the concept has been used by pursued by several research institutions throughout the world but though they have demonstrated that the technology works, none of these reactors have have achieved breakeven performance to deliver more power than was consumed in initiating the fusion. The best that has been achieved so far in a Tokamak type reactor was achieved in 1997 by the Joint European Torus (JET) reactor at Culham in the UK which produced a fusion power output of 16 MWatts from an input power of 24 MWatts giving a conversion gain Q of 0.65.

The NIF Laser Fusion reactor at the Lawrence Livermore National Laboratory (LLNL) in the USA first went live in June 2009 and up to now it is the only reactor to have exceeded breakeven performance. In 2013 it achieved a conversion gain of 1.4 but the technology but its output power is much lower than the Tokamak’s and is still a long way from producing commercial power.

The quest for commercially viable fusion power continues.

Fusion Fuels

The most promising fuels for achieving practical fusion energy release on Earth are the two isotopes of Hydrogen, Deuterium and Tritium, which may be fused together to produce a positively charged Helium nucleus, also called an alpha particle, and a surplus neutron in a so called D-T reaction. The energy released by the fusion is shared between the alpha particle which carries 20% of the total energy released and the neutron which carries 80%. Hydrogen nuclides carry the lowest charge of all atoms since they have the fewest protons. They therefore have the lowest Coulomb barrier to fusion and so offer the potential to achieve fusion with the minimum amount of applied energy.

The D-T reaction yields 17.6 MeV of energy from the fusion of just two atoms, but to give them enough energy to overcome the Coulomb barrier and initiate the fusion requires the energy of each of the Deuterium and Tritium atoms to be raised to between 10 KeV and 20 Kev. This corresponds to a temperature of 100 to 200 Million °C which is over six times hotter than the 15 Million °C temperature at the center of the Sun. At these high temperatures all matter is in the plasma state, the fourth state of matter, in which the kinetic energy of the particles strips the electrons from the atomic nuclei leaving positively charged ions producing an ionised plasma.

Deuterium is naturally abundant constituting 0.015%, or one in every 6,700 atoms, of seawater from which it is easily extracted. The Earth’s oceans contain enough Deuterium to supply the World’s energy needs for millions of years.

Tritium on the other hand is an unstable isotope of hydrogen in the form of a radioactive gas with a half life of 12.3 years and is not found naturally but would have to be manufactured. Tritium is actually produced by the fusion plant itself as an essential part of the neutron capture system which extracts the heat generated by the fusion reaction. The bombardment of Lithium with neutrons splits the Lithium into Helium and Tritium and since neutrons are produced in abundance by the D-T fusion reaction, the reactor can provide its own Tritium source. Tritium is also produced by similar processes commercially.

Lithium is a fairly common metal, also found in seawater as well as many of the world’s salt flats. Thus there is sufficient available fusion fuel to supply the world’s power for millions of years.

Other possible fusion fuels include the following combinations, Deuterium-Deuterium used in the D-D reaction and Deuterium with the isotope Helium-3 in the D-He3 reaction but up to now almost all reactors have been based on the D-T reaction which requires the lowest fusion temperature. See the list of other fusion reactions which also shows the corresponding energy release of each reaction.

Fusion Energy Release

Theoretically, the fusion of one atom of Deuterium with one atom of Tritium releases 17.6 Million electronVolts of energy in the following reaction.

2H1    +    3H1    ⇒    4He2    +   1 n0    +    @ 17.6 MeV

Scaling this up, the fusion of 1 kilogram of D-T fuel will thus release enough energy to provide a constant 10 MegaWatts of heating power, which can be converted into electricity, for a full year. Similarly the fusion of just 1 milligram (0.000035 ounces) releases 337 MJoules of energy which is equivalent to 80.7 kg of the explosive TNT, enough to blow a fusion reactor apart. See Fusion Energy Release and the table of Energy Content of Fuels.

Fusion Power

The potential energy available from nuclear fusion is unlimited, but in reality, delivering this energy is proving to be an elusive goal. The actual energy delivered by fusion from the various experimental reactors rarely approaches the amount of energy used to create the fusion reaction with the very best reactors just breaking even.

Fusion or Burning
Fusion is the combination of the two fusion fuel elements, as the result of externally supplied energy, to produce a new element with a consequent release of energy. This is often called the burning of the fuel.

Ignition Point
As the temperature of the burning fuel rises, the fusion reaction rate increases so that the fusion eventually becomes self-sustaining. Ignition is defined as the state in which the energy released by the fusion reactions is sufficient to produce self-sustaining fusion of new fuel nuclei without the need for an external energy supply. Note that ignition is not a necessary condition for a practical reactor since burning alone can release more energy than the energy supplied from external sources.

There is no critical mass for sustained fusion explosion. The fuel mass can be as small as desired.

Conversion Gain
The fusion conversion gain factor, or quality factor, Q is defined as the ratio of the energy released by the fusion or "burning" process and the energy used to create and sustain the fusion in a steady state. Sometimes the ratio is defined in terms of power rather than energy.

The condition of Q = 1 is referred to as breakeven. Unless Q > 1 there will be no surplus usable energy.

Note: The conversion gain refers to the input and output of the fusion reaction only. It does not include the energy consumed in generating the driver power used to initiate the fusion, nor does it include the efficiency loss associated with capturing and converting the energy output of the reactor to usable electricity if that is its purpose. Since the surplus energy usually appears in the form of heat there will be a further conversion loss involved in generating electricity from the heat. This means that only 35% to 45% of this surplus energy can be extracted as electricity after taking into account the conversion efficiency of steam turbine generating plants. The economic generation of electricity by means of nuclear fusion requires a fusion reactor with a conversion factor of at least Q>10.

See how the measuring point influences the fusion system efficiency calculation.

Break-even Point
The breakeven point is the point at which the fusion power generated is equal to the power needed to maintain plasma temperature so that Q=1. However, this is not sufficient for ignition since energy still has to be supplied to overcome losses, due to radiation, conduction and the energy carried away from the fusion mass by dispersion of the neutrons, in order to maintain the plasma temperature.

For ignition the input energy is zero and Q is infinite.

System Dimensioning and the Lawson Criterion

In order to obtain more energy from a fusion reaction than is required for heating the fuel, three conditions must apply simultaneously. These conditions are usually stated in terms of the "triple product" of ion density, confinement time and temperature, known as the Lawson criterion after the British scientist John D. Lawson who first outlined it. For D-T fusion these conditions are:

Plasma Ignition Temperature: (T) The fuel temperature must be high enough so that the particles (ions) have sufficient energy to enable them to overcome the Coulomb barrier (the critical ignition temperature) and fuse with each other. For Deuterium-Tritium fuel, this is 100 to 200 Million °C or 10 to 20 KeV.

Ion Density at the center of the fuel: (n) The particle (ion) density of the fuel is specified as the number of particles / m3 or the number of fuel ions /m3 (not mass / m3) and must be very high to provide as many opportunities as possible for collisions between the Deuterium and Tritium ions to increase the probability of fusion occurring.

For D-T plasma fuel the particle density is around 1020 particles / m3. For solid D-T fuel, it is 1030 particles / m3 after compression.

Energy Confinement Time: (τE) For sustainable fusion to take place, the rate of rate of energy supplied to the fuel must be greater than the rate of energy loss to the environment from the burning fuel. The confinement time is an indirect measure of the rate of this energy loss and is defined as the total amount of energy in the burning fuel divided by the rate at which energy is lost. It corresponds to the time constant of the rate of energy loss from the reaction. A short time constant means very rapid energy loss. It is often incorrectly interpreted as the necessary time duration for which the temperature of the fuel must be maintained for fusion to take place. The confinement time depends on the physical nature of the fuel.

For fusion of the D-T fuel supplied in gaseous form, with magnetic confinement of the heated plasma, the confinement time is around 3-6 seconds. For the fusion of solid D-T fuel using inertial confinement, the confinement time is less than 1 nanosecond (10-9 seconds).

The Lawson Triple Product
The triple product n T τE is an empirical measure of the conditions necessary for sustained fusion to take place. It is often used as a useful figure of merit to characterize or compare fusion reactions. It depends on factors such as the type of fuel, the method of fusion, the type and method of energy supply and the particle sizes and densities and is valid only for fusion temperatures between 10 KeV and 20 KeV.

In practical terms this means that for the reaction to be sustainable, the temperature, or energy, of the fusion fuel has to be very high. The particle density of the fuel must also be very high for reactions to occur reasonably often. At the same time the energy lost from the system per unit time must be relatively small (slow loss rate) which means that the τE confinement time (time constant) equivalent will be relatively long.

For ignition to occur, the energy input rate must be equal to or greater than the energy loss rate 1/τE.

Since the units of Temperature X Density are equivalent to a Pressure (From the Gas Laws PV=nRT) the units of the Triple Product are often stated as Atmospheres*Seconds

The following graph shows the value of the "triple product" necessary for sustained fusion to occur over a range of fuel temperatures for three different fuel combinations.

It shows that, as the temperature is increased the corresponding triple product necessary for fusion decreases. This is due to an increase in the fusion reaction rate which occurs as the temperature rises. However the fusion rate eventually reaches a maximum or "sweet spot"around 100 to 200 Million °K after which it gradually begins to fall. This sweet spot corresponds to the lowest triple product value at which sustained fusion can occur. For the D-T reaction this optimum condition occurs at a temperature of just over 10 keV. This is six times the temperature at the core of the Sun. See why Solar fusion seems to be possible at a lower temperature.

Note that to initiate fusion, both the D-D and the D-He3 fusion reactions require a greater triple product, or greater energy, than for D-T fusion.

Lawson Criteria for Nuclear Fusion

The engineering challenge is to find practical fusion methods which satisfy the Lawson technical conditions.

Fusion Methods

To initiate fusion, the amount of energy in the form of heat and pressure from external sources applied to the fuels must be sufficient to raise the energy levels of the fuel nuclei to a sufficient level to overcome the Coulomb barrier between the nuclei. For significant fusion reactions to take place, these high energy levels of the fuel elements must be maintained for a period long enough for a sufficient number of collisions between the atoms of fuel to occur. Such conditions prevail at the center of a star where the massive gravitational forces compress the matter, mostly Hydrogen, in its core to extremely high densities and temperatures causing fusion to take place.

To produce self-sustaining fusion, the rate at which energy is released by the fusion reaction itself must be greater than the rate of energy loss to the environment from the burning fuel. In the Sun or a star, the gravitational field balances the enormous thermal expansion forces resulting from the fusion, holding the fuel in place and maintaining the thermonuclear reactions in a controlled and steady rate. This stellar process of keeping the fuel in place is called gravitational confinement.


Various methods have been tried for generating and controlling the high temperatures and huge energy flows involved in keeping the fuel dense enough and hot enough for long enough to undergo sustained fusion in practical reactors. Two of the most successful reactor technologies are described here. Known as magnetic confinement and inertial confinement, they are optimized for the physical nature of the fuel.

The Earth does not have the immense gravitational pressure of the Sun to contain the fuel and compress it to a very high density. For fusion to take place on Earth, to compensate for the lower densities of the available fuels, the fuel or plasma must be be heated to temperatures six or more times higher than those in the Sun in order to achieve a sufficient number of fusion reactions. This is consistent with meeting the requirements of the Lawson triple product.

Creating the conditions necessary to initiate and maintain D-T and similar fusion reactions places severe requirements on the fusion reactor design. Unfortunately there are no materials for containing the plasma which can withstand the temperatures required of over 100 Million degrees Kelvin. Furthermore the plasma must be prevented from coming into direct contact with any solid material which could lead to contamination of the fuel so that the plasma must be enclosed in a vacuum. Obtaining a high enough particle density of gas molecules confined within a vacuum chamber for fusion is a major problem. Since the high temperatures also imply high pressures, and fusion causes very fast expansion of the plasma, some external force is required to act against this thermal pressure and keep the plasma in place.

In the stars the necessary confinement force is provided by gravitation. On Earth the force can be provided by magnetic fields in magnetic confinement plasma fusion reactors.

Alternatively the fusion reaction may be triggered in solid fuel pellets by a high intensity energy pulse in the very short period before the resulting plasma starts to expand. In this case there is nothing to counteract the expansion of the plasma but its inertia keeps the material together long enough for fusion to occur. The inertial confinement time is simply the time it takes the plasma pressure to overcome the inertia of the particles before they are dispersed, hence the name.

In general, increasing any one of the three factors ( n T τE) of Lawson’s triple product should allow the requirements on the other two factors to be reduced. As an example the fuel used in the magnetic confinement reactor has a very low density because it is a plasma of gas ions and it is contained in a vacuum. It also has a high rate of energy loss. It therefore needs longer confinement times for sufficient particle collisions to take place. Inertial confinement by contrast uses solid fuel which has a much higher density so that it can work with very short confinement times.

Fuel in Plasma Form – Magnetic Confinement Fusion (MCF)

Fusion of the Deuterium and Tritium fuel is designed to take place in a high temperature plasma circulating in a toroidal vacuum chamber such as the Tokamak reactor. Since the plasma consists of moving charged particles, it constitutes an electrical conductor carrying a current, hence it can be affected by magnetic fields. The tendency of the hot plasma to expand can therefore be counteracted by the Lorenz force, arising from its reaction with a magnetic field of appropriate geometry.

The plasma is created by injecting a small puff of the gaseous fuels into the toroidal chamber where they are heated to over 100 Million °C by electrical induction created by a transformer, with its inner poloidal magnetic coils acting as the primary winding and the plasma itself as the secondary winding. See diagram of the MCF magnetic fields below.

Strong magnetic fields around the torus serve two purposes. They are used to increase the plasma density to a level necessary to achieve fusion. At the same time, since they are not affected by heat, these fields act as a container confining the extremely hot conductive plasma to the center of the toroidal chamber so that it does not touch or damage the chamber walls.

After compression the particle density is greater than about 1020/m3 and the corresponding confinement time must be longer than 1 second.

Note that a particle density of 1020 particles (fuel ions)/m3 is very low corresponding to a mass density of around 1 milligram/m3 which is about one millionth of the density of air of 1.225 kg/m3 (at sea level and 15 °C).
The minimum Lawson’s triple product ( n T τE) required for sustained D-T fusion in an MCF reactor is approximately 3.5 X 1028 °K seconds/m3 ≡ 3 X 1021 keV seconds/m3.

See how this is implemented in the Tokamak Reactor

Fuel in Solid Form – Internal Confinement Fusion (ICF)

Before compression in an inertial fusion reactor, the density of the solid fuel used for ICF, at atmospheric pressure, is about 2 X 108 times denser (by mass) than same fuel in the form of a plasma. Solidifying the gaseous Deuterium and Tritium fuel by cooling it to -255 °C, to create small, dense, solid pellets gives the reactor an energy efficient head start in reaching the density required to satisfy the Lawson criteria for fusion.

The fuel pellets are bombarded from all directions, to provide uniform illumination of the target, by simultaneous pulses of high energy such as intense UV laser radiation, X-rays, or ion beams, with a duration of around one nanosecond and sufficient total energy to cause the pellet to implode. This sends a shock wave through the solid fuel pellet compressing it by 30 times or more causing the inner core to reach such a temperature and pressure that it fuses the D-T fuel in a mini thermonuclear explosion. After compression the particle density is around than 1030/m3, which is around 1010 times denser than the plasma used in magnetic confinement fusion. Because the density is so high, and the energy loss rate is relatively low compared with the plasma fuel, the confinement time can be 1010 times less to compensate and still satisfy the Lawson triple product requirement for fusion. This means that the confinement time can be as low as 10-11 seconds or more.

The inertia of the fuel ions within the pellet keeps the pellet together only long enough for fusion to take place under the influence of the high energy pulses before the explosive fusion reaction blows the pellet apart. There is therefore an upper limit of less than a nanosecond (10-9 seconds) to the possible confinement times for inertial confinement reactions because fusion must occur during the very short period before disintegration of the fuel pellet.

The minimum Lawson’s triple product (n T τE) required for sustained D-T fusion in an ICF reactor is approximately 1028 °K s/m3 ≡ 0.9 X 1021 keV seconds/m3.

See how this is implemented in the NIF Reactor

Inertial confinement was first used in the hydrogen bomb where the driver was x-rays created by a fission bomb.

The Tokamak Reactor – Magnetic Confinement

The principles of the Tokamak reactor are described here but it important to note that this is based on experience with small scale experimental units designed to verify the feasibility of key sub-system designs. There is still much work to do to scale up the system to deliver commercial power generation.

Benefits of D-T Fusion and the Tokamak
  • Nuclear fusion has the potential to provide much more energy for a given weight of fuel than any technology currently in use.
  • Secure and inexhaustible supply of low cost fuel.
  • No chemical effluent combustion products
  • Waste is less radioactive and in much lower volume than waste from fission reactors
  • No radiation leaks above normal background levels
  • No possibility of nuclear runaway (Chain reaction)
  • Shutting of the energy or the fuel supply causes the reaction to stop
  • Intrinsically safe system, does not require the elaborate safety systems needed for fission reactors
  • No after-heat problems associated with loss of coolant as in fission reactors
  • No use of, or production of, weapons grade nuclear materials
  • Major technical challenges still to be overcome
  • Tokamak technology (and alternative fusion technologies) still not ready after over 40 years of parallel development programmes by several nations.
  • Needs huge amounts of energy to initiate and control the fusion process
  • The plasma is prone to instabilities. See more about plasmas.
  • Produces radioactive waste though in much smaller amounts than fission reactions
  • Produces pulsed not continuous power.(Using a heat engine (steam turbine) to generate electricity makes this irrelevant.)
  • Requires immense pulsed power to start the reaction. This could affect the grid supply unless local, isolated, short term energy storage is provided.
  • Economic viability not yet proven
  • Tokamak System Principle

    Deuterium and Tritium atoms are heated and fused together in a high temperature plasma circulating in a vacuum chamber where the fusion reaction produces Helium and a surplus neutron. The plasma is maintained in place by powerful magnetic fields. Large amounts of electric power are needed to heat the plasma and to power the electromagnets. See diagram below.


    Surplus neutrons from the fusion reaction are captured by a Lithium blanket where they react with the Lithium producing more Tritium which is one of the two fusion fuels as well as alpha particles (Helium nuclei). The heat energy released by the fusion should be enough to maintain the fusion reaction and to provide a surplus which can be used to generate electricity. The surplus heat from the fusion and the neutron capture by the Lithium is used to raise steam in a heat exchanger and the steam is used to drive a conventional turbine generator.

    Engineering Challenges

    The quest for cheap, renewable energy using nuclear fusion is pushing the limits of technology in several directions simultaneously. Immense technical problems have to be overcome and solutions proposed and progress is painfully slow since it could take several years just to implement and verify a major sub-system change.

    • Containment
      The design of the reactor is dictated by the requirements for containment of the D-T reaction since there are no materials which could possibly withstand the extremely high temperatures necessary for fusion to take place. The solution is to confine the Deuterium and Tritium fuels in a plasma circulating within a toroidal chamber and kept from touching the walls by powerful magnetic fields.

      Note that the confinement time is measured in seconds. This indicates the order of magnitude of the engineering aspirations. A few seconds of fusion is currently regarded as a great success with the best achievement so far measured in minutes, albeit at a low efficiency.

      At higher plasma densities the required confinement time could be shorter but the ability to achieve higher plasma densities is limited by the ability to achieve higher magnetic fields.

      Only the Helium atoms are confined (neutrons, having no charge, escape the magnetic field) and therefore only 20% of the total fusion power is available for plasma heating

    • The Fuel
      The enormous JET Tokamak fusion reactor is designed to deliver megaWatts of power from a plasma of only a few grams of Deuterium and Tritium circulating within the torus.
    • The Plasma
      The temperature of the D-T plasma in the Tokamak is over 100 Million °C. Since the plasma comprises charged particles it becomes conductive and can be controlled by electrical and magnetic fields. These fields confine the plasma to the centre of the torus so that it cannot come into contact with, or damage the chamber walls.

      Instabilities of the plasma are a serious nuisance rather than a major disaster.

    • The Plasma Chamber
      The fusion needs to take place in a vacuum to avoid contamination by other elements. Since the plasma circulates in a toroidal shape, it needs a toroidally shaped vacuum chamber to contain it. Though the amount of fuel is very small, only a few grams, the cross section of the chamber needs to be very large to allow sufficient separation of the extremely hot plasma from the chamber walls . The outer diameter of the chamber ring in the JET Tokamak for example is over 10 metres. The cross section of the toroidal ring through which the plasma flows is "D" shaped with an internal height of over 4 metres. This is a small scale demonstration plant!
      The physical requirements of this huge structure are severe.

      • It must maintain a very high leak free vacuum inside
      • The chamber walls must allow the externally applied magnetic fields to pass through.
      • It must accommodate access for fuel and instrumentation while maintaining the vacuum boundary.
      • It must absorb the thermal radiation coming from the extremely hot plasma allowing for the occasional momentary contact of the plasma with the walls in case of temporary instability.
      • When heated to extremely high temperatures, the chamber walls should not release impurities into the plasma which would contaminate and cool it.
      • More seriously, it must allow the neutron flux resulting from the fusion reaction to pass through chamber walls to the Lithium blanket surrounding the chamber. The neutron flux in a D-T fusion reactor is about 100 times that of fission power reactors and some of these neutrons are unavoidably absorbed by the chamber structure causing it to become radioactive. Once this has occurred, any subsequent activity in the chamber must be done using remote handling equipment.
    The Magnetic Fields

    Magnetic confinement is used to contain the high temperature plasma preventing it from touching the chamber walls.

    Since the plasma comprises charged particles, its location can be fixed by two superimposed external magnetic fields interacting with the magnetic field of the plasma current itself as shown in the diagram below.

    The toroidal chamber carrying the plasma passes through a series of toroidal field coils (shown in green) mounted vertically around the circumference of the chamber. These coils create a toroidal magnetic field along the center line of the plasma chamber. Electrons and ions in this field will tend to follow helical paths along the magnetic field as they circulate around the inside of the chamber. This field provides the primary mechanism of confinement of the plasma particles.

    Toroidal Magnetic Field

    The poloidal coils, also confusingly called vertical coils since they are mounted horizontally parallel to the plane of the toroidal chamber, are located around the perimeter of the chamber. The inner poloidal field coils serve a dual purpose, acting as the multi-turn primary of a transformer whose secondary is the plasma itself which is essentially a single short circuited turn. In this way a large current can be induced in the plasma causing it to flow along the inside of the chamber, winding its way through the torus in a helical path. At the same time the secondary current raises the plasma temperature by Joule (I2R) heating.

    Poloidal Magnetic FieldSource ENS European Nuclear Society (Modified)

    The interaction of the external poloidal and toroidal magnetic fields and the field due to the plasma current serves to locate the plasma within the cross section of the chamber at the same time squeezing it towards the centre line and away from the walls

    TokamaK Magnetic Fields

    Tokamak Magnetic CircuitsSource – European Fusion Development Agreement (EFDA)

    The diagram opposite provides an alternative view showing the iron core of the transformer poloidal magnetic circuit.

    The dependence of the system on the transformer raises other problems since transformers only work with varying currents, whereas DC is required for continuous power generation. This limits the existing Tokamak design to the production of pulsed power. The actual waveform is a sawtooth current ramp.

    Sawtooth Wave

    The main plasma current in the JET reactor (See below) is around 5 Million Amperes.

    Energy consumption in the magnetic field coils is minimized by using superconducting technologies which require very low temperature operation.

    Plasma Heating

    In current Tokamak designs the Joule heating supplied by by the poloidal transformer is insufficient to raise the temperature to the necessary 100 Million °C or to maintain it there. Consequently, the heating must be supplemented from other sources.

    Magnetic Compression
    The gas laws tell us that the temperature of a fixed volume of gas is directly proportional to its pressure. The same compression heating effect can be achieved in the Tokamak by increasing the magnetic field confining the plasma. At the same time this compression increases the plasma density facilitating the fusion reaction.

    Radio frequency (RF) Heating
    RF heating is another technology which is used for plasma heating.

    Plasma Self Heating
    Once fusion starts the fusion products contribute to the overall heating.

    The high speed neutrons produced by the fusion carry 80% of the energy released, but having no charge, they escape from the magnetic field. Because they have high penetrating power, most of the neutrons pass through the chamber wall and are eventually captured by the Lithium blanket to which they give up their energy. A neat way of passing the fusion energy through the chamber walls without heating them up. The neutrons which don’t make it through the chamber wall react with the materials in the wall causing them to become radioactive.

    The positively charged Helium ions (alpha particles) on the other hand carrying 20% of the fusion energy remain trapped by the magnetic field in the plasma where they give up their energy in collisions with the Deuterium and Tritium ions increasing their temperature in the process.

    If the heat energy is sufficient and there are enough D-T ions to accept it and given enough time for collisions to occur then fusion can occur. This is the basis of the Lawson criterion.

    Only the Helium ions are confined (neutrons escape magnetic field and plasma) and therefore only 20% of the total fusion power is available for plasma heating

    Additional heating is needed to raise the temperature of the plasma
    RF heating with radio/micro-wave radiation (~25-55MHz)
    Neutral beam heating: accelerate beam of H or D ions then neutralisation + collision with plasma

    The Lithium Blanket
    The Lithium blanket serves several purposes:

    • It captures the neutrons emitted by the fusion reaction and extracts their energy converting it into heat.
    • It reacts with the neutrons emerging from the plasma to form Tritium, which is fed back into the reactor as fuel.
    • It is an essential part of the heat exchanger in which the heat energy is transferred to a water/steam circuit, raising steam for conventional electricity generation while at the same time cooling the reactor.
    • It contains the radiation from the radioactive structure.

    Alternative designs for of the blanket are still being investigated. Options are pellets of Lithium or pebbles of Lithium alloys which help facilitate the extraction of the Tritium and the purging of the Helium produced in the blanket. This is complicated by the fact that Lithium melts at 180 °C  and boils at 1347 °C. More likely, Lithium will be used in liquid form which simplifies the heat transfer in the heat exchanger.

    Extracting the power

    The first stage is to extract energy from the fusion process. Up to now, no fusion reactors, including Tokamaks have produced significant power with a conversion gain better than unity.

    The Plasma

    The main difficulty is in producing and maintaining a sufficiently high temperature for fusion to occur. So far this has been, and can only be, possible in short pulses with Tokamak designs dependent on transformer heating. The pulse durations achieved, that is the duration of controlled maintenance of the plasma, have been only a few tens of seconds. The confinement time which is the average time that the ions and electrons remain in the plasma (as specified in the Lawson criterion) is generally much shorter than this. Commercial power plants will need pulse lengths of many hours or days.

    The Heat Exchanger

    The heat exchanger is an essential component in the energy conversion chain, designed to take the heat out of the Lithium blanket as explained above. The electricity generating equipment does not see the power pulses coming from the reactor. By converting the energy to heat, the energy pulses are simply smoothed out in the heat exchanger.

    Generating electricity by nuclear fusion or nuclear fission involves three energy conversion stages, each with its own efficiency losses. While direct energy conversion from a nuclear reaction in a single stage may not yet be practical, it seems that the possibility of a two stage energy conversion by combining fusion with MagnetoHydroDynamics (MHD) is still beyond reach. MHD is designed to extract electricity directly from a charged plasma by Faraday induction. The Tokamak already provides the plasma, but it would need to use a different pair of fusion elements which didn’t produce a troublesome neutron. It’s a pity a way has not been found for using it to generate electricity directly by MHD techniques.


    Compared with a fission reactor in which a serious nuclear accident could result if the chain reaction gets out of control, a fusion reactor is intrinsically much safer. The processes involved in a fusion reactor are all set to work at optimum conditions of temperature, pressure and magnetic field. Any deviation from these optimum values, for whatever reason, will immediately cause the fusion energy release to fall and the conditions for maintaining fusion, the Lawson criteria, will rapidly be breached causing the fusion to stop. There is thus no possibility of nuclear runaway and the basic high energy fusion reaction is intrinsically safe.

    • The active plasma is kept in a finely balanced equilibrium position by the applied magnetic fields. Any malfunction in the system or external damage would upset the equilibrium and the plasma would collapse into the walls of the chamber, immediately ending the fusion reaction.
    • The self sustaining fusion action occurs in pulses and energy must be applied to initiate each fusion pulse. In the absence of heating energy pulses there could be no fusion.
    • In the case of a serious accident, the only radioactive product which could be released into the atmosphere is the Tritium fuel. The total amount of Tritium circulating or stored in the plant is only about 1 Kg and this would be diluted to legally acceptable safety limits by the time it reached the plant boundary.
    • The amount of fuel circulating within the reactor at any time is only a few grams. Turning off the fuel supply stops the reaction in seconds.
    • The amount of nuclear waste produced by the Tokamak is much lower than with fission reactors and what waste there is has a much shorter half-life
    Current Experience

    The largest current experiment for controlled nuclear fusion in the world is the Joint European Torus (JET) at Culham in England.

    The JET Tokamak

    Source – European Fusion Development Agreement (EFDA)

    Work on the JET project began in january 1983 and by 1991, it was possible for the first time in the history of fusion research to release considerable energy by controlled nuclear fusion using the JET. For a period of two seconds, the facility generated a fusion power of 1.8 megawatt. In 1997, JET produced a peak of 16.1 MW of fusion power (65% of input power), from an input power of 24 MW sustained for over 0.5 seconds. After a quarter of a century we may know a lot more about fusion and Tokamaks, but we still can not deliver sustained power even on a laboratory scale.

    In June 2005, the construction in France of a much larger Tokamak, the International Thermonuclear Experimental Reactor (ITER), was announced by the European Fusion Development Agreement (EFDA). Designed to produce several times more fusion power than the power put into the plasma over many minutes it dwarfs the JET. Described as “an experimental step between today’s studies of plasma physics and future electricity-producing fusion power plants” it is expected to deliver 500 megawatts of fusion power from an input power of 50 megawatts with a conversion gain Q of 10 and is expected to cost $16 billion while still not delivering commercial power. Full Deuterium-Tritium fusion experiments are not scheduled to start until 2027.

    The Future

    While the demonstration units may verify the technical feasibility of generating electricity by nuclear fusion, the economic viability is yet unproven. Proving out all of the necessary subsystems and scaling up the design from the demonstration systems to commercial generating plants is far from complete and industry experts don’t expect to achieve the goal of commercial exploitation until 2030 or 2040. Meanwhile engineers and physicists have a new set of expensive toys to play with.

    Nice work if you can get it!
    Tokamak History

    Inertial Confinement Reactors

    Inertial confinement fusion (ICF) is loosely based on the principles used in the Hydrogen bomb only on a much, much smaller scale. The fusion fuel is subjected to very high pressure and temperature in order to initiate fusion. In the case of the Hydrogen bomb these necessary operating conditions are created by the nuclear fission explosion of an Atom bomb.

    For controlled ICF, the extreme operating conditions are achieved instead by bombarding a small, solid pellet of fuel with a very high pulse of energy causing its outer layer to be rapidly heated to the necessary 100 million degrees Kelvin and at the same time causing the inner part of the pellet to be compressed very quickly with huge pressure to a density 20 times that of solid lead. The intense heat coupled with the increase in density of the fuel is sufficient for fusion to take place. This all happens in around one to three nanoseconds. The energy pulse could be derived from a variety of sources, known as drivers, including, ultra violet (UV) lasers, X-rays, electron beams and plasma (ion) beams.

    The first fusion reactor ever to successfully achieve a conversion gain greater than unity was the National Ignition Facility (NIF) reactor at the US Lawrence Livermore National Laboratory. The operating principles and challenges of inertial confinement fusion are explained here using the technology of the NIF reactor, and the results of its breakthrough "over unity" fusion demonstration, as an example.

    The NIF Reactor – Inertial Confinement Fusion (ICF)

    In its simplest configuration, a small pellet of frozen Deuterium-Tritium mixture (D-T) held in a plastic shell is irradiated evenly from all sides by intense bursts of energy from very high power laser beams, or X-rays, focused directly on the target, explosively detonating its outer layers and initiating a mini thermonuclear explosion at the core of the pellet. The diagram below illustrates the stages of the process.

    Other inertial fusion drivers include heavy or light ion accelerators.

    Nuclear Fusion Using Laser Energy and Inertial Confinement

    Inertial Confinement Key
    Source: U.S. LANL – Los Alamos National Laboratory (Modified)

    The alpha particles (helium nuclei) produced by the D-T fusion reaction carrying 20% of the released fusion energy deposit this energy within the fuel mass further heating the fuel and increasing the rate of the fusion reactions. The neutrons with 80% of the energy escape from the fuel carrying their energy with them.

    The Confinement Time

    The confinement time of the plasma is mostly determined by the radius of the capsule. The inward shockwave travels approximately at the speed of sound. The inertial confinement time depends on the outward movement of the ions. It is typically only a few nanoseconds and is roughly the time that it takes an ion to travel at its thermal speed across the radius of the fuel pellet. The higher the temperature and density, the more vigorous the reaction and the more difficult it is to contain the plasma.

    The Fuel Target

    The fuel pellet is a 60/40 mixture by weight of Deuterium and Tritium enclosed in a small plastic capsule and frozen to its solid state at -255 °C (18 °K) to keep it solid. The capsule is necessarily small, typically about 2 mm in diameter and only a few milligrams or less in weight, for two reasons. Larger fuel volumes will require larger input energies to bring about ignition and the ignition of larger pellets releases so much energy that it could result in damaging the reactor chamber. For example, the fusion of 1 milligram (0.000035 ounces) of D-T fuel releases 337 MegaJoules (93.6 KWh) of energy, equivalent to 80.7 kg of TNT.

    Typically only a small proportion of the fuel will undergo fusion unless full ignition is achieved since the very short confinement times limit the duration of the fuel burn.

    The Reactor Chamber

    The target must be precisely located at the center of a vacuum chamber where it can be irradiated evenly from all sides by laser beams positioned in apertures in the chamber wall. The NIF chamber is for experimental use only and is 10 meters (33 feet) across with a wall thickness of 10 cm of aluminium and 30 cm (1 foot) of concrete which absorbs neutrons from fusion reactions and contains explosions. The walls in commercial reactors will be designed to incorporate heat exchangers to capture the energy released by the fusion.

    The NIF Laser Driver

    The driver is the mechanism by which energy is delivered to the fuel capsule. The NIF reactor uses a laser for this purpose. With an output of 1.8 MegaJoules (MJ), it is the world’s largest and most energetic laser. To put this energy output into perspective, 1.8 MJ is equivalent to only 500 Watthours or 0.5 "units" of domestic electricity. But the NIF laser can deliver this energy in 3.6 nanoseconds. This means that it can supply a continuous power of 500 TeraWatts (trillion Watts) for 3.6 nanoseconds. This is almost 1000 times more than the 0.535 TeraWatts average instantaneous of electrical power consumption of the entire USA.

    • The Laser
      The process starts with a Neodymium:glass laser which generates pulses of infrared light with precise frequency and pulse shape control. The pulse duration can be varied between 1 and 15 nanoseconds and it is shaped to provide precise timing of the energy flow to optimize the timing of the heating of the plastic ablator surface followed by the implosion of the fuel. Instabilities which cause the uncontrolled break-up of the fuel pellet are suppressed by starting with a low energy intensity followed by a rapid rise to maximum intensity for around 3 nanoseconds during the second half of the pulse.
    • The Splitters and Amplifiers
      After launch, the laser pulse is split into 48 separate beams and passed through 48 preamplifiers each with a gain of 109 times. Each beam is further split into 4 beams to give a total of 192 beams which are passed back and forth several times through 192 main amplifiers consisting of reflective Neodymium doped glass slabs (lasing material) surrounded by Xenon flash lamps powered by a large capacitor bank. The intense flash of light from the lamps pumps the Neodymium atoms up to a higher energy state so that the laser beam gathers more light and energy as it passes through giving a further gain of 106 for an overall gain of 1015.
    • The Frequency Converters
      In the final optical assemblies, the laser’s infrared (IR) light with a wavelength of 1053 nm is converted into ultraviolet (UV) light with a wavelength of 351 nm in Potassium Dihydrogen Phosphate (KDP) crystal frequency converters which merge groups of three of the incoming photons into a new photons with three times the energy and one third of the wavelength. The shorter wavelength beams are absorbed more readily by the fuel targets and cause less uncontrolled preheating of the fuel by electrons.

Laser Beam Alignment
An array of mirrors and optical assemblies positioned around the reactor chamber converge the beams and focus them with great precision on the tiny 2mm target, held on a supporting arm, at the centre of the 10 meter chamber.

National Ignition Facility - Laser Bay, Lawrence Livermore National Laboratory
Source: LLNL – Public domain.
The NIF Laser

The NIF’s 192 laser beams and their amplifiers are housed in two separate laser bays, each the size of a football field and each containing 96 of the beams.

The photograph shows one of the laser bays.
Note the size of the operating personnel.

Direct Drive

With direct drive, the fuel pellets are irradiated directly by the laser beams fired from the chamber walls 5 meters away. To maximise the effect of the incident radiation and ensure controlled fusion, the energy must be precisely concentrated into the centre of the pellet. It is not enough that the beams merely hit the pellet. The 192 beams must enter the 2 mm fuel pellet, at precise angles, at 192 points evenly distributed around its surface. Misalignment will result in insufficent energy being concentrated on the centre of the fuel pellet to initiate fusion and will instead cause breakup of the pellet. In practice, it is very difficult to achieve the necessary uniform illumination of the target simply by focussing the multiple laser beams directly on the pellet.

According to Bruno Van Wonterghem, operations manager for NIF “The precision NIF is designed to achieve is similar to throwing a dime from Livermore to San Francisco [a distance of about 64 kilometers] and landing it perfectly inside the coin slot of a parking meter.”

Indirect Drive

The NIF overcame this alignment problem by using indirect irradiation by means of X-rays derived from the laser beams to initiate fusion instead of the laser beams. Its breakthrough experiment, in which it achieved the first ever over unity conversion gain, used a fuel pellet weighing 0.17 mg, contained in a 2mm diameter plastic capsule held at the center of a, hollow, open ended, cylindrical shaped cavity made of gold called a hohlraum .(German "hollow space"). The 192 laser beams are fired through the holes at each end of the cavity at such an angle that they don’t touch the capsule but instead hit the inside wall of the hohlraum.

The laser pulses heat the gold of the hohlraum to such a high temperature that it in turn radiates a pulse of X-rays which are more dispersed than the laser beams and which spread more uniformly around the capsule, not just focusing on the 192 points. About 15% of the incident energy is lost in this process.

Only about 15% of the resulting X-rays actually impinge on, and are absorbed by, the target capsule but this is enough to initiate the blow off of the plastic ablator and the implosion of the fuel.

Direct and Indirect Fusion Drive
Direct and Indirect Fusion Drives
Source: LLNL
The NIF Hohlraum
Source: LLNL NIF

Measuring about 10 mm long and 5.5 mm in diameter, with a 2.8 mm diameter laser entrance hole at each end, the hohlraum converts the light energy to X-ray energy and provides a much more uniform energy distribution.

NIF Fusion Energy Flow Summary

(The 2013 demonstration)

Approximate energy levels at different process steps of the NIF reactor

Infrared master oscillator (laser) output: 10-9 J

Energy of the infrared light pulse emerging from the Neodymium:glass laser.

Input energy of the laser amplification process: 422 MJ
The energy consumed by the amplifiers and beam splitters in raising the energy in the beams is 422 MJ.
(Efficiency 0.85%)

Laser Infrared output: 3.6 MJ
Energy output from the laser amplifiers applied to the frequency converter.

Laser UV output: 1.8 MJ
Combined output energy after conversion to UV radiation of the 192 beams impinging on the hohlraum target.

Laser energy absorbed by the hohlraum: <1.5 MJ
Theoretical prediction of the energy remaining after the UV radiation is converted to X-rays, about 85%.

Laser energy absorbed by the outer layers of the DT target pellet: <220 kJ
Theoretical prediction of the estimated percentage of the available X-ray energy in the hohlraum which is absorbed by the outer layers of the target, about 15%.

Actual energy absorbed by the DT target pellet: ~10 kJ
Like the X-ray energy in the hohlraum, this is difficult to measure and so is an estimated value which is equivalent to 2.8 Watthours. It is less than 0.6% of the laser energy fired at the hohlraum target.

NIF reactor – Energy out

Energy released by fusion reaction: ~14 kJ
Calculated from the count of neutrons emitted. Neutrons are a product of fusion reactions so they are used as a measure of the energy output. The output energy is equivalent to 3.9 Watthours and is released in the form of heat.

4 Watthours of electrical energy is just enough to power a 60 Watt electric light bulb for 4 minutes.

Conversion Gain and System Efficiency The final fusion energy output of 14 kJ compared with the energy supplied, measured at different points in the conversion chain is as follows:

  • 1.4 times the 10 kJ of energy absorbed directly by the DT fuel – (the fusion gain).
  • 0.8 % of the 1.8 MJ laser energy irradiating the target – (the target efficiency)
  • 3.3×10-5 fraction of the 422 MJ of input energy consumed in amplifying the the output of the master laser – ignoring the small amount of energy used to power the laser. (the system efficiency)
  • Note that the system conversion gain or efficiency just refers to the production of heat from the fusion reaction. It does not include any further system thermodynamic and efficiency losses incurred, typically 35%, if the heat would be used in applications such as generating electricity from the heat of fusion.
  • Sources: The European Fusion Education Network (fusenet), LLNL and others.

    The NIF 2013 Demonstration – Performance Evaluation

    The results of the NIF demonstration are often misinterpreted as having produced net energy. This is plainly not true but the experiment did achieve a most important milestone: The amount of energy released through the fusion reaction exceeded the amount of energy being absorbed by the fuel. The demonstration thus achieved a fusion gain greater than unity which enabled the "burning" of the fuel but this is still a step short of the lab’s goal of “ignition” or self sustained burning. Burning only occurred while the fuel was being irradiated by energy from an external source, in this case, during the pulse of X-rays derived from the laser pulse. See note about Conversion Gain and Breakeven.

    The results indicate that, using the NIF reactor, the overall fusion "system" gain would have to be of the order of 30,000 just to breakeven or 100,000 if the desired system output was the generation of electricity. The biggest factor adversely affecting the system conversion gain however is not the low gain of the fusion reaction, but the poor efficiency of the optical amplification and frequency conversion systems which consume 422 MJ of energy just to provide the 1.8 MJ laser power output, – an efficiency of only 0.4%. Improved laser, or alternative drive, technology could thus make a dramatic improvement in system efficiency.

    Since the results of the 2013 demonstration were published, NIF fusion development has continued. Two months after the first successful shot, modifying the shape and timing of the laser pulse used to detonate the fuel has enabled the conversion gain to be increased by over 20%. Subsequently the efficiency losses in the laser driver chain have been reduced by 25%.

    For comparison, in 1997 the JET Tokamak produced 16.1 MWatts of power for 5 seconds equivalent to 22.4 kWh or 80.5 MJoules.

    Alternative Drivers

    The method of providing the driver energy for detonating the fuel in ICF reactors was pioneered with lasers, but the limited efficiency of these systems and the difficulty of scaling up the technology and modifying it for commercial applications has prompted research into other methods. Both heavy and light ion beam driver systems offer significant advantages over laser drivers. Reactor designs can be greatly simplified and they are capable of higher energy pulses, better driver efficiencies and higher repetition rates.

    Multiple ion beams are accelerated through a series of linear accelerators and made to converge on the target. Heavy ions deposit more energy per ion than lighter species, and therefore a smaller ion current is needed to deposit a given total energy.

    Scaling Up Laser Fusion Systems for Commercial Applications

    While the experimental results are encouraging and demonstrate the feasibility of inertial confinement fusion, there’s still a long way to go to scale up the immense demonstration system into a commercially viable heat source for powering an electricity generating plant. The following are some of the issues which need to be considered.

    • Driver System
      The existing NIF driver system is over complicated and very inefficient. A simpler, more efficient system needs to be developed. Besides producing the required power density, a commercial driver must also have an adequate repetition rate and be efficient and reliable. These requirements are more likely to be satisfied by ion accelerators. There’s lots of scope for improvement here.
    • Capturing the Heat Output
      The demonstration system generates inconsequential amounts of heat energy which is carried away by neutrons which strike the reactor chamber walls. It does not have a method of capturing the heat. Some of the materials in the chamber walls are unfortunately susceptible to radiation damage from the neutrons produced by the fusion, becoming radioactive as well as mechanically weakened. In a commercial reactor where the production of neutrons will be considerably higher than in the experimental reactor, the chamber wall should be able to withstand this neutron bombardment otherwise it would have to be replaced regularly. It must also incorporate a heat exchanger to capture and extract the energy from the neutrons. Such problems have been investigated in depth in the Tokamak reactor whose walls include a Lithium blanket which serves the dual purpose of generating Tritium as well as capturing the neutrons.
    • Continuous Output
      Just as the ICF reactor receives its energy in pulses, so it also delivers its energy in pulses. Currently it is only capable of carrying out one fusion shot per day, each of which delivers only a small amount of energy. For commercial use, continuous energy flow is required so that the fusion repetition rate with an output of 14kJ per shot would need to be increased to at least ten shots per second. This would generate an output 3.36 MWh of heat energy per day. But this is not the net energy gain of the system. The overall inefficiencies prevailing in the 2103 "state of the art" system would have to be taken into account and this would have changed the fusion energy gain to a substantial system energy loss. Progress to eliminate system losses and to improve the fusion gain continues.

      The large number of fuel pellets needed has consequences for fuelling the system.

    • Pellet Production
      To carry out ten shots per second would require production of 864000 pellets and hohlraums per day of the size used in the demonstration unit. A smaller number of larger pellets could be used but the practical maximum pellet size is limited by the potential explosive power of the fusion.
    • Conversion Gain
      Ii is not unreasonable to expect that with further development the fusion energy conversion gain could be increased high enough to cause self sustaining ignition rather than simply burning. This has the dual benefit of improving the overall system gain and while it would still be necessary to have manageable, low fuel weights, the self sustaining reaction would make more efficient use of the fuel by consuming a greater proportion of the pellet mass thus reducing the number of pellets required.
    • Fuel Feed System
      This could be a major problem. The fuel pellets must be refrigerated and fed at high rate into the target holder which will be very hot from previous fusions. The pellets nust also must be placed and aligned very precisely at the convergence point of the laser or ion beams.
      The debris from the fusion must also be collected and removed on a continuous basis.
    • Fuel Costs
      The cost of the gold used in the hohlraums which are destroyed in every shot is not insignificant though much of it could be recovered and recycled. Nevertheless, it will probably be more cost effective to use an alternative driver system.
    • Capital Costs
      The cost of the NIF demonstration system has been over $4 billion. Considering the further development which needs to take place and the complexity of the added technical facilities needed by a commercial reactor, it may turn out that though the system is technically viable, it may be difficult to produce a commercially viable system.
    • Safety
      The ICF system has the same safety issues as the Tokamak, though working at a lower pressure, without the high temperature plasma, it could be considered slightly safer.

    The Way Forward

    We know inertial confinement fusion using lasers works. We also know laser systems have their drawbacks and the technology is still in its infancy. Development work is however continuing at various research institutions throughout the world, across the whole spectrum of fusion technology, to come up with alternative reactor designs with more efficient driver systems, practical heat capture systems and fuel feed systems. There’s a long way to go but we are getting there.

    About the author, Barrie Lawson:

    Barrie graduated from Birmingham University with a degree in Electrical and Electronic Engineering in 1964. Since then he as has worked at Director level in many branches of the electronics industry including military electronics, telecommunications, computers, automotive and consumer electronics. During the last 10 years he has been involved in the battery business, originally as Chairman of MPower Batteries, a custom battery pack making company in Scotland which he helped to found and later in China where he set up a similar business. He is currently Chairman of CHE EVC, another battery startup company pioneering some interesting new technologies. In his spare time he writes and maintains the Electropaedia web site, a comprehensive knowledge base about batteries and energy sources.