Initial research into fusion power plants has focused on deuterium-tritium or deuterium-He3 reactions.
The ocean is a good source of deuterium (from heavy water), but tritium and He3 are in short supply.
Other materials such as boron 11, which is 80% of the boron on earth, can be found in commercial
quantitites in Nevada (20 mule team borax) and other states. This section of our web site describes
the potential fusion fuels.
There are a few fusion reactions that have no neutrons as products on any of their branches. Those
with the largest cross sections are these:
D + 3He ? 4He (3.6 MeV) + p (14.7 MeV)
D + 6Li ? 2 4He + 22.4 MeV
p + 6Li ? 4He (1.7 MeV) + 3He (2.3 MeV)
3He + 6Li ? 2 4He + p + 16.9 MeV
3He + 3He ? 4He + 2 p
p + 7Li ? 2 4He + 17.2 MeV
p + 11B ? 3 4He + 8.7 MeV
The first two of these use deuterium as a fuel, and D-D side reactions will produce some neutrons.
Although these can be minimized by running hot and deuterium-lean, the fraction of energy released
as neutrons will probably be several percent, so that these fuel cycles, although neutron-poor, do not
classify as aneutronic according to the 1% threshold.
The rates of the next two reactions (involving p, 3He, and 6Li) are not particularly high in a thermal
plasma. When they are treated as a chain, however, they offer the possibility of an enhanced
reactivity due to a non-thermal distribution. The product 3He from the first reaction could participate in
the second reaction before thermalizing, and the product p from the second reaction could participate
in the first reaction before thermalizing. Unfortunately, detailed analyses have not shown sufficient
reactivity enhancement to overcome the inherently low cross section.
The pure 3He reaction suffers from a fuel-availability problem. 3He occurs naturally on the Earth in
only minuscule amounts, so it would either have to be bred from reactions involving neutrons
(counteracting the potential advantage of aneutronic fusion), or mined from extraterrestrial bodies.
The top several meters of the surface of the Moon is relatively rich in 3He, on the order of 0.01 parts
per million by weight, but mining this resource and returning it to Earth would be very difficult and
expensive. 3He could in principle be recovered from the atmospheres of the gas giant planets, but
this would be even more challenging.
The p-7Li reaction has no advantage over p-11B. On the contrary, its cross section is somewhat
For the above reasons, most studies of aneutronic fusion concentrate on the last reaction, p-11B.
Neutronicity, confinement requirement, and power density
The only fusion reactions thus far produced by humans to achieve ignition are those which have been
created in hydrogen bombs; the first of which, shot Ivy Mike, is shown here.Any of the reactions above
can in principle be the basis of fusion power production. In addition to the temperature and cross
section discussed above, we must consider the total energy of the fusion products Efus, the energy of
the charged fusion products Ech, and the atomic number Z of the non-hydrogenic reactant.
Specification of the D-D reaction entails some difficulties, though. To begin with, one must average
over the two branches (2) and (3). More difficult is to decide how to treat the T and 3He products. T
burns so well in a deuterium plasma that it is almost impossible to extract from the plasma. The D-3He
reaction is optimized at a much higher temperature, so the burnup at the optimum D-D temperature
may be low, so it seems reasonable to assume the T but not the 3He gets burned up and adds its
energy to the net reaction. Thus we will count the DD fusion energy as Efus = (4.03+17.6+3.27)/2 =
12.5 MeV and the energy in charged particles as Ech = (4.03+3.5+0.82)/2 = 4.2 MeV.
Another unique aspect of the D-D reaction is that there is only one reactant, which must be taken into
account when calculating the reaction rate.
With this choice, we tabulate parameters for four of the most important reactions.
fuel Z Efus [MeV] Ech [MeV] neutronicity
D-T 1 17.6 3.5 0.80
D-D 1 12.5 4.2 0.66
D-3He 2 18.3 18.3 ~0.05
p-11B 5 8.7 8.7 ~0.001
The last column is the neutronicity of the reaction, the fraction of the fusion energy released as
neutrons. This is an important indicator of the magnitude of the problems associated with neutrons
like radiation damage, biological shielding, remote handling, and safety. For the first two reactions it is
calculated as (Efus-Ech)/Efus. For the last two reactions, where this calculation would give zero, the
values quoted are rough estimates based on side reactions that produce neutrons in a plasma in
Of course, the reactants should also be mixed in the optimal proportions. This is the case when each
reactant ion plus its associated electrons accounts for half the pressure. Assuming that the total
pressure is fixed, this means that density of the non-hydrogenic ion is smaller than that of the
hydrogenic ion by a factor 2/(Z+1). Therefore the rate for these reactions is reduced by the same
factor, on top of any differences in the values of <sv>/T². On the other hand, because the D-D
reaction has only one reactant, the rate is twice as high as if the fuel were divided between two
Thus there is a "penalty" of (2/(Z+1)) for non-hydrogenic fuels arising from the fact that they require
more electrons, which take up pressure without participating in the fusion reaction. (It is usually a
good assumption that the electron temperature will be nearly equal to the ion temperature. Some
authors, however discuss the possibility that the electrons could be maintained substantially colder
than the ions. In such a case, known as a "hot ion mode", the "penalty" would not apply.) There is at
the same time a "bonus" of a factor 2 for D-D due to the fact that each ion can react with any of the
other ions, not just a fraction of them.
We can now compare these reactions in the following table.
fuel <sv>/T² penalty/bonus reactivity Lawson criterion power density
D-T 1.24×10-24 1 1 1 1
D-D 1.28×10-26 2 48 30 68
D-3He 2.24×10-26 2/3 83 16 80
p-11B 3.01×10-27 1/3 1240 500 2500
The maximum value of <sv>/T2 is taken from a previous table. The "penalty/bonus" factor is that
related to a non-hydrogenic reactant or a single-species reaction. The values in the column
"reactivity" are found by dividing 1.24×10-24 by the product of the second and third columns. It
indicates the factor by which the other reactions occur more slowly than the D-T reaction under
comparable conditions. The column "Lawson criterion" weights these results with Ech and gives an
indication of how much more difficult it is to achieve ignition with these reactions, relative to the
difficulty for the D-T reaction. The last column is labeled "power density" and weights the practical
reactivity with Efus. It indicates how much lower the fusion power density of the other reactions is
compared to the D-T reaction and can be considered a measure of the economic potential.
Bremsstrahlung losses in quasineutral, isotropic plasmas
The ions undergoing fusion in many systems will essentially never occur alone but will be mixed with
electrons that neutralize the ions' electrical charge and form a plasma. The electrons will generally
have a temperature comparable to or greater than that of the ions, so they will collide with the ions
and emit Bremsstrahlung. The Sun and stars are opaque to Bremsstrahlung, but essentially any
terrestrial fusion reactor will be optically thin at relevant wavelengths. Bremsstrahlung is also difficult
to reflect and difficult to convert directly to electricity, so the ratio of fusion power produced to
Bremsstrahlung radiation lost is an important figure of merit. This ratio is generally maximized at a
much higher temperature than that which maximizes the power density (see the previous subsection).
The following table shows the rough optimum temperature and the power ratio at that temperature for
fuel Ti (keV) Pfusion/PBremsstrahlung
D-T 50 140
D-D 500 2.9
D-3He 100 5.3
3He-3He 1000 0.72
p-6Li 800 0.21
p-11B 300 0.57
The actual ratios of fusion to Bremsstrahlung power will likely be significantly lower for several
reasons. For one, the calculation assumes that the energy of the fusion products is transmitted
completely to the fuel ions, which then lose energy to the electrons by collisions, which in turn lose
energy by Bremsstrahlung. However because the fusion products move much faster than the fuel
ions, they will give up a significant fraction of their energy directly to the electrons. Secondly, the
plasma is assumed to be composed purely of fuel ions. In practice, there will be a significant
proportion of impurity ions, which will lower the ratio. In particular, the fusion products themselves
must remain in the plasma until they have given up their energy, and will remain some time after that
in any proposed confinement scheme. Finally, all channels of energy loss other than Bremsstrahlung
have been neglected. The last two factors are related. On theoretical and experimental grounds,
particle and energy confinement seem to be closely related. In a confinement scheme that does a
good job of retaining energy, fusion products will build up. If the fusion products are efficiently
ejected, then energy confinement will be poor, too.
The temperatures maximizing the fusion power compared to the Bremsstrahlung are in every case
higher than the temperature that maximizes the power density and minimizes the required value of the
fusion triple product. This will not change the optimum operating point for D-T very much because the
Bremsstrahlung fraction is low, but it will push the other fuels into regimes where the power density
relative to D-T is even lower and the required confinement even more difficult to achieve. For D-D
and D-3He, Bremsstrahlung losses will be a serious, possibly prohibitive problem. For 3He-3He, p-6Li
and p-11B the Bremsstrahlung losses appear to make a fusion reactor using these fuels with a
quasineutral, anisotropic plasma impossible. Some ways out of this dilemma are considered — and
rejected — in Fundamental limitations on plasma fusion systems not in thermodynamic equilibrium by
Todd Rider. This limitation does not apply to non-neutral and anisotropic plasmas; however, these
have their own challenges to contend with.