Nuclear fusion
In nuclear physics, nuclear fusion is a nuclear
reaction in which two or more atomic nuclei
collide at a very high speed and join to form
a new type of atomic nucleus. During this
process, matter is not conserved because some
of the matter of the fusing nuclei is converted
to photons . Fusion is the process that powers
active or "main sequence" stars.
The fusion of two nuclei with lower masses
than iron (which, along with nickel, has the
largest binding energy per nucleon) generally
releases energy, while the fusion of nuclei
heavier than iron absorbs energy. The opposite
is true for the reverse process, nuclear fission.
This means that fusion generally occurs for
lighter elements only, and likewise, that
fission normally occurs only for heavier elements.
There are extreme astrophysical events that
can lead to short periods of fusion with heavier
nuclei. This is the process that gives rise
to nucleosynthesis, the creation of the heavy
elements during events such as supernovae.
Following the discovery of quantum tunneling
by Friedrich Hund, in 1929 Robert Atkinson
and Fritz Houtermans used the measured masses
of light elements to predict that large amounts
of energy could be released by fusing small
nuclei. Building upon the nuclear transmutation
experiments by Ernest Rutherford, carried
out several years earlier, the laboratory
fusion of hydrogen isotopes was first accomplished
by Mark Oliphant in 1932. During the remainder
of that decade the steps of the main cycle
of nuclear fusion in stars were worked out
by Hans Bethe. Research into fusion for military
purposes began in the early 1940s as part
of the Manhattan Project. Fusion was accomplished
in 1951 with the Greenhouse Item nuclear test.
Nuclear fusion on a large scale in an explosion
was first carried out on November 1, 1952,
in the Ivy Mike hydrogen bomb test.
Research into developing controlled thermonuclear
fusion for civil purposes also began in earnest
in the 1950s, and it continues to this day.
Two projects, the National Ignition Facility
and ITER, have the goal of high gains, that
is, producing more energy than required to
ignite the reaction, after 60 years of design
improvements developed from previous experiments.
While these ICF and Tokamak designs became
popular in recent times, experiments with
Stellarators are gaining international scientific
attention again, like Wendelstein 7-X in Greifswald,
Germany.
Overview
The origin of the energy released in fusion
of light elements is due to an interplay of
two opposing forces, the nuclear force which
combines together protons and neutrons, and
the Coulomb force which causes protons to
repel each other. The protons are positively
charged and repel each other but they nonetheless
stick together, demonstrating the existence
of another force referred to as nuclear attraction.
This force, called the strong nuclear force,
overcomes electric repulsion in a very close
range. The effect of this force is not observed
outside the nucleus, hence the force has a
strong dependence on distance, making it a
short-range force. The same force also pulls
the neutrons together, or neutrons and protons
together. Because the nuclear force is stronger
than the Coulomb force for atomic nuclei smaller
than iron and nickel, building up these nuclei
from lighter nuclei by fusion releases the
extra energy from the net attraction of these
particles. For larger nuclei, however, no
energy is released, since the nuclear force
is short-range and cannot continue to act
across still larger atomic nuclei. Thus, energy
is no longer released when such nuclei are
made by fusion; instead, energy is absorbed
in such processes.
Fusion reactions of light elements power the
stars and produce virtually all elements in
a process called nucleosynthesis. The fusion
of lighter elements in stars releases energy
(and the mass that always accompanies it).
For example, in the fusion of two hydrogen
nuclei to form helium, 0.7% of the mass is
carried away from the system in the form of
kinetic energy or other forms of energy (such
as electromagnetic radiation).
Research into controlled fusion, with the
aim of producing fusion power for the production
of electricity, has been conducted for over
60 years. It has been accompanied by extreme
scientific and technological difficulties,
but has resulted in progress. At present,
controlled fusion reactions have been unable
to produce break-even (self-sustaining) controlled
fusion reactions. Workable designs for a reactor
that theoretically will deliver ten times
more fusion energy than the amount needed
to heat up plasma to required temperatures
are in development (see ITER). The ITER facility
is expected to finish its construction phase
in 2019. It will start commissioning the reactor
that same year and initiate plasma experiments
in 2020, but is not expected to begin full
deuterium-tritium fusion until 2027.
It takes considerable energy to force nuclei
to fuse, even those of the lightest element,
hydrogen. This is because all nuclei have
a positive charge due to their protons, and
as like charges repel, nuclei strongly resist
being put close together. Accelerated to high
speeds, they can overcome this electrostatic
repulsion and be forced close enough for the
attractive nuclear force to be sufficiently
strong to achieve fusion. The fusion of lighter
nuclei, which creates a heavier nucleus and
often a free neutron or proton, generally
releases more energy than it takes to force
the nuclei together; this is an exothermic
process that can produce self-sustaining reactions.
The US National Ignition Facility, which uses
laser-driven inertial confinement fusion,
is thought to be capable of break-even fusion.
The first large-scale laser target experiments
were performed in June 2009 and ignition experiments
began in early 2011.
Energy released in most nuclear reactions
is much larger than in chemical reactions,
because the binding energy that holds a nucleus
together is far greater than the energy that
holds electrons to a nucleus. For example,
the ionization energy gained by adding an
electron to a hydrogen nucleus is 13.6 eV—less
than one-millionth of the 17.6 MeV released
in the deuterium–tritium (D–T) reaction
shown in the diagram to the right (one gram
of matter would release 339 GJ of energy).
Fusion reactions have an energy density many
times greater than nuclear fission; the reactions
produce far greater energy per unit of mass
even though individual fission reactions are
generally much more energetic than individual
fusion ones, which are themselves millions
of times more energetic than chemical reactions.
Only Direct conversion of mass into energy,
such as that caused by the annihilatory collision
of matter and antimatter, is more energetic
per unit of mass than nuclear fusion.
Requirements
A substantial energy barrier of electrostatic
forces must be overcome before fusion can
occur. At large distances, two naked nuclei
repel one another because of the repulsive
electrostatic force between their positively
charged protons. If two nuclei can be brought
close enough together, however, the electrostatic
repulsion can be overcome by the attractive
nuclear force, which is stronger at close
distances.
When a nucleon such as a proton or neutron
is added to a nucleus, the nuclear force attracts
it to other nucleons, but primarily to its
immediate neighbours due to the short range
of the force. The nucleons in the interior
of a nucleus have more neighboring nucleons
than those on the surface. Since smaller nuclei
have a larger surface area-to-volume ratio,
the binding energy per nucleon due to the
nuclear force generally increases with the
size of the nucleus but approaches a limiting
value corresponding to that of a nucleus with
a diameter of about four nucleons. It is important
to keep in mind that the above picture is
a toy model because nucleons are quantum objects,
and so, for example, since two neutrons in
a nucleus are identical to each other, distinguishing
one from the other, such as which one is in
the interior and which is on the surface,
is in fact meaningless, and the inclusion
of quantum mechanics is necessary for proper
calculations.
The electrostatic force, on the other hand,
is an inverse-square force, so a proton added
to a nucleus will feel an electrostatic repulsion
from all the other protons in the nucleus.
The electrostatic energy per nucleon due to
the electrostatic force thus increases without
limit as nuclei get larger.
The net result of these opposing forces is
that the binding energy per nucleon generally
increases with increasing size, up to the
elements iron and nickel, and then decreases
for heavier nuclei. Eventually, the binding
energy becomes negative and very heavy nuclei
(all with more than 208 nucleons, corresponding
to a diameter of about 6 nucleons) are not
stable. The four most tightly bound nuclei,
in decreasing order of binding energy per
nucleon, are 62Ni, 58Fe, 56Fe, and 60Ni. Even
though the nickel isotope, 62Ni, is more stable,
the iron isotope 56Fe is an order of magnitude
more common. This is due to the fact that
there is no easy way for stars to create 62Ni
through the alpha process.
An exception to this general trend is the
helium-4 nucleus, whose binding energy is
higher than that of lithium, the next heaviest
element. This is because protons and neutrons
are fermions, which according to the Pauli
exclusion principle cannot exist in the same
nucleus in exactly the same state. Each proton
or neutron energy state in a nucleus can accommodate
both a spin up particle and a spin down particle.
Helium-4 has an anomalously large binding
energy because its nucleus consists of two
protons and two neutrons; so all four of its
nucleons can be in the ground state. Any additional
nucleons would have to go into higher energy
states. Indeed, the helium-4 nucleus is so
tightly bound that it is commonly treated
as a single particle in nuclear physics, namely,
the alpha particle.
The situation is similar if two nuclei are
brought together. As they approach each other,
all the protons in one nucleus repel all the
protons in the other. Not until the two nuclei
actually come in contact can the strong nuclear
force take over. Consequently, even when the
final energy state is lower, there is a large
energy barrier that must first be overcome.
It is called the Coulomb barrier.
The Coulomb barrier is smallest for isotopes
of hydrogen, as their nuclei contain only
a single positive charge. A diproton is not
stable, so neutrons must also be involved,
ideally in such a way that a helium nucleus,
with its extremely tight binding, is one of
the products.
Using deuterium-tritium fuel, the resulting
energy barrier is about 0.1 MeV. In comparison,
the energy needed to remove an electron from
hydrogen is 13.6 eV, about 7500 times less
energy. The (intermediate) result of the fusion
is an unstable 5He nucleus, which immediately
ejects a neutron with 14.1 MeV. The recoil
energy of the remaining 4He nucleus is 3.5 MeV,
so the total energy liberated is 17.6 MeV.
This is many times more than what was needed
to overcome the energy barrier.
The reaction cross section σ is a measure
of the probability of a fusion reaction as
a function of the relative velocity of the
two reactant nuclei. If the reactants have
a distribution of velocities, e.g. a thermal
distribution with thermonuclear fusion, then
it is useful to perform an average over the
distributions of the product of cross section
and velocity. This average is called the 'reactivity',
denoted less than σvgreater than. The reaction
rate (fusions per volume per time) is less
than σvgreater than times the product of
the reactant number densities:
If a species of nuclei is reacting with itself,
such as the DD reaction, then the product
must be replaced by.
increases from virtually zero at room temperatures
up to meaningful magnitudes at temperatures
of 10–100 keV. At these temperatures, well
above typical ionization energies (13.6 eV
in the hydrogen case), the fusion reactants
exist in a plasma state.
The significance of as a function of temperature
in a device with a particular energy confinement
time is found by considering the Lawson criterion.
This is an extremely challenging barrier to
overcome on Earth, which explains why fusion
research has taken many years to reach the
current high state of technical prowess.
Methods for achieving fusion
Thermonuclear fusion
If the matter is sufficiently heated (hence
being plasma), the fusion reaction may occur
due to collisions with extreme thermal kinetic
energies of the particles. In the form of
thermonuclear weapons, thermonuclear fusion
is the only fusion technique so far to yield
undeniably large amounts of useful fusion
energy. Usable amounts of thermonuclear fusion
energy released in a controlled manner have
yet to be achieved.
Inertial confinement fusion
Inertial confinement fusion (ICF) is a type
of fusion energy research that attempts to
initiate nuclear fusion reactions by heating
and compressing a fuel target, typically in
the form of a pellet that most often contains
a mixture of deuterium and tritium.
Beam-beam or beam-target fusion
If the energy to initiate the reaction comes
from accelerating one of the nuclei, the process
is called beam-target fusion; if both nuclei
are accelerated, it is beam-beam fusion.
Accelerator-based light-ion fusion is a technique
using particle accelerators to achieve particle
kinetic energies sufficient to induce light-ion
fusion reactions. Accelerating light ions
is relatively easy, and can be done in an
efficient manner—all it takes is a vacuum
tube, a pair of electrodes, and a high-voltage
transformer; fusion can be observed with as
little as 10 kV between electrodes. The key
problem with accelerator-based fusion (and
with cold targets in general) is that fusion
cross sections are many orders of magnitude
lower than Coulomb interaction cross sections.
Therefore the vast majority of ions end up
expending their energy on bremsstrahlung and
ionization of atoms of the target. Devices
referred to as sealed-tube neutron generators
are particularly relevant to this discussion.
These small devices are miniature particle
accelerators filled with deuterium and tritium
gas in an arrangement that allows ions of
these nuclei to be accelerated against hydride
targets, also containing deuterium and tritium,
where fusion takes place. Hundreds of neutron
generators are produced annually for use in
the petroleum industry where they are used
in measurement equipment for locating and
mapping oil reserves.
Muon-catalyzed fusion
Muon-catalyzed fusion is a well-established
and reproducible fusion process that occurs
at ordinary temperatures. It was studied in
detail by Steven Jones in the early 1980s.
Net energy production from this reaction cannot
occur because of the high energy required
to create muons, their short 2.2 µs half-life,
and the high chance that a muon will bind
to the new alpha particle and thus stop catalyzing
fusion.
Other principles
Some other confinement principles have been
investigated, some of them have been confirmed
to run nuclear fusion while having lesser
expectation of eventually being able to produce
net power, others have not yet been shown
to produce fusion.
Sonofusion or bubble fusion, a controversial
variation on the sonoluminescence theme, suggests
that acoustic shock waves, creating temporary
bubbles (cavitation) that expand and collapse
shortly after creation, can produce temperatures
and pressures sufficient for nuclear fusion.
The Farnsworth–Hirsch fusor is a tabletop
device in which fusion occurs. This fusion
comes from high effective temperatures produced
by electrostatic acceleration of ions.
The Polywell is a non-thermodynamic equilibrium
machine that uses electrostatic confinement
to accelerate ions into a center where they
fuse together.
Antimatter-initialized fusion uses small amounts
of antimatter to trigger a tiny fusion explosion.
This has been studied primarily in the context
of making nuclear pulse propulsion, and pure
fusion bombs feasible. This is not near becoming
a practical power source, due to the cost
of manufacturing antimatter alone.
Pyroelectric fusion was reported in April
2005 by a team at UCLA. The scientists used
a pyroelectric crystal heated from −34 to
7 °C (−29 to 45 °F), combined with a tungsten
needle to produce an electric field of about
25 gigavolts per meter to ionize and accelerate
deuterium nuclei into an erbium deuteride
target. At the estimated energy levels, the
D-D fusion reaction may occur, producing helium-3
and a 2.45 MeV neutron. Although it makes
a useful neutron generator, the apparatus
is not intended for power generation since
it requires far more energy than it produces.
Hybrid nuclear fusion-fission (hybrid nuclear
power) is a proposed means of generating power
by use of a combination of nuclear fusion
and fission processes. The concept dates to
the 1950s, and was briefly advocated by Hans
Bethe during the 1970s, but largely remained
unexplored until a revival of interest in
2009, due to the delays in the realization
of pure fusion. Project PACER, carried out
at Los Alamos National Laboratory (LANL) in
the mid-1970s, explored the possibility of
a fusion power system that would involve exploding
small hydrogen bombs (fusion bombs) inside
an underground cavity. As an energy source,
the system is the only fusion power system
that could be demonstrated to work using existing
technology. However it would also require
a large, continuous supply of nuclear bombs,
making the economics of such a system rather
questionable.
Important reactions
Astrophysical reaction chains
The most important fusion process in nature
is the one that powers stars. The net result
is the fusion of four protons into one alpha
particle, with the release of two positrons,
two neutrinos (which changes two of the protons
into neutrons), and energy, but several individual
reactions are involved, depending on the mass
of the star. For stars the size of the sun
or smaller, the proton-proton chain dominates.
In heavier stars, the CNO cycle is more important.
Both types of processes are responsible for
the creation of new elements as part of stellar
nucleosynthesis.
At the temperatures and densities in stellar
cores the rates of fusion reactions are notoriously
slow. For example, at solar core temperature
(T ≈ 15 MK) and density (160 g/cm3), the
energy release rate is only 276 μW/cm3—about
a quarter of the volumetric rate at which
a resting human body generates heat. Thus,
reproduction of stellar core conditions in
a lab for nuclear fusion power production
is completely impractical. Because nuclear
reaction rates strongly depend on temperature
(exp(−E/kT)), achieving reasonable energy
production rates in terrestrial fusion reactors
requires 10–100 times higher temperatures
(compared to stellar interiors): T ≈ 0.1–1.0
GK.
Criteria and candidates for terrestrial reactions
In man-made fusion, the primary fuel is not
constrained to be protons and higher temperatures
can be used, so reactions with larger cross-sections
are chosen. This implies a lower Lawson criterion,
and therefore less startup effort. Another
concern is the production of neutrons, which
activate the reactor structure radiologically,
but also have the advantages of allowing volumetric
extraction of the fusion energy and tritium
breeding. Reactions that release no neutrons
are referred to as aneutronic.
To be a useful energy source, a fusion reaction
must satisfy several criteria. It must:
Be exothermic: This may be obvious, but it
limits the reactants to the low Z (number
of protons) side of the curve of binding energy.
It also makes helium 4He the most common product
because of its extraordinarily tight binding,
although 3He and 3H also show up.
Involve low Z nuclei: This is because the
electrostatic repulsion must be overcome before
the nuclei are close enough to fuse.
Have two reactants: At anything less than
stellar densities, three body collisions are
too improbable. In inertial confinement, both
stellar densities and temperatures are exceeded
to compensate for the shortcomings of the
third parameter of the Lawson criterion, ICF's
very short confinement time.
Have two or more products: This allows simultaneous
conservation of energy and momentum without
relying on the electromagnetic force.
Conserve both protons and neutrons: The cross
sections for the weak interaction are too
small.
Few reactions meet these criteria. The following
are those with the largest cross sections:
For reactions with two products, the energy
is divided between them in inverse proportion
to their masses, as shown. In most reactions
with three products, the distribution of energy
varies. For reactions that can result in more
than one set of products, the branching ratios
are given.
Some reaction candidates can be eliminated
at once. The D-6Li reaction has no advantage
compared to p+-11
5B because it is roughly as difficult to burn
but produces substantially more neutrons through
2
1D-2
1D side reactions. There is also a p+-7
3Li reaction, but the cross section is far
too low, except possibly when Ti greater than
1 MeV, but at such high temperatures an endothermic,
direct neutron-producing reaction also becomes
very significant. Finally there is also a
p+-9
4Be reaction, which is not only difficult
to burn, but 9
4Be can be easily induced to split into two
alpha particles and a neutron.
In addition to the fusion reactions, the following
reactions with neutrons are important in order
to "breed" tritium in "dry" fusion bombs and
some proposed fusion reactors:
The latter of the two equations was unknown
when the U.S. conducted the Castle Bravo fusion
bomb test in 1954. Being just the second fusion
bomb ever tested (and the first to use lithium),
the designers of the Castle Bravo "Shrimp"
had understood the usefulness of Lithium-6
in tritium production, but had failed to recognize
that Lithium-7 fission would greatly increase
the yield of the bomb. While Li-7 has a small
neutron cross-section for low neutron energies,
it has a higher cross section above 5 MeV.
Li-7 also undergoes a chain reaction due to
its release of a neutron after fissioning.
The 15 Mt yield was 150% greater than the
predicted 6 Mt and caused heavy casualties
from the fallout generated.
To evaluate the usefulness of these reactions,
in addition to the reactants, the products,
and the energy released, one needs to know
something about the cross section. Any given
fusion device has a maximum plasma pressure
it can sustain, and an economical device would
always operate near this maximum. Given this
pressure, the largest fusion output is obtained
when the temperature is chosen so that less
than σvgreater than /T2 is a maximum. This
is also the temperature at which the value
of the triple product nTτ required for ignition
is a minimum, since that required value is
inversely proportional to less than σvgreater
than /T2 (see Lawson criterion). (A plasma
is "ignited" if the fusion reactions produce
enough power to maintain the temperature without
external heating.) This optimum temperature
and the value of less than σvgreater than
/T2 at that temperature is given for a few
of these reactions in the following table.
Note that many of the reactions form chains.
For instance, a reactor fueled with 3
1T and 3
2He creates some 2
1D, which is then possible to use in the 2
1D-3
2He reaction if the energies are "right".
An elegant idea is to combine the reactions
(8) and (9). The 3
2He from reaction (8) can react with 6
3Li in reaction (9) before completely thermalizing.
This produces an energetic proton, which in
turn undergoes reaction (8) before thermalizing.
Detailed analysis shows that this idea would
not work well, but it is a good example of
a case where the usual assumption of a Maxwellian
plasma is not appropriate.
Neutronicity, confinement requirement, and
power density
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 2
1D-2
1D reaction entails some difficulties, though.
To begin with, one must average over the two
branches (2i) and (2ii). More difficult is
to decide how to treat the 3
1T and 3
2He products. 3
1T burns so well in a deuterium plasma that
it is almost impossible to extract from the
plasma. The 2
1D-3
2He reaction is optimized at a much higher
temperature, so the burnup at the optimum
2
1D-2
1D temperature may be low, so it seems reasonable
to assume the 3
1T but not the 3
2He gets burned up and adds its energy to
the net reaction. Thus the total reaction
would be the sum of (2i), (2ii), and (1):
We count the 2
1D-2
1D fusion energy per D-D reaction (not per
pair of deuterium atoms) 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. (Note:
if the tritium ion reacts with a deuteron
while it still has a large kinetic energy,
then the kinetic energy of the helium-4 produced
may be quite different from 3.5 MeV, so this
calculation of energy in charged particles
is only approximate.)
Another unique aspect of the 2
1D-2
1D 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
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 thermal equilibrium.
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 less than σvgreater than /T2. On the other
hand, because the 2
1D-2
1D reaction has only one reactant, its rate
is twice as high as when the fuel is divided
between two different hydrogenic species,
thus creating a more efficient reaction.
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 2
1D-2
1D because 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.
The maximum value of less than σvgreater
than /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 2
1D-3
1T 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 2
1D-3
1T 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 2
1D-3
1T 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 in aggregate
neutralize the ions' bulk 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 x-ray radiation of
10–30 keV energy (Bremsstrahlung). The Sun
and stars are opaque to x-rays, but essentially
any terrestrial fusion reactor will be optically
thin for x-rays of this energy range. X-rays
are difficult to reflect but they are effectively
absorbed (and converted into heat) in less
than mm thickness of stainless steel (which
is part of a reactor's shield). The ratio
of fusion power produced to x-ray radiation
lost to walls 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 estimates of the
optimum temperature and the power ratio at
that temperature for several reactions.
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 ions
in the plasma are assumed to be purely fuel
ions. In practice, there will be a significant
proportion of impurity ions, which will then
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
2
1D-3
1T very much because the Bremsstrahlung fraction
is low, but it will push the other fuels into
regimes where the power density relative to
2
1D-3
1T is even lower and the required confinement
even more difficult to achieve. For 2
1D-2
1D and 2
1D-3
2He, Bremsstrahlung losses will be a serious,
possibly prohibitive problem. For 3
2He-3
2He, p+-6
3Li and p+-11
5B the Bremsstrahlung losses appear to make
a fusion reactor using these fuels with a
quasineutral, isotropic 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.
