FYI
- From: Me <agnescherry@xxxxxxxxx>
- Date: Mon, 16 Jun 2008 14:56:57 -0700 (PDT)
Overview
Nuclear physics
Radioactive decay
Nuclear fission
Nuclear fusion [show]Classical decays
Alpha decay · Beta decay · Gamma radiation · Cluster decay
[show]Advanced decays
Double beta decay · Double electron capture · Internal conversion ·
Isomeric transition
[show]Emission processes
Neutron emission · Positron emission · Proton emission
[show]Capturing
Electron capture · Neutron capture
R · S · P · Rp
[show]Fission
Spontaneous fission · Spallation · Cosmic ray spallation ·
Photodisintegration
[show]Nucleosynthesis
Stellar Nucleosynthesis
Big Bang nucleosynthesis
Supernova nucleosynthesis
[show]Scientists
Becquerel · Bethe · Marie Curie · Pierre Curie · Fermi
This box: view • talk • edit
Fusion reactions power the stars and produce all but the lightest
elements in a process called nucleosynthesis. While the fusion of
lighter elements in stars releases energy, production of the heavier
elements absorbs energy.
When the fusion reaction is a sustained uncontrolled chain, it can
result in a thermonuclear explosion, such as that generated by a
hydrogen bomb. Reactions which are not self-sustaining can still
release considerable energy, as well as large numbers of neutrons.
Research into controlled fusion, with the aim of producing fusion
power for the production of electricity, has been conducted for over
50 years. It has been accompanied by extreme scientific and
technological difficulties, but resulted in steady progress. As of the
present, break-even (self-sustaining) controlled fusion reaction have
been demonstrated in a few tokamak-type reactors around the world and
resulted in producing workable design of the reactor which will
deliver ten times more fusion energy than the amount of energy needed
to heat up its plasma to required temperatures (see ITER which is
scheduled to be operational in 2016).
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 too close together. Accelerated to
high speeds (that is, heated to thermonuclear temperatures), they can
overcome this electromagnetic repulsion and get close enough for the
attractive nuclear force to be sufficiently strong to achieve fusion.
The fusion of lighter nuclei, creating a heavier nucleus and a free
neutron, will generally release more energy than it took to force them
together-an exothermic process that can produce self-sustaining
reactions.
The energy released in most nuclear reactions is much larger than that
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 electron volts - less than one-
millionth of the 17 MeV released in the D-T (deuterium-tritium)
reaction shown to the top right. Fusion reactions have an energy
density many times greater than nuclear fission-that is, per unit of
mass the reactions produce far greater energies, even though
individual fission reactions are generally much more energetic than
individual fusion reactions-which are themselves millions of times
more energetic than chemical reactions. Only the direct conversion of
mass into energy, such as with collision of matter and antimatter, is
more energetic per unit of mass than nuclear fusion.
[edit] Requirements
A substantial energy barrier 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 neighbors 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 strong force
generally increases with the size of the nucleus but approaches a
limiting value corresponding to that of a fully surrounded nucleon.
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 electrostatic force caused by positively charged nuclei is very
strong over long distances, but at short distances the nuclear force
is stronger. As such, the main technical difficulty for fusion is
getting the nuclei close enough to fuse. Distances not to scale.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 are not
stable. The four most tightly bound nuclei, in decreasing order of
binding energy, are 62Ni, 58Fe, 56Fe, and 60Ni.[1] Even though the
nickel isotope ,62Ni, is more stable, the iron isotope 56Fe is an
order of magnitude more common. This is due to a greater
disintegration rate for 62Ni in the interior of stars driven by photon
absorption.
A notable exception to this general trend is the helium-4 nucleus,
whose binding energy is higher than that of lithium, the next heavier
element. The Pauli exclusion principle provides an explanation for
this exceptional behavior—it says that because protons and neutrons
are fermions, they cannot exist 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.
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—they contain
only a single positive charge in the nucleus. A bi-proton 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
0.01 MeV.[citation needed] In comparison, the energy needed to remove
an electron from hydrogen is 13.6 eV, about 750 times less energy. The
(intermediate) result of the fusion is an unstable 5He nucleus, which
immediately ejects a neutron with 14.1 MeV.[citation needed] The
recoil energy of the remaining 4He nucleus is 3.5 MeV,[citation
needed] so the total energy liberated is 17.6 MeV.[citation needed]
This is many times more than what was needed to overcome the energy
barrier.
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. If the nuclei are part of a
plasma near thermal equilibrium, one speaks of thermonuclear fusion.
Temperature is a measure of the average kinetic energy of particles,
so by heating the nuclei they will gain energy and eventually have
enough to overcome this 0.01 MeV. Converting the units between
electronvolts and kelvins shows that the barrier would be overcome at
a temperature in excess of 120 million kelvins, obviously a very high
temperature.
There are two effects that lower the actual temperature needed. One is
the fact that temperature is the average kinetic energy, implying that
some nuclei at this temperature would actually have much higher energy
than 0.01 MeV, while others would be much lower. It is the nuclei in
the high-energy tail of the velocity distribution that account for
most of the fusion reactions. The other effect is quantum tunneling.
The nuclei do not actually have to have enough energy to overcome the
Coulomb barrier completely. If they have nearly enough energy, they
can tunnel through the remaining barrier. For this reason fuel at
lower temperatures will still undergo fusion events, at a lower rate.
The fusion reaction rate increases rapidly with temperature until it
maximizes and then gradually drops off. The DT rate peaks at a lower
temperature (about 70 keV, or 800 million kelvins) and at a higher
value than other reactions commonly considered for fusion energy.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. The reaction rate (fusions per volume per time)
is <σv> 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 n1n2 must be replaced by (1 / 2)n2.
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 <σv> as a function of temperature in a device with
a particular energy confinement time is found by considering the
Lawson criterion.
[edit] Gravitational confinement
One force capable of confining the fuel well enough to satisfy the
Lawson criterion is gravity. The mass needed, however, is so great
that gravitational confinement is only found in stars (the smallest of
which are brown dwarfs). Even if the more reactive fuel deuterium were
used, a mass greater than that of the planet Jupiter would be needed.
[edit] Magnetic confinement
See Magnetic confinement fusion for more information.
The charged ions of fusion fuel follow spiral orbits around magnetic
field lines (see Guiding center#Gyration), and the fuel is therefore
trapped along the field lines. A variety of magnetic configurations
exist, including the toroidal geometries of tokamaks and stellarators
and open ended mirror confinement systems.
[edit] Inertial confinement
See Inertial fusion energy for more information.
A third confinement principle is to apply a rapid pulse of energy to a
large part of the surface of a pellet of fusion fuel, causing it to
simultaneously "implode" and heat to very high pressure and
temperature. If the fuel is dense enough and hot enough, the fusion
reaction rate will be high enough to burn a significant fraction of
the fuel before it has dissipated. To achieve these extreme
conditions, the initially cold fuel must be explosively compressed.
Inertial confinement is used in the hydrogen bomb, where the driver is
x-rays created by a fission bomb. Inertial confinement is also
attempted in "controlled" nuclear fusion, where the driver is a laser,
ion, or electron beam, or a Z-pinch.
Some confinement principles have been investigated, such as muon-
catalyzed fusion, the Farnsworth-Hirsch fusor and Polywell (inertial
electrostatic confinement), and bubble fusion.
[edit] Production methods
A variety of methods are known to affect nuclear fusion. Some are
"cold" in the strict sense that no part of the material is hot (except
for the reaction products), some are "cold" in the limited sense that
the bulk of the material is at a relatively low temperature and
pressure but the reactants are not, and some are "hot" fusion methods
that create macroscopic regions of very high temperature and pressure.
[edit] Locally cold 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. It has not been reported to
produce net energy. Net energy production from this reaction is not
believed to be possible because of the energy required to create
muons, their 2.2 µs half-life, and the chance that a muon will bind to
the new alpha particle and thus stop catalyzing fusion.
"Cold fusion" also refers to a simple method using electrodes
(generally palladium) in heavy water, which many claim has not been
verified to be possible. Anomalous excess heat and residual traces of
Tritium and Helium in the deuterated electrolyte, have been reported
in numerous replicated[citation needed] experiments, but peer
consensus is still divided.
[edit] Generally cold, locally hot fusion
Accelerator based light-ion fusion. Using particle accelerators it is
possible to achieve particle kinetic energies sufficient to induce
many light ion fusion reactions. Accelerating light ions is relatively
easy, cheap, 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 kilovolt 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
vast majority of ions ends 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 which 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. Despite periodic reports in the popular press by
scientists claiming to have invented "table-top" fusion machines,
neutron generators have been around for half a century. The sizes of
these devices vary but the smallest instruments are often packaged in
sizes smaller than a loaf of bread. These devices do not produce a net
power output.
In sonoluminescence, acoustic shock waves create temporary bubbles
that collapse shortly after creation, producing very high temperatures
and pressures. In 2002, Rusi P. Taleyarkhan reported the possibility
that bubble fusion occurs in those collapsing bubbles (aka
sonofusion). As of 2005, experiments to determine whether fusion is
occurring give conflicting results. If fusion is occurring, it is
because the local temperature and pressure are sufficiently high to
produce hot fusion.[2] In an episode of Horizon, on BBC television,
results were presented showing that, although temperatures were
reached which could initiate fusion on a large scale, no fusion was
occurring, and inaccuracies in the measuring system were the cause of
anomalous results.
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 device can be built
inexpensively, but it too is unable to produce a net power output.
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 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 (−30 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. Though the energy of the deuterium
ions generated by the crystal has not been directly measured, the
authors used 100 keV (a temperature of about 109 K) as an estimate in
their modeling.[3] At these energy levels, two deuterium nuclei can
fuse together to produce a helium-3 nucleus, a 2.45 MeV neutron and
bremsstrahlung. Although it makes a useful neutron generator, the
apparatus is not intended for power generation since it requires far
more energy than it produces.[4][5][6][7]
[edit] Hot fusion
In "standard" "hot" fusion, the fuel reaches tremendous temperature
and pressure inside a fusion reactor or nuclear weapon.
The methods in the second group are examples of non-equilibrium
systems, in which very high temperatures and pressures are produced in
a relatively small region adjacent to material of much lower
temperature. In his doctoral thesis for MIT, Todd Rider did a
theoretical study of all quasineutral, isotropic, non-equilibrium
fusion systems. He demonstrated that all such systems will leak energy
at a rapid rate due to bremsstrahlung radiation produced when
electrons in the plasma hit other electrons or ions at a cooler
temperature and suddenly decelerate. The problem is not as pronounced
in a hot plasma because the range of temperatures, and thus the
magnitude of the deceleration, is much lower. Note that Rider's work
does not apply to non-neutral and/or anisotropic non-equilibrium
plasmas.
[edit] Important reactions
[edit] Astrophysical reaction chains
The proton-proton chain dominates in stars the size of the Sun or
smaller.
The CNO cycle dominates in stars heavier than the Sun.The most
important fusion process in nature is that which powers the 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. [8] 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)), then in order to achieve reasonable rates of
energy production in terrestrial fusion reactors 10–100 times higher
temperatures (compared to stellar interiors) are required T ≈ 0.1–1.0
GK.
[edit] 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.
In order to be useful as a source of energy, 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. It should be noted that 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:
(1) 2
1D + 3
1T → 4
2He ( 3.5 MeV ) + n0 ( 14.1 MeV )
(2i) 2
1D + 2
1D → 3
1T ( 1.01 MeV ) + p+ ( 3.02 MeV ) 50%
(2ii) → 3
2He ( 0.82 MeV ) + n0 ( 2.45 MeV ) 50%
(3) 2
1D + 3
2He → 4
2He ( 3.6 MeV ) + p+ ( 14.7 MeV )
(4) 3
1T + 3
1T → 4
2He + 2 n0 + 11.3 MeV
(5) 3
2He + 3
2He → 4
2He + 2 p+ + 12.9 MeV
(6i) 3
2He + 3
1T → 4
2He + p+ + n0 + 12.1 MeV 51%
(6ii) → 4
2He ( 4.8 MeV ) + 2
1D ( 9.5 MeV ) 43%
(6iii) → 4
2He ( 0.5 MeV ) + n0 ( 1.9 MeV ) + p+ ( 11.9 MeV ) 6%
(7i) 2
1D + 6
3Li → 2 4
2He + 22.4 MeV
(7ii) → 3
2He + 4
2He + n0 + 2.56 MeV
(7iii) → 7
3Li + p+ + 5.0 MeV
(7iv) → 7
4Be + n0 + 3.4 MeV
(8) p+ + 6
3Li → 4
2He ( 1.7 MeV ) + 3
2He ( 2.3 MeV )
(9) 3
2He + 6
3Li → 2 4
2He + p+ + 16.9 MeV
(10) p+ + 11
5B → 3 4
2He + 8.7 MeV
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.[9]The D-6Li
reaction has no advantage compared to p+-11
5Bbecause it is roughly as difficult to burn but produces
substantially more neutrons through 2
1D-2
1Dside reactions. There is also a p+-7
3Lireaction, but the cross section is far too low, except possibly
when Ti> 1 MeV, but at such high temperatures an endothermic, direct
neutron-producing reaction also becomes very significant. Finally
there is also a p+-9
4Bereaction, which is not only difficult to burn, but 9
4Becan 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:
n0 + 6
3Li → 3
1T + 4
2He
n0 + 7
3Li → 3
1T + 4
2He + n0
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 will have a
maximum plasma pressure that it can sustain, and an economical device
will always operate near this maximum. Given this pressure, the
largest fusion output is obtained when the temperature is chosen so
that <σv>/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 <σv>/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 <σv>/T² at that
temperature is given for a few of these reactions in the following
table.
Nucleosynthesis
fuel T [keV] <σv>/T² [m³/s/keV²]
2
1D-3
1T 13.6 1.24×10-24
2
1D-2
1D 15 1.28×10-26
2
1D-3
2He 58 2.24×10-26
p+-6
3Li 66 1.46×10-27
p+-11
5B 123 3.01×10-27
Note that many of the reactions form chains. For instance, a reactor
fueled with 3
1T and 3
2He will create 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. A detailed analysis shows that this idea will not really
work well, but it is a good example of a case where the usual
assumption of a Maxwellian plasma is not appropriate.
[edit] 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, 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 2
1D-2
1D 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 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 we
will count the 2
1D-2
1D 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 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.
fuel Z Efus [MeV] Ech [MeV] neutronicity
2
1D-3
1T 1 17.6 3.5 0.80
2
1D-2
1D 1 12.5 4.2 0.66
2
1D-3
2He 2 18.3 18.3 ~0.05
p+-11
5B 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 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 <σv>/T². On the other hand,
because the 2
1D-2
1D reaction has only one reactant, the rate is twice as high as if the
fuel were divided between two hydrogenic species.
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.
fuel <σv>/T² penalty/bonus reactivity Lawson criterion power density
2
1D-3
1T 1.24×10-24 1 1 1 1
2
1D-2
1D 1.28×10-26 2 48 30 68
2
1D-3
2He 2.24×10-26 2/3 83 16 80
p+-11
5B 3.01×10-27 1/3 1240 500 2500
The maximum value of <σv>/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.
[edit] 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 the rough optimum temperature and the power
ratio at that temperature for several reactions.[10]
fuel Ti (keV) Pfusion/PBremsstrahlung
2
1D-3
1T 50 140
2
1D-2
1D 500 2.9
2
1D-3
2He 100 5.3
3
2He-3
2He 1000 0.72
p+-6
3Li 800 0.21
p+-11
5B 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 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, 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.[11] This limitation does not apply to non-neutral and
anisotropic plasmas; however, these have their own challenges to
contend with.
[edit] See also
Physics Portal
Energy Portal
Fusion power
Nuclear physics
Nuclear fission
Nuclear reactor
Nucleosynthesis
Helium fusion
Helium-3
Neutron source
Neutron generator
Timeline of nuclear fusion
Periodic table
[edit] References
^ The Most Tightly Bound Nuclei
^ Access : Desktop fusion is back on the table : Nature News
^ http://www.nature.com/nature/journal/v434/n7037/extref/nature03575-s1.pdf
^ UCLA Crystal Fusion
^ Physics News Update 729
^ Coming in out of the cold: nuclear fusion, for real | csmonitor.com
^ Nuclear fusion on the desktop ... really! - Science - MSNBC.com
^ FusEdWeb | Fusion Education
^ http://theses.mit.edu/Dienst/UI/2.0/Page/0018.mit.theses/1995-130/30?npages=306
^ http://theses.mit.edu/Dienst/UI/2.0/Page/0018.mit.theses/1995-130/26?npages=306
^ http://fusion.ps.uci.edu/artan/Posters/aps_poster_2.pdf Portable
Document Format (PDF)
[edit] External links
International Fusion Research and Prototype reactor
IEC Fusion Video Presentation – Presentation on inertial electrostatic
confinement fusion from Dr. Robert Bussard
Fusion.org.uk – A guide to fusion from the UKAEA
Fusion Power Associates A Washington, DC area lobbying organization;
"a non-profit, tax-exempt research and educational foundation,
providing timely information on the status of fusion development."
Edits the Journal of Fusion Energy.
Fusion Science and Technology– Journal published by the American
Nuclear Society.
Impulse Devices A small California based company researching table top
sonic bubble fusion.
MIT Article on table top fusion
JET– Nuclear Fusion Research at the Joint European Torus
Nuclear Files.org What is Nuclear Fusion?
Nuclear Fusion Animation
Nuclear Fusion Explained
Chaos could keep fusion under control
Nuclear fusion reactions First chapter of The Physics of Inertial
Fusion, Stefano Atzeni and Jürgen Meyer-ter-Vehn
Nuclear Fusion for Beginners
Low energy transmutation reactions in deuterium loaded thin film metal
hydrides
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