what element marks the boundary between using fusion and fission to release energy?

Procedure naturally occurring in stars where atomic nucleons combine

Nuclear fusion is a reaction in which 2 or more atomic nuclei are combined to form 1 or more than different diminutive nuclei and subatomic particles (neutrons or protons). The divergence in mass between the reactants and products is manifested as either the release or the absorption of energy. This departure in mass arises due to the difference in nuclear binding energy between the nuclei before and after the reaction. Nuclear fusion is the process that powers active or principal sequence stars and other high-magnitude stars, where big amounts of energy are released.

A nuclear fusion process that produces atomic nuclei lighter than iron-56 or nickel-62 volition mostly release energy. These elements take a relatively pocket-size mass and a relatively large bounden energy per nucleon. Fusion of nuclei lighter than these releases energy (an exothermic process), while the fusion of heavier nuclei results in energy retained by the production nucleons, and the resulting reaction is endothermic. The opposite is true for the opposite process, called nuclear fission. Nuclear fusion uses lighter elements, such as hydrogen and helium, which are in general more fusible; while the heavier elements, such as uranium, thorium and plutonium, are more fissionable. The extreme astrophysical result of a supernova can produce plenty free energy to fuse nuclei into elements heavier than atomic number 26.

History [edit]

In 1920, Arthur Eddington suggested hydrogen-helium fusion could exist the principal source of stellar free energy. Quantum tunneling was discovered past Friedrich Hund in 1929, and shortly afterward Robert Atkinson and Fritz Houtermans used the measured masses of light elements to show that large amounts of energy could be released past fusing small nuclei. Building on the early experiments in bogus nuclear transmutation by Patrick Blackett, laboratory fusion of hydrogen isotopes was accomplished by Marking Oliphant in 1932. In the remainder of that decade, the theory of the chief bicycle of nuclear fusion in stars was worked out past Hans Bethe. Research into fusion for military purposes began in the early 1940s equally part of the Manhattan Projection. Self-sustaining nuclear fusion was commencement carried out on ane November 1952, in the Ivy Mike hydrogen (thermonuclear) flop exam.

Research into developing controlled fusion within fusion reactors has been ongoing since the 1940s, but the engineering is still in its evolution stage.

Process [edit]

The release of energy with the fusion of calorie-free elements is due to the interplay of two opposing forces: the nuclear strength, which combines together protons and neutrons, and the Coulomb force, which causes protons to repel each other. Protons are positively charged and repel each other past the Coulomb force, but they tin can nonetheless stick together, demonstrating the being of some other, brusque-range, force referred to every bit nuclear attraction.^[2] Low-cal nuclei (or nuclei smaller than iron and nickel) are sufficiently small and proton-poor allowing the nuclear force to overcome repulsion. This is because the nucleus is sufficiently small that all nucleons feel the curt-range attractive force at to the lowest degree as strongly as they feel the infinite-range Coulomb repulsion. Edifice up nuclei from lighter nuclei by fusion releases the extra free energy from the internet attraction of particles. For larger nuclei, however, no energy is released, since the nuclear forcefulness is short-range and cannot continue to act across longer nuclear length scales. Thus, energy is not released with the fusion of such nuclei; instead, free energy is required as input for such processes.

Fusion powers stars and produces well-nigh all elements in a process chosen nucleosynthesis. The Sun is a main-sequence star, and, as such, generates its energy past nuclear fusion of hydrogen nuclei into helium. In its cadre, the Sun fuses 620 million metric tons of hydrogen and makes 616 million metric tons of helium each 2nd. The fusion of lighter elements in stars releases energy and the mass that always accompanies it. For example, in the fusion of 2 hydrogen nuclei to form helium, 0.645% of the mass is carried abroad in the form of kinetic free energy of an alpha particle or other forms of energy, such as electromagnetic radiation.^[3]

It takes considerable free energy to force nuclei to fuse, even those of the lightest chemical element, hydrogen. When accelerated to high plenty speeds, nuclei can overcome this electrostatic repulsion and be brought close enough such that the bonny nuclear forcefulness is greater than the repulsive Coulomb force. The strong strength grows rapidly once the nuclei are close enough, and the fusing nucleons tin can essentially "fall" into each other and the result is fusion and net energy produced. The fusion of lighter nuclei, which creates a heavier nucleus and often a costless 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.

Energy released in most nuclear reactions is much larger than in chemical reactions, because the binding free energy that holds a nucleus together is greater than the free energy that holds electrons to a nucleus. For example, the ionization energy gained by adding an electron to a hydrogen nucleus is thirteen.half dozen eV—less than i-millionth of the 17.6 MeV released in the deuterium–tritium (D–T) reaction shown in the adjacent diagram. Fusion reactions take an energy density many times greater than nuclear fission; the reactions produce far greater free energy per unit of mass even though individual fission reactions are generally much more energetic than private fusion ones, which are themselves millions of times more than energetic than chemical reactions. Merely direct conversion of mass into energy, such equally that acquired past the annihilatory collision of matter and antimatter, is more energetic per unit of mass than nuclear fusion. (The consummate conversion of 1 gram of matter would release 9×10¹³ joules of free energy.)

Research into using fusion for the production of electricity has been pursued for over 60 years. Although controlled fusion is generally manageable with current technology (eastward.chiliad. fusors), successful accomplishment of economic fusion has been stymied by scientific and technological difficulties;^{[ which? ]} still, of import progress has been made. At present, controlled fusion reactions have been unable to produce break-fifty-fifty (cocky-sustaining) controlled fusion.^[four] The two about advanced approaches for it are magnetic confinement (toroid designs) and inertial confinement (light amplification by stimulated emission of radiation designs).

Workable designs for a toroidal reactor that theoretically will deliver ten times more fusion energy than the corporeality needed to heat plasma to the required temperatures are in evolution (run across ITER). The ITER facility is expected to terminate its construction phase in 2025. It will start commissioning the reactor that same twelvemonth and initiate plasma experiments in 2025, but is not expected to begin full deuterium-tritium fusion until 2035.^[5]

Similarly, Canadian-based General Fusion, which is developing a magnetized target fusion nuclear energy system, aims to build its demonstration plant by 2025.^[6]

The United states of america National Ignition Facility, which uses light amplification by stimulated emission of radiation-driven inertial confinement fusion, was designed with a goal of break-even fusion; the showtime big-calibration laser target experiments were performed in June 2009 and ignition experiments began in early 2011.^[7] ^[8]

Nuclear fusion in stars [edit]

The CNO cycle dominates in stars heavier than the Dominicus.

An of import fusion procedure is the stellar nucleosynthesis that powers stars, including the Sun. In the 20th century, it was recognized that the free energy released from nuclear fusion reactions accounts for the longevity of stellar heat and lite. The fusion of nuclei in a star, starting from its initial hydrogen and helium abundance, provides that energy and synthesizes new nuclei. Different reaction chains are involved, depending on the mass of the star (and therefore the pressure and temperature in its core).

Around 1920, Arthur Eddington anticipated the discovery and machinery of nuclear fusion processes in stars, in his paper The Internal Constitution of the Stars.^[9] ^[10] At that time, the source of stellar energy was a consummate mystery; Eddington correctly speculated that the source was fusion of hydrogen into helium, liberating enormous energy according to Einstein's equation $Due east = mc 2$ . This was a particularly remarkable development since at that fourth dimension fusion and thermonuclear free energy had not even so been discovered, nor even that stars are largely composed of hydrogen (run across metallicity). Eddington's paper reasoned that:

The leading theory of stellar energy, the contraction hypothesis, should cause stars' rotation to visibly speed up due to conservation of angular momentum. But observations of Cepheid variable stars showed this was not happening.
The just other known plausible source of energy was conversion of matter to energy; Einstein had shown some years earlier that a small corporeality of matter was equivalent to a large amount of free energy.
Francis Aston had likewise recently shown that the mass of a helium cantlet was about 0.8% less than the mass of the four hydrogen atoms which would, combined, form a helium atom (co-ordinate to the then-prevailing theory of atomic structure which held atomic weight to exist the distinguishing belongings between elements; piece of work by Henry Moseley and Antonius van den Broek would later bear witness that nucleic charge was the distinguishing property and that a helium nucleus, therefore, consisted of two hydrogen nuclei plus additional mass). This suggested that if such a combination could happen, information technology would release considerable energy every bit a byproduct.
If a star independent merely 5% of fusible hydrogen, information technology would suffice to explain how stars got their energy. (We now know that near 'ordinary' stars contain far more 5% hydrogen.)
Further elements might also be fused, and other scientists had speculated that stars were the "crucible" in which light elements combined to create heavy elements, but without more than authentic measurements of their atomic masses cypher more could be said at the time.

All of these speculations were proven correct in the following decades.

The primary source of solar free energy, and that of similar size stars, is the fusion of hydrogen to course helium (the proton–proton chain reaction), which occurs at a solar-core temperature of xiv one thousand thousand kelvin. The net outcome is the fusion of four protons into one alpha particle, with the release of 2 positrons and two neutrinos (which changes two of the protons into neutrons), and energy. In heavier stars, the CNO cycle and other processes are more important. Every bit a star uses up a substantial fraction of its hydrogen, it begins to synthesize heavier elements. The heaviest elements are synthesized past fusion that occurs when a more massive star undergoes a violent supernova at the end of its life, a process known as supernova nucleosynthesis.

Requirements [edit]

A substantial energy barrier of electrostatic forces must be overcome earlier fusion can occur. At large distances, two naked nuclei repel one another considering of the repulsive electrostatic strength between their positively charged protons. If two nuclei tin can be brought shut plenty together, nonetheless, the electrostatic repulsion can be overcome by the quantum consequence in which nuclei tin tunnel through coulomb forces.

When a nucleon such as a proton or neutron is added to a nucleus, the nuclear strength attracts it to all the other nucleons of the nucleus (if the atom is small enough), but primarily to its immediate neighbors due to the short range of the strength. The nucleons in the interior of a nucleus take more neighboring nucleons than those on the surface. Since smaller nuclei accept a larger surface-area-to-book ratio, the bounden energy per nucleon due to the nuclear force more often than not increases with the size of the nucleus but approaches a limiting value corresponding to that of a nucleus with a diameter of about 4 nucleons. It is important to go along in mind that nucleons are breakthrough objects. So, for instance, since two neutrons in a nucleus are identical to each other, the goal of distinguishing ane from the other, such equally which one is in the interior and which is on the surface, is in fact meaningless, and the inclusion of breakthrough mechanics is therefore necessary for proper calculations.

The electrostatic force, on the other hand, is an inverse-square force, so a proton added to a nucleus volition feel an electrostatic repulsion from all the other protons in the nucleus. The electrostatic free energy per nucleon due to the electrostatic strength thus increases without limit every bit nuclei atomic number grows.

The electrostatic strength between the positively charged nuclei is repulsive, merely when the separation is pocket-sized enough, the breakthrough effect volition tunnel through the wall. Therefore, the prerequisite for fusion is that the 2 nuclei exist brought close enough together for a long enough fourth dimension for quantum tunneling to act.

The net event of the opposing electrostatic and strong nuclear forces is that the binding energy per nucleon generally increases with increasing size, upward to the elements iron and nickel, and then decreases for heavier nuclei. Eventually, the bounden energy becomes negative and very heavy nuclei (all with more than 208 nucleons, corresponding to a bore of most 6 nucleons) are not stable. The iv virtually tightly bound nuclei, in decreasing order of binding energy per nucleon, are ⁶²
Ni
, ⁵⁸
Fe
, ⁵⁶
Atomic number 26
, and ⁶⁰
Ni
.^[xi] Even though the nickel isotope, ⁶²
Ni
, is more stable, the iron isotope ⁵⁶
Fe
is an lodge of magnitude more common. This is due to the fact that there is no easy mode for stars to create ⁶²
Ni
through the blastoff process.

An exception to this general tendency is the helium-iv nucleus, whose bounden energy is higher than that of lithium, the next heavier chemical 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'due south free energy state in a nucleus can accommodate both a spin up particle and a spin down particle. Helium-four has an anomalously big binding energy because its nucleus consists of two protons and 2 neutrons (information technology is a doubly magic nucleus), 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 quantum mechanical particle in nuclear physics, namely, the alpha particle.

The situation is similar if two nuclei are brought together. Every bit they arroyo each other, all the protons in one nucleus repel all the protons in the other. Non until the two nuclei actually come close enough for long enough so the strong nuclear force can have over (by fashion of tunneling) is the repulsive electrostatic force overcome. Consequently, even when the final energy country is lower, there is a large energy barrier that must first be overcome. Information technology is called the Coulomb barrier.

The Coulomb barrier is smallest for isotopes of hydrogen, as their nuclei contain only a single positive accuse. A diproton is non stable, so neutrons must also be involved, ideally in such a fashion that a helium nucleus, with its extremely tight binding, is ane of the products.

Using deuterium–tritium fuel, the resulting energy barrier is about 0.one MeV. In comparison, the free energy needed to remove an electron from hydrogen is thirteen.6 eV. The (intermediate) result of the fusion is an unstable ^vHe nucleus, which immediately ejects a neutron with 14.one MeV. The recoil energy of the remaining ^ivHe nucleus is 3.v MeV, then the total energy liberated is 17.half-dozen MeV. This is many times more than than what was needed to overcome the energy bulwark.

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 kelvin) and at a higher value than other reactions commonly considered for fusion free energy.

The reaction cantankerous section (σ) is a measure of the probability of a fusion reaction equally a role of the relative velocity of the ii reactant nuclei. If the reactants have a distribution of velocities, e.thousand. a thermal distribution, then it is useful to perform an average over the distributions of the product of cross-department and velocity. This average is called the 'reactivity', denoted $⟨ σv ⟩$ . The reaction charge per unit (fusions per book per time) is $⟨ σv ⟩$ times the product of the reactant number densities:

f=n_{one}n_{2}\langle \sigma v\rangle .

If a species of nuclei is reacting with a nucleus like itself, such as the DD reaction, then the production $n_{1}n_{2}$ must be replaced by $northward^{2}/two$ .

$\langle \sigma v\rangle$ increases from virtually zero at room temperatures up to meaningful magnitudes at temperatures of ten–100 keV. At these temperatures, well higher up typical ionization energies (13.6 eV in the hydrogen example), the fusion reactants exist in a plasma state.

The significance of $\langle \sigma five\rangle$ equally a function of temperature in a device with a particular energy confinement time is institute 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 electric current avant-garde technical state.^[12]

Artificial fusion [edit]

Thermonuclear fusion [edit]

If matter is sufficiently heated (hence being plasma) and bars, fusion reactions may occur due to collisions with farthermost thermal kinetic energies of the particles. Thermonuclear weapons produce what amounts to an uncontrolled release of fusion energy. Controlled thermonuclear fusion concepts apply magnetic fields to confine the plasma.

Inertial confinement fusion [edit]

Inertial confinement fusion (ICF) is a method aimed at releasing fusion free energy by heating and compressing a fuel target, typically a pellet containing deuterium and tritium.

Inertial electrostatic confinement [edit]

Inertial electrostatic confinement is a set up of devices that use an electric field to estrus ions to fusion weather. The well-nigh well known is the fusor. Starting in 1999, a number of amateurs have been able to do apprentice fusion using these homemade devices.^[thirteen] ^[14] ^[fifteen] ^[xvi] Other IEC devices include: the Polywell, MIX POPS^[17] and Marble concepts.^[xviii]

Beam-axle or axle-target fusion [edit]

Accelerator-based calorie-free-ion fusion is a technique using particle accelerators to achieve particle kinetic energies sufficient to induce calorie-free-ion fusion reactions. Accelerating light ions is relatively easy, and can exist done in an efficient manner—requiring merely a vacuum tube, a pair of electrodes, and a loftier-voltage transformer; fusion can be observed with equally little as x kV betwixt the electrodes. The system tin can be arranged to accelerate ions into a static fuel-infused target, known as beam-target fusion, or by accelerating two streams of ions towards each other, beam-beam fusion.

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 expend their energy emitting bremsstrahlung radiation and the 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 those nuclei to be accelerated against hydride targets, too containing deuterium and tritium, where fusion takes identify, releasing a flux of neutrons. 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.

A number of attempts to recirculate the ions that "miss" collisions accept been made over the years. One of the ameliorate-known attempts in the 1970s was Migma, which used a unique particle storage ring to capture ions into circular orbits and render them to the reaction area. Theoretical calculations made during funding reviews pointed out that the arrangement would accept meaning difficulty scaling up to incorporate enough fusion fuel to be relevant every bit a ability source. In the 1990s, a new organisation using a field-reverse configuration (FRC) as the storage arrangement was proposed by Norman Rostoker and continues to be studied by TAE Technologies as of 2021^[update]. A closely related arroyo is to merge two FRC's rotating in reverse directions,^[19] which is beingness actively studied by Helion Energy. Because these approaches all have ion energies well beyond the Coulomb barrier, they often suggest the use of alternative fuel cycles like p-¹¹B that are too difficult to endeavor using conventional approaches.^[twenty]

Muon-catalyzed fusion [edit]

Muon-catalyzed fusion is a fusion procedure that occurs at ordinary temperatures. Information technology was studied in detail past Steven Jones in the early on 1980s. Internet energy production from this reaction has been unsuccessful because of the high energy required to create muons, their brusque 2.2 µs half-life, and the high risk that a muon will bind to the new alpha particle and thus finish catalyzing fusion.^[21]

Other principles [edit]

Some other confinement principles have been investigated.

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 viable. This is not near becoming a practical power source, due to the toll of manufacturing antimatter lonely.
Pyroelectric fusion was reported in April 2005 by a team at UCLA. The scientists used a pyroelectric crystal heated from −34 to vii °C (−29 to 45 °F), combined with a tungsten needle to produce an electric field of nigh 25 gigavolts per meter to ionize and advance deuterium nuclei into an erbium deuteride target. At the estimated energy levels,^[22] 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.^[23] ^[24] ^[25] ^[26] D-T fusion reactions accept been observed with a tritiated erbium target.^[27]
Hybrid nuclear fusion-fission (hybrid nuclear ability) is a proposed means of generating power past 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.^[28]
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) within an underground crenel. Every bit an free energy source, the system is the only fusion power system that could be demonstrated to piece of work using existing applied science. Even so it would also require a large, continuous supply of nuclear bombs, making the economics of such a organisation rather questionable.
Bubble fusion as well chosen sonofusion was a proposed mechanism for achieving fusion via sonic cavitation which rose to prominence in the early 2000s. Subsequent attempts at replication failed and the principal investigator, Rusi Taleyarkhan, was judged guilty of research misconduct in 2008.^[29]

Of import reactions [edit]

Stellar reaction chains [edit]

At the temperatures and densities in stellar cores, the rates of fusion reactions are notoriously irksome. For example, at solar core temperature (T ≈ 15 MK) and density (160 g/cm^three), the free energy release charge per unit is only 276 μW/cm³—most a quarter of the volumetric rate at which a resting man body generates oestrus.^[30] Thus, reproduction of stellar core conditions in a lab for nuclear fusion power production is completely impractical. Because nuclear reaction rates depend on density as well as temperature and well-nigh fusion schemes operate at relatively depression densities, those methods are strongly dependent on higher temperatures. The fusion rate as a function of temperature (exp(−East/kT)), leads to the demand to achieve temperatures in terrestrial reactors 10–100 times higher than in stellar interiors: T ≈ 0.1–1.0×10⁹ Thou.

Criteria and candidates for terrestrial reactions [edit]

In bogus fusion, the primary fuel is non constrained to be protons and higher temperatures can be used, so reactions with larger cantankerous-sections are chosen. Another business organisation is the production of neutrons, which activate the reactor construction radiologically, but likewise accept the advantages of allowing volumetric extraction of the fusion free energy and tritium convenance. 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:

Exist exothermic: This limits the reactants to the low Z (number of protons) side of the curve of binding energy. Information technology as well makes helium ^four
He
the most common product because of its extraordinarily tight bounden, although ³
He
and ^three
H
as well prove upward.
Involve low atomic number (Z) nuclei: This is considering the electrostatic repulsion that must be overcome before the nuclei are close plenty to fuse is straight related to the number of protons information technology contains - its atomic number.^{[ citation needed ]}
Have two reactants: At annihilation less than stellar densities, 3-body collisions are too improbable. In inertial confinement, both stellar densities and temperatures are exceeded to recoup for the shortcomings of the tertiary parameter of the Lawson criterion, ICF's very short solitude fourth dimension.
Have ii or more products: This allows simultaneous conservation of free 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:^[31] ^[32]

(one)

²
₁ D

^three
₁ T

→

^four
₂ He

(

three.52 MeV

)

northward⁰

(

14.06 MeV

)

(2i)

²
₁ D

→

ⁱⁱⁱ
_ane T

(

1.01 MeV

)

p⁺

(

3.02 MeV

)

50%

(2ii)

→

ⁱⁱⁱ
₂ He

(

0.82 MeV

)

n⁰

(

ii.45 MeV

)

50%

(3)

²
₁ D

³
₂ He

→

⁴
₂ He

(

three.vi MeV

)

p⁺

(

14.vii MeV

)

(4)

³
_one T

³
₁ T

→

⁴
₂ He

2 northward⁰

11.3 MeV

(5)

³
₂ He

→

^four
₂ He

2 p⁺

12.ix MeV

(6i)

³
₂ He

³
₁ T

→

⁴
₂ He

p⁺

n⁰

12.i MeV

57%

(6ii)

→

⁴
₂ He

(

4.8 MeV

)

²
_one D

(

9.5 MeV

)

43%

(7i)

²
_one D

⁶
_three Li

→

2 ⁴
_two He

22.4 MeV

(7ii)

→

³
_ii He

^four
₂ He

n⁰

2.56 MeV

(7iii)

→

⁷
₃ Li

p⁺

v.0 MeV

(7iv)

→

⁷
₄ Be

n⁰

3.4 MeV

(8)

p⁺

^six
₃ Li

→

^iv
₂ He

(

i.7 MeV

)

^three
_two He

(

two.three MeV

)

(nine)

³
_ii He

⁶
₃ Li

→

2 ^four
₂ He

p⁺

16.9 MeV

(ten)

p⁺

^eleven
_five B

→

3 ⁴
_two He

eight.7 MeV

For reactions with two products, the energy is divided between them in inverse proportion to their masses, every bit shown. In most reactions with iii products, the distribution of energy varies. For reactions that tin can result in more than than 1 set of products, the branching ratios are given.

Some reaction candidates can be eliminated at once. The D-^sixLi reaction has no advantage compared to p⁺- ^eleven
₅ B
because it is roughly as difficult to burn but produces substantially more neutrons through ²
₁ D
- ²
₁ D
side reactions. There is besides a p⁺- ⁷
₃ Li
reaction, but the cross section is far also low, except possibly when T _i > ane MeV, but at such high temperatures an endothermic, direct neutron-producing reaction likewise becomes very pregnant. Finally there is also a p⁺- ^nine
_iv Be
reaction, which is not only difficult to burn, only ⁹
₄ Be
tin be hands induced to split into two alpha particles and a neutron.

In improver to the fusion reactions, the following reactions with neutrons are important in guild to "breed" tritium in "dry" fusion bombs and some proposed fusion reactors:

northward⁰	+	⁶ _iii Li	→	³ _one T	+	^iv ₂ He + 4.784 MeV
n⁰	+	⁷ ₃ Li	→	³ ₁ T	+	⁴ ₂ He + northward⁰ – 2.467 MeV

The latter of the 2 equations was unknown when the U.Due south. conducted the Castle Bravo fusion bomb exam in 1954. Being only the second fusion bomb ever tested (and the outset to use lithium), the designers of the Castle Bravo "Shrimp" had understood the usefulness of ^half-dozenLi in tritium production, merely had failed to recognize that ⁷Li fission would greatly increase the yield of the bomb. While ^viiLi has a small neutron cross-section for low neutron energies, it has a college cantankerous section above v MeV.^[33] The 15 Mt yield was 250% greater than the predicted vi Mt and caused unexpected exposure to fallout.

To evaluate the usefulness of these reactions, in addition to the reactants, the products, and the free energy released, one needs to know something nearly the nuclear cantankerous department. Whatsoever 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 then that $⟨ σv ⟩/ T 2$ is a maximum. This is besides 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 $⟨ σv ⟩/ T 2$ (run across Lawson criterion). (A plasma is "ignited" if the fusion reactions produce enough ability to maintain the temperature without external heating.) This optimum temperature and the value of $⟨ σv ⟩/ T 2$ at that temperature is given for a few of these reactions in the post-obit table.

fuel	T [keV]	$⟨ σv ⟩/ T ii$ [m³/southward/keV²]
ⁱⁱ _one D - ⁱⁱⁱ ₁ T	13.6	1.24×ten⁻²⁴
ⁱⁱ ₁ D - ² ₁ D	15	1.28×10⁻²⁶
² _ane D - ³ _two He	58	two.24×10⁻²⁶
p⁺- ^vi ₃ Li	66	1.46×10⁻²⁷
p⁺- ¹¹ ₅ B	123	3.01×10⁻²⁷

Note that many of the reactions grade bondage. For instance, a reactor fueled with ⁱⁱⁱ
_ane T
and ³
_ii He
creates some ²
_i D
, which is then possible to employ in the ²
₁ D
- ⁱⁱⁱ
₂ He
reaction if the energies are "right". An elegant thought is to combine the reactions (8) and (ix). The ⁱⁱⁱ
_ii He
from reaction (8) can react with ⁶
₃ Li
in reaction (9) before completely thermalizing. This produces an energetic proton, which in plow undergoes reaction (8) before thermalizing. Detailed assay shows that this idea would not piece of work well,^{[ citation needed ]} but it is a good example of a case where the usual assumption of a Maxwellian plasma is not advisable.

Neutronicity, confinement requirement, and power density [edit]

Any of the reactions higher up can in principle be the basis of fusion ability product. In addition to the temperature and cantankerous section discussed above, we must consider the full energy of the fusion products E _fus, the energy of the charged fusion products East _ch, and the atomic number Z of the non-hydrogenic reactant.

Specification of the ²
_i D
- ⁱⁱ
₁ D
reaction entails some difficulties, though. To begin with, i must average over the two branches (2i) and (2ii). More difficult is to decide how to treat the ³
₁ T
and ³
₂ He
products. ³
₁ T
burns so well in a deuterium plasma that it is well-nigh impossible to extract from the plasma. The ⁱⁱ
₁ D
- ³
₂ He
reaction is optimized at a much college temperature, so the burnup at the optimum ²
₁ D
- ⁱⁱ
_i D
temperature may be low. Therefore, information technology seems reasonable to assume the ³
₁ T
but not the ³
₂ He
gets burned up and adds its energy to the internet reaction, which means the total reaction would exist the sum of (2i), (2ii), and (1):

v ^two
₁ D
→ ^four
₂ He
+ 2 n⁰ + ³
₂ He
+ p⁺, E _fus = four.03+17.6+3.27 = 24.9 MeV, E _ch = iv.03+3.five+0.82 = 8.35 MeV.

For calculating the power of a reactor (in which the reaction rate is determined by the D-D step), we count the ²
_i D
- ²
₁ D
fusion energy per D-D reaction every bit Due east _fus = (four.03 MeV + 17.six MeV)×50% + (3.27 MeV)×fifty% = 12.v MeV and the energy in charged particles as E _ch = (4.03 MeV + 3.5 MeV)×l% + (0.82 MeV)×l% = iv.ii MeV. (Note: if the tritium ion reacts with a deuteron while it still has a large kinetic energy, so the kinetic free energy of the helium-4 produced may exist quite different from 3.v MeV,^[34] so this calculation of energy in charged particles is only an approximation of the average.) The amount of energy per deuteron consumed is 2/5 of this, or 5.0 MeV (a specific energy of about 225 million MJ per kilogram of deuterium).

Another unique aspect of the ²
₁ D
- ²
₁ D
reaction is that there is but ane reactant, which must be taken into business relationship when computing the reaction rate.

With this choice, nosotros tabulate parameters for 4 of the nigh important reactions

fuel	Z	East _fus [MeV]	E _ch [MeV]	neutronicity
² _i D - ³ ₁ T	ane	17.6	3.5	0.lxxx
² _i D - ² _i D	1	12.5	4.2	0.66
² ₁ D - ^three ₂ He	2	18.3	18.iii	≈0.05
p⁺- ^xi ₅ B	five	8.7	viii.7	≈0.001

The terminal column is the neutronicity of the reaction, the fraction of the fusion free energy released as neutrons. This is an important indicator of the magnitude of the problems associated with neutrons like radiation impairment, biological shielding, remote handling, and condom. For the start 2 reactions information technology is calculated as (E _fus-Due east _ch)/Eastward _fus. For the final ii reactions, where this adding would requite nothing, the values quoted are rough estimates based on side reactions that produce neutrons in a plasma in thermal equilibrium.

Of course, the reactants should likewise be mixed in the optimal proportions. This is the case when each reactant ion plus its associated electrons accounts for half the pressure. Bold that the full pressure level is fixed, this means that particle density of the not-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 aforementioned factor, on superlative of whatever differences in the values of $⟨ σv ⟩/ T two$ . On the other hand, because the ²
_ane D
- ⁱⁱ
₁ D
reaction has simply one reactant, its rate is twice as loftier as when the fuel is divided between two different hydrogenic species, thus creating a more efficient reaction.

Thus there is a "penalty" of (two/(Z+1)) for non-hydrogenic fuels arising from the fact that they require more electrons, which take up force per unit area 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 every bit a "hot ion mode", the "penalty" would not apply.) There is at the same fourth dimension a "bonus" of a factor 2 for ²
_i D
- ²
₁ D
considering each ion tin react with any of the other ions, not just a fraction of them.

We tin can at present compare these reactions in the following table.

fuel	$⟨ σv ⟩/ T 2$	penalisation/bonus	inverse reactivity	Lawson criterion	power density (W/g³/kPa²)	changed ratio of power density
² ₁ D - ³ ₁ T	one.24×10⁻²⁴	1	1	ane	34	ane
ⁱⁱ ₁ D - ² ₁ D	1.28×x⁻²⁶	two	48	30	0.five	68
² _i D - ⁱⁱⁱ ₂ He	2.24×10⁻²⁶	ii/three	83	16	0.43	80
p⁺- ⁶ ₃ Li	one.46×10⁻²⁷	1/2	1700		0.005	6800
p⁺- ¹¹ ₅ B	3.01×10⁻²⁷	1/3	1240	500	0.014	2500

The maximum value of $⟨ σv ⟩/ T 2$ 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 cavalcade "inverse reactivity" are found past dividing 1.24×x⁻²⁴ past the product of the 2nd and third columns. It indicates the factor by which the other reactions occur more slowly than the ²
_i D
- ³
₁ T
reaction under comparable conditions. The column "Lawson criterion" weights these results with E _ch and gives an indication of how much more difficult it is to achieve ignition with these reactions, relative to the difficulty for the ²
₁ D
- ³
₁ T
reaction. The next-to-last cavalcade is labeled "power density" and weights the applied reactivity by E _fus. The terminal column indicates how much lower the fusion power density of the other reactions is compared to the ²
_one D
- ³
_i T
reaction and tin be considered a measure of the economic potential.

Bremsstrahlung losses in quasineutral, isotropic plasmas [edit]

The ions undergoing fusion in many systems will essentially never occur lone but will be mixed with electrons that in aggregate neutralize the ions' majority electrical charge and class 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 radiations of 10–30 keV free energy, a process known as Bremsstrahlung.

The huge size of the Sun and stars means that the x-rays produced in this process will non escape and will eolith their energy back into the plasma. They are said to be opaque to x-rays. Just any terrestrial fusion reactor will be optically thin for 10-rays of this free 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 role of a reactor'due south shield). This means the bremsstrahlung procedure is conveying energy out of the plasma, cooling it.

The ratio of fusion power produced to 10-ray radiation lost to walls is an of import effigy of merit. This ratio is generally maximized at a much college temperature than that which maximizes the power density (come across the previous subsection). The following table shows estimates of the optimum temperature and the ability ratio at that temperature for several reactions:

fuel	T _i (keV)	P _fusion/P _{Bremsstrahlung}
² _i D - ⁱⁱⁱ _ane T	50	140
² _ane D - ^two _i D	500	2.9
² _i D - ³ _two He	100	five.3
³ _ii He - ^three ₂ He	g	0.72
p⁺- ⁶ ₃ Li	800	0.21
p⁺- ¹¹ _v B	300	0.57

The bodily ratios of fusion to Bremsstrahlung power volition likely exist significantly lower for several reasons. For ane, the adding 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. All the same, 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 practise, 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 upwards their energy, and will remain for some time after that in any proposed confinement scheme. Finally, all channels of energy loss other than Bremsstrahlung take been neglected. The final two factors are related. On theoretical and experimental grounds, particle and free energy solitude seem to exist closely related. In a confinement scheme that does a good job of retaining free energy, fusion products volition build up. If the fusion products are efficiently ejected, then energy solitude will exist poor, also.

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 volition non change the optimum operating signal for ^two
₁ D
- ³
₁ T
very much because the Bremsstrahlung fraction is low, but it will button the other fuels into regimes where the power density relative to ²
₁ D
- ³
_ane T
is even lower and the required confinement fifty-fifty more hard to achieve. For ²
₁ D
- ^two
₁ D
and ⁱⁱ
₁ D
- ⁱⁱⁱ
₂ He
, Bremsstrahlung losses will be a serious, possibly prohibitive problem. For ³
₂ He
- ³
₂ He
, p⁺- ^six
₃ Li
and p⁺- ^xi
₅ B
the Bremsstrahlung losses appear to make a fusion reactor using these fuels with a quasineutral, isotropic plasma incommunicable. Some ways out of this dilemma have been considered but rejected.^[35] ^[36] This limitation does non apply to not-neutral and anisotropic plasmas; however, these have their own challenges to debate with.

Mathematical description of cross section [edit]

Fusion under classical physics [edit]

In a classical flick, nuclei can be understood as difficult spheres that repel each other through the Coulomb force but fuse once the ii spheres come up close enough for contact. Estimating the radius of an atomic nuclei equally about one femtometer, the energy needed for fusion of two hydrogen is:

E_{\ce {thresh}}={\frac {one}{iv\pi \epsilon _{0}}}{\frac {Z_{1}Z_{two}}{r}}{\ce {->[{\text{two protons}}]}}{\frac {1}{4\pi \epsilon _{0}}}{\frac {e^{2}}{1\ {\ce {fm}}}}\approx 1.iv\ {\ce {MeV}}

This would imply that for the cadre of the sun, which has a Boltzmann distribution with a temperature of around 1.four keV, the probability hydrogen would attain the threshold is $10^{-290}$ , that is, fusion would never occur. However, fusion in the sun does occur due to breakthrough mechanics.

Parameterization of cross section [edit]

The probability that fusion occurs is profoundly increased compared to the classical picture, cheers to the smearing of the effective radius equally the DeBroglie wavelength also as quantum tunnelling through the potential bulwark. To determine the rate of fusion reactions, the value of most interest is the cross section, which describes the probability that particles will fuse by giving a characteristic area of interaction. An estimation of the fusion cross-sectional surface area is frequently cleaved into three pieces:

\sigma \approx \sigma _{geometry}\times T\times R

Where $\sigma _{geometry}$ is the geometric cross section, $T$ is the barrier transparency and $R$ is the reaction characteristics of the reaction.

$\sigma _{geometry}$ is of the gild of the square of the de-Broglie wavelength $\sigma _{geometry}\approx \lambda ^{2}={\bigg (}{\frac {\hbar }{m_{r}v}}{\bigg )}^{2}\propto {\frac {i}{\epsilon }}$ where $m_{r}$ is the reduced mass of the system and $\epsilon$ is the center of mass free energy of the organisation.

$T$ tin can be approximated by the Gamow transparency, which has the form: $T\approx due east^{-{\sqrt {\epsilon _{One thousand}/\epsilon }}}$ where $\epsilon _{Grand}=(\pi \blastoff Z_{one}Z_{two})^{2}\times 2m_{r}c^{ii}$ is the Gamow factor and comes from estimating the quantum tunneling probability through the potential barrier.

$R$ contains all the nuclear physics of the specific reaction and takes very different values depending on the nature of the interaction. However, for most reactions, the variation of $R(\epsilon )$ is minor compared to the variation from the Gamow gene and then is approximated by a function called the Astrophysical South-cistron, $Due south(\epsilon )$ , which is weakly varying in energy. Putting these dependencies together, i approximation for the fusion cross section as a office of energy takes the form:

\sigma (\epsilon )\approx {\frac {South(\epsilon )}{\epsilon }}e^{-{\sqrt {\epsilon _{Chiliad}/\epsilon }}}

More detailed forms of the cross-section tin can be derived through nuclear physics-based models and R-matrix theory.

Formulas of fusion cross sections [edit]

The Naval Research Lab'due south plasma physics formulary^[37] gives the total cross section in barns as a function of the free energy (in keV) of the incident particle towards a target ion at residual fit by the formula:

\sigma ^{\text{NRL}}(\epsilon )={\frac {A_{five}+{\big (}(A_{4}-A_{3}\epsilon )^{2}+1{\big )}^{-1}A_{two}}{\epsilon (east^{A_{1}\epsilon ^{-1/2}}-ane)}}

with the following coefficient values:

NRL Formulary Cantankerous Section Coefficients
	DT(i)	DD(2i)	DD(2ii)	DHe³(iii)	TT(iv)	THeⁱⁱⁱ(6)
A1	45.95	46.097	47.88	89.27	38.39	123.ane
A2	50200	372	482	25900	448	11250
A3	1.368×10⁻²	4.36×10^−four	iii.08×10^−iv	3.98×10⁻³	one.02×10^−three	0
A4	1.076	1.22	1.177	i.297	2.09	0
A5	409	0	0	647	0	0

Bosch-Hale^[38] too reports a R-matrix calculated cantankerous sections fitting ascertainment data with Padé rational approximating coefficients. With energy in units of keV and cross sections in units of millibarn, the factor has the form:

S^{\text{Bosch-Hale}}(\epsilon )={\frac {A_{1}+\epsilon {\bigg (}A_{2}+\epsilon {\big (}A_{3}+\epsilon (A_{4}+\epsilon A_{5}){\big )}{\bigg )}}{1+\epsilon {\bigg (}B_{1}+\epsilon {\large (}B_{2}+\epsilon (B_{3}+\epsilon B_{4}){\big )}{\bigg )}}}

, with the coefficient values:

Bosch-Unhurt coefficients for the fusion cantankerous section
	DT(ane)	DD(2ii)	DHeⁱⁱⁱ(iii)	THe^iv
$\epsilon _{M}$	31.3970	68.7508	31.3970	34.3827
A1	5.5576×10⁴	5.7501×10^{half dozen}	5.3701×10⁴	6.927×10^four
A2	ii.1054×10^two	ii.5226×x^three	3.3027×x^two	seven.454×10⁸
A3	−3.2638×10^−two	iv.5566×10¹	−1.2706×10^−one	2.050×ten^six
A4	1.4987×10^−six	0	2.9327×10⁻⁵	five.2002×10^iv
A5	i.8181×10^−ten	0	−2.5151×ten^−ix	0
B1	0	−3.1995×x⁻ⁱⁱⁱ	0	6.38×10¹
B2	0	−8.5530×ten⁻⁶	0	−9.95×10⁻¹
B3	0	5.9014×10⁻⁸	0	6.981×10^−v
B4	0	0	0	i.728×10⁻⁴
Applicable Energy Range [keV]	0.5-5000	0.three-900	0.5-4900	0.five-550
$(\Delta S)_{\text{max}}\%$	2.0	two.2	2.5	one.ix

where $\sigma ^{\text{Bosch-Hale}}(\epsilon )={\frac {South^{\text{Bosch-Hale}}(\epsilon )}{\epsilon \exp(\epsilon _{G}/{\sqrt {\epsilon }})}}$

Maxwell-averaged nuclear cross sections [edit]

In fusion systems that are in thermal equilibrium, the particles are in a Maxwell–Boltzmann distribution, meaning the particles have a range of energies centered around the plasma temperature. The sun, magnetically confined plasmas and inertial confinement fusion systems are well modeled to exist in thermal equilibrium. In these cases, the value of involvement is the fusion cantankerous-section averaged across the Maxwell-Boltzmann distribution. The Naval Research Lab's plasma physics formulary tabulates Maxwell averaged fusion cantankerous sections reactivities in $\mathrm {cm^{3}/sec}$ .

NRL Formulary fusion reaction rates averaged over Maxwellian distributions
Temperature [keV]	DT(i)	DD(2ii)	DHe³(3)	TT(4)	Theⁱⁱⁱ(6)
one	five.five×x⁻²¹	1.5×ten⁻²²	1.0×10⁻²⁶	3.3×10⁻²²	1.0×10⁻²⁸
2	2.6×10⁻¹⁹	5.4×10⁻²¹	1.4×x⁻²³	7.1×ten⁻²¹	1.0×10⁻²⁵
5	1.3×10⁻¹⁷	1.eight×10⁻¹⁹	6.7×10⁻²¹	1.4×x⁻¹⁹	2.1×ten⁻²²
ten	one.1×10^−xvi	i.2×10^−xviii	2.3×x^−nineteen	vii.2×x⁻¹⁹	1.2×10⁻²⁰
20	4.2×10⁻¹⁶	5.2×10^−xviii	iii.viii×10⁻¹⁸	ii.5×ten^−eighteen	2.half-dozen×10⁻¹⁹
50	8.7×ten⁻¹⁶	ii.1×ten⁻¹⁷	5.iv×ten⁻¹⁷	8.7×ten⁻¹⁸	five.three×10^−eighteen
100	8.five×10^−sixteen	iv.5×10⁻¹⁷	i.6×ten^−xvi	i.ix×10⁻¹⁷	two.7×10⁻¹⁷
200	vi.three×10⁻¹⁶	8.8×x⁻¹⁷	two.4×ten⁻¹⁶	4.2×10⁻¹⁷	ix.2×10⁻¹⁷
500	three.seven×10⁻¹⁶	one.viii×10⁻¹⁶	2.3×10⁻¹⁶	8.four×10⁻¹⁷	2.nine×10⁻¹⁶
chiliad	2.7×10^−sixteen	ii.ii×10⁻¹⁶	one.8×10⁻¹⁶	8.0×10⁻¹⁷	v.2×10⁻¹⁶

For energies $T\leq 25{\text{ keV}}$ the data can exist represented by:

({\overline {\sigma v}})_{DD}=2.33\times 10^{-14}\cdot T^{-2/three}\cdot e^{-eighteen.76T^{-ane/3}}{{\text{ cm}}^{3}}/{\text{sec}}

({\overline {\sigma five}})_{DT}=three.68\times 10^{-12}\cdot T^{-ii/3}\cdot due east^{-19.94T^{-ane/3}}{{\text{ cm}}^{iii}}/{\text{sec}}

with $T$ in units of keV.

References [edit]

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^ Kramer, David (March 2011). "DOE looks over again at inertial fusion as potential clean-energy source". Physics Today. 64 (3): 26–28. Bibcode:2011PhT....64c..26K. doi:ten.1063/ane.3563814.
^ Eddington, A. S. (October 1920). "The Internal Constitution of the Stars". The Scientific Monthly. eleven (four): 297–303. Bibcode:1920Sci....52..233E. doi:10.1126/science.52.1341.233. JSTOR 6491. PMID 17747682.
^ Eddington, A. S. (1916). "On the radiative equilibrium of the stars". Monthly Notices of the Majestic Astronomical Society. 77: 16–35. Bibcode:1916MNRAS..77...16E. doi:x.1093/mnras/77.1.16.
^ The Most Tightly Bound Nuclei. Hyperphysics.phy-astr.gsu.edu. Retrieved 17 Baronial 2011.
^ Report, Science World (23 March 2013). "What Is The Lawson Criteria, Or How to Brand Fusion Ability Viable". Science World Report.
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^ "Build a Nuclear Fusion Reactor? No Problem". Clhsonline.net. 23 March 2012. Archived from the original on xxx Oct 2014. Retrieved 24 August 2014.
^ Danzico, Matthew (23 June 2010). "Extreme DIY: Building a bootleg nuclear reactor in NYC". Retrieved 30 October 2014.
^ Schechner, Sam (18 Baronial 2008). "Nuclear Ambitions: Amateur Scientists Get a Reaction From Fusion". The Wall Street Journal . Retrieved 24 August 2014.
^ Park J, Nebel RA, Stange S, Murali SK (2005). "Experimental Observation of a Periodically Oscillating Plasma Sphere in a Gridded Inertial Electrostatic Confinement Device". Phys Rev Lett. 95 (ane): 015003. Bibcode:2005PhRvL..95a5003P. doi:10.1103/PhysRevLett.95.015003. PMID 16090625.
^ "The Multiple Ambipolar Recirculating Axle Line Experiment" Poster presentation, 2011 U.s.a.-Japan IEC conference, Dr. Alex Klein
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^ A. Asle Zaeem et al "Aneutronic Fusion in Standoff of Oppositely Directed Plasmoids" Plasma Physics Reports, Vol. 44, No. 3, pp. 378–386 (2018).
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^ UCLA Crystal Fusion. Rodan.physics.ucla.edu. Retrieved 17 August 2011. Archived 8 June 2015 at the Wayback Car
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^ A momentum and energy balance shows that if the tritium has an energy of Eastward_T (and using relative masses of ane, 3, and 4 for the neutron, tritium, and helium) and then the energy of the helium can exist anything from [(12E_T)^1/ii−(5×17.6MeV+2×E_T)^ane/2]^two/25 to [(12E_T)^ane/2+(5×17.6MeV+two×E_T)^i/2]²/25. For Due east_T=1.01 MeV this gives a range from ane.44 MeV to vi.73 MeV.
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^ Bosch, H. S (1993). "Improved formulas for fusion cross-sections and thermal reactivities". Nuclear Fusion. 32 (4): 611–631. doi:10.1088/0029-5515/32/4/I07. S2CID 55303621.

External links [edit]

NuclearFiles.org – A repository of documents related to nuclear ability.
Annotated bibliography for nuclear fusion from the Alsos Digital Library for Nuclear Issues
NRL Fusion Formulary

chatawaybefold87.blogspot.com

Source: https://en.wikipedia.org/wiki/Nuclear_fusion

Chataway Befold87

what element marks the boundary between using fusion and fission to release energy?

History [edit]

Process [edit]

Nuclear fusion in stars [edit]

Requirements [edit]

Artificial fusion [edit]

Thermonuclear fusion [edit]

Inertial confinement fusion [edit]

Inertial electrostatic confinement [edit]

Beam-axle or axle-target fusion [edit]

Muon-catalyzed fusion [edit]

Other principles [edit]

Of import reactions [edit]

Stellar reaction chains [edit]

Criteria and candidates for terrestrial reactions [edit]

Neutronicity, confinement requirement, and power density [edit]

Bremsstrahlung losses in quasineutral, isotropic plasmas [edit]

Mathematical description of cross section [edit]

Fusion under classical physics [edit]

Parameterization of cross section [edit]

Formulas of fusion cross sections [edit]

Maxwell-averaged nuclear cross sections [edit]

See also [edit]

References [edit]

Further reading [edit]

External links [edit]

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