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{{shortShort description|Fusion energypower concepts based on intersecting beams of fusion fuel ions}}
'''Colliding beam fusion''' ('''CBF'''), or '''colliding beam fusion reactor''' ('''CBFR'''), is a class of [[fusion energypower]] concepts that are based on two or more intersecting beams of [[fusionFusion power#Fuels|fusion fuel]] [[ion]]s that are independently accelerated to fusion energies using a variety of [[particle accelerator]] designs or other means. One of the beams may be replaced by a static target, in which case the approach is known astermed '''accelerator based fusion''' or '''beam-target fusion''', but the physics is the same as colliding beams.<ref name=":0">{{Cite book |url=https://link.springer.com/book/10.1007/978-3-030-62308-1 |title=Accelerator Technology |series=Particle Acceleration and Detection |year=2020 |language=en |doi=10.1007/978-3-030-62308-1|isbn=978-3-030-62307-4 |s2cid=229610872 }}</ref>
 
CBFRs sufferface from a series ofseveral problems that have limited their ability to be seriously considered as a candidatecandidates for [[fusion energypower]]. When two ions collide, they are more likely to [[scattering|scatter]] than to fuse. [[Magnetic fusionconfinement energyfusion]] reactors overcome this problem using a bulk plasma and confining it for some time so that the ions have many thousands of chances to collide. Two beams colliding do not give the ions muchlittle time to interact before the beams fly apart. This limits how much [[fusion energy]]power a beam-beam machine can make. In addition, beams do not remain focussed; in the 1950s [[Marshall Rosenbluth]] showed that it takes more energy to hold the beams together than what can be expected from their fusion reactions.
 
CBFR does offeroffers more efficient ways to heatprovide plasmathe activation energy for fusion, by directly accelerating individual particles rather than heating a bulk fuel. The CBFR plasmareactants isare naturally non-thermal which gives itthem advantages, especially asthat they can directly supplycarry enough energy to overcome the [[Coulomb barrier]] of [[Aneutronicaneutronic fusion|anuetronic fuel]]s fuels. A number ofSeveral designs have been attemptedsought to overcomingaddress the shortcomings of CBFR;earlier theseCBFRs, include theincluding [[Migma]], MARBLE, MIX, and other beam-based concepts. These concepts attempt to overcome the fundamental problemschallenges withof CBFR by applying radiowaves[[radio wave]]s, bunching the beams together, increasing re-circulationrecirculation, or applying some quantum effects. - noneNone of these approaches have succeeded yet. A micro-fission event at an intersecting apical deuterium particle stream could overcome this energy limitation.
 
==Conventional fusion==
{{mainFurther|Nuclear fusion}}
 
Fusion takes place when atoms come into close proximity and the [[nuclear force]] pulls their nuclei together to form a single larger nucleus. Counteracting this process is the positive charge of the nuclei, which repel each other due to the [[electrostatic force]]. In order forFor fusion to occur, the nuclei must have enough energy to overcome this ''[[coulomb barrier]]''. The barrier is loweredlower for atoms with less positive charge,: those with the fewest [[proton]]s. The nuclear force is increasedincreases with additionalmore nucleons,: the total number of protons and [[neutron]]s. This means that a combination of [[deuterium]] and [[tritium]] has the lowest coulomb barrier, at about 100&nbsp;keV (see [[Nuclear fusion#Requirements for fusion|requirements for fusion]]).{{sfn|WNA|2019}}
 
When the fuel is heated to high energies the [[electron]]s disassociate from the nuclei, which are left as individual ions and electrons mixed in a gas-like [[Plasma (physics)|plasma]]. Particles in a gas are distributed across a wide range of energies in a spectrum known as the [[Maxwell–Boltzmann distribution]]. At any given temperature the majority of the particles are at lower energies, with a "[[long tail]]" containing smaller numbers of particles at much higher energies. So while 100&nbsp;keV represents a temperature of over one billion degrees, in order to produce fusion events, the fuel does not haveneed to be heated to this temperature as a whole;: some reactions will occur even at lower temperatures due to the small number of high-energy particles in the mix.{{sfn|WNA|2019}}
 
As the fusion reactions give off large amounts of energy, and some of that energy will be deposited back in the fuel, these reactions heat the fuel. There is a critical temperature at which the rate of reactions, and thus the energy deposited, balances losses to the environment. At this point the reaction becomes self-sustaining, a point known as ''[[fusion ignition|ignition]]''. For D-T fuel, that temperature is between 50 and 100&nbsp;million&nbsp;degrees. The overall rate of fusion and net energy release is dependent on the combination of temperature, density and energy confinement time, known as the [[fusion triple product]].{{sfn|WNA|2019}}
 
Two primary approaches have developed to attack the [[fusion energypower]] problem. In the [[inertial confinement fusion|inertial confinement]] approach, the fuel is quickly squeezed to extremely high densities, which also increases the internal temperature through the [[adiabatic process]]. There is no attempt to maintain these conditions for any period of time, the fuel explodes outward as soon as the force is released. The confinement time is on the order of microseconds, so the temperatures and density have tomust be very high in order tofor any appreciable amount of the fuel to undergo fusion. This approach has been successful in producing fusion reactions, but to date, the devices that can provide the compression, typically [[laser]]s, require muchfar more energy than the reactions produce.{{sfn|WNA|2019}}
 
The more widely studied approach is [[magnetic confinement fusion|magnetic confinement]]. Since the plasma is electrically charged, it will follow magnetic lines of force and a suitable arrangement of fields can keep the fuel away from the container walls. The fuel is then heated over an extended period until some of the fuel in the tail starts undergoing fusion. At the temperatures and densities that are possible using magnets the fusion process is fairly slow, so this approach requires long confinement times on the order of tens of seconds, or minutes. Confining a gas at millions of degrees for this sort of time scale has proven difficult, although modern experimental machines are approaching the conditions needed for net power production, or "[[fusion gain factor|breakeven]]".{{sfn|WNA|2019}}
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The original earthbound fusion reactions were created by such a device at the [[Cavendish Laboratory]] at [[Cambridge University]]. In 1934, [[Mark Oliphant]], [[Paul Harteck]] and [[Ernest Rutherford]] used a new type of [[power supply]] to power a device not unlike an electron gun to shoot [[deuterium]] nuclei into a metal foil infused with [[deuterium]], [[lithium]] or other light elements. This apparatus allowed them to study the [[nuclear cross section]] of the various reactions, and it was their work that produced the 100&nbsp;keV figure.{{sfn|Oliphant|Harteck|Rutherford|1934}}
 
The chance that any given deuteron will hit one of the deuterium atoms in the metal foil is vanishingly small. The experiment only succeeded because it ran for extended periods, and the rare reactions that did occur were so powerful that they could not be missed. But as the basis of a system for power production it simply wouldn't work; the vast majority of the accelerated deuterons goes right through the foil without undergoing a collision, and all the energy put into accelerating it is lost. The small number of reactions that do occur give off far less energy thatthan what is fed into the accelerator.{{sfn|Oliphant|Harteck|Rutherford|1934}}<ref name=":0" />
 
A somewhat related concept was explored by [[Stanislaw Ulam]] and [[James L. Tuck|Jim Tuck]] at [[Los Alamos National Laboratory|Los Alamos]] shortly after [[World War II]]. In this system, deuterium was infused into metal like the Cavendish experiments, but then formed into a cone and inserted into [[shaped charge]] warheads. Two such warheads were aimed at each other and fired, forming rapidly moving jets of deuterized metal that collided. These experiments were carried out in 1946 but failed to turn up any evidence of fusion reactions.{{sfn|Tuck|1958}}
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To illustrate the difficulty of building a beam-target fusion system, we will consider one promising fusion fuel, the proton-boron cycle, or p-B11.{{sfn|Ruggiero|1992|p=1}}
 
Boron can be formed into highly purified solid blocks, and [[proton]]s easily produced by ionizing [[hydrogen]] gas. The protons can be accelerated and fired into the boron block, and the reactions will cause several [[alpha particle]]s to be released. These can be collected in an electrostatic system to directly produce electricity without having to use a [[Rankine cycle]] or a similar heat-driven system. As the reactions create no [[neutron]]s directly, they have many practical advantages in terms offor safety as wellalso.{{sfn|Ruggiero|1992|pp=1,2}}
 
The chance of a collision is maximized when the protons have an energy of about 675&nbsp;keV. When they fuse, the alphas carry away a total of 8.7&nbsp;MeV. Some of that energy, 0.675&nbsp;MeV, needs tomust be recycled into the accelerator to produce new protons to continue the process, and the generation and acceleration process is unlikely to be much more than 50% efficient. This still leaves ample net energy to close the cycle. However, this assumes every proton causes a fusion event, which isdoes not the caseoccur. Considering the probability of a reaction, the resultant cycle is:
 
{{math|E<sub>net</sub> {{=}} 8.7&nbsp;MeVζ<sub>p</sub>ζ<sub>B</sub> - 0.675&nbsp;MeV}}{{sfn|Ruggiero|1992|p=3}}
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{{math|ζ<sub>p</sub>ζ<sub>B</sub> {{=}} 0.67&nbsp;MeV / 8.6&nbsp;MeV {{=}} {{frac|13}}}}{{sfn|Ruggiero|1992|p=3}}
 
That means that in order to break even, the system has to haveneeds at least {{frac|13}} of the particles to undergo fusion. In order toTo ensure that a proton has a chance to collide with a boron, it has tomust travel past a number ofmany boron atoms. The collision rate of collisions is:
 
{{math|n<sub>events</sub> {{=}} σ ρ d}}{{sfn|Ruggiero|1992|p=3}}
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===Colliding beams===
Things can be improved somewhat improved by using two accelerators firing at each other instead of a single accelerator and a non-moving target. In this case, the second fuel, boron in the example above, is already ionized, so the "ionization drag" seen by the protons entering the solid block is eliminated.{{sfn|Ruggiero|1992|p=4}}
 
In this case, however, the concept of a characteristic interaction length has no meaning as there is no solid target. Instead, for these types of system, the typical measure is to use the [[Luminosity (scattering theory)|beam luminosity]], L, a term that combines the reaction cross-section with the number of events. The term is normally defined as:
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{{math|L {{=}} {{sfrac|P|σ 8.76&nbsp;MeV}}}}{{sfn|Ruggiero|1992|p=7}}
 
If we set P to 1&nbsp;MW, equivalent to a small [[wind turbine]], this requires an L of 10<sup>42</sup>&nbsp;cm<sup>−2</sup>s<sup>−1</sup>.{{sfn|Ruggiero|1992|p=5}} For comparison, the world record for luminosity set by the [[Large Hadron Collider]] in 2017 was 2.06 x 10<sup>34</sup>&nbsp;cm<sup>−2</sup>s<sup>−1</sup>, tenmore than seven orders of magnitude too low.<ref>{{cite web |url=https://home.cern/news/news/accelerators/record-luminosity-well-done-lhc |title=The LHC's 2017 proton run has ended with record luminosity |date=13 November 2017 |first= Corinne |last=Pralavorio |website=CERN}}</ref>
 
==Intersecting beams==
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One such solution would be to place the reaction area of a two-beam system between the poles of a powerful magnet. The field will cause the electrically charged particles to bend around into circular paths and come back into the reaction area again. However, such systems naturally defocus the particles, so this will not lead them back to their original trajectories accurately enough to produce the densities desired.{{sfn|Ruggiero|1992|p=4}}
 
A better solution is to use a dedicated [[storage ring]] which includes focusing systems to maintain the beam accuracy. However, these only accept particles in a relatively narrow selection of original trajectories. If two particles approach closely and scatter off at an angle, they will no longer recycle into the storage area.<ref name=":0" /> It is easy to show that the loss rate from such scatterings is far greater than the fusion rate.{{sfn|Ruggiero|1992|p=4}}
 
SeveralMany attempts have been made to address this scattering problem.▼
 
▲Several attempts have been made to address this scattering problem.
===Migma===
{{mainFurther|Migma}}
 
The [[Migma]] device is perhaps the first significant attempt to solve the recirculation problem. It useduses a storage system that was, in effect, an infinite number of storage rings arranged at different locations and angles. This wasis not accomplisheddone physicallyby butadded throughcomponents theor hardware configurations, but via careful arrangement of the magnetic fields within a wide but flat cylindrical vacuum chamber. Only ions undergoing very high angle scattering events would be lost, and accordingcalculations tosuggest calculations,that the rate of these events was such that any given ion would pass through the reaction area 10<sup>8</sup> times before scattering out. This would be enough to sustain positive energy output.{{sfn|Maglich|1973|pp=213-215}}
 
Several Migma devices were built and showed some promise, but it did not progress beyond moderately sized devices. A number ofSeveral theoretical concerns were raised based on [[space charge]] limit considerations, which suggested that increasing the density of the fuel to useful levels would require enormous magnets to confine it. During funding rounds the system became mired in an acrimonious debate with the various energy agencies and further development ended in the 1980s.{{sfn|Crease|1989}}
 
===Tri-Alpha===
{{mainFurther|TAE Technologies}}
 
A similar concept is being attempted by [[TAE Technologies|]], formerly Tri-Alpha Energy]] (TAE), based largely on the ideas of Norman Rostoker, a professor at [[University of California, Irvine]]. Early publications from the early 1990s show devices using conventional intersecting storage rings and refocussing arrangements, but later documents from 1996 on use a completelyvery different system firing fuel ions into a [[field-reversed configuration]] (FRC).{{sfn|Rostoker|Binderbauer|Monkhorst|1997}}
 
The FRC is a self-stable arrangement of plasma thatwhich geometry looks something like a mix of a [[vortex ring]] and a thick-walled tube. The magnetic fields keep the particles trapped between the tube walls, circulating rapidly. TAE intends to first produce a stable FRC, and then use accelerators to fire additional fuel ions into it so they become trapped. The ions make up for any radiative losses from the FRC, as well asand inject more [[magnetic helicity]] into the FRC to keep its shape. The ions from the accelerators collide to produce fusion.{{sfn|Rostoker|Binderbauer|Monkhorst|1997}}
 
When the concept was first revealed, it garnered a number ofseveral negative reviews in the journals.{{sfn|Nevins|Carlson|1998}}{{sfn|Wong}} These issues were explained away and the construction of several small experimental devices followed. {{asofAs of|2018}}, the best-reported performance of the system is approximately 10<sup>−12</sup> away from breakeven. In early 2019, it was announced that the system would instead be developed using conventional D-T fuels and the company changed its name to TAE.{{sfn|McMahon|2019}}
 
==Inertial electrostatic confinement==
==IEC==
Several types of [[inertial electrostatic confinement]] (IEC) devices are proposed as reactors.
 
===Fusor===
{{mainFurther|fusorFusor}}
The classic example of an IEC device is a [[fusor]]. A typical Fusor has two spherical metal cages, one inside the otheranother, in a vacuum. A high [[voltage]] is placed between the two cages. Fuel gas injected .{{sfn|Spangler|2013}}{{sfn|Fusor}} The fuel ionizes and is accelerated towardstoward the inner cage. IfIons the ionsthat miss the inner cage, they can fuse together.
 
Fusors are not considered part of the CBFR family, because they do not traditionally use beams.
 
There are numerousmany problems with the fusor as a [[fusion power]] reactor. One is that the electrical grids are charged to the point where there is a strong mechanical force pulling them together, which limits how small the grid materials can be. This results in a minimum rate of collisions between the ions and the grids, removing energy from the system. Additionally, these collisions spall off metal into the fuel, which causes it to rapidly lose energy through radiation. It may be that the smallest possible grid material is still large enough that collisions with the ions will remove energy from the system faster than the fusion rate. Beyond that, there are several loss mechanisms that suggest X-ray radiation from such a system will likewise remove energy faster than fusion can supply it.{{sfn|Fusor}}
 
===N-Body IEC===
In 2017, the University of Maryland simulated an N-Body beam system to determine if recirculating ion-beams could reach fusion conditions. Models showed that the concept was fundamentally limited because it could not reach sufficient densities needed for fusion power.
 
===Polywell===
{{mainFurther|polywellPolywell}}
 
An attempt to avoid the grid-collision problems was made by [[Robert Bussard]] in his [[polywellPolywell]] design. This uses a cusp magnetic field arrangements to produce "virtual electrodes" consisting of trapped electrons. The result is to produce an accelerating field notsimilar unlike theto one produced by the grid wires in the fusor, but with no wires. Collisions with the electrons in the virtual electrodes are possible, but unlike the fusor, these do not cause additionalno losses throughvia spalled-off metal ions.{{sfn|NBC|2013}}
 
The polywell's biggest flaw is its ability to hold a plasma negative for any significant amount of time. In practice, any significant amount of negative charge vanishes quickly. AdditionallyFurther, analysis by Todd Rider in 1995 suggests that any system that has non-equilibrium plasmas will suffer from rapid losses of energy due tovia [[bremsstrahlung]]. Bremsstrahlung occurs when a charged particle is rapidly accelerated, causing it to radiate x-rays, and thereby lose energy. In the case of IEC devices, including both the fusor and polywell, the collisions between recently accelerated ions entering the reaction area and low-energy ions and electrons forms a lower limit on bremsstrahlung that appears to be far higher than any possible rate of fusion.{{sfn|Rider|1995}}
 
==Notes==
{{notelistNotelist}}
 
==References==
===Citations===
{{reflistReflist|30em}}
 
===Bibliography===
* {{cite magazine
|title=Visionary Physicist's Crusade Serves As Lesson Inin Futility
|first= Robert |last=Crease
|date=27 November 1989
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* {{cite web
|website=Forbes
|title=Energy Fromfrom Fusion Inin 'A Couple Years,' CEO Says, Commercialization Inin Five
|date=14 January 2019
|first=Jeff |last=McMahon
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|date=June 1995
|journal=Physics of Plasmas
|volume=2| |number=6
|pages=1853–1872
|doi=10.1063/1.871273
|bibcode=1995PhPl....2.1853R
|hdl=1721.1/29869
|s2cid=12336904
|hdl-access=free
}}
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|date=1 November 2013
|url=https://makezine.com/projects/make-36-boards/nuclear-fusor/
|magazine=MAKEMake
|volume=36
|page=90
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|ref=CITEREFFusor
}}
* {{cite techreporttech report
|first1=H. Vernon |last1=Wong |first2=B.N. |last2=Breizman |first3=J.W. |last3=Van Dam
|title=Proton-Boron (p − B11) colliding beam fusion reactor
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|volume=133 |issue=413
|pages=413 |date=17 March 1934
|doi=10.1038/133413a0 |bibcode=1934Natur.133..413O |s2cid=4078529 |doi-access=free }}
* {{cite techreporttech report
|first=James |last=Tuck
|citeseerx=10.1.1.455.1581
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