Physics:Aneutronic fusion

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Short description: Form of fusion power
Lithium-6–deuterium fusion reaction: an aneutronic fusion reaction, with energy released carried by alpha particles, not neutrons.

Aneutronic fusion is any form of fusion power in which very little of the energy released is carried by neutrons. While the lowest-threshold nuclear fusion reactions release up to 80% of their energy in the form of neutrons, aneutronic reactions release energy in the form of charged particles, typically protons or alpha particles. Successful aneutronic fusion would greatly reduce problems associated with neutron radiation such as damaging ionizing radiation, neutron activation, reactor maintenance, and requirements for biological shielding, remote handling and safety.

Since it is simpler to convert the energy of charged particles into electrical power than it is to convert energy from uncharged particles, an aneutronic reaction would be attractive for power systems. Some proponents see a potential for dramatic cost reductions by converting energy directly to electricity, as well as in eliminating the radiation from neutrons, which are difficult to shield against.[1][2] However, the conditions required to harness aneutronic fusion are much more extreme than those required for deuterium-tritium fusion such as at ITER.

History

The first experiments in the field started in 1939, and serious efforts have been continual since the early 1950s.

An early supporter was Richard F. Post at Lawrence Livermore. He proposed to capture the kinetic energy of charged particles as they were exhausted from a fusion reactor and convert this into voltage to drive current.[3] Post helped develop the theoretical underpinnings of direct conversion, later demonstrated by Barr and Moir. They demonstrated a 48 percent energy capture efficiency on the Tandem Mirror Experiment in 1981.[4]

Polywell fusion was pioneered by the late Robert W. Bussard in 1995 and funded by the US Navy. Polywell uses inertial electrostatic confinement. He founded EMC2 to continue polywell research.[5][6]

A picosecond pulse of a 10-terawatt laser produced hydrogen–boron aneutronic fusions for a Russian team in 2005.[7] However, the number of the resulting α particles (around 103 per laser pulse) was low.

In 2006, the Z-machine at Sandia National Laboratory, a z-pinch device, reached 2 billion kelvins and 300 keV.[8]

In 2011, Lawrenceville Plasma Physics published initial results and outlined a theory and experimental program for aneutronic fusion with the dense plasma focus (DPF).[9][10] The effort was initially funded by NASA's Jet Propulsion Laboratory.[11] Support for other DPF aneutronic fusion investigations came from the Air Force Research Laboratory.[12]

A French research team fused protons and boron-11 nuclei using a laser-accelerated proton beam and high-intensity laser pulse.[13] In October 2013 they reported an estimated 80 million fusion reactions during a 1.5 nanosecond laser pulse.[13]

In 2016, a team at the Shanghai Chinese Academy of Sciences produced a laser pulse of 5.3 petawatts with the Superintense Ultrafast Laser Facility (SULF) and expected to reach 10 petawatts with the same equipment.[14]

In 2021, TAE Technologies field-reversed configuration announced that its Norman device was regularly producing a stable plasma at temperatures over 50 million degrees.[15]

In 2021, a Russian team reported experimental results in a miniature device with electrodynamic (oscillatory) plasma confinement. It used a ~1–2 J nanosecond vacuum discharge with a virtual cathode. Its field accelerates boron ions and protons to ~100–300 keV under oscillating ions' collisions. α particles of about 5×104/4π (~10 α particles/ns) were obtained during the 4 μs of applied voltage.[16]

Australian spin-off company HB11 Energy was created in September 2019.[17] In 2022, they claimed to be the first commercial company to demonstrate fusion.[18][19]

Definition

Fusion reactions can be categorized according to their neutronicity: the fraction of the fusion energy released as energetic neutrons. The State of New Jersey defined an aneutronic reaction as one in which neutrons carry no more than 1% of the total released energy,[20] although many papers on the subject[21] include reactions that do not meet this criterion.

Coulomb barrier

The Coulomb barrier is the minimum energy required for the nuclei in a fusion reaction to overcome their mutual electrostatic repulsion. Repulsive force between a particle with charge +Z1 and one with +Z2 is proportional to (Z1×Z2)/r2, where r is the distance between them. The Coulomb barrier facing a pair of reacting, charged particles depends both on total charge and on how equally those charges are distributed; the barrier is lowest when a low-Z particle reacts with a high-Z one and highest when the reactants are of roughly equal charge. Barrier energy is thus minimized for those ions with the fewest protons.

Once the nuclear potential wells of the two reacting particles are within two proton radii of each other, the two can begin attracting one another via nuclear force. Because this interaction is much stronger than electromagnetic interaction, the particles will be drawn together despite the ongoing electrical repulsion, releasing nuclear energy. Nuclear force is a very short-range force, though, so it is a little oversimplified to say it increases with the number of nucleons. The statement is true when describing volume energy or surface energy of a nucleus, less true when addressing Coulomb energy, and does not speak to proton/neutron balance at all. Once reactants have gone past the Coulomb barrier, they're into a world dominated by a force that does not behave like electromagnetism.

In most fusion concepts, the energy needed to overcome the Coulomb barrier is provided by collisions with other fuel ions. In a thermalized fluid like a plasma, the temperature corresponds to an energy spectrum according to the Maxwell–Boltzmann distribution. Gases in this state have some particles with high energy even if the average energy is much lower. Fusion devices rely on this distribution; even at bulk temperatures far below the Coulomb barrier energy, the energy released by the reactions is great enough that capturing some of that can supply sufficient high-energy ions to keep the reaction going.

Thus, steady operation of the reactor is based on a balance between the rate that energy is added to the fuel by fusion reactions and the rate energy is lost to the surroundings. This concept is best expressed as the fusion triple product, the product of the temperature, density and "confinement time", the amount of time energy remains in the fuel before escaping to the environment. The product of temperature and density gives the reaction rate for any given fuel. The rate of reaction is proportional to the nuclear cross section (σ).[1][22]

Any given device can sustain some maximum plasma pressure. An efficient device would continuously operate near this maximum. Given this pressure, the largest fusion output is obtained when the temperature is such 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. A plasma is "ignited" if the fusion reactions produce enough power to maintain the temperature without external heating.

Because the Coulomb barrier is proportional to the product of proton counts (Z1×Z2) of the two reactants, varieties of heavy hydrogen, deuterium and tritium (D–T), give the fuel with the lowest total Coulomb barrier. All other potential fuels have higher Coulomb barriers, and thus require higher operational temperatures. Additionally, D–T fuels have the highest nuclear cross-sections, which means the reaction rates are higher than any other fuel. This makes D–T fusion the easiest to achieve. Comparing the potential of other fuels to the D–T reaction. The table below shows the ignition temperature and cross-section for three of the candidate aneutronic reactions, compared to D–T:

Candidate reactions
Reaction Ignition
T [keV]		 Cross-section

<σv>/T2 [m3/s/keV2]

21D–31T 13.6 1.24×10−24
21D–32He 58 2.24×10−26
p+–63Li 66 1.46×10−27
p+–115B 123 3.01×10−27

The easiest to ignite of the aneutronic reactions, D–3He, has an ignition temperature over four times as high as that of the D–T reaction, and correspondingly lower cross-sections, while the p–11B reaction is nearly ten times more difficult to ignite.

Candidate reactions

Several fusion reactions produce no neutrons on any of their branches. Those with the largest cross sections are:

High nuclear cross section aneutronic reactions[1]
Isotopes Reaction
Deuterium - 3He 2D + 3He →   4He + 1p + 18.3 MeV
Deuterium - 6lithium 2D + 6Li → 2 4He     + 22.4 MeV
Proton - 6lithium 1p + 6Li → 4He + 3He + 4.0 MeV
3He – 6lithium 3He + 6Li → 2 4He + 1p + 16.9 MeV
3He - 3He 3He + 3He →   4He + 2 1p + 12.86 MeV
Proton – Lithium-7 1p + 7Li → 2 4He     + 17.2 MeV
Proton – Boron-11 1p + 11B → 3 4He     + 8.7 MeV
Proton – Nitrogen 1p + 15N →   12C + 4He + 5.0 MeV

Candidate fuels

3He

The 3He–D reaction has been studied as an alternative fusion plasma because it has the lowest energy threshold.

The p–6Li, 3He–6Li, and 3He–3He reaction rates are not particularly high in a thermal plasma. When treated as a chain, however, they offer the possibility of enhanced reactivity due to a non-thermal distribution. The product 3He from the p–6Li reaction could participate in the second reaction before thermalizing, and the product p from 3He–6Li could participate in the former before thermalizing. Detailed analyses, however, do not show sufficient reactivity enhancement to overcome the inherently low cross section.[citation needed]

The 3He reaction suffers from a 3He availability problem. 3He occurs in only minuscule amounts on Earth, so it would either have to be bred from neutron reactions (counteracting the potential advantage of aneutronic fusion)[clarification needed] or mined from extraterrestrial sources.

The amount of 3He needed for large-scale applications can also be described in terms of total consumption: according to the US Energy Information Administration, "Electricity consumption by 107 million U.S. households in 2001 totaled 1,140 billion kW·h" (1.14×1015 W·h). Again assuming 100% conversion efficiency, 6.7 tonnes per year of 3He would be required for that segment of the energy demand of the United States, 15 to 20 tonnes per year given a more realistic end-to-end conversion efficiency. Extracting that amount of pure 3He would entail processing 2 billion tonnes of lunar material per year, even assuming a recovery rate of 100%.[citation needed]

In 2022, Helion Energy claimed that their 7th fusion prototype (Polaris; fully funded and under construction as of September 2022) will demonstrate "net electricity from fusion", and will demonstrate "helium-3 production through deuterium-deuterium fusion" by means of a "patented high-efficiency closed-fuel cycle".[23]

Deuterium

Although the deuterium reactions (deuterium + 3He and deuterium + 6lithium) do not in themselves release neutrons, in a fusion reactor the plasma would also produce D-D side reactions that result in reaction product of 3He plus a neutron. Although neutron production can be minimized by running a plasma reaction hot and deuterium-lean, the fraction of energy released as neutrons is probably several percent, so that these fuel cycles, although neutron-poor, do not meet the 1% threshold. See 3He. The D-3He reaction also suffers from the 3He fuel availability problem, as discussed above.

Lithium

Fusion reactions involving lithium are well studied due to the use of lithium for breeding tritium in thermonuclear weapons. They are intermediate in ignition difficulty between the reactions involving lower atomic-number species, H and He, and the 11B reaction.

The p–7Li reaction, although highly energetic, releases neutrons because of the high cross section for the alternate neutron-producing reaction 1p + 7Li → 7Be + n[24]

Boron

Many studies of aneutronic fusion concentrate on the p–11B reaction,[25][26] which uses easily available fuel. The fusion of the boron nucleus with a proton produces energetic alpha particles (helium nuclei).

Since igniting the p–11B reaction is much more difficult than D-T, alternatives to the usual tokamak fusion reactors are usually proposed, such as inertial confinement fusion.[27] One proposed method uses one laser to create a boron-11 plasma and another to create a stream of protons that smash into the plasma. The proton beam produces a tenfold increase of fusion because protons and boron nuclei collide directly. Earlier methods used a solid boron target, "protected" by its electrons, which reduced the fusion rate.[28] Experiments suggest that a petawatt-scale laser pulse could launch an 'avalanche' fusion reaction,[27][29] although this remains controversial.[30] The plasma lasts about one nanosecond, requiring the picosecond pulse of protons to be precisely synchronized. Unlike conventional methods, this approach does not require a magnetically confined plasma. The proton beam is preceded by an electron beam, generated by the same laser, that strips electrons in the boron plasma, increasing the protons' chance to collide with the boron nuclei and fuse.[28]

Residual radiation

Calculations show that at least 0.1% of the reactions in a thermal p–11B plasma produce neutrons, although their energy accounts for less than 0.2% of the total energy released.[31]

These neutrons come primarily from the reaction:[32]

11B + α → 14N + n + 157 keV

The reaction itself produces only 157 keV, but the neutron carries a large fraction of the alpha energy, close to Efusion/3 = 2.9 MeV. Another significant source of neutrons is:

11B + p → 11C + n − 2.8 MeV.

These neutrons are less energetic, with an energy comparable to the fuel temperature. In addition, 11C itself is radioactive, but quickly decays to 11B with a half life of only 20 minutes.

Since these reactions involve the reactants and products of the primary reaction, it is difficult to lower the neutron production by a significant fraction. A clever magnetic confinement scheme could in principle suppress the first reaction by extracting the alphas as they are created, but then their energy would not be available to keep the plasma hot. The second reaction could in principle be suppressed relative to the desired fusion by removing the high energy tail of the ion distribution, but this would probably be prohibited by the power required to prevent the distribution from thermalizing.

In addition to neutrons, large quantities of hard X-rays are produced by bremsstrahlung, and 4, 12, and 16 MeV gamma rays are produced by the fusion reaction

11B + p → 12C + γ + 16.0 MeV

with a branching probability relative to the primary fusion reaction of about 10−4.[note 1]

The hydrogen must be isotopically pure and the influx of impurities into the plasma must be controlled to prevent neutron-producing side reactions such as:

11B + d → 12C + n + 13.7 MeV
d + d → 3He + n + 3.27 MeV

The shielding design reduces the occupational dose of both neutron and gamma radiation to a negligible level. The primary components are water (to moderate the fast neutrons), boron (to absorb the moderated neutrons) and metal (to absorb X-rays). The total thickness is estimated to be about one meter, mostly water.[33]

Approaches

Using the patents of UNSW's theoretical physicist Heinrich Hora,[34][35][36] HB11 Energy uses two petawatt-class, chirped pulse lasers[37] to drive low-temperature proton-boron fusion using an "in-target" approach. One laser drives hydrogen atoms via target normal sheath acceleration towards a boron plasma confined by a kilotesla magnetic field powered by the other laser. The resulting He+ ions are directly converted to electricity. The pico-second laser produces an avalanche reaction that offers a 109 time increased fusion yield improvement compared to other ICF systems. The company claims an alpha particle flux of 1010/sr, 4 orders of magnitude below net energy gain.[18][19]

Energy capture

Aneutronic fusion produces energy in the form of charged particles instead of neutrons. This means that energy from aneutronic fusion could be captured using direct conversion instead of thermally. Direct conversion can be either inductive, based on changes in magnetic fields, electrostatic, based on pitting charged particles against an electric field, or photoelectric, in which light energy is captured in a pulsed mode.[38]

Electrostatic direct conversion uses the motion of charged particles to create voltage. This voltage drives electricity in a wire which becomes electrical power. It is the reverse of phenomena that use a voltage to put a particle in motion. It has been described as a linear accelerator running backwards.[39]

Aneutronic fusion loses much of its energy as light. This energy results from the acceleration and deceleration of charged particles. These speed changes can be caused by bremsstrahlung radiation or cyclotron radiation or synchrotron radiation or electric field interactions. The radiation can be estimated using the Larmor formula and comes in the X-ray, UV, visible, and IR spectra. Some of the energy radiated as X-rays may be converted directly to electricity. Because of the photoelectric effect, X-rays passing through an array of conducting foils transfer some of their energy to electrons, which can then be captured electrostatically. Since X-rays can go through far greater material thickness than electrons, many hundreds or thousands of layers are needed to absorb them.[40]

Technical challenges

Many challenges confront the commercialization of aneutronic fusion.

Temperature

The large majority of fusion research has gone toward D-T fusion, which is the easiest to achieve. Fusion experiments typically use deuterium-deuterium fusion (D-D) because deuterium is cheap and easy to handle, being non-radioactive. Experimenting with D-T fusion is more difficult because tritium is expensive and radioactive, requiring additional environmental protection and safety measures.

The combination of lower cross-section and higher loss rates in D-3He fusion is offset to a degree because the reactants are mainly charged particles that deposit their energy in the plasma. This combination of offsetting features demands an operating temperature about four times that of a D-T system. However, due to the high loss rates and consequent rapid cycling of energy, the confinement time of a working reactor needs to be about fifty times higher than D-T, and the energy density about 80 times higher. This requires significant advances in plasma physics.[41]

Proton–boron fusion requires ion energies, and thus plasma temperatures, some nine times higher than those for D-T fusion. For any given density of the reacting nuclei, the reaction rate for proton-boron achieves its peak rate at around 600 keV (6.6 billion degrees Celsius or 6.6 gigakelvins)[42] while D-T has a peak at around 66 keV (765 million degrees Celsius, or 0.765 gigakelvin). For pressure-limited confinement concepts, optimum operating temperatures are about 5 times lower, but the ratio is still roughly ten-to-one.

Power balance

The peak reaction rate of p–11B is only one third that for D-T, requiring better plasma confinement. Confinement is usually characterized by the time τ the energy is retained so that the power released exceeds that required to heat the plasma. Various requirements can be derived, most commonly the Lawson criterion, the product of the density, nτ, and the product with the pressure nTτ. The nτ required for p–11B is 45 times higher than that for D-T. The nTτ required is 500 times higher.[note 2] Since the confinement properties of conventional fusion approaches, such as the tokamak and laser pellet fusion are marginal, most aneutronic proposals use radically different confinement concepts.

In most fusion plasmas, bremsstrahlung radiation is a major energy loss channel. (See also bremsstrahlung losses in quasineutral, isotropic plasmas.) For the p–11B reaction, some calculations indicate that the bremsstrahlung power will be at least 1.74 times larger than the fusion power. The corresponding ratio for the 3He-3He reaction is only slightly more favorable at 1.39. This is not applicable to non-neutral plasmas, and different in anisotropic plasmas.

In conventional reactor designs, whether based on magnetic or inertial confinement, the bremsstrahlung can easily escape the plasma and is considered a pure energy loss term. The outlook would be more favorable if the plasma could reabsorb the radiation. Absorption occurs primarily via Thomson scattering on the electrons,[43] which has a total cross section of σT = 6.65×10−29 m2. In a 50–50 D-T mixture this corresponds to a range of 6.3 g/cm2.[44] This is considerably higher than the Lawson criterion of ρR > 1 g/cm2, which is already difficult to attain, but might be achievable in inertial confinement systems.[45]

In megatesla magnetic fields a quantum mechanical effect might suppress energy transfer from the ions to the electrons.[46] According to one calculation,[47] bremsstrahlung losses could be reduced to half the fusion power or less. In a strong magnetic field cyclotron radiation is even larger than the bremsstrahlung. In a megatesla field, an electron would lose its energy to cyclotron radiation in a few picoseconds if the radiation could escape. However, in a sufficiently dense plasma (ne > 2.5×1030 m−3, a density greater than that of a solid[48]), the cyclotron frequency is less than twice the plasma frequency. In this well-known case, the cyclotron radiation is trapped inside the plasmoid and cannot escape, except from a very thin surface layer.

While megatesla fields have not yet been achieved, fields of 0.3 megatesla have been produced with high intensity lasers,[49] and fields of 0.02–0.04 megatesla have been observed with the dense plasma focus device.[50][51]

At much higher densities (ne > 6.7×10−34 m−3), the electrons will be Fermi degenerate, which suppresses bremsstrahlung losses, both directly and by reducing energy transfer from the ions to the electrons.[52] If necessary conditions can be attained, net energy production from p–11B or D–3He fuel may be possible. The probability of a feasible reactor based solely on this effect remains low, however, because the gain is predicted to be less than 20, while more than 200 is usually considered to be necessary.

Power density

In every published fusion power plant design, the part of the plant that produces the fusion reactions is much more expensive than the part that converts the nuclear power to electricity. In that case, as indeed in most power systems, power density is an important characteristic.[note 3] Doubling power density at least halves the cost of electricity. In addition, the confinement time required depends on the power density.

It is, however, not trivial to compare the power density produced by different fusion fuel cycles. The case most favorable to p–11B relative to D-T fuel is a (hypothetical) confinement device that only works well at ion temperatures above about 400 keV, in which the reaction rate parameter <σv> is equal for the two fuels, and that runs with low electron temperature. p–11B does not require as long a confinement time because the energy of its charged products is two and a half times higher than that for D-T. However, relaxing these assumptions, for example by considering hot electrons, by allowing the D-T reaction to run at a lower temperature or by including the energy of the neutrons in the calculation shifts the power density advantage to D-T.

The most common assumption is to compare power densities at the same pressure, choosing the ion temperature for each reaction to maximize power density, and with the electron temperature equal to the ion temperature. Although confinement schemes can be and sometimes are limited by other factors, most well-investigated schemes have some kind of pressure limit. Under these assumptions, the power density for p–11B is about 2,100 times smaller than that for D-T. Using cold electrons lowers the ratio to about 700. These numbers are another indication that aneutronic fusion power is not possible with mainline confinement concepts.

See also

Notes

  1. ↑ As with the neutron dose, shielding is essential with this level of gamma radiation. The neutron calculation in the previous note would apply if the production rate is decreased a factor of ten and the quality factor is reduced from 20 to 1. Without shielding, the occupational dose from a small (30 kW) reactor would still be reached in about an hour.
  2. ↑ Both figures assume the electrons have the same temperature as the ions. If operation with cold electrons is possible, as discussed below, the relative disadvantage of p–11B would be a factor of three smaller, as calculated here.
  3. ↑ Comparing two different types of power systems involves many factors in addition to the power density. Two of the most important are the volume in which energy is produced in comparison to the total volume of the device, and the cost and complexity of the device. In contrast, the comparison of two different fuel cycles in the same type of machine is generally much more robust.

References

  1. ↑ 1.0 1.1 1.2 Harms, A. A.; Schoepf, Klaus F.; Kingdon, David Ross (2000). Principles of Fusion Energy: An Introduction to Fusion Energy for Students of Science and Engineering. World Scientific. pp. 8–11. ISBN 978-981-238-033-3. https://books.google.com/books?id=DD0sZgutqowC&pg=PA8. 
  2. ↑ Larry T. Cox Jr., Franklin B. Mead Jr. and Chan K. Choi Jr., (1990). "Thermonuclear Reaction Listing with Cross-Section Data for Four Advanced Reactions"], Fusion Technology, Volume 18, no. 2. Retrieved 2019-05-07.
  3. ↑ "Mirror Systems: Fuel Cycles, Loss Reduction and Energy Recovery" R.F. Post, BNES nuclear Fusion Reactor Conference at Culham Labs, September 1969
  4. ↑ "Experimental Results from a beam Direct Converter at 100 kV" W. L. Barr, R. W. Moir and G Hamilton, December 3, 1981, Journal of Fusion Energy Vol 2, No. 2, 1982
  5. ↑ Bussard, R. W. & Jameson L. W., Inertial-Electrostatic-Fusion Propulsion Spectrum: Air-Breathing to Interstellar Flight , Journal of Propulsion and Power Vol. 11, No. 2, March–April 1995
  6. ↑ "Should Google Go Nuclear? Clean, cheap, nuclear power (no, really)" (in en). November 9, 2006. https://www.youtube.com/watch?v=rk6z1vP4Eo8. 
  7. ↑ Belyaev, V.S. (2005). "Observation of neutronless fusion reactions in picosecond laser plasmas". Physical Review E 72 (2): 026406. doi:10.1103/physreve.72.026406. PMID 16196717. Bibcode: 2005PhRvE..72b6406B. http://fire.pppl.gov/fusion_pb11_belyaev_082605.pdf. , mentioned in news@nature.com on August 26, 2005 : Lasers trigger cleaner fusion
  8. ↑ Malcolm Haines et al., Viscous Heating of Ions through Saturated Fine-Scale MHD Instabilities in a Z-Pinch at 200–300 keV Temperature; Phys. Rev. Lett. 96, 075003 (2006)
  9. ↑ Lerner, Eric J. (January 28, 2011). "Theory and Experimental Program for p-B11 Fusion with the Dense Plasma Focus". Journal of Fusion Energy 30 (5): 367–376. doi:10.1007/s10894-011-9385-4. Bibcode: 2011JFuE...30..367L. 
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  13. ↑ 13.0 13.1 "Record proton-boron fusion rate achieved | FuseNet". 2014-12-02. Archived on 2014-12-02. Error: If you specify |archivedate=, you must also specify |archiveurl=. http://www.fusenet.eu/node/575. 
  14. ↑ Biran Wang (2 February 2018). "100 Petawatt lasers could generate antimatter from vacuum and create commercial nuclear fusion". https://www.nextbigfuture.com/2018/02/100-petawatt-lasers-could-generate-antimatter-from-vacuum-and-create-commercial-nuclear-fusion.html. 
  15. ↑ "Claiming a landmark in fusion energy, TAE Technologies sees commercialization by 2030" (in en-US). 8 April 2021. https://social.techcrunch.com/2021/04/08/claiming-a-landmark-in-fusion-energy-tae-technologies-sees-commercialization-by-2030/. 
  16. ↑ Kurilenkov, Yu. K.; Oginov, A. V.; Tarakanov, V. P.; Gus'kov, S. Yu.; Samoylov, I. S. (2021-04-22). "Proton-boron fusion in a compact scheme of plasma oscillatory confinement". Physical Review E 103 (4): 043208. doi:10.1103/PhysRevE.103.043208. PMID 34005891. Bibcode: 2021PhRvE.103d3208K. https://link.aps.org/doi/10.1103/PhysRevE.103.043208. 
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  19. ↑ 19.0 19.1 Blain, Loz (2022-03-29). "HB11's hydrogen-boron laser fusion test yields groundbreaking results" (in en-US). https://newatlas.com/energy/hb11-laser-fusion-demonstration/. 
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  23. ↑ "Helion FAQ". https://www.helionenergy.com/faq/. Retrieved 29 September 2022. 
  24. ↑ S. G. Mashnik, M. B. Chadwick, H. G. Hughes, R. C. Little, R. E. MacFarlane, L. S. Waters, and P. G. Young, "7Li(p,n) NUCLEAR DATA LIBRARY FOR INCIDENT PROTON ENERGIES TO 150 MEV", Feb. 8, 2008. ArXiv (retrieved 17 January 2017)
  25. ↑ Nevins, W. M. (1998). "A Review of Confinement Requirements for Advanced Fuels". Journal of Fusion Energy 17 (1): 25–32. doi:10.1023/A:1022513215080. Bibcode: 1998JFuE...17...25N. 
  26. ↑ Pilcher, Pat (2010-01-11). "Fusion breakthrough a magic bullet for energy crisis?". The Independent (London). https://www.independent.co.uk/news/science/fusion-breakthrough-a-magic-bullet-for-energy-crisis-1864275.html. 
  27. ↑ 27.0 27.1 "Functional hydrogen-boron fusion could be here "within the next decade", powered by huge lasers" (in en-US). ZME Science. 2017-12-15. https://www.zmescience.com/science/hydrogen-boron-laser-fusion-15122017. 
  28. ↑ 28.0 28.1 Cowen, R.. (2013). "Two-laser boron fusion lights the way to radiation-free energy". Nature. doi:10.1038/nature.2013.13914. 
  29. ↑ Hora, H.; Eliezer, S.; Kirchhoff, G. J.; Nissim, N.; Wang, J. X.; Lalousis, P.; Xu, Y. X.; Miley, G. H. et al. (December 2017). "Road map to clean energy using laser beam ignition of boron-hydrogen fusion". Laser and Particle Beams 35 (4): 730–740. doi:10.1017/s0263034617000799. ISSN 0263-0346. Bibcode: 2017LPB....35..730H. 
  30. ↑ Belloni, F.; Margarone, D.; Picciotto, A.; Schillaci, F.; Giuffrida, L. (February 2018). "On the enhancement of p-11B fusion reaction rate in laser-driven plasma by α → p collisional energy transfer". Physics of Plasmas 25 (2): 020701. doi:10.1063/1.5007923. Bibcode: 2018PhPl...25b0701B. 
  31. ↑ Heindler and Kernbichler, Proc. 5th Intl. Conf. on Emerging Nuclear Energy Systems, 1989, pp. 177–82. Even though 0.1% is a small fraction, the dose rate is still high enough to require very good shielding, as illustrated by the following calculation. Assume we have a very small reactor producing 30 kW of total fusion power (a full-scale power reactor might produce 100,000 times more than this) and 30 W in the form of neutrons. If there is no significant shielding, a worker in the next room, 10 m away, might intercept (0.5 m2)/(4 pi (10 m)2) = 4×10−4 of this power, i.e., 0.012 W. With 70 kg body mass and the definition 1 gray = 1 J/kg, we find a dose rate of 0.00017 Gy/s. Using a quality factor of 20 for fast neutrons, this is equivalent to 3.4 millisieverts. The maximum yearly occupational dose of 50 mSv will be reached in 15 s, the fatal (-1">50) dose of 5 Sv will be reached in half an hour. If very effective precautions are not taken, the neutrons would also activate the structure so that remote maintenance and radioactive waste disposal would be necessary.
  32. ↑ W. Kernbichler, R. Feldbacher, M. Heindler. "Parametric Analysis of p–11B as Advanced Reactor Fuel" in Plasma Physics and Controlled Nuclear Fusion Research (Proc. 10th Int. Conf., London, 1984) IAEA-CN-44/I-I-6. Vol. 3 (IAEA, Vienna, 1987).
  33. ↑ El Guebaly, Laial, A., Shielding design options and impact on reactor size and cost for the advanced fuel reactor Aploo, Proceedings- Symposium on Fusion Engineering, v.1, 1989, pp.388–391. This design refers to D–He3, which actually produces more neutrons than p–11B fuel.
  34. ↑ Hora, H.; Eliezer, S.; Kirchhoff, G.J. et al. (12 December 2017). "Road map to clean energy using laser beam ignition of boron-hydrogen fusion". Laser and Particle Beams 35 (4): 730–740. doi:10.1017/S0263034617000799. Bibcode: 2017LPB....35..730H. 
  35. ↑ Brian Wang (13 December 2017). "Breakthroughs could make commercial laser nuclear fusion through billion times improvements in yield". https://www.nextbigfuture.com/2017/12/billion-times-improvement-with-laser-nuclear-fusion-using-avalanche-reaction-effect.html. 
  36. ↑ Wilson Da Silva (14 December 2017). "Laser-boron fusion now 'leading contender' for energy". UNSW Newsroom. https://newsroom.unsw.edu.au/news/science-tech/laser-boron-fusion-now-'leading-contender'-energy. 
  37. ↑ Blain, Loz (February 21, 2020). "Radical hydrogen-boron reactor leapfrogs current nuclear fusion tech" (in en-US). https://newatlas.com/energy/hb11-hydrogen-boron-fusion-clean-energy/. 
  38. ↑ Miley, G.H., et al., Conceptual design for a B-3He IEC Pilot plant, Proceedings—Symposium on Fusion Engineering, v. 1, 1993, pp. 161–164; L.J. Perkins et al., Novel Fusion energy Conversion Methods, Nuclear Instruments and Methods in Physics Research, A271, 1988, pp. 188–96
  39. ↑ Moir, Ralph W. "Direct Energy Conversion in Fusion Reactors." Energy Technology Handbook 5 (1977): 150-54. Web. 16 Apr. 2013.
  40. ↑ Quimby, D.C., High Thermal Efficiency X-ray energy conversion scheme for advanced fusion reactors, ASTM Special technical Publication, v.2, 1977, pp. 1161–1165
  41. ↑ Motevalli, Seyed Mohammad; Fadaei, Fereshteh (7 February 2015). "A Comparison Between the Burn Condition of Deuterium–Tritium and Deuterium–Helium-3 Reaction and Stability Limits". Zeitschrift für Naturforschung 70 (2): 79–84. doi:10.1515/zna-2014-0134. Bibcode: 2015ZNatA..70...79M. 
  42. ↑ Lerner, Eric J.; Terry, Robert E. (2007-10-16). "Advances towards pB11 Fusion with the Dense Plasma Focus". arXiv:0710.3149 [physics.plasm-ph].
  43. ↑ Lecture 3 : Accelerated charges and bremsstrahlung, lecture notes in astrophysics from Chris Flynn, Tuorla Observatory
  44. ↑ mi/σT = 2.5×1.67×10−24 g/6.65×10−25 cm2 = 6.28 g/cm2
  45. ↑ Robert W. B. Best. "Advanced Fusion Fuel Cycles". Fusion Technology, Vol. 17 (July 1990), pp. 661–5.
  46. ↑ G.S. Miller, E.E. Salpeter, and I. Wasserman, Deceleration of infalling plasma in the atmospheres of accreting neutron stars. I. Isothermal atmospheres, Astrophysical Journal, 314: 215–233, 1987 March 1. In one case, they report an increase in the stopping length by a factor of 12.
  47. ↑ Lerner, Eric J. (January 26, 2004). "Prospects for P11B Fusion with the Dense Plasma Focus: New Results". arXiv:physics/0401126.
  48. ↑ Assuming 1 MT field strength. This is several times higher than solid density.
  49. ↑ "X-ray Polarization Measurements at Relativistic Laser Intensities" , P. Beiersdorfer, et al.
  50. ↑ Bostick, W.H. et al., Ann. NY Acad. Sci., 251, 2 (1975)
  51. ↑ The magnetic pressure at 1 MT would be 4×1011 MPa. For comparison, the tensile strength of stainless steel is typically 600 MPa.
  52. ↑ Son, S.; Fisch, N.J. (2004). "Aneutronic fusion in a degenerate plasma". Physics Letters A 329 (1–2): 76–82. doi:10.1016/j.physleta.2004.06.054. Bibcode: 2004PhLA..329...76S. http://w3.pppl.gov/~fisch/fischpapers/2004/Son_PLA_04.pdf. 

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