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By Charles Rhodes, P.Eng., Ph.D.

The available prime energy sources are fossil fuels, renewable energy and nuclear energy. The world consumption of fossil fuels is constrained by the rise in the atmospheric/ocean CO2 concentration. The use of uranium/thorium in water cooled nuclear fission reactors is constrained by the limited natural uranium/thorium resource. As compared to CANDU reactors the efficiency of uranium usage can be enlarged about 100 fold and the long lived toxic waste reduced over 1000 fold through the use of liquid sodium cooled fast neutron reactors (FNRs). However, the rate of deployment of FNRs is limited by the net plutonium breeding rate. Other issues with FNRs are a requirement for a highly educated work force, a requirement for a scientifically educated general population and a requirement for international oversight to ensure that the related fuel reprocessing capacity not used for nuclear weapon production.

Absent widespread adoption of nuclear power and/or a major reduction in human population the present per capita rate of energy usage is unsustainable.

There are four fusion reaction sequences of possible interest for bulk power generation.
H-2 + H-3 = He-4 + n
n + Li-7 = Li-6 + 2 n
2 n + 2 Li-6 = 2 H-3 + 2 He-4

H-2 + He-3 = He-4 + p
p + Li-6 = He-3 + He-4

H-2 + H-2 = He-3 + n
n + Li-6 = H-3 + He-4
H-2 + H-2 = H-3 + p
p + Li-6 = He-3 + He-4

B-11 + H = 3 He-3

Each of these reaction sequences has major practical challenges. The #1 reaction sequence yields most of the fusion energy as high kinetic energy neutrons. This neutron kinetic energy cannot be captured by the reacting plasma so there are serious challenges with plasma temperature maintenance. This reaction requires initial 120 keV particle energies to run. If the fuel for the #1 reaction sequence is kept in storage sufficiently long the H-3, which has a half life of 12.6 years, spontaneously decays to He-3, enabling the #2 reaction sequence if the initial particle energies are sufficient. Reference: Fusion 2022

The #2 reaction sequence requires an ongoing supply of He-3 which is a rare isotope on Earth. Although He-3 appears to be in balance various side reactions consume part of it. This reaction may become important for power generation in the future if He-3 is mined from the surface of the moon or made in sufficient quantities in Fast Neutron Reactors or by reaction sequence #1. Reaction sequence #2 requires about 450 keV particle energies to run.

In theory reaction sequence #3 could be potentially be used to produce more H-3 and He-3 to feed reaction sequences #1 and #2. However, reaction sequence #3 requires initial particle energies of about 3000 keV to run. In addition the cross sections of reaction sequence #3 are relatively small so there is no certainty that this reaction can practically be made to run on Earth, even under favorable circumstances.

In theory the plutonium production rate required to support a large fast neutron reactor fleet might be enhanced through the use of deuterium-tritium (D-T) fusion as in reaction #1 above. D-T fusion produces high energy neutrons. These high energy neutrons impacting U-238 or Li-7 or Be produce multiple lower energy neutrons that in turn can be used to convert U-238 into fissionable Pu-239, to convert Th-232 into fissionable U-233 and to convert Li-6 into H-3 to sustain the fusion process. However all that assumes that the D-T reaction can be made to run sustainably in the first place.

This web site outlines the design of a pulsed fusion reactor based on an array of electrically powered flywheel guns. These flywheel guns form a hollow rapidly collapsing shell of liquid lead that compresses a D-H-3 mixture to fusion conditions. The flywheel guns involve state of the art high speed microcontrollers and related mechanical systems that must be synchronized on a millisecond time scale. The mechanical efficiency of the flywheel guns must be high to give a net energy gain.

A major issue with all Earth based fusion processes is that much of the gross electricity generated must be fed back into the fusion process to either sustain the fusion reaction or energize the next plasma compression. As compared to a fission reactor, which requires relatively little electricity feedback, this issue at least doubles the size of the heat source and generation equipment per net kWhe produced, making fusion uneconomic for primary electricity generation as long as fission fuel remains readily available. If D-T fusion can be made to work its primary application might be production of more Pu-239 start fuel for fast neutron fission reactors.

As of 2020 there is new hope for fusion based on an improvement in superconducting materials which allows higher magnetic field strengths. This work is being led by Commonwealth Fusion and MIT and is described at: Fusion FHRs Tritium FLiBe Challenges and Opportunities.

Reaction sequence #4 is unique insofar as it does not produce neutrons. However, as compared to reaction sequences #1 amd #2 the energy output of reaction sequence #4 is small. Other than via a proton accelerator it is difficult to visualize how this reaction sequence can be scaled up for practical electric power production. Proton accelerators are inherently current limited by space charge issues.

Nuclear fusion reactions are the source of energy emitted by the sun and the stars.

Deuterium (H-2) is formed in the sun via the fusion reaction:
H-1 + H-1 = H-2 + e+
where e+ is a positron. The positron is soon annihilated by interaction with a free electron. This fusion reaction has a very low cross section and requires reactant particle energies in excess of 1.02 MeV and hence only occurs at extremely high temperatures and pressures that cannot be duplicated on Earth. However, the deuterium (H-2) formed via this reaction is a suitable fusion fuel for mankind to use on Earth.

Deuterium is ejected by the sun and forms part of the solar wind. A portion of the ejected deuterium is captured by the Earth's gravitational field and accumulates in the Earth's lakes and oceans. For the purpose of fuelling nuclear fusion equipment the supply of deuterium in lakes and the oceans is almost unlimited.

Deuterium (H-2) reacts with itself, with helium-3 (He-3) and with tritium (H-3) via the following nuclear reactions:
H-2 + H-2 = He-3 + n + 3.268 MeV
H-2 + He-3 = He-4 + H-1 + 18.354 MeV
H-2 + H-2 = H-3 + H-1 + 4.032 MeV
H-2 + H-3 = He-4 + n + 17.591 MeV

The (H-2 + H-2) reactions occur at particle energies of about 3,000 keV. The (H-2 + He-3) reactions occur at particle energies of about 450 keV. The (H-2 + H-3) reactions occur at particle energies of about 120 keV. Plots of the fusion cross sections as a function of particle energy are available at Kaye & Laby.

In a practical Earthbound fusion system operated at a nominal particle energy of 120 keV the fusion cross sections for (H-2 + He-3) and (H-2 + H-2) reactions are two orders of magnitude less than the fusion cross section for the (H-2 + H-3) reaction. Hence from a practical pulsed energy production perspective the (H-2 + He-3) and (H-2 + H-2) reactions can be ignored.

One way of heating a (H-2 + H-3) plasma is to inject 500 keV He-3 ions. The resulting (He-3 + H-2) reactons will liberate high energy protons that will cause plasma heating provided that the ion path length is long enough. Realizing the required ion path length requires a strong toroidal magnetic field. This methodology can be applied in a magnetic field plasma confinement apparatus but is impractical in a mechanical compression apparatus.

For (H-2 + H-3) reactions the dominant net waste products are He-4 and n of which He-4 is a stable gas and the initial high energy (> 13.6 MeV) neutron n is used for production of Pu-239 using the reaction-decay chain:
n + 3 U-238 = 2 n + U-237 + 2 U-238
= U-237 + 2 U-239
= Np-237 + e + 2 Np-239 + 2 e
= Np-237 + 3 e + 2 Pu-239 + 2 e

This reaction-decay chain takes place within the liquid lead-uranium compression and heat transfer fluid used in the fusion reactor. The liquid lead must contain a dense suspension of metallic U-Np-Pu particles.

When due to cumulative nuclear reactions the plutonium to uranium ratio in this fluid reaches 20% this fluid is electrochemically processed to extract the Pu, Np and U from the lead for use as Fast neutron Reactor (FNR) core fuel.

Note that if the Np-237 does not directly fission within the fusion apparatus then within the FNR it follows the reaction-decay path:
Np-237 + n = Np-238
= Pu-238 + e
(86.4 year half life)
= U-234 + He-4 + e

Thus the FNR relies on fast neutron triggered fission of Np-237 or Pu-238 or U-234 to dispose of these isotopes, all of which have long half lives.

In the breeding blanket of a FNR tritium is produced using the reaction:
Li-6 + n = H-3 + He-4
Hence, some of the FNR blanket rods must contain Li-6. This Li-6 may be in the form of stable LiF to prevent it chemically interacting with other blanket rod materials. When due to neutron absorption the Li-6 converts to H-3 + He-4, the released F can react with the liquid Na in the blanket tube to form stable NaF.

The isotope Li-6 is available on Earth in large quantities.

The natural radioactive decay reaction:
H-3 = He-3 + e
takes place with a half life of 12.6 years. This reaction limits the shelf life of H-3 and hence requires that the FNR blanket bundles containing Li-6 be processed frequently. One way to exploit He-3 that forms as a results natural decay of H-3 and (H-2 + H-2) reactions is to cryogenically separate the He-3 and sell it as a process byproduct. An alternative strategy is to develop magnetically confined fusion reactors that operate at a higher temperature with a D-He-3 fuel mix.

This web site addresses a fusion power methodology known as Plasma Impact Fusion (PIF). The concept can be griefly summarized as follows:

1) Using electricity a semi-stable deuterium plasma spheromak is formed which stores at least 3000 J of energy in its electric and magnetic fields.

2)This plasma spheromak is injected into a robust spherical reaction chamber and the spheromak injection ports are rapidly closed.

3) This plasma spheromak is then surrounded by a radially collapsing liquid lead shell containing a uranium particle suspension. This shell is formed by the simultaneous discharge of a spherical array of inward pointing flywheel guns. Every lead and uranium atom has inward radial momentum which tends to direct that atom toward the center of the sphere.

4) A deuterium-tritium gas mixture is injected into the collapsing liquid lead shell.

5) The deuterium-tritium gas mixture absorbs energy from the deuterium plasma spheromak and forms a random deuterium-tritium plasma within the spherical liquid lead-uranium shell.

6) The inrushing liquid lead-uranium adiabatically compresses and heats this random deuterium-tritium plasma to fusion conditions.

7) Near the instant of maximum plasma compression the deuterium-tritium plasma density, temperature and pressure are sufficient to enable fusion reactions.

8) When the initial kinetic energy contained in the liquid lead-uranium is converted into plasma particle kinetic energy the liquid lead has no remaining inward momentum and the liquid lead radial movement reverses. The hot high pressure random plasma expands accelerating the liquid lead-uranium radially outward.

9) The plasma gains energy from the high energy He-4 nuclei released by the deuterium-tritium fusion reaction. The liquid lead-uranium is heated by the high energy neutrons released by the deuterium-tritium fusion reaction. The inner surface layer of the lead-uranium shell is heated by x-ray and gamma ray absorption.

10) Most of the fusion energy is immediately captured by the liquid lead-uranium as heat. However, some of the liquid lead forms contained high pressure hot lead vapor. This high pressure hot lead vapor propels the balance of the liquid lead-uranium radially outward.

11) The radially moving liquid lead-uranium impacts the spherical reaction chamber wall and flywheel gun ports, which must be made very robust and must be surface contoured for safe and repeated kinetic energy absorption.

12) The fusion energy is harvested by pumping the liquid lead-uranium through a heat exchanger.

13) Lead vapor remaining in the reaction chamber is condensed using a relatively cool liquid lead-uranium spray.

14) The residual gases H-2, H-3, He-3 and He-4 are vacuum extracted and cryogenically separated. The He-3 and He-4 are sold to others and the H-2 and H-3 are recycled as fusion fuel

15) The above described process repeats as rapidly as possible to maximize the average fusion energy flux and the average Pu-239 production rate.

16) At least half of the heat released by each fusion energy pulse must be used to generate sufficient electricity to trigger the next fusion energy pulse. Hence much of the fusion process economic value lies in conversion of U-238 into Pu-239 to enable more rapid deployment of Fast Neutron Reactors (FNRs).

This web page last updated March 3, 2022.

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