Toroidal solenoid

The toroidal solenoid was an early 1946 design for a fusion power device designed by George Paget Thomson and Moses Blackman of Imperial College London. It proposed to confine a deuterium fuel plasma to a toroidal chamber using magnets, and then heating it to fusion temperatures using radio frequency energy in the fashion of a microwave oven. It is notable for being the first such design to be patented, filing a secret patent on 8 May 1946 and receiving it in 1948.
A critique by Rudolf Peierls noted several problems with the concept. Over the next few years, Thomson continued to suggest starting an experimental effort to study these issues, but was repeatedly denied as the underlying theory of plasma diffusion was not well developed. When similar concepts were suggested by Peter Thonemann that included a more practical heating arrangement, John Cockcroft began to take the concept more seriously, establishing small study groups at Harwell. Thomson adopted Thonemann's concept, abandoning the radio frequency system.
When the patent had still not been granted in early 1948, the Ministry of Supply inquired about Thomson's intentions. Thomson explained the problems he had getting a program started and that he did not want to hand off the rights until that was clarified. As the directors of the UK nuclear program, the Ministry quickly forced Harwell's hand to provide funding for Thomson's program. Thomson then released his rights the patent, which was granted late that year. Cockcroft also funded Thonemann's work, and with that, the UK fusion program began in earnest. After the news furor over the Huemul Project in February 1951, significant funding was released and led to rapid growth of the program in the early 1950s, and ultimately to the ZETA reactor of 1958.

Conceptual development

The basic understanding of nuclear fusion was developed during the 1920s as physicists explored the new science of quantum mechanics. George Gamow's 1928 work on quantum tunnelling demonstrated that nuclear reactions could take place at lower energies than classical theory predicted. Using this theory, in 1929 Fritz Houtermans and Robert Atkinson demonstrated that expected reaction rates in the core of the Sun supported Arthur Eddington's 1920 suggestion that the Sun is powered by fusion.
In 1934, Mark Oliphant, Paul Harteck and Ernest Rutherford were the first to achieve fusion on Earth, using a particle accelerator to shoot deuterium nuclei into a metal foil containing deuterium, lithium or other elements. This allowed them to measure the nuclear cross section of various fusion reactions, and determined that the deuterium-deuterium reaction occurred at a lower energy than other reactions, peaking at about 100,000 electronvolts.
This energy corresponds to the average energy of particles in a gas heated to a billion Kelvin. Materials heated beyond a few tens of thousand Kelvin dissociate into their electrons and nuclei, producing a gas-like state of matter known as plasma. In any gas the particles have a wide range of energies, normally following the Maxwell–Boltzmann statistics. In such a mixture, a small number of particles will have much higher energy than the bulk.
This leads to an interesting possibility; even at temperatures well below 100,000 eV, some particles will randomly have enough energy to undergo fusion. Those reactions release huge amounts of energy. If that energy can be captured back into the plasma, it can heat other particles to that energy as well, making the reaction self-sustaining. In 1944, Enrico Fermi calculated this would occur at about 50,000,000 K.

Confinement

Taking advantage of this possibility requires the fuel plasma to be held together long enough that these random reactions have time to occur. Like any hot gas, the plasma has an internal pressure and thus tends to expand according to the ideal gas law. For a fusion reactor, the problem is keeping the plasma contained against this pressure; any known physical container would melt at temperatures in the thousands of Kelvin, far below the millions needed for fusion.
A plasma is electrically conductive, and is subject to electric and magnetic fields. In a magnetic field, the electrons and nuclei orbit the magnetic field lines. A simple confinement system is a plasma-filled tube placed inside the open core of a solenoid. The plasma naturally wants to expand outwards to the walls of the tube, as well as move along it, towards the ends. The solenoid creates a magnetic field running down the centre of the tube, which the particles will orbit, preventing their motion towards the sides. Unfortunately, this arrangement does not confine the plasma along the length of the tube, and the plasma is free to flow out the ends.

Initial design

The obvious solution to this problem is to bend the tube, and solenoid, around to form a torus. Motion towards the sides remains constrained as before, and while the particles remain free to move along the lines, in this case, they will simply circulate around the long axis of the tube. But, as Fermi pointed out, when the solenoid is bent into a ring, the electrical windings of the solenoid would be closer together on the inside than the outside. This would lead to an uneven field across the tube, and the fuel will slowly drift out of the centre. Some additional force needs to counteract this drift, providing long-term confinement.
Thomson began development of his concept in February 1946. He noted that this arrangement caused the positively charged fuel ions to drift outward more rapidly than the negatively charged electrons. This would result in a negative area in the center of the chamber that would develop over a short period. This net negative charge would then produce an attractive force on the ions, keeping them from drifting too far from the center, and thus preventing them from drifting to the walls. It appeared this could provide long-term confinement.
This leaves the issue of how to heat the fuel to the required temperatures. Thomson proposed injecting a cool plasma into the torus and then heating it with radio frequency signals beamed into the chamber. The electrons in the plasma would be "pumped" by this energy, transferring it to the ions though collisions. If the chamber held a plasma with densities on the order of 10¹⁴ to 10¹⁵ nuclei/cm³, it would take several minutes to reach the required temperatures.

Filing a patent

In early March, Thomson sent a copy of his proposal to Rudolf Peierls, then at the University of Birmingham. Peierls immediately pointed out a concern; both Peierls and Thomson had been to meetings at the Los Alamos in 1944 where Edward Teller held several informal talks, including the one in which Fermi outlined the basic conditions needed for fusion. This was in the context of an H-bomb, or "the super" as it was then known. Peierls noted that the US might claim priority on such information and consider it highly secret, which meant that while Thomson was privy to the information, it was unlikely others at Imperial were.
Considering the problem, Thomson decided to attempt to file a patent on the concept. This would ensure the origins of the concepts would be recorded, and prove that the ideas were due to efforts in the UK and not his previous work on the atom bomb. At the time, Thomson was not concerned with establishing personal priority for the concept nor generating income from it. At his suggestion, on 26 March 1946 they met with Arthur Block of the Ministry of Supply, which led to B.L. Russel, the MoS' patent agent, beginning to write a patent application that would be owned entirely by the government.

Peierls' concerns

Peierls then followed up with a lengthy critique of the concept, noting three significant issues.
The major concern was that the system as a whole used a toroidal field to confine the electrons, and the electric field resulting to confine the ions. Peierls pointed out that this "cross field" would cause the particles to be forced across the magnetic lines due to the right hand rule, causing the electrons to orbit around the chamber in the poloidal direction, eliminating the area of increased electrons in the center, and thereby allowing the ions to drift to the walls. Using Thomson's own figures for the conditions in an operating reactor, Peierls demonstrated that the resulting neutralized region would extend all the way to the walls, by less than the radius of the electrons in the field. There would be no confinement of the ions.
He also included two additional concerns. One involved the issue of the deuterium fuel ions impacting with the walls of the chamber and the effects that would have, and the other that having electrons leave the plasma would cause an ion to be forced out to maintain charge balance, which would quickly "clean up" all of the gas in the chamber.

Pinch emerges

Thomson was not terribly concerned about the two minor problems but accepted that the primary one about the crossed fields was a serious issue. Considering the issue, a week later he wrote back with a modified concept. In this version, the external magnets producing the toroidal field were removed, and confinement was instead provided by running a current through the plasma. He proposed inducing this current using radio signals injected through slots cut into the torus at spaces that would create a wave moving around the torus similar to the system used in linear accelerators used to accelerate electrons.
A provisional patent was filed on 8 May 1946, updated to use the new confinement system. In the patent, Thomson noted that the primary problem would be overcoming energy losses through bremsstrahlung. He calculated that a plasma density of 10¹⁵ would remain stable long enough for the energy of the pumped electrons to heat the D fuel to the required 100 keV over the time of several minutes. Although the term "pinch effect" is not mentioned, except for the current generation concept, the description was similar to the pinch machines that would become widespread in the 1950s.