Colliding beam fusion

Colliding beam fusion (CBF), or colliding beam fusion reactor (CBFR), is any member of a class of fusion energy concepts that are based on two or more intersecting beams of fusion fuel ions 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 as accelerator based fusion or beam-target fusion, but the physics is the same as colliding beams. CBFR designs have parallels with the inertial electrostatic confinement, or IEC, which can be thought of a CBFR with an infinite number of beams.

CBFR approaches contrast with the more common magnetic fusion energy concepts in that they do not attempt to heat the fuel to fusion energies in bulk, but provide the required energies one particle at a time. This process can be much more efficient than bulk heating. However, these designs all suffer from the problem that it is difficult to get the ions to hit each other. Particles that miss may be lost, taking their energy with them, whereas in magnetic systems the particles remain in the system for seconds or minutes, giving them ample opportunity to undergo a reaction.

A number of design concepts attempt to address this problem of leaking particles. One of the better-researched concepts was the Migma, which used a unique particle storage ring to capture any particles that did not collide and circulate them back into the reaction area so they would get multiple chances. A more modern version of this concept uses a field-reversed configuration to retain the particles, with TAE Technologies developing such a system as a commercial venture.

In spite of no present CFBR approaching the energy levels seen in modern magnetic fusion machines, the colliding beam concept remains popular because it does not suffer from energy losses to the environment in the same way as magnetic machines. This makes it more suitable for aneutronic fusion fuels like p-B11, which lose energy at a much higher rate than the deuterium-tritium (D-T) fuel used in most designs. Aneutronic fuels have the advantage that they do not give off high-energy neutrons, a problem in conventional designs. However, recent works cast doubt on the energy balance of such approaches and suggest that the loss mechanisms are actually higher in these systems than conventional designs.

Conventional fusionEdit

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 for fusion to occur, the nuclei must have enough energy to overcome this coulomb barrier. The barrier is lowered for atoms with less positive charge, those with the fewest protons. The nuclear force is increased with additional nucleons, the total number of protons and neutrons. This means that a combination of deuterium and tritium has the lowest coulomb barrier, at about 100 keV (see requirements for fusion).[1]

When the fuel is heated to high energies the electrons disassociate from the nuclei, which are left as individual ions and electrons mixed in a gas-like 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 keV represents a temperature of over one billion degrees, in order to produce fusion events the fuel does not have 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.[1]

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 ignition. For D-T fuel, that temperature is between 50 and 100 million degrees. The overall rate of fusion and net energy release is dependent on the combination of temperature, density and confinement time, known as the fusion triple product.[1]

Two primary approaches have developed to attack the fusion energy problem. In the 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 to be very high in order to 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 lasers, require much more energy than the reactions produce.[1]

The more widely studied approach is 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 "breakeven".[1]

Direct accelerationEdit

The energy levels needed to overcome the coulomb barrier, about 100 keV for D-T fuel, corresponds to millions of degrees, but is within the energy range that can be provided by even the smallest particle accelerators. For instance, the very first cyclotron, built in 1932, was capable of producing 4.8 MeV in a device that fit on a tabletop.[2]

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 keV figure.[3]

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 that what is fed into the accelerator.[3]

A somewhat related concept was explored by Stanislaw Ulam and Jim Tuck at 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.[4]

Beam-target systemsEdit

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.[5]

Boron can be formed into highly purified solid blocks, and protons easily produced by ionizing hydrogen gas. The protons can be accelerated and fired into the boron block, and the reactions will cause several alpha particles 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 neutrons directly, they have many practical advantages in terms of safety as well.[6]

The chance of a collision is maximized when the protons have an energy of about 675 keV. When they fuse, the alphas carry away a total of 8.7 MeV. Some of that energy, 0.675 MeV, needs to 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 is not the case. Considering the probability of a reaction, the resultant cycle is:

Enet = 8.7 MeVζpζB - 0.675 Mev[7]

where ζp and ζB are the probabilities that any given proton or boron will undergo a reaction. Re-arranging, we can show that:

ζpζB = 0.67 MeV / 8.6 MeV = ​113[7]

That means that in order to break even, the system has to have at least ​113 of the particles undergo fusion. In order to ensure that a proton has a chance to collide with a boron, it has to travel past a number of boron atoms. The rate of collisions is:

nevents = σ ρ d[7]

where σ is the nuclear cross section between a proton and boron, ρ is the density of boron, and d is the average distance the proton travels through the boron before undergoing a fusion reaction. For p-B11, σ is 0.9 x 10-24 cm-2, ρ is 2.535 g/cm3, and thus d ~ 8 cm. However, travelling through the block causes the proton to ionize the boron atoms it passes, which slows the proton. At 0.675 MeV, this process slows the proton to sub-keV energies in about 10-4 cm, many orders of magnitude less than what is required.[7]

Colliding beamsEdit

Things can be improved somewhat 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.[8]

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 beam luminosity, L, a term that combines the reaction cross-section with the number of events. The term is normally defined as:

L = 1/σdN/dt[9]

For this discussion, we will re-arrange it to extract the collisional frequency:

dN/dt = σ L[9]

Each of these collisions will produce 8.7 MeV, so multiplying by dN/dt gives the power. To generate N collisions one requires luminosity L, generating L requires power, so one can calculate the amount of power needed to produce a given L through:

L = P/σ 8.76 MeV[10]

If we set P to 1 MW, equivalent to a small wind turbine, this requires an L of 1042 cm-2s-1.[9] For comparison, the world record for luminosity set by the Large Hadron Collider in 2017 was 2.06 x 1034 cm-2s-1, ten orders of magnitude too low.[11]

Intersecting beamsEdit

Given the extremely low interaction cross-sections, the number of particles required in the reaction area is enormous, well beyond any existing technology. However, this assumes that the particles in question only get one pass through the system. If the particles that missed collisions can be recycled in a way that their energy can be retained and the particles have multiple chances to collide, the energy imbalance can be reduced.[8]

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 defocus the particles, so this will not lead them back to their original trajectories accurately enough.[8]

A better solution is to use a dedicated storage ring which includes focussing 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. It is easy to show that the loss rate from such scatterings is far greater than the fusion rate.[8]

Several attempts have been made to address this scattering problem.

MigmaEdit

The Migma device is perhaps the first significant attempt to solve the recirculation problem. It used a storage system that was, in effect, an infinite number of storage rings arranged at different locations and angles. This was not accomplished physically, but through careful arrangement of the magnetic fields within a cylindrical vacuum chamber. Only ions undergoing very high angle scattering events would be lost, and according to calculations, the rate of these events was such that any given ion would pass through the reaction area 108 times before scattering out. This would be enough to sustain positive energy output.[12]

Several Migma devices were built and showed some promise, but it did not progress beyond moderately sized devices. A number of 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. During funding rounds the system became mired in an acrimonious debate with the various energy agencies and further development ended in the 1980s.[13]

Tri-AlphaEdit

A similar concept is being attempted 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 completely different system firing fuel ions into a field-reversed configuration (FRC).[14]

The FRC is a self-stable arrangement of plasma that looks something like 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 as inject more magnetic helicity into the FRC to keep its shape. The ions from the accelerators collide to produce fusion.[14]

When the concept was first revealed it garnered a number of negative reviews in the journals.[15][16] These issues were explained away and the construction of several small experimental devices followed. As of 2018, the best-reported performance of the system is approximately 10-12 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.[17]

IECEdit

Another approach using the same basic concept relies not on beams, but a more random distribution of accelerated particles. These approaches are known generally as inertial electrostatic confinement, or IEC for short. There are two major approaches to IEC being explored, the fusor and polywell.

FusorEdit

One of the earliest attempts to address the energy loss due to missed collisions was developed in the 1960s as the fusor. Modern fusor designs generally consist of two spherical metal grids, one inside the other in a vacuum chamber. A high voltage is placed between the two grids and the fuel gas injected.[18][19]

When the gas approaches the grids it is ionized, at which point it is rapidly accelerated inward. When it passes the inner grid the electric field drops to (near) zero and the ion is left traveling through the center of the chamber at high speed. Other ions are similarly traveling inwards from all directions, so the chance of collision in the center where they are all aimed is higher. In the case they miss, the ions travel back into the area between the two grids, where they are once again circulated into the center. In this way any one ion has many chances to undergo a collision.[18][19]

There are numerous problems with this approach. 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.[19]

PolywellEdit

An attempt to avoid the grid-collision problems was made by Robert Bussard in his polywell design. This uses complex magnetic field arrangements to produce "virtual electrodes" consisting of trapped electrons. The result is to produce an accelerating field not unlike the 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 additional losses through spalled-off metal ions.[20]

The polywell does not fall prey to the issues with grid collisions, but the other considerations of energy loss mechanisms still apply. In particular, a broad consideration published by Todd Rider in 1995 suggests that any system that has non-equilibrium plasmas will suffer from rapid losses of energy due to 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.[21]

ReferencesEdit

CitationsEdit

  1. ^ a b c d e WNA 2019.
  2. ^ "The First Cyclotrons". American Institute of Physics.
  3. ^ a b Oliphant, Harteck & Rutherford 1934.
  4. ^ Tuck 1958.
  5. ^ Ruggiero 1992, p. 1.
  6. ^ Ruggiero 1992, pp. 1,2.
  7. ^ a b c d Ruggiero 1992, p. 3.
  8. ^ a b c d Ruggiero 1992, p. 4.
  9. ^ a b c Ruggiero 1992, p. 5.
  10. ^ Ruggiero 1992, p. 7.
  11. ^ Pralavorio, Corinne (13 November 2017). "The LHC's 2017 proton run has ended with record luminosity". CERN.
  12. ^ Maglich 1973, pp. 213-215.
  13. ^ Crease 1989.
  14. ^ a b Rostoker, Binderbauer & Monkhorst 1997.
  15. ^ Nevins & Carlson 1998.
  16. ^ Wong.
  17. ^ McMahon 2019.
  18. ^ a b Spangler 2013.
  19. ^ a b c Fusor.
  20. ^ NBC 2013.
  21. ^ Rider 1995.

BibliographyEdit