Colliding Beam Fusion Reactor

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Science  21 Nov 1997:
Vol. 278, Issue 5342, pp. 1419-1422
DOI: 10.1126/science.278.5342.1419


Recent results with Tokamak experiments provide insights into the problem of magnetic confinement. They demonstrate how to avoid anomalous transport and thus solve the major problems of Tokamak reactors: size, the production of 14-megaelectron volt neutrons, and maintenance. An alternate confinement system, the field-reversed configuration, confines beams of protons and boron-11. For the proton–boron-11 fusion reaction, the fusion products are all charged particles for which direct conversion is feasible and neutron flux is negligible.

For more than 40 years, research toward a fusion reactor has been pursued in most of the industrialized countries of the world. During the last 30 years, most of the resources have been focused on the Tokamak, culminating in the International Thermonuclear Experimental Reactor (ITER), which will cost about $10 billion (1). The Tokamak has been a research facility of great value, but a reactor based on this concept has three major disadvantages.

1) Magnetic confinement in such a reactor is much less effective than expected. The phenomenon of anomalous transport leads to a large minimum size for adequate confinement. This limit implies a minimum plant size of about 10 GW.

2) The deuterium-tritium fuel yields most of its fusion energy in the form of 14-MeV neutrons, which create a great deal of radioactivity. Low-activation materials have been suggested to reduce this problem, but it is not certain that they can be developed with adequate physical properties. In addition, the 14-MeV neutrons cause radiation damage to materials. The neutron flux must be less than about 2 MW m−2 for the first wall to have a reasonable lifetime. Then, massive shielding is required to protect the superconducting magnets.

3) The Tokamak is toroidal. Therefore, the construction of the coils, vacuum system, and so forth make maintenance difficult and expensive.

Alternative concepts have been proposed to solve one or more of these problems. We describe the concept of a colliding beam fusion reactor (CBFR) (2), which in principle solves the three problems of size, neutrons, and maintenance.

Minimum Reactor Size

In a Tokamak (Fig. 1), the plasma has a strong toroidal magnetic field, produced by the coils, and a poloidal field, produced by the toroidal current in the plasma. The resultant field is helical. Particles in this field, to first approximation, follow the field lines with a small radius of gyration about the field line. The collective behavior of many particles in such a plasma results in modes of oscillation that may grow, that is, instabilities. Long-wavelength oscillations must be stable or the plasma will escape magnetic confinement in a few microseconds. There are short-wavelength oscillations that cannot be stabilized because they are due to, for example, a density gradient that is fundamental for isolation of the plasma from the material walls. Such oscillations will grow and saturate to a nonlinear limit, which leads to a spectrum of fluctuations. The fluctuations are called anomalous because they are much greater than would be expected from discrete particle effects. The fluctuations lead to anomalous transport, which is a collective effect, whereas classical transport involves two-body Coulomb scattering.

Figure 1

Tokamak design and typical particle orbit.

The containment time of a plasma is τ =R 2/2D (3), whereR is the minor radius of a Tokamak plasma and Dis the diffusion coefficient. The classical value isD c =a i 2ie, wherea i is the ion gyroradius and τieis the ion-electron scattering time. The Bohm diffusion coefficient attributed to short-wavelength instabilities isD B = (1/16)a i 2Ωi, where Ωi is the ion gyrofrequency. For fusion conditions (particle density n = 1015cm−3, temperature T = 100 keV, and magnetic field B = 100 kG), D B≈ 108 D c. If Bohm diffusion prevails, R must be very large in order to have an adequate containment time for fusion. In early experiments with toroidal confinement, Bohm diffusion was consistently observed. The fusion effort would surely have been terminated were it not for the work of Artsimovich, who proved that the containment time was τ ≈ 100R 2/2D B. Recent experiments with Tokamaks suggest that τ =R 2/2D c ≈ 108 R 2/2D B is possible, in which case the minimum dimension of a reactor would be reduced from meters to centimeters. These experiments involved the injection of energetic beams (about 50 keV) in order to heat the plasma in the large Tokamak experiments (4) at Princeton, General Atomic, and the Joint European Torus in England. In addition, the Joint European Torus was used for experiments with a burning plasma in which energetic fusion products such as tritium (about 1 MeV) were followed. In all cases, energetic ions from about 100 keV to 3 MeV slowed down and diffused classically, although the containment time of the thermal plasma was anomalously short. The energetic beam ion density was about 1% of the density and 10 to 100 times the mean energy of the ions of the thermal plasma. The physical reason for the classical behavior of the energetic ions was that such ions have a large gyroradiusa i, and they average the fluctuations so that only wavelengths larger than a i cause anomalous transport. The large orbit ions are insensitive to the short-wavelength fluctuations that cause anomalous transport. This interpretation is supported by computer simulations (5). These results lead to the conjecture that if most of the ions in a plasma were energetic, classical transport (6) would prevail if long-wavelength modes were stable.

The problem is how to make such a plasma. The density of the injected beam in Tokamaks was increased. It was found that there is a threshold beam density above which the beam drives Alfvén modes in the background plasma; these long-wavelength modes cause anomalous beam transport (4). Earlier attempts to make such a plasma by injecting and trapping energetic beams also failed because of instabilities with a low threshold beam density (7). However, the field-reversed configuration (FRC) (Fig.2) was successful (8).

Figure 2

Field-reversed configuration with typical particle orbits.

Research into the FRC design started at the Naval Research Laboratories around 1960; it was also studied at Los Alamos National Laboratory (1975 to 1990), and there is a current experiment at the University of Washington. The contained particles (Fig. 2) in the FRC normally follow betatron orbits, which are typical in accelerator physics rather than plasma physics. The orbits with v θ < 0 (the diamagnetic direction) always curve toward the null surface, where the magnetic field vanishes. This result obtains for particles of different charge, mass, or energy, so that their orbits always overlap. Such overlap is important for fusion reactions to take place and would not be the case for a constant magnetic field. The drift orbits havev θ > 0 and would not be contained. They rotate in a direction opposite to the betatron orbits, and the radial magnetic field at the ends of the plasma produces a Lorentz force that expels these particles. In typical experiments at Los Alamos, the ion gyroradius was about half the plasma radius, and about half of the current was carried by energetic ions.

The FRC is surprisingly stable. Various magnetohydrodynamic (long wavelength) instabilities that had been predicted do not occur. This plasma is physically different from previously studied plasmas, which are dominated by small gyroradius particles and are described by magnetohydrodynamics (MHD). It is the starting point for the creation of a plasma with classical transport. It is already halfway there because the average gyroradius is about half the size of the plasma. Injecting and trapping beams should increase the fraction of large orbit ions because the particles are better contained. Excitation of long-wavelength modes by energetic ions is not expected, otherwise the FRC could not have been formed: There are no Alfvén waves or other MHD modes to excite.


The nuclear fuels that can be used in an FRC reactor include deuterium (D) and tritium (T)Embedded Image(1)which produce α particles and neutrons. The reactivity 〈σv〉 ≈ 8 × 10−16cm3 s−1 has a broad peak at a temperature of about 100 keV. This is the only reaction that has been considered seriously because of its large reactivity and because the fuel has atomic number Z = 1, which implies the least radiation loss. However, most of the energy is produced in 14.1-MeV neutrons, which implies that induced radioactivity will be a serious problem, and conversion of the neutron energy to electric power will involve heat management, turbines, and so forth, and an efficiency of not more than 40%.

The reactionEmbedded Image(2)producing α particles and protons, can be a considerable improvement over D-T, but the reactivity 〈σv〉 = 2 × 10−16 cm3s−1 at 200 keV is much less, and neutrons are produced by secondary D-D reactions.

The reaction of protons with boron-11Embedded Image(3)produces no radioactivity, and radioactivity from side reactions is negligible. The reactivity has a broad peak if the energy of the proton relative to 11B is 580 ± 140 keV. If the temperatures of the proton and11B beams are much less than 140 keV, the reactivity can be even greater than it is for D-T. The energy produced per reaction is half as much as that for D-T; however, direct conversion of particle energy to electric power is possible at an efficiency that is more than twice that of heat conversion. For a thermal p-11B reactor, the electromagnetic radiation energy is greater than the nuclear energy produced, and a reactor that produces net energy is possible only if the conversion efficiency is nearly 100% (9). However, by maintaining the relative energy of the protons and 11B to maximize 〈σv〉, the nuclear energy produced is much greater, and recent research indicates that this process is possible in an FRC. Preliminary designs of D-T, D-3He, and p-11B reactors have been investigated (10).


Tokamak reactors are expensive and difficult to maintain because of their toroidal design. The confined plasma in the FRC has a toroidal geometry, but the reactor is a linear system (Fig.3): All of the components can be mounted on rails and easily separated for repairs and maintenance. Therefore, such a reactor should prove to be much easier and less expensive to maintain than a Tokamak.

Figure 3

Artist's conception of 100-MW beam fusion reactor. The inverse cyclotron is indicated at the ends of the generators; the size is indicated for a 50-MW output.

Issues and Solutions

Confinement of the energy of electrons. The electron temperature must be maintained at a high level (tens of kiloelectron volts), or the proton beam slows down too rapidly. If there is significant plasma density at the first wall, electron transport of energy becomes important, reducing the electron temperature. The beam plasma equilibria that have been studied involve a reduction in plasma density at the wall of about 10 orders of magnitude compared to the peak density (10). Thus, there is a broad insulation region (a vacuum) between the plasma and the wall. In addition, the plasma has a positive charge, so that electrons are electrostatically confined by electric fields of the order of 10 kV cm−1. In a steady-state reactor, the fusion product plasma extends beyond the fuel plasma. However, the FRC configuration has a natural diverter surrounding the fuel plasma because the magnetic field lines beyond the fuel plasma are open (Fig. 2). Particles that reach the open field lines rapidly scatter out of the plasma region into the direct converter generators (Fig. 3).

Reactivity of the p-11B reaction. In order to exploit resonance in a steady-state reactor, it is necessary to maintain the proton and boron beams at an average energy difference of 580 keV. In addition, the temperatures of the beams must be substantially less than 140 keV. The proton beam is slowed down by the electrons and the boron beam. The boron beam, on the other hand, is speeded up by the proton beam and the electrons. In addition, the beam temperatures are increased because of scattering, most importantly the scattering of the proton beam by the boron beam. These kinetic effects drive the plasma toward thermal equilibrium. Nevertheless, it is possible to exploit the resonance.

It is important to adjust the fuel mix to minimize bremsstrahlung radiation and scattering because the atomic number Z of boron is 5. The fusion power density is proportional ton 1 n 2〈σv〉, where n 1 is the proton density andn 2 is the boron density. The radiation is proportional to (n 1 +Zn 2)(n 1 +Z 2 n 2). The scattering heats the proton beam. There is also a cooling effect because electrons are cooled by radiation and electrons cool the proton beam. This effect is well known in accelerator physics (11). The term most sensitive to n 2/n 1 is 〈σv〉, which depends strongly on the proton beam temperature. For example ifn 2/n 1 is about 0.0025 andn 1 ≈ 4 × 1015cm−3, the temperature is T e ≈ 20 keV for electrons and T 1 ≈ 25 keV for protons. Then, 〈σv〉 ≈ 8 × 10−16cm3 s−1, the same as the maximum reactivity for a D-T thermal reactor.

It is also necessary to maintain the average values of azimuthal beam velocities v θ = v 1(for protons) and v θ =v 2 (for boron) so that (1/2)m 1(v 1v 2)2 = 580 keV. In addition to the fuel plasma, it is necessary to consider the fusion product plasma, which consists of selectively confined α particles (12). Particles with v θ < 0 (Fig. 2) are confined and particles with v θ > 0 are released promptly, so that the confined α particles carry a current comparable to the current of the fuel plasma. In addition, the contained α particles have angular momentum. There can be a significant transfer of momentum to the protons by means of collisions, which keep them from slowing down. Fine-tuning can be accomplished by continuously injecting the fuel protons at an energy that is larger or smaller than the design energy. It is more difficult to keep the boron from speeding up as a result of collisions with the protons and α particles. This problem can be prevented by injecting low-energy protons, which couple strongly with the boron but not with the high-energy particles. This process requires only a low density of low-energy protons, so that the investment is trivial. The low-energy protons would be subject to anomalous transport, so that they would not be contained long enough to increase their energy significantly by collision processes (13). If we assume that v 1 andv 2 are constant, electron-ion collisions will affect the azimuthal electron velocity v e and therefore the current, bremsstrahlung, and other parameters. In a steady state, the electron velocity will reach a compromise betweenv 1 and v 2, that is,v e = (n 1 v 1 +n 2 Z 2 v 2)/(n 1+ n 2 Z 2), which will be closer to v 1. This effect reduces the net current and the energy transfer from fuel protons to electrons. The net current is called the Ohkawa current (12, 13).

Energy extraction. Direct converters involving collector plates (14) and venetian blinds are not suitable for fusion product ions with energies above 1 MeV. Several types of inverse accelerators have been studied for the high-energy ions.

In the conceptual design of the D-3He reactor “Artemis,” a traveling-wave direct converter (15) for 14-MeV protons was designed with an efficiency of 75%. The device is 30 m long. Peniotron and Gyrotron converters (16) guide fusion product ions into a microwave cavity to generate 155-MHz microwaves; rectifying antennas produce a dc output. Efficiency as high as 90% is projected. The cavity dimensions are 1.5 m by 1.5 m by 10 m, and a magnetic field of 102 kG is involved.

We have proposed an inverse cyclotron (13, 17) that operates at a lower frequency (about 5 MHz) and requires a much smaller magnetic field (about 6 kG) (Fig. 3). The linear motion of fusion product ions is converted to circular motion by a magnetic cusp. The circular motion makes the device much shorter than a linear device. Collectors are also used for particles with energy less than 1 MeV.

Energy balance. The quantity Q, the ratio of fusion power to radiation loss, is important in determining the feasibility of a reactor. Estimates (10) for the CBFR areQ = 35 for D-T, 3 for D-3He, and 2.7 for p-11B (18). Spin polarization of the fuel would (13) increase Q for the p-11B reactor to 4.3, and a further increase may result from the nuclear quadrupole moment (19) of 11B. The design of a 100-MW (electric) reactor (13) has been considered on the basis ofQ = 4.3 by assuming a converter efficiency of 0.9 for α particles, 0.4 for radiation, and 0.7 for accelerators. The coils are assumed to be superconducting and to sustain magnetic fields of about 100 kG. The dimensions of Fig. 3 are based on these calculations.


The main emphasis of fusion research to date has been on the D-T Tokamak because of the large value of Q. Such a value makes the design of such a reactor much easier and much less dependent on exotic technologies. From this research has come most of the considerable body of knowledge required for fusion reactors, including the behavior of beams, which forms the basis of our present research. The purpose of this article has been to indicate another option for fusion reactor development, based on the p-11B reaction. In the light of recent discoveries about the classical behavior of high-energy particles (4), the p-11B reactor seems possible and has many engineering advantages concerning size, radioactivity, and maintenance.


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