DIRD Inertial Electrostatic Confinement Fusion

Inertial Electrostatic Confinement Fusion

Defense Intelligence Reference Document, Acquisition Threat Support. DIA-08-1003-006, 10 March 2010 (ICOD: 1 December 2009).

Prepared by the Defense Intelligence Agency. This product is one in a series of advanced technology reports produced in FY 2009 under the Defense Intelligence Agency Advanced Aerospace Weapon System Applications (AAWSA) Program.

Copyright warning: further dissemination of the photographs in the original publication is not authorized.

Preface

This report is intended to provide the reader with an overview of the basics, current experimental status, supporting theory, and potential applications of inertial electrostatic confinement (IEC) fusion. Emphasis is placed on work in these areas at the University of Illinois Urbana-Champaign, although some other research is brought in.

The report shows that IEC is a unique approach to fusion in that it offers a number of spin-off applications, such as a small neutron source for neutron activation analysis on the route to fusion power. The report further shows that IEC is one of the few potential fusion approaches that can potentially burn aneutronic fuels like proton-boron-11. In aneutronic fusion, neutrons carry no more than 1 percent of the total released energy, greatly reducing problems associated with neutron radiation. That ability, combined with its simple mechanical structure and small size, make the IEC reactor, if achieved, an ideal fusion power unit.

Present experimental devices are four to five orders of magnitude below breakeven — energy out over energy in equal to 1 — energy gain for proton-boron-11. However, it is argued that the ability to study the physics in very-small-volume plasmas makes it possible to rapidly investigate scale-up to a power-producing device. As an example, the report concludes with a conceptual experiment proposed for demonstration of breakeven conditions for proton-boron-11 using a hydrogen plasma simulation.

The author has purposely tried to avoid use of equations in this report to enhance readability and to stress concepts rather than analysis. However, considerable analysis is provided in a number of the source references cited.

Section I. IEC Background and Basics

Before considering detail, it is helpful to obtain a rough idea of how inertial electrostatic confinement fusion works.

Figure 1.1 shows a University of Illinois spherical IEC: a spherical vacuum chamber with a gas feed line, a grid on a high-voltage feedthrough, a vacuum pump and a high-voltage power supply. The plasma discharge between the grid and the vacuum wall creates an ion source that is extracted and directed towards the center by the highly charged negative grid. A photograph of the discharge through the view port shows the star mode discharge where ion beams are created that pass through the grid openings. This is important for long run times since ion bombardment of the grids, hence grid wire sputtering, is minimized.

This gridded type IEC has a spherical mesh grid suspended on a high voltage feedthrough in the center of a metal vacuum vessel. The fusion fuel, for example deuterium gas, is first fed into the chamber, originally prepared at high vacuum of about 10⁻⁷ torr. The fuel gas brings the pressure up into the tens of millitorr region. Then the voltage on the grid is raised into the many negative kilovolt range, creating a plasma discharge between the high voltage grid and the electrically grounded chamber wall. The high negative voltage on the grid serves to extract the ions from the plasma, accelerating them towards the center of the grid where in principle they interact and fuse.

In practice, however, the scattering cross section is larger than the fusion cross section. Thus many ions scatter without reacting. Many near misses essentially pass straight through the center of the plasma core and exit. This dominance of scattering over fusion reactions is the central issue of all fusion confinement approaches, forcing use of strong confinement so the ions have many passes and hence a good probability of fusing before being lost from the fusion reaction chamber.

In the IEC, multiple passes occur because the ions are trapped in a potential well created by the buildup of positive charge due to the large flow of the accelerated ions into a small core region in the center of the negative grid. Viewed in another way, the ions extracted from the region between the grid and the wall can scatter and pass back through the grid, but can only return to the same potential surface they were born on. Thus they cannot reach the vessel wall, but instead lose their kinetic energy, stop, and are accelerated by the grid potential back into the center of the grid. This then provides many recirculations through the center of the grid volume where they have a finite probability of fusing. If not for the existence of various loss channels such as hitting the grid, charge exchange, or up-scattering in energy, the ions would be trapped in the potential well until they fused.

The conventional requirement for fusion confinement is given in terms of the confinement parameter, the ion density times the confinement time. Also the ion energy must be in the 20 or more keV range assuming deuterium-tritium fuel. For breakeven, J. Lawson developed his famous criterion: a density-time product of 10¹⁴ per cm³ per second at a temperature above 15 keV for deuterium-tritium fusion.

The Lawson criterion is independent of the confinement method, but does depend on the fuel via the selection of cross sections in the derivation. Magnetic confinement is generally limited to a density of about 10¹⁴ per cm³ by pressure balance; then a confinement time of about 1 second is required. For inertial confinement fusion, or laser fusion, compression of targets can achieve about 10²⁴ per cm³, so a confinement time of only 10⁻¹⁰ seconds is needed, corresponding to the disassembly time of the compressed target.

Now consider the IEC. In principle, the ions focused on the center of the IEC can achieve a density of about 10¹⁶, giving a required confinement time of 10⁻² seconds for deuterium-tritium breakeven. This time can be restated in terms of the number of ion recirculations in the IEC potential well by dividing the well diameter by the average velocity of the recirculating ion. In later cases discussed in this report, this number is typically quite large, usually about 1,000 recirculations. Achievement of this large number of recirculations requires strong reduction of all of the loss channels noted earlier. Grid losses can be reduced by star mode operation, discussed later, where the recirculating ions possess beam-like trajectories passing through the center of the grid opening. The ideal, however, is the elimination of the grid altogether, which can be done via formation of virtual potential structures, originally proposed by Farnsworth.

The temperature requirement also leads to a fundamental difference in the IEC physics versus other confinement approaches. Note that temperature is not a proper term here, since it implies an equilibrium distribution while the IEC is far from that with its beam-like ions; the reader should view temperature as meaning average energy of the ions. Most ions in the IEC are born near the chamber wall, so are accelerated to an energy close to the applied voltage on the grid during the extraction process. A reasonable estimate is that the ions reaching the fusion region in the center have an energy near 80 percent of the grid voltage on average. Thus it becomes relatively easy to achieve the Lawson deuterium-tritium requirement by applying a voltage of about 25 kV. In fact most IEC neutron sources discussed later operate at voltages above 80 kV to get into an energy range giving a higher fusion cross section. In sharp contrast, magnetic fusion devices struggle to obtain a temperature in the 10 keV range since the entire plasma population must be heated, versus direct ion acceleration in the IEC, due to the equilibrium distribution maintained in these plasmas.

Another very important point is that Lawson assumed that the ions and electrons were in thermal equilibrium, at the same temperature. This is a reasonable approximation for magnetic confinement, but not so for the IEC. In the latter, the electrons form a distorted Maxwellian distribution at an effective temperature well below that of the beam-like ions. Since electron energy loss processes such as radiation emission are serious, the Lawson temperature criterion must be modified for the IEC. A first rough estimate is that the electron-to-ion temperature ratio must be under one third for deuterium-tritium.

In later sections use of proton-boron-11 fuel in the IEC is considered. This is very attractive since it provides all charged particle reaction products, making this a unique aneutronic system. Such a reactor represents a truly ideal system from an environmental and energy sustainability perspective. However, for such fuels, the Lawson criterion becomes much more demanding, increasing the density-time product by two orders of magnitude and the energy to 150 kV. Also, for the IEC, an electron-to-ion temperature ratio under one ninth becomes essential.

(A paragraph here qualifying the temperature ratio is omitted for length: radiation losses are quite sensitive to deviations in the actual energy distributions, since electron bremsstrahlung comes primarily from the high energy tail of the electron distribution while energy transfer with ions is dominated by its foot, so at high powers these regions can burn out and the losses saturate — beneficial, but complex to evaluate numerically and little reported for IECs to date. The complete text is at the source.)

IEC Background

Inertial electrostatic confinement was conceived of by Philo Farnsworth, the inventor of electronic television, as an approach to fusion power using electrostatic fields for confinement. When he did this in 1955, the prime approaches being pursued worldwide were magnetic confinement or inertial, laser-compression, confinement. Electrostatic confinement had in fact been written off by most scientists due to Earnshaw’s theorem, which stated that plasma could not be confined by electrostatic fields alone — an expression of the fact that a biased plate used to confine one species would automatically attract the other, so that the whole plasma would transport to the plate. Farnsworth seemed to intuitively understand that this theorem assumed steady state, so that if, as in the IEC, the ions were dynamically moving and confined, they would electrostatically confine the electrons. He went further and realized that in a spherical system virtual electrodes would form a high density plasma region if the confined ions were focused at the center of the sphere.

While Hirsch worked with Farnsworth to demonstrate early experimental success with IEC experiments, the concept passed from view as magnetic and inertial confinement research exponentiated. Then in the late 1990s R. W. Bussard revived the concept with the hybrid IEC magnetic approach. In this approach the electrons were confined in the magnetic field, forming a potential trap for ions. Upon invitation by Bussard to join this effort, the author, George Miley, undertook supporting experiments that were a variation of the original Hirsch approach, using electrostatic grids to form a trap with ions that then brought electrons in. He realized that this approach could result in a very attractive low level neutron source for neutron activation applications, and began that development. Such work was soon taken up in several other laboratories, including Los Alamos National Laboratory, the University of Wisconsin and Kyoto University.

Meanwhile Bussard’s work continued with strong funding from the military. However, little was published or known about this until 2008 when he made public appeals to regain funding stopped just when the experiment achieved a major success. Subsequently, funding resumed but Bussard passed away shortly thereafter due to a long battle with cancer. His company and work were then taken over by R. Nebel, who took leave from Los Alamos to undertake this new work. That effort is now in progress and represents the largest IEC power-oriented project in the US or elsewhere, but still modest with a half dozen senior scientists involved. Meanwhile, laboratories elsewhere working on IEC neutron sources have continued, while the University of Wisconsin has added an IEC proton source as an option using similar technology. The labs, including Illinois, have fusion power as an ultimate goal, but must focus on their funded near-term spin-off projects.

At this point the IEC still receives no funding from the Department of Energy, which remains focused on the tokamak route to fusion power. Thus, with little funding, slow progress has been made in answering the key question of whether or not the IEC can be developed for fusion power. If it can, the device would be simpler and smaller than a tokamak, making it an extremely attractive option. In addition, its beam-like reactions, highly non-Maxwellian, make the IEC very well suited for burning alternate — advanced — fuels like deuterium-helium-3 and proton-boron-11, which are much more environmentally favorable than conventional deuterium-tritium fusion. Unfortunately tokamaks are not well equipped to go forward to such fuels.

On the other hand, the use of non-power-producing IECs for other applications, such as small neutron, proton, and x-ray sources, has been amply demonstrated. Now, the issue is how well and in what applications the IEC sources compete commercially with other options such as accelerator target sources.

One other limitation of this report is that it largely provides details based on the author’s work on IECs over the last decade. Thus it will not do justice to the ongoing work by others, notably at EMC2 on the Bussard Polywell device or the advanced gridded IEC neutron and proton source development work at the University of Wisconsin, Kyoto University, and the Tokyo Institute of Technology.

IEC Basics

We begin by presenting the early very basic theoretical study by Elmore, Tuck, and Watson. That addresses the key question of the fusion power density obtainable with potential well confinement. One of their basic assumptions is that the potential well is dug by electrons which trap ions. Certain added assumptions lead to well depth, and finally they conclude that the system is unstable for ion densities sufficiently high that appreciable thermonuclear yield is expected. They qualify this conclusion saying that admittedly, a more thorough investigation is required to obtain a complete understanding of stability of this electrostatic device.

This result was quite negative for electron formation of potential wells, but left the route possibly open since the subject needed a more thorough investigation. Later, for various reasons, Bussard still pursued this concept by introducing the High-Energy Power Source, or Polywell, device, which uses a spherical simulated magnetic field to stabilize the potential well formed by electrons. This represents a hybrid magnetic-IEC confinement system where electrons are confined by the magnetic fields, forming the potential well which traps ions. Apparently, Bussard’s view was that this added magnetic stabilization would overcome the earlier Elmore and Tuck criticism. Subsequently, some of his reports used particle-in-cell simulations to support the view that such a stabilized electron potential well would allow adequate density for attractive fusion densities.

However, the next IEC experiments following the Elmore analysis, prior to Bussard’s, were the Hirsch-Farnsworth experiments, which used ion-injected rather than electron-injected traps, as does the present author’s work. This selection was largely driven by the desire to gain added stability by the large momentum of recirculating ions that form the potential well. Next, it is important to review the multiple well — poissors — solution Farnsworth and Hirsch found for ion-injected formation of potential wells in spherical geometry.

Figure 1.2 shows the idealized potential structure calculated by Hirsch for monoenergetic ions with no angular momentum. The nested virtual anodes and cathodes observed were originally termed poissors by the inventor, Philo Farnsworth. As seen from it, monoenergetic ions with angular momentum drag in electrons to create onion-skin-like nested potential wells around the center of the sphere such that the ion density goes to infinity in zero volume at the origin.

This is a very striking result that enthused these researchers to push on with this research. It in effect circumvents the Elmore restriction by changing the potential well physics fundamentally. Of course in practice there will be a spread in energy and angular momentum, so one would not expect more than a single potential well to form in practice. The questions remaining then were, and still are: how deep can such a well be in practice, and how high an ion density can be trapped in it?

Various studies followed, using simulation codes. Klevens and Black developed a model of an electrostatic confinement device with ion injection that correlates well with experiment, determining the ion density profile in position and velocity throughout two concentric grids by accounting for charge transfer and grid capture. Their ion distribution function had three parts: a beam created at the anode and accelerated by the applied cathode voltage, a low-energy group produced by charge transfer near the cathode or in the center, and an intermediate group from charge transfer between anode and cathode; the electrons were taken as isotropic in velocity space and uniform in total energy within the well. Substituting these into Poisson’s equation, the resulting potential profile exhibited no more than a shallow potential well — a result consistent with beam deflection measurements in the ion injection mode experiments.

It has been found that for the medium level of ion currents under discussion, the most critical factors which inhibit deep well formation are inadequate spherical focusing and charge neutralization. The focusing is determined to a great extent by the degree to which the grids are spherical potential surfaces. The grid must approach a spherical shape within a few percent before other factors such as grid transparency and background pressure play an important role. However, as the current is increased, the requirements for sphericity are somewhat relaxed. For a grid construction error of less than 5 percent, increasing the grid transparency and decreasing the pressure will also lead to significant improvement in well depth.

These results were somewhat encouraging. However, they showed that grid deformation could be very harmful. The present author later showed that design of grids with larger openings provided the star mode, where ion beams passed through the center of the openings, avoiding grid collisions and making sphericity of the grid itself less important. This is important for small neutron and proton source type devices. However, the assumption of grids fails to address the question of how a grid could survive in a power reactor, or whether grids could be eliminated to use a potential well with virtual electrode formation. The use of grids cannot be completely ruled out for power reactors: magnetic field protection techniques, active cooling and so on are conceivable.

Another question relates to the role of background gas in the IEC. When Miley moved to simplify the device for small neutron sources, he used the discharge between the grid and vessel to form the ions needed for acceleration and fusion. This inherently forces use of a modest background neutral gas pressure of the fuel, typically deuterium, inside the reaction vessel. That in turn results in ion reactions with the background gas becoming a dominant process. Such interactions include fusion itself, scattering and charge exchange. This greatly changes the plasma physics of the IEC as opposed to the ideal of a potential well with zero background pressure.

Some key differences were brought out by Tim Thorson in his experimental study. He noted that in present gridded systems convergence is not important, since beam-target fusion reactions dominate the reactivity — as evidenced by the linear scaling of reactivity with cathode current — and convergence may even reduce reactivity by forming a virtual anode that limits the central ion density, though this space charge effect can be overcome by proper introduction of electrons. Good convergence is required to achieve optimal beam-beam reactivity scaling for applications needing higher fusion rates, and the importance of symmetry in determining convergence constrains any spherical device planned for them. The observed loss of convergence with decreasing pressure and increasing current makes achieving significant beam-beam scaling far less favorable. He also pointed out the importance of energetic ions undergoing charge exchange and being lost from the system.

In addition to the issue of beam-background fusion dominating in the gridded systems at higher pressures, Thorson pointed out the importance of energetic ions undergoing charge exchange and being lost from the system. These problems are best understood by considering beam-background versus beam-beam fusion scaling. The former scales as the beam density times the background density, hence as beam density times pressure, while beam-beam fusion goes as the square of the beam density.

If ions are produced, as done in most small gridded experiments, by electron ionization collisions with neutral gas during a plasma discharge between the grid and vacuum vessel wall, reduction of background gas pressure will also reduce the ion source, reducing the reaction rate. Thus it becomes apparent that to get the favorable beam-beam scaling needed to go into the power reactor regime, ions must be produced externally while the main reaction chamber is kept at very low background pressure to avoid charge exchange losses. Indeed, without explaining that this was the reason, Hirsch used external ion guns in his early experiments at Farnsworth labs. The present author, however, went back to the internal discharge ion source technique to simplify the device for portable neutron source applications. Power devices will need to go back to external production of some type.

While earlier workers sought small grid openings designed to provide uniform ion flows for good core plasma convergence, Miley disclosed that the star mode could be produced with wider grid openings. In fact, three key modes can be formed in gridded IECs depending on the pressure and grid openings — star, central spot, and halo. These names are quite descriptive of the visual appearances of the visible light emitted from the discharges. All three modes are reproducible and stable; each is associated with a different potential well structure, hence neutron production rate.

The star mode is distinguished by microchannels or spokes radiating outward from a bright center spot. As verified by magnetic deflection experiments, the spokes are primarily composed of ion beams aligned so that they pass through the center of the openings delineated by the grid wires. This mode is very efficient for neutron production, since the large effective grid transparency allows numerous passes of ions through the center spot before being intercepted by the grid or lost by charge exchange. The star mode is typically obtained at lower operating pressures, under 10 millitorr, and higher voltages, above 30 kV, using a carefully formed grid with good sphericity and high transparency above 95 percent. The halo, or jet, mode occurs when one of the grid openings is slightly enlarged compared to the others.

Figure 1.3 illustrates the discharge modes in gridded devices identified by Miley; Figure 1.4 is a photograph of the star mode seen through a reaction vessel port window.

In summary, the basic IEC approach is to create a potential well through electrostatic confinement of one of the plasma species in a dynamic, inertial configuration. Inertial effects associated with dynamic motion of the confined species are essential to avoid the plasma losses predicted by Earnshaw. The two primary approaches can be termed ion injected or electron injected, the injected species being the one forming the potential well. In order to maintain the well, the second species brought in with the injected one must not completely neutralize the plasma; that is, the IEC plasma is inherently quasi-neutral. This well then provides trapping and convergence of the ions streaming towards the center of the trap region, forming a dense fusing plasma there.

For a power reactor the objective is to obtain ion beam-beam collisions in this central core. For neutron and proton production, satisfactory reaction rates can come from beam-background collisions. However, this scaling with injected current would require excessive input power for a practical power-producing unit. Thus beam-beam scaling of the reaction rate as the current squared, or higher powers as noted earlier due to nonlinear effects, is essential. The vision of a power reactor seeks a zero background pressure, thus generally involves an external ion source with acceleration into the trap at ultra low pressure to obtain beam-beam collisions. The issue of whether the trap should be formed by ion injection or by digging a well with electrons remains open, but involves stability and reaction volume optimization issues.

Bussard HEPS (or Polywell) Concept

In Bussard’s Polywell IEC, a spherical magnetic field termed a Polywell is approximately obtained with a multi-pole cusp magnetic field. One of the key physics questions revolves around electron losses from the poles in the cusp field. Krall and Bussard argue that a plasma waffle-ball effect causes the loss cone angle to be reduced due to the high pressure developed in the IEC plasma. The issue still needs further experimental verification. The Polywell approach is very important and is currently pursued by R. Nebel’s EMC2 company in Santa Fe with significant Department of Defense funding.

Barnes-Nebel Penning Trap

The Penning fusion device confines a nonneutral electron plasma in a modified Penning trap by a combination of applied magnetostatic and electrostatic fields; the electron space charge in turn electrostatically confines a minority, unmagnetized ion species. To apply this to fusion energy production the applied voltages must reach 100 kV or more, and even then, in a practically sized system, the electron density — and to a greater degree the ion density — falls short of that required for reasonable fusion reactivity. Ion focusing, in space or in time, is therefore intrinsic to the concept being interesting.

Penning fusion is strongly related to the IEC but attempts to address two of its limitations. Following the Bussard-Krall theory, the grid is replaced by an electron cloud forming a virtual cathode, avoiding ion-grid collisions, secondary electron emission and grid heating. And high rates of ion-ion collisions, which limit the theoretically achievable gain to around unity, are avoided to some extent with this type of well. However, electron loss and cone losses, radiation damage of the magnets and cooling, and the ability to circumvent the Elmore density limit remain as questions.

Nebel POPS Device

Theoretical studies by Barnes and Nebel show that a small internal oscillating ion cloud may undergo a self-similar collapse in a harmonic oscillator potential formed by a uniform electron background. This then forms a dynamic IEC device, but with a quite different ion distribution function versus the conventional beam-like one. A key issue for this Periodically Oscillating Plasma Sphere concept is how much plasma compression can be achieved by the oscillations. Recent work has shown that by properly programming the distribution function of the injected electrons it is possible to significantly improve the space dynamic charge neutralization and the plasma compression. Results indicate that although the formalism works well during the early phases of compression, when the compression gets large the solution bifurcates and becomes unphysical. Subsequent experiments at Lawrence Livermore National Laboratory were encouraging, but have not been continued at a high level of effort due to key staff leaving for EMC2. Thus, the practicality of this concept remains an open question which deserves more research.

Miley’s Ion-Injected Device

The key to developing an IEC power device is to use external ion guns to form and inject ions into the spherical IEC chamber. This eliminates the need for a grid, and differential pumping between the gun and chamber allows the high vacuum needed in the chamber. The ion formation is done in the high pressure gun discharge region outside of the chamber. Miley at Illinois has been studying such a system both theoretically and experimentally. The theoretical studies confirm that such an IEC plasma can exist stably and has sufficient confinement time for aneutronic fusion. This assumes, however, that very precise control is maintained over the energy and angular momentum of injected ions and a balanced supply of electrons is provided. A radio-frequency ion injector, or gun, capable of such operation has already been developed.

Figure 1.5 is a schematic of the Illinois radio-frequency gun injector: a magnetic focusing lens, a coaxial copper resonator, a helical antenna and glass tube driven by a radio-frequency generator, magnetic differential coils, a deuterium gas feed, and an ion beam extracted at negative potential into the positively charged wall of the vacuum chamber. Figure 1.6 shows the gun attached to an IEC chamber in the Illinois laboratory, and Figure 1.7 a photograph of center spot formation, in which the main beam observed is a direct path along the injector angle and other faint light channels indicate beams scattered from the central core region.

In this radio-frequency gun, a graded index magnetic field is used to increase the ionization efficiency. A key component is the magnetic focusing lens at the extraction port. This allows very efficient differential pumping between the high pressure gun chamber and the low pressure IEC chamber. It also provides some control of the angular velocity of entering ions.

These studies did include differential pumping, so that the number of recirculating passes by an ion was very low, roughly 2. The injected ion current was about 50 mA. Still, based on measurements of neutrons emitted using deuterium fuel, the gain — fusion energy out over energy in — was remarkable for such a small device, of order 10⁻⁶. Based on these results, an aggressive proton-boron-11 breakeven experiment using this type of IEC is discussed in Section VI.

Closing Remarks

As seen, a wealth of information has been developed in studies of gridded IEC devices. However, the beam-background fusion used in these devices involves important differences in physics compared to what is needed for future beam-beam IEC reactors. Most notable is the need to maintain an extremely low background pressure to prevent interactions with background neutrals. Further, physical grids are subject to damage at high power levels. Some studies show grids can survive at modest powers. But for aggressive power units such as the proton-boron-11 plant of Section VI, they must be replaced with virtual electrode surfaces creating a deep potential well for ion confinement. Up-scattering out of the well must be minimized while electron temperatures are suppressed.

Section II. Select Experiments

In this section some select experiments are briefly reviewed with the main focus on ion-injected IECs, beginning with the early Hirsch gun-injected experiments that are important both historically and from a physics perspective.

Hirsch disclosed experimental results with very high deuterium-tritium neutron rates from an ion-injected IEC. Six ion guns were used to create a low energy ion beam that entered the chamber and was trapped via electrostatic structures to form the potential well structure desired for IEC operation. However, differential pumping was not used, so beam-background and charge-exchange collisions must have still played a significant role. Still, Hirsch obtained record neutron rates for deuterium-tritium fusion.

Figure 2.1 shows the historic early IEC ion injection experiment of R. Hirsch working with Philo Farnsworth. Figure 2.2 shows that neutron rates measured with it exceeded 10⁹ deuterium-tritium neutrons per second at 150 kV. For perspective, Illinois gridded devices routinely produce about 10⁸ deuterium-deuterium neutrons per second at 80 kV — slightly above Hirsch’s result, but using higher ion currents.

The key point about this remarkable result is that the neutron production rates are well above that predicted by simple beam-background fusion reactions, implying that benefit was obtained from recirculating beam-beam reactions in a potential well. Indeed, to further confirm the existence of a potential well, Hirsch did both collimated neutron and gamma measurements, and found structure for both consistent with well formation. One possible explanation is that the ion-electron densities obtained were high enough to burn out — completely ionize — the background neutrals in the potential well. There is no direct evidence to support this view, however.

These important results have never been fully explained. Attempts to reproduce them by Gardner and co-workers at Brigham Young University, using Hirsch’s original device, gave significantly lower neutron production, which they attributed to a failure to regain the gun alignment necessary for a highly converged plasma core.

(A passage here on ion injection is omitted for length: that the terms injector and gun are misleading — the objective is simply to flow low energy ions into the device so that they are then accelerated to fusion energies by the grid or the virtual electrode structure, which requires a loss of excess energy after injection so the ion does not pass straight through the well and strike the opposite wall. How best to introduce ions so that their energy falls below the escape energy is a key design question. The complete text is at the source.)

(A group of subsections here is omitted for length: the star-mode discharge photograph and the defocusing optics of open grid structures; the use of Marx-bank pulsed power to reach peak currents of tens of amps and exploit the current-squared scaling of beam-beam fusion; the metallic getter developed with Robert Anderl at the Idaho National Engineering and Environmental Laboratory, which replaced external pumping and allowed a sealed unit — technology Daimler-Chrysler licensed through Illinois and used in Germany on ore delivery belts for neutron activation analysis, directly replacing californium-252 sources and allowing on-off operation, simpler licensing and lower costs; the Kyoto University crane-mounted landmine detection project with its hybrid magnetron ion source; and the University of Wisconsin helium-3 helicon ion source producing steady-state ion currents of 10 mA into IEC systems at background pressures as low as 200 microtorr. The complete text is at the source.)

Closing Comments

The experiments selected for this section are far from exhaustive. They were selected to explain some issues and status relative to gridded devices for near-term applications such as neutron sources, and also to address some issues such as ion injection related to future fusion power units. The latter issues revolve around how to create deep potential wells in the IEC and trap the reacting ions in the well while excluding neutral gas atoms. The use of external ion sources with differential pumping then becomes a key approach for production of ions while keeping ultra low background pressure in the reacting chamber. However, introduction of the source into the configuration such that the ions are born at potentials below the well depth is another possibility, as shown by the hybrid magnetron source work in Japan. Another point noted is the advantage of using pulsed operation to obtain high peak ion currents to take advantage of the ion density squared scaling for beam-beam reactions.

Section III. Other Geometries

A unique feature of the IEC is the ability to vary its geometry to adapt to a number of important near-term and future applications. Here we consider cylindrical IEC geometries, the IEC jet extraction geometry, the dipole-assisted device, and the magnetically-coupled IEC unit.

Cylindrical IECs

The prime alternate geometry studied is cylindrical. Developed at Illinois and since taken up at the University of Wisconsin, Kyoto University and the Tokyo Institute of Technology, its objective is a dense core region extending along the axis — valuable for neutron sources because it offers a long source covering a large object such as a shipping container, at the cost of high input power. It is not clear the cylinder is useful for a power reactor: as a two-dimensional version of the spherical unit, its beam convergence and hence core density are lower. Two types have been studied — a gridded version, essentially the spherical unit converted into a cylinder, and a hollow cathode design with an alternating series of hollow cylindrical cathodes and anodes along a common axis and biased end plates as particle reflectors. The latter produces about 10⁷ deuterium-deuterium neutrons per second in steady state and 10⁹ per second pulsed.

Electrically-Driven IEC Jet Thruster

The use of an IEC design for space propulsion was originally proposed by Bussard. Here we discuss a near-term electrically driven IEC designed for space applications, with electrical power coming from a solar panel.

The IEC jet thruster is intended as an ultra-maneuverable space thruster for satellite and small probe operations, covering a wide range of powers from a few watts to kilowatts with good efficiency, while providing a plasma jet that can start with a large diameter but be narrowed directionally to focus on targets. Ions are generated and accelerated towards the center of a spherical vacuum chamber; a virtual cathode forms in the high-density central core, and combined with a locally distorted cathode grid potential field it extracts accelerated ions into an intense quasi-neutral ion jet.

A plasma jet is extracted from the gridded spherical device simply by enlarging one grid opening, which distorts the potential surfaces. The local gradient initiates electron flow that in turn drags ions out across the surface, forming an intense space-charge-neutralized ion beam directed outward from the central core. Such operation has been routinely obtained in laboratory devices under steady state, with the jet maintained for hours. The power carried by the jet has been demonstrated by heating a target plate placed in its path: with a device drawing about 2 kW of input power, over 1.5 kW is carried out by the jet flow, and no major losses of ions to the vacuum chamber wall or grid are observed.

Both experimental data and particle-in-cell simulations show that the energetic ions can be maintained in microchannels for hundreds of passes, while the jet opening allows escape in less than ten passes; consequently more than 95 percent of the ions escape at full energy. Thus the star-jet provides a very good method to both store and direct the energetic ions. Against a conventional planar ion thruster, the advantages are much more open grid structures — which with microchannel focusing prevent ion-grid collisions and greatly reduce grid erosion — a more compact unit per unit ion source volume, and reduced neutral propellant leakage.

(Two subsections here are omitted for length: the detailed jet extraction electrostatics — the trough cut in the potential profile, the insulated channel grid, the servo-hinged grid axis and bias control of jet focus — and the experimental jet design, a 30 cm chamber with an 8 cm tungsten or tantalum grid of about 90 percent transparency, a 1 cm extraction port and xenon propellant. The complete text is at the source.)

Table 3.1. Estimated performance parameters of the IEC ion thruster

| Parameter | IEC ion thruster | |---|---| | Propellant | Xenon | | Molecular weight (amu) | 131.3 | | Specific impulse (s) | 3000 | | Thrust (mN) | 34 | | Jet power (W) | 500 | | Net accelerating potential (V) | 600 | | Beam current (mA) | 832 | | Power loss to grid (W) | 50 or less | | Power loss to bremsstrahlung radiation (W) | under 1 | | Power loss to ionization of propellant (W) | 200-250 | | Input power (W) | 750-800 | | Thruster efficiency (percent) | 62-68 |

In summary, the power efficiency of the IEC thruster appears to be competitive with existing ion thrusters. The advantages are a more compact design, a large heat rejection area, an exhaust jet closer to quasi-neutrality, reduced neutral propellant leakage, and reduced grid erosion.

Scale-up to a Proton-Boron-11 Space Power Unit and Thruster

The electrically driven IEC jet thruster provides an important data base for a next-step proton-boron-11 jet thruster. Jumping to that fuel for this application may appear overly ambitious. However, neutronless fusion seems essential in a small space thruster to avoid excessive weight from shielding of electronics. Considerable experience with fusing plasmas in IECs has been gained through development of deuterium-deuterium neutron sources. These devices operate with about 80 keV deuterium ion beams, using the non-Maxwellian character of the IEC. This important characteristic makes use of proton-boron-11 a realistic goal. In fact, operation with circulating ion energies at the desired 150 keV energy for proton-boron-11 has already been achieved at Illinois and several other laboratories working on IECs. The issue then is how to achieve adequate confinement times. The approach being pursued at Illinois is the formation of deep potential wells with angular ion injection using a differentially pumped radio-frequency ion gun.

The Dipole Assisted IEC

The dipole assisted IEC places a dipole magnet in the center of two hemispherical grids. First proposed by Miley and under investigation at Illinois, it is closely related to the levitated dipole reactor but much simpler, being smaller and not requiring levitation. Two ion sources inject 40 keV deuterium and helium-3 ion beams toward the center of the dipole magnet; the magnetic field compresses the beams by trapping ions along the field lines, so they fuse within the dipole. The products of the deuterium-helium-3 reaction are 14.7 MeV protons and 4 MeV alpha particles, which can be used for direct charged particle propulsion or direct conversion to electricity. Since the magnetic field does not close at the nozzle but is open, the exhausted particles are not required to be neutralized.

By applying the desired voltage to the cathode grid, high-energy ions are easily obtained, so fusion is dominated by beam-beam, non-Maxwellian reactions, and the dipole field traps and compresses ions within its inner radius so that very high ion density can be achieved. Biasing the dipole magnet to the same potential as the cathode grid solves the problem of space charge build-up. Experiments at Illinois using two split spherical grids have confirmed an order of magnitude density increase in the center region compared with no dipole present; measured against magnetic field strength, the electron density increases about 17 times more than in the non-magnetic-field measurement, very close to the theoretical estimates.

Khachan’s Studies at the University of Sydney

Joe Khachan’s research at the University of Sydney has stressed optical emission spectroscopy of gridded devices. Using Doppler spectroscopy of the hydrogen alpha line, his group showed that the microchannels in a discharge at tens of millitorr and below 30 kV are mostly molecular ions with approximately 20 percent atomic hydrogen, and developed a collisional radiative model to measure ion densities and electron energies and predict fusion rates from a hydrogen discharge — which removes the radiation hazard from laboratory work. A dusty plasma measurement confirmed that charged micron-sized spheres feel a force away from the cathode centre, attributed to a local potential maximum at the center of the cathode that accelerates ions outward; after charge exchange they leave as neutrals along the microchannels. From that observation Khachan engineered the collimated beam of exiting neutrals into a simple electric propulsion thruster in which a unidirectional microchannel emerges from a conical cathode, and claims its specific impulse and efficiency greatly exceed existing electric propulsion thrusters.

Section IV. IEC Theory

Section IV turns to some more recent studies, starting with an early study by Bill Nevins that has caused concern in the community about the suitability of the IEC for a fusion power reactor. Nevins did a semi-analytic analysis where IEC systems are predicated including a non-equilibrium ion distribution function. Coulomb collisions between ions cause this distribution to relax to a Maxwellian on the ion-ion collisional time scale. His analysis suggests that the input power required to prevent this relaxation, thus maintaining the IEC configuration for times beyond the ion-ion collisional time scale, is greater than the fusion power produced. Thus, he concluded that IEC systems show little promise for the development of commercial electric power plants. Nevins’s analysis appears to be very thorough; however, it suffers from several key but subtle assumptions that may force the pessimistic results.

Later, to further explore issues raised by Nevins, Luis Chacon, doing his thesis with Miley, decided to use a Fokker-Planck model for analysis of the IEC so that some of the questionable assumptions used by Nevins could be relaxed. This study specifically dealt with a Penning-type IEC due to interest in the Penning trap experiment at Los Alamos. It should be stressed, however, that the conclusions still apply in principle to the ion-injected IEC, since the issues involve the potential well trapping common to both. The Penning trap and the ion-injected devices differ in how the well is formed and stabilized, but the physics of trapped plasma confinement is the same. Namely, the time scale for collisional degradation of the beam-like ion distribution function is crucial, since short times, as short as the fusion time, would prevent a power reactor.

Figure 4.1 gives a cross section of the experimental layout of the PFX-I experiment: the emitter electron source, the onion-shaped anode and the reflector form an axial electrostatic well for electron axial confinement, radial confinement is provided by the axial magnetic field, and the reflector is biased slightly more negative than the emitter to avoid electron losses to it. Figure 4.2 details the anode and the ion injection port, with ion and electron divertors and the equipotential lines that define the ion confinement region.

Nevins addressed this issue by calculating collisional relaxation rates from a beam-like, monoenergetic ion population, absolutely confined in a square potential well. From his analysis, he concluded that the IEC will thermalize and lose ion focusing before enough fusion events take place, and predicted that the gain — the ratio of fusion power out to ion input power — of a device operating with a 50/50 percent deuterium-tritium mixture would be about 0.21 for a 50 kV square well. This conclusion would rule out the possibility of a fusion reactor, but would leave open the development of driven neutron sources.

However, this analysis contains several questionable assumptions. For example, a tightly focused monoenergetic ion beam is in fact a pessimistic scenario, because different co-moving ion species — such as deuterium and tritium with the same energy — result in a finite speed difference, thus fostering ion-ion collisions and the degradation of the ion distribution function. It would be more realistic to consider that, in a square well, friction between species would homogenize the speed within the ion beam after some time, making the speed difference infinitesimal. This line of argument was pursued earlier by Barnes and colleagues, who found a gain of about 1.3 for the same system.

Table 4.1. Comparison of analytical and numerical estimates of gain in a beam-dominated solution, for a 50 kV square well

| Case | Analytical | Bounce-averaged Fokker-Planck (Chacon) | |---|---|---| | With co-moving ions | Gain about 0.21 (Nevins) | — | | Without co-moving ions | Gain about 1.3 (Chacon) | Gain about 1 |

In Chacon’s work, a bounce-averaged Fokker-Planck model was employed to obtain steady-state solutions for the ion distribution function and to calculate associated fusion energy gains in a variety of operating conditions, in terms of source and sink strengths, ion injection energies, well depths, and electrostatic potential shapes. Thus the limiting assumptions by Nevins — that ions are confined in a square potential well, and that their distribution is tightly focused and monoenergetic — are relaxed. When these restrictive assumptions are removed, it is found that large energy gains, in the hundreds, for beam-like solutions in square wells are possible in Penning IEC devices provided that the electrostatic well is deep enough, above about 100 kV; the ion confinement time is long enough; and the ion source strength is moderate, with the ion injection energy slightly below the potential-well maximum.

Calculated gains from the bounce-averaged simulation for the beam-like cases are also about five to ten times larger than Nevins’s, an inconsistency traceable to the treatment of the two hydrogen species: the bounce-averaged model treats them as one species of average mass, while Nevins treats them separately but assumes a common monoenergetic distribution, which leaves a finite velocity difference that boosts collisionality and lowers the gain. The inconsistency disappears when the two are compared against theoretical estimates with a similar multispecies treatment.

These results again confirm that proper formation of the electrostatic well is essential to achieve large fusion gains, and demonstrate that the distorted Maxwellian ion distribution — neglected in previous analyses — can play a positive role in the IEC gain. Results also show that the square well assumption used in previous analytical estimates is in fact a pessimistic one. Parabolic wells result in larger density peaks at the center, yielding gains three to five times larger, for a well depth around 150 kV, than those obtained with square wells. Parabolic wells are also more forgiving with respect to the source-to-sink ratio requirement. Operating regimes with gain above 100 have been identified. These results ignore electron bremsstrahlung loss; that effect was addressed heuristically by Chacon using a semi-analytic model, indicating that quite large gains are still possible, provided that electron particle losses are kept small and well depths are large.

The source-to-sink balance behind these results is a competition between up-scattering of the Maxwellian ion component confined in the well, which grows as the Maxwellian temperature rises and tends to empty it, and down-scattering of the beam, which tends to fill it. Weak sinks and strong sources give a large beam population, raising the down-scattering rate and hence the effective Maxwellian temperature; weak sources and strong sinks give the opposite.

In summary, unlike the original Nevins calculations, the subsequent Chacon results are quite encouraging, but leave open the issue of whether or not satisfactory deep potential wells can be created.

Potential Well Structure

The potential structures are called double potentials because two extrema — outer and inner wells — are observed in the plots of electrostatic potential versus IEC radius, excluding the real cathode grid minimum. The virtual anode is defined as that position where the potential increases from its minimum value at the real cathode up to about 95 percent of its maximum value. The virtual cathode is defined as the position where the potential is 95 percent as deep as its minimum value in the center of the device. The depth of the inner potential minimum is called the double well depth, defined as a percentage of the height of the outer potential maximum. In spherical geometry, the velocity component perpendicular to the radius axis represents the angular momentum.

Figures 4.5 and 4.6 define the double well depth for a 30 keV injection case, where the double well has a depth of about 60 percent, and the parallel and perpendicular velocities at the IEC cathode grid.

Tzonev and Colleagues — Deep Well Study

Tzonev and colleagues used IXL, a one-dimensional electrostatic Poisson-Vlasov solver for spherical geometry, originally developed by Mission Research Corporation for Bussard, to determine an electrostatic potential consistent with the dynamics of the charged particles within that same potential and the resulting charge density distribution inside the spherical cathode. IXL neglects collisional effects, so it provides an important limiting case where space charge effects dominate; each particle population is characterised by injected beam current, average injection energy, energy spread in the parallel and perpendicular directions, and the number of recirculations through the core.

Earlier studies had assumed that very low angular momentum — zero in the ideal case — is necessary to trap energetic ions. In contrast, Tzonev and colleagues considered high-current ion beams as having a significant angular-momentum spread, and found that deep double electrostatic potential wells can occur at high ion and electron currents of 30 to 50 amperes, high perpendicular ion energy spread of 3 to 14 keV, low perpendicular electron energy spread of about 3 eV, and low radial ion energy spread of 0.1 to 0.5 eV.

An important new insight revealed that these potential profiles create ion density distribution functions completely different from the ones observed when a single well electrostatic potential exists. Two ion density peaks were commonly observed — one in the central core region, and one near the cathode wire grid. In this manner the single ion peak created by the single well potential is split into two peaks. The central ion peak has a much smaller radius than the original peak. This causes higher ion densities to occur in the central potential well, which is essential for the achievement of high fusion rates. However, since the fusion core radius in these calculations is very small, on the order of 0.4 to 0.9 cm, the total number of neutrons emitted per second is too low to create useful fusion power. Still, the physics principles illustrated provide important insight into injection issues.

A reduced angular momentum spread and higher injection energies would be required to correct the well volume problem. Still, the deuterium-deuterium fusion rate scaling as the current to the fifth power is encouraging, and it is indeed surprising that this large angular momentum spread achieves such distinct double well structures. The current scaling for beam-beam reactions is strictly the square of the current. However, as shown by Tzonev, nonlinear changes in the potential well shape and ion density profile combine to cause the higher power current scaling law. It would be anticipated that this effect would saturate at some current, tending back to the fundamental square relation. Prior investigators also predicted scaling laws with exponents greater than 2: the first suggestion was by Bussard on theoretical grounds, and later particle-in-cell studies by M. Ohnishi at Kyoto University also showed such strong scaling. The unanswered question is at what current level this occurs.

Momota and Miley — Study of Virtual Electrode Structure

(A subsection here on Momota and Miley’s analytic study of virtual electrode structure is omitted for length: using the nonlinear Poisson equation with particle densities from kinetic theory, and a novel method for a spherically symmetric stationary distribution function, it finds that the angular momentum of the ions, together with the smaller one of the electrons, creates a virtual cathode — a double-well structure of the electrostatic potential on a potential hill near the center — and it gives the density limit of the well and the conditions relevant to forming a deep one. The trends are roughly similar to Tzonev’s numerical results. The complete text is at the source.)

Kim — Stability Analysis

In addition to achieving adequate potential well trapping for net energy production, the question of stability of the non-Maxwellian plasma in the well must be considered. Krall did earlier studies showing that the distribution in the Bussard-type Polywell is stable against key instabilities such as two-stream, but these were internal company reports and not openly published. More recently, H. J. Kim, in his thesis done with Miley, did an in-depth study of two-stream-like instabilities in the ion-injected device. His work is very encouraging in that he identifies a possible window of stability which depends on the injected energy distribution and angular velocity spread.

(A passage here describing Kim’s numerical method — a fully implicit particle-in-cell scheme implemented with a Jacobian-free Newton-Krylov algorithm, its energy conservation properties, its agreement with linear dispersion relations for counter-streaming instabilities, Landau damping and ion acoustic waves, and the two-dimensional delta-f algorithm with an immersed boundary to avoid the singularity at the spherical center — is omitted for length; the complete text is at the source.)

Kim performed a normal mode analysis of the ion-ion counter-streaming instability in a spherical inertial electrostatic confinement in order to gain insight into the ion-injected equilibrium configuration. From the analysis of cold ion beams, two-stream instability in finite spherical systems may be excited for small beam velocities compared with those of homogeneous and infinite plasma. When an ion beam is hot, the waves excited are ion acoustic type, and a certain temperature ratio is required before the wave will go unstable. The growth rate is a decreasing function of the longitudinal energy spread of the ion distribution, because a large spread induces strong Landau damping; and a more monoenergetic beam can also stabilize the instability, since the growth rate falls for a higher beam density at fixed beam speed. The growth rate does not change dramatically as the mode of angular perturbation increases.

The results indicate that the two-stream instability is stabilized if the angular momentum spread of the beam ions is small enough, due to enhanced ion densification at the center of the device. This is very encouraging for future IEC development. However, an experimental study should be performed to verify this result.

Rider — Energy Balance Study

Todd Rider reports a quite different type of energy balance analysis. Where the prior papers concentrated on up-scattering and down-scattering in various potential well configurations, Rider considered a block-diagram energy flow balance to determine the net gain from a power unit. In such an analysis the reaction, scattering and electron-ion equilibration rates enter as averages over the distribution functions, so those functions are not calculated explicitly. In traditional magnetic confinement analyses a Maxwellian distribution has generally been assumed, and for tokamaks that is reasonable because such systems are near thermal equilibrium. In sharp contrast, as stressed repeatedly here, the IEC is not.

That uncertainty makes an analysis of Rider’s type very challenging. It appears he used Maxwellian averages, and critics generally cite this as the cause of his pessimistic results. He was particularly interested in the claim that its beam-like non-Maxwellian plasma lets the IEC burn advanced fuels more easily than Maxwellian devices, and considered deuterium-tritium, deuterium-deuterium, deuterium-helium-3, helium-3-helium-3, proton-boron-11 and proton-lithium-6. All of these must battle large bremsstrahlung losses, evaluated using the traditional formula — but that evaluation has a built-in bias, since the losses depend heavily on the electron-to-ion temperature ratio, which in turn depends strongly on the averaged rates assumed, and deviation from an equilibrium electron energy distribution also strongly affects radiation emission.

Using the Maxwellian averages, he found bremsstrahlung prohibitively large for helium-3-helium-3, proton-boron-11 and proton-lithium-6, and a considerable fraction of the fusion power for deuterium-helium-3 and deuterium-deuterium, limiting use to deuterium-tritium; and he concluded that the dense central region of a reactor-grade device could not maintain a significantly non-Maxwellian ion distribution or a low electron-to-ion temperature ratio. The problem is that the assumed rate constants would naturally force that conclusion. The analysis should be redone with rates averaged over the non-Maxwellian distribution characteristic of an IEC reactor, which has not been reported to date. Despite that, Rider’s recommendations of issues to study and overcome — especially reducing radiation losses — remain quite valid.

Neutron Source Simulations

Several simulation studies have focused on neutron source type devices. Here, unlike a future power reactor, the background gas pressure is high enough that the fusion rate follows beam-background scaling — theoretically a current times pressure scaling — and charge exchange becomes a significant factor. Miley and colleagues used an analytical model of charge-exchange collisions including ion time-of-flight: simulating 10 mA of deuterium ion current in a 30 cm diameter device at 50 kV, it matched the experimental result of 10⁶ fusion neutrons per second, and it gives a neutron yield scaling as the grid diameter raised to the power minus 0.41, very close to the experimental scaling observed at Illinois. For higher pressure operation, charge exchange severely limits the number of passes despite the star mode’s high effective transparency: at 4.6 millitorr about half the atomic deuterium ions charge-exchange within the cathode region on their first pass, and after only four passes the fusion rate from subsequent passes is negligible. Molecular deuterium ions have a smaller cross section and survive about 20 passes.

In summary, the design of an optimal IEC neutron source is quite different from that of a power-producing device. In the source design, the grid parameters, grid-to-vessel diameter ratio, chamber diameter, surface conditions, background pressure, current and voltage all become important parameters. In power-producing devices the ion injection parameters — including ion current, ion energy relative to the height of the well potential, the ion angular momentum, and the ion-to-electron temperature ratio, along with the chamber diameter — determine performance.

Section V. Potential Applications

The ultimate application for IECs is electrical power production. Section V concentrates on various near-term spin-off applications of neutron, proton and x-ray sources, and also non-electrical power applications such as space propulsion.

Neutron, Proton and X-ray Sources

The main application of the IEC to date has been as a small portable neutron source for neutron activation analysis. Since both deuterium-deuterium and deuterium-helium-3 reactions can be used for proton production, IECs have also been pursued for medical and positron-emission-tomography isotope production, though the source strengths needed to compete are still a research question. Another novel application is simulating the implantation of deuterium and helium ions in candidate fusion reactor first wall materials. Yet another involves running the device with reverse polarity, so that the trapped electrons produce soft x-rays extracted through a thin low-atomic-number window — a small-scale version of a national laboratory synchrotron light source.

The cylindrical IEC, like the spherical one, converts to a tunable x-ray source with minimal alteration: reverse the electrode polarities, add electron emitters along the vessel wall, and substitute hydrogen for deuterium, since here the function of the gas ions is to provide electron bremsstrahlung. Intense emission is concentrated in a small volume surrounding the central axis because of the high electron density formed there, and the spectrum peaks at about two-thirds of the applied voltage — so a 120 kV setting yields about 80 kV x-rays.

Space Propulsion

The IEC can be used for both near-term electrically driven thrusters for satellite operations, using the jet mode discussed earlier, and for fusion-powered deep space propulsion. The latter is illustrated by a design in which a deuterium-helium-3 reactor was utilized.

Figures 5.5 and 5.6 show Fusion Ship II, a 750 MW-electric IEC fusion-powered manned spacecraft with ion thruster propulsion, in image and scale schematic.

The overall spaceship length is 300 metres and the initial mass at mission start is 500 metric tons. Crew and avionics are in the central compartment at the forward end, in a 12 m diameter chamber that could contain a rotating centrifuge for sleep and exercise. Twin 175-metre assemblies, each comprising five deuterium-helium-3 spherical IEC reactors and traveling wave direct energy converters, generate 1,394 MW of 14.7 MeV proton flux and 469 MW of thermal heat, converted to 1,197 MW of radio-frequency electric power; 242 MW recirculates to run the reactors, 750 MW drives the ion thrusters, and the remainder is rejected as waste heat. A fuel recirculation and separation system continuously removes the helium-4 product from the reactants, and unburned fuel is collected by the direct energy converters and returned, conserving the valuable helium-3.

The ion thrusters run on argon propellant at a specific impulse of 35,000 seconds and an efficiency of 90 percent, producing 4,370 newtons of thrust and an initial acceleration of 0.0087 m/s². A typical out-and-back mission to Jupiter is 210 days out and 153 days to return, comparable to or faster than prior fusion studies predicted. Of the initial 500 metric tons, 222 are argon propellant for a velocity change of 220 km/s and 178 are the reactors, converters and thrusters; the rest is crew areas, electronics, life support, shielding and antenna, with a 30 percent dry-mass contingency. Fusion Ship II would be one of the largest propelled vehicles ever built, at one quarter the mass of the Space Shuttle at liftoff.

Table 5.2. Comparison of IEC design and magnetic fusion design

| | Fusion Ship I | Fusion Ship II | Spherical tokamak | |---|---|---|---| | Overall mass (metric tons) | 300 | 500 | 1690 | | Overall length (m) | 174 | 300 | 240 | | Number of crew | 10 | 10 | 6-12 | | Thrust power (MW) | 86 | 750 | 4830 | | Reactor gain | 4 | 9 | 73 | | Reactor power (MW) | 296 | 2175 | 7895 | | Thrust system | Krypton ion | Argon ion | Magnetic nozzle | | Specific impulse (s) | 16,000 | 35,000 | 35,435 | | Jupiter one-way trip time (days) | 400 | 210 | 118 |

The tokamak has a shorter trip time by employing a power level that is six times that of the IEC units. Further, it is designed for deuterium-tritium use, since deuterium-helium-3 is difficult to burn in such tokamaks, but tritium handling, radiation damage, and radioactivity issues are not addressed. Thus, if the IEC and tokamak were compared on the same operational basis — same fuels and power levels — the IEC would clearly show a distinct advantage. Note that this is even true with the tokamak using a very advanced conceptual design well beyond the reach of ITER technology.

Magnetically-Channeled Spherical IEC Array

The Magnetically-Channeled Spherical IEC Array keeps the basic ion-injected reactor but adds magnetic channels that couple exhaust plasma and reaction products between units. Each spherical IEC sits in a hexapole field — different from the hexapole used in Bussard’s Polywell — inside a field channel created by a column of Helmholtz coils, with the coil sets adjusted so the fields cancel at the center of each unit, giving a larger field null region than a cusp. The array retains the stability of good field curvature and effectively closes the belt loss cone: because the field lines that exit the cusp reconnect to the confinement region within the coils, particles leaving through the belt cusp recirculate back in, which significantly increases confinement time over a simple cusp device.

Particles lost axially, out through the spindle cone of one unit, should be retrapped in the next. Passing through the high field region between units, a particle has a small gyroradius; on reaching the low field region it moves in a straight line along the vector direction at the edge of the null, and because the phase of its gyro motion is random at that point, the direction it takes across the null is random. The result is a random, collisionless scattering that leaves the particle confined in the neighbouring unit. This retrapping increases the confinement time of the array roughly in proportion to the number of units.

An additional benefit is that in a reactor embodiment, both leaking fuel plasma and energetic charged fusion products — for example the 14 MeV proton from deuterium-helium-3 — can be collimated and aimed into a direct energy converter, giving high overall conversion efficiency; alternately, for propulsion, the proton beam, augmented by heavy atoms to increase the flow mass, can be directly exhausted for thrust. These principles have not yet been demonstrated experimentally, but initial tests could be done with a modest size experiment and stepped up to a full-scale prototype.

Section VI. Possible Next Step Breakeven Experiment

The prior sections have presented much information about the existing data base and theory for IEC operation. The potential for use in applications such as a neutron source and related radiation sources is well established. However the ultimate goal is to develop a power-producing IEC — better yet, to do this taking advantage of the unique ability of the IEC to use non-Maxwellian plasma to burn advanced fuels, minimizing radioactive and radiation involvement. However the best current device results are 5 or 6 orders of magnitude down in energy gain from breakeven. Thus it may appear that such a hope is many years off.

Fortunately, the IEC can be scaled up in energy gain while keeping a small size, since the losses are in velocity space — that is, via ion up-scattering out of the potential well trap. This is in sharp contrast to tokamaks, where losses occur via diffusion across the outer surface, so increased confinement times have been achieved by going to the massively large ITER type devices. The problems and costs for construction of ITER have thrown its development into the distant future.

Demonstration of Net Energy Gain using IEC Aneutronic Fusion

The IEC is one of the few approaches to fusion that has the potential of burning aneutronic fuels such as deuterium-helium-3 and proton-boron-11 in a reasonable scale device. This fuel results in charged-particle reaction products which allow efficient use of direct energy conversion technology with no direct greenhouse emissions and minimal radioactivity or radioactive wastes. The experiment proposed here would provide verifiable and reproducible proof of the break-even conditions necessary to burn proton-boron-11 as a practical aneutronic fuel in an IEC fusion power-generating device.

The proposal is to develop a revolutionary small IEC fusion power unit that could be commercialized in time to impact the energy crisis we now face. This device would have the aggressive goal of burning relatively inexpensive aneutronic proton-boron-11 fuel, avoiding issues of tritium breeding and radioactivity that deuterium-tritium burning ITER-type devices face. This technology is the result of new understanding of ways to create a deep electrostatic potential well for improved confinement in an ion-injected IEC. This will be done with specially designed ion guns to inject ions into the device with strong focus and controlled angular momentum. The concept builds on a combination of prior small scale experiments with gun-injected IECs and simulation of their scale-up to power production using particle-in-cell codes and particle tracking analysis.

The small size of the IEC is a key characteristic. If rapid development is to be achieved, the ability to employ small size experiments is essential. Fortunately, confinement scaling in the IEC is in velocity space rather than physical space, allowing breakeven and power production in small-volume plasmas. Thus in principle, energy breakeven could be demonstrated in a very dense plasma core occupying only a few cubic centimetres with only a few hundred watts in and out. This extreme is not currently possible, but use of the new gun-injected technology to obtain breakeven in a dense plasma core of hundreds of cubic centimetres with 20 to 25 kW input power seems practical. This proof-of-principle device would demonstrate the physics of energy production and provide the basis for rapidly going to practical IEC power plants. This route could lead to power reactors for distributed power applications in the megawatt range that are only a fraction of the size of an ITER-type plant or even current fission nuclear plants.

Vision of a Future Proton-Boron-11 Fusion Plant

In the ultimate power plant, the preferred fusion reaction would employ aneutronic proton-boron-11 fuel, which fuses to produce energetic alpha particles with no neutrons and minimal radioactivity. This eliminates radioactive tritium breeding and corresponding tritium inventory, activation and damage to reactor structural materials, and the massive shielding and radiation protection in traditional fission and deuterium-tritium fusion reactor systems. In this case, proton-boron-11 reactions in the central IEC core result in MeV-energy alpha particles according to the reaction: a proton plus boron-11 yields three alphas.

Due to its inherent non-Maxwellian, beam-like plasma, the IEC is especially well suited for burning a fuel such as proton-boron-11 which requires high energies of about 150 keV. In operation, the bulk of the driving energy is given to ions, so an applied voltage of about 180 kV provides ion energies near the peak of the proton-boron-11 cross section. In contrast, in Maxwellian-type plasmas typical of magnetic confinement devices, energy is expended to create ions over a wide distribution of energies; thus tokamaks are designed to operate at much lower ion energies of 20 to 30 keV, suitable for deuterium-tritium fusion.

Figure 6.1 plots the proton-boron-11 fusion cross section energy requirements against well depth: the reaction rate approaches that of deuterium-tritium at very high energies, that is, deep potential wells.

The key physics challenge then for the IEC is to achieve good ion confinement via strong ion trapping — that is, a large number of recirculations — in the potential well. This trapped plasma must meet the Lawson criterion for energy breakeven with proton-boron-11: a density-time product of about 10¹⁶ per cm³ per second, two orders of magnitude above the requirement for deuterium-tritium fusion. Assuming a converged core density in the potential well of about 10¹⁶ per cm³, ion trap times of about 1 second are required. While very demanding, plasma simulations show that carefully controlled injection can provide the potential well formation required to achieve this goal.

Proposed Breakeven Experiment

Studies of gridded configurations discussed earlier have achieved reaction rates of up to 10¹² reactions per second, about 1 watt of fusion power. Although these power levels fall well below the requisite break-even condition for power production, the corresponding neutron production makes the IEC an excellent compact source for practical neutron activation analysis. Consequently this application, and then related spin-off type projects, have continued to advance IEC basic physics understanding to the point where a pathway to a power reactor can now be envisioned.

Present experiments at Illinois are designed to baseline the impact of ion injection conditions combined with supplemental electron sources to maintain the desired quasi-neutrality. One current experiment consists of a 16-inch diameter spherical vacuum system with a spherical grid held at a high potential. This system produces about 10⁸ reactions per second based on neutron counting experiments. A specially designed radio-frequency ion gun is installed on the side of the chamber to study controlled ion injection and corresponding potential well formation for ion trapping.

These studies did not yet include differential pumping, so the number of recirculation passes by an ion was low, roughly 2, due to major charge exchange losses. The injected ion current with one gun was only about 50 mA. Still, based on measurements of neutrons emitted using deuterium fuel, the gain was of order 10⁻⁶, which is remarkable for such a small device. These results, plus supporting computer simulation studies, show that the scale-up of this device to 12 injector guns plus strong differential pumping could potentially achieve breakeven.

Figure 6.2 shows the IEC system with radio frequency ion gun; Figure 6.3 the multiple ion gun concept; Figure 6.4 a differentially pumped radio-frequency-driven ion gun, drawn with six guns for simplicity, though twelve are proposed for the breakeven study.

The key to achieving breakeven conditions in this device is to inject ions with good focus and the desired angular momentum. The radio-frequency ion gun has a unique magnetic nozzle to achieve that. Electrons are simultaneously introduced in a measured fashion. This eliminates the need for a grid by formation of a deep potential well. Also, differential pumping between the guns and the main chamber provides the high vacuum needed to avoid charge exchange. This configuration is highly non-Maxwellian due to the beam-dominated nature of the trapped ions, although, as pointed out in the discussion of Chacon’s work, thermalized ions build up an additional quasi-Maxwellian distribution in the trap. Still, detailed analysis such as done by Momota and Kim shows that the beam ion momentum provides sufficient stiffness to the system to maintain stability. This assumes, however, that very precise control is maintained over the energy and angular momentum of injected ions and a balanced supply of electrons is provided.

A key component is the magnetic focusing lens at the gun extraction port. This allows very efficient differential pumping between the high pressure gun chamber and the low pressure IEC chamber and provides focus control. This experiment will involve very high power inputs, about a megawatt. To avoid excessive power supply and thermal controls, a Marx bank pulsed power input with peak powers of about 1 MW over 1 millisecond at 0.01 Hz will be used. Pulsed experiments with equivalent power inputs on one gun have already been performed successfully. The pulse length is set long enough to provide quasi-equilibrium physics conditions in the trapped plasma during the flat top region of the pulse. Thus the data obtained are relevant to eventual steady-state reactors where the internal fusion power production alleviates the input power supply requirement.

The energy gain scaling for such a device goes as the number of recirculations times the injected current, divided by the square of the radius of the dense core spot formed in the sphere. The 12-gun breakeven design will provide an increase in recirculations to about 1,000 due to differential pumping effects; the current will increase to 6,000 mA due to multiple pulsed guns; and the core radius will be cut down by a factor of 10 due to improvements in focusing and reduced collisionality. This predicts an increase in gain, compared to the prior gun experiment, of about 10⁸ — giving a gain of 1, breakeven, as required for a proton-boron-11 plasma. As noted earlier, this breakeven gain assumes a Lawson breakeven confinement parameter that exceeds the deuterium-tritium requirement by a factor of 100; in other words, this could also be thought of as a deuterium-tritium equivalent gain of 100.

To accomplish this result quickly on a modest budget, we need to simplify the work by avoiding the need to develop new injection technology for hydrogen-boron fuel, plus avoid the need to handle the fusion energy produced. Thus we propose to confirm the achievement of breakeven conditions using a hydrogen plasma and diagnostics to show that the density-time product and temperature corresponding to a gain of 1 for proton-boron-11 are obtained. An alternate approach might be to use deuterium, as is done in present neutron source studies; however, that would require massive shielding and other access restrictions for the neutron flux levels. Modern plasma diagnostics can make quite precise measurement of the plasma conditions needed for the confirmation, so the hydrogen equivalent approach is recommended.

Concluding Remarks

Once achieved in hydrogen, these conditions could be fairly quickly confirmed with proton-boron-11 fuel in later experiments, once the needed fuel handling system is added. Thus the proposed hydrogen simulation of proton-boron-11 breakthrough conditions would be a landmark achievement, leading the way to rapid deployment of the technology needed to build small fusion power plants.

The technology development needed to proceed largely involves the design and engineering of subsystems for the balance of plant. Many of these can employ conventional equipment, but several require new developments. These include the hydrogen-boron fuel injection system, the direct energy conversion system to convert the charged particle product energy to electricity, and the exhaust plasma collection and recovery system. Also the chamber wall must incorporate advanced cooling methods to handle the large surface heat loads caused by near-surface absorption of the bremsstrahlung emission. There are no show stoppers, however, so the road map to IEC fusion power seems clear. The main challenge is to find funding sources with the will to proceed.

(The report’s six per-section reference lists are omitted here; the complete text is at the source.)