DIRD Advanced Nuclear Propulsion for Manned Deep Space Missions

Advanced Nuclear Propulsion for Manned Deep Space Missions

Defense Intelligence Reference Document, Acquisition Threat Support. DIA-08-1003-007, 11 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

My interest in space flight dates to when I was about 10 years old and received as a birthday gift a popular book about the feasibility of space flight. From it I learned for the first time about Oberth and Goddard and of the possibility of reaching the Moon with a multistage rocket. This occurred at the same time that Hahn and Strassmann announced the discovery of nuclear fission, with the possibility of an atomic bomb by a fission chain reaction.

Having been born in Germany in 1929, I received my Ph.D. in physics under Heisenberg in 1955. Inspired by the 15-megaton hydrogen bomb test conducted by the United States in 1952, I have been deeply interested in the nonfission ignition of thermonuclear reactions by inertial confinement since 1954. At the time all fusion research in the United States was still classified, but I had quite independently discovered the basic principles of inertial confinement, the Guderley convergent shock wave, and the Rayleigh imploding shell solutions. In 1956 I presented my findings at a meeting organized by Von Weizsäcker at the Max Planck Institute in Göttingen. The abstracts of this meeting reside today in the University of Stuttgart library.

In 1958 I had delivered a paper at the 2nd United Nations Conference on the Peaceful Use of Atomic Energy on Nerva-type nuclear rocket reactors. The paper turned out to be of some importance as I was invited by the U.S. government to come to the United States under Operation Paperclip. In San Diego I met Ted Taylor and Freeman Dyson, who were working on the famous Orion nuclear bomb propulsion concept. This concept is generally credited to Stanislaw Ulam, but I know from conversations I had with Heisenberg that a similar idea had been presented to Heisenberg by Wernher von Braun in Berlin in or around 1942. Because of my idea to use the Guderley convergent shock wave solution for thermonuclear ignition, Ted Taylor and Freeman Dyson were interested in my joining their group. But because at that time this work was classified and I was not yet a U.S. citizen, this was not possible.

In 1967 I saw a new possibility for the nonfission ignition of thermonuclear microexplosions by intense relativistic electron and ion beams, driven by a high-voltage Marx generator. This ignition concept could be used not only to control the release of energy by nuclear fusion, but also to propel a spacecraft, replacing the pusher plate of the Orion concept with a magnetic mirror, reflecting the plasma-fireball of the thermonuclear microexplosion. This idea was adopted by the British Interplanetary Society in its 1978 Project Daedalus starship study, replacing a neutron-rich deuterium-tritium thermonuclear explosive with a neutron-poor deuterium-helium-3 explosive. Unlike the deuterium-tritium reaction, in which 80 percent of the released energy goes into neutrons, most of the energy in the deuterium-helium-3 reaction goes into alpha particles, which can be deflected by a magnetic mirror. But because helium-3 is not abundantly available everywhere, it was proposed to mine it from Jupiter’s atmosphere.

Studies have been conducted on spacecraft propulsion with the matter-antimatter annihilation reaction; however, it is an enormous technical challenge to produce antimatter in appreciable quantities. The idea of using nanogram amounts of antimatter for the ignition of fission-fusion microexplosions appears to have credible potential, but even there the production and storage of nanogram quantities of antimatter pose serious technical problems.

We have little reason to expect that new fundamental laws of physics that could lead to a breakthrough in propulsion still await discovery. Very much as America was discovered only once, it is quite possible that all the fundamental laws of physics relevant to propulsion have been discovered, challenging our imagination to find out if they are sufficient to invent propulsion systems that ultimately might bring us to Earthlike planets of nearby solar systems.

I conclude this preface with an imaginary talk by Ted Taylor to Freeman Dyson as recorded by the latter’s son, George Dyson, in his book Project Orion — The True Story of the Atomic Spaceship, followed by a dream of Ted Taylor’s. Freeman’s hope for the Orion had rested on the fact that there seems to be no law of nature forbidding the construction of fission-free bombs, and on the belief that improvements in the design of the nuclear devices, by reducing the fraction of total yield due to fission, might achieve reduction factors of 10² to 10³. This belief in small, fission-free bombs has largely evaporated. One exception is Ted Taylor. He remains convinced that small, clean bombs could propel Orion — but he still fears more than ever that such devices would be irresistible as weapons, until we outgrow the habit of war. There are lots of different routes to that final result of a very clean bomb. Could you make a one-kiloton explosion in which the fission yield was zero, which is bad news on the proliferation front, but could turn Orion into something quite clean? Freeman thinks Ted is wrong — and Ted hopes Freeman is right. I for my part think Freeman is wrong.

Many years later, shortly before his death, Ted Taylor reported: I had a dream last night, about a new form of nuclear weapon, and I am really scared of it. He reported that when he woke up, he wrote down his dream, and it appeared scientifically sound and feasible. What was it? We never will know with certainty, but I have a guess: it is the possibility of chemical superexplosives, explained in the appendix, powerful enough to ignite a thermonuclear bomb.

Introduction

As Hermann Oberth proved for chemical rockets in his 1923 book The Rocket into Planetary Space, this paper will try to prove for thermonuclear rockets the following:

• At the present state of science and technology one can build spaceships driven by deuterium thermonuclear reactions, able to reach the outer limits of the solar system.
• Such spaceships permit the manned exploration of the entire solar system and beyond, with the ultimate potential to reach nearby solar systems.
• The cost in research and development to build such spaceships will be high but still well within what is economically feasible.
• Using the same physical principles as for deuterium fusion rockets will also lead to the realization of clean nuclear energy, justifying the expenditures for these large projects.

Deuterium can be used as the rocket fuel of choice in addition to any inert material that is suitable as a propellant. This propellant material is available on most planetary bodies and particularly on the comets of the Oort cloud. The main idea is that by gradual radial expansion from the Sun by building bridges over the Oort clouds, which presumably surround all suns, Earthlike planets in neighboring solar systems can eventually be reached.

The first and most important step toward this goal is to reach the focus of the Einstein gravitational lens at 550 astronomical units. At this location, one can use the Sun as the lens of a super telescope, an idea first proposed by Claudio Maccone in 1993. Present knowledge is that there are planets in nearby solar systems that are likely Earthlike planets. It is only with this gigantic telescope that one can determine if life on these planets is possible. But because of the complexity of this task, a manned mission to the Einstein gravitational lens focus is likely to be needed, possible only with advanced nuclear rocket propulsion.

Deuterium, Argon Ion Lasers, and KeV Superexplosives

The goal is a spacecraft that can be refueled while landing on a planetary body, which can be a planet, an asteroid, or a comet. With heavy water available on many planetary bodies but in particular on comets, this suggests the use of deuterium as the thermonuclear rocket fuel. Ignition of deuterium, though, is more difficult than ignition of the deuterium-tritium reaction or of the deuterium-helium-3 reaction.

The deuterium-tritium reaction is the easiest to ignite, but 80 percent of the energy goes into neutrons, which cannot be deflected by a magnetic mirror. In the deuterium-helium-3 reaction all the energy goes into charged fusion products, but in a mixture of deuterium with helium-3 there are still some neutron-producing deuterium-deuterium reactions. More important is the fact that, unlike deuterium, helium-3 is largely unavailable. There is some indication of helium-3 on the surface of the Moon. In the Daedalus starship study by the British Interplanetary Society, it was proposed to mine helium-3 from the atmosphere of Jupiter. In either case, the cost to recover appreciable amounts of helium-3 would be very high.

For the deuterium-deuterium reaction, the situation is quite different because there the instantaneous burn with deuterium of the tritium and helium-3 reaction products of deuterium makes possible a detonation wave in dense deuterium. In this detonation wave, only 38 percent of the energy released goes into neutrons, compared with 80 percent for the deuterium-tritium reaction.

Deuterium can be extracted from water with relative ease in three steps. Water is electrolytically split into hydrogen and oxygen. The hydrogen gas, composed of ordinary hydrogen and hydrogen deuteride, is cooled down until it liquefies, whereby the heavier hydrogen deuteride is separated by the force of gravity from the lighter hydrogen. The newly produced hydrogen deuteride is heated and passed through a catalyst, splitting two molecules of hydrogen deuteride into one of hydrogen and one of deuterium.

Since the gravitational field on the surface of a comet or small planet, from which the deuterium shall be extracted, is small, the apparatus separating the liquid hydrogen deuteride from hydrogen must be set into rapid rotation.

The comparatively small amount of energy needed for the separation can ideally be drawn from a ferroelectric capacitor — for example, a barium-titanate capacitor with a dielectric constant of about 5,000 — to be charged up to many kilovolts by a small fraction of the electric energy drawn from the deuterium fusion explosions through a magnetohydrodynamic loop. One can also draw this energy from a small onboard nuclear reactor requiring only a small radiator, slowly charging the capacitor. Alternatively, one may store the needed energy in the magnetic field of a superconductor.

For the launching of the spacecraft into Earth orbit, a very different scheme is proposed. It requires special materials that are readily available on Earth but not on extraterrestrial bodies serving as landing points to refuel the spacecraft. There the primary resource is water from which deuterium is obtained.

In the Orion bomb propulsion project, a large number of fission bombs, or fission-triggered fusion bombs, were proposed to lift the spacecraft into space. Since this would release a large amount of highly radioactive fission products into the atmosphere, it was one of the causes that killed Orion. Even though large payloads can be brought into Earth orbit by chemical rockets, this remains very expensive, and an acceptable less expensive nuclear alternative is highly desirable.

There appear to be two possibilities. The first is a laser driven by a high explosive, powerful enough to ignite a deuterium-tritium microexplosion, which in turn can initiate a thermonuclear detonation in deuterium. The second, more speculative, possibility is the conjectured existence of chemical kiloelectronvolt superexplosives. These are chemical compounds formed under high pressure, resulting in keV bridges between inner electron shells and able to release intense bursts of keV X-rays capable of igniting a deuterium-tritium thermonuclear reaction, which in turn could ignite a larger deuterium detonation.

To realize the first possibility, one might consider pumping a solid argon rod with a convergent cylindrical shock wave driven by a high explosive. If the argon rod is placed in the center of convergence and reaches a temperature of 90,000 K, the upper ultraviolet laser level of the argon will be populated. Following this heating, the argon cylinder radially expands and cools, with the upper laser level frozen into the argon. The energy thus stored in the upper laser level can then be removed from the rod by a small Q-switched laser, the resulting powerful laser pulse optically focused onto a thermonuclear target.

To realize the second possibility, one would have to subject suitable materials to very high pressure. These energetic states can be reached only if during their compression the materials are not appreciably heated, because such heating would prevent the electrons from forming the bridges between the inner electron shells. Details of the second possibility are provided in the appendix.

Magnetic Insulation and Inductive Charging

Two concepts are of great importance for the envisioned realization of a deuterium fusion-driven starship: the concept of magnetic insulation, which permits the attainment of ultrahigh voltages in high vacuum; and the concept of inductive charging, by which a magnetically insulated conductor can be charged up to very high electric potentials.

Magnetic Insulation

In a greatly simplified way, magnetic insulation can be understood as follows. If the electric field on the surface of a negatively charged conductor reaches a critical field on the order of 10⁷ V/cm, the conductor becomes the source of electrons emitted by field emission. The critical electric field for the emission of ions from a positively charged conductor is about 10⁸ V/cm. Therefore, if in a high-voltage diode the electric field reaches about 10⁷ V/cm, breakdown will occur by electric field emission from the cathode to the anode.

But if a magnetic field of strength B measured in gauss is applied in a direction parallel to the negatively charged surface, and if B exceeds E, where E like B is measured in electrostatic cgs units, the field-emitted electrons make a drift motion parallel to the surface of the conductor with a velocity proportional to the ratio of the electric to the magnetic field. To keep that drift velocity below the velocity of light then requires that E stay below B. Let us assume a field of 2 by 10⁴ gauss, which can be reached with ordinary electromagnets: this means E can be as large as 2 by 10⁴ electrostatic units, or 6 by 10⁶ V/cm. For a conductor with a radius of about 10 m — an example for a small starship configuration — one can reach a voltage on the order of 6 by 10⁹ volts.

Inductive Charging

To charge the spacecraft to the required gigavolt potentials, we choose for its architecture a large but hollow cylinder, which at the same time acts as a large magnetic field coil. If thermionic electron emitters are placed inside this coil and the magnetic field of the coil rises in time, Maxwell’s induction law induces an azimuthal electric field inside the coil, proportional to the radial distance from the axis and to the rate of change of the axial field.

In combination with the axial magnetic field, the electrons from the thermionic emitters make a radial inward-directed motion. By Gauss’s law this leads to the buildup of an electron cloud inside the cylinder, and hence to a radial electric field proportional to the electron number density and radius. That radial field leads to an additional azimuthal drift motion superimposed on the radially directed inward drift.

For the newly formed electron cloud to be stable, its maximum electron number density must be below the Brillouin limit, set by the magnetic field and the electron rest mass energy of 8.2 by 10⁻⁷ erg. For a field of 2 by 10⁴ gauss, one finds a maximum density of about 4 by 10¹³ per cm³. To reach a potential of 10⁹ volts with a cylindrical electron cloud of radius 10³ cm requires a density of about 2 by 10⁹ per cm³, well below that maximum.

Deuterium as the Preferred Nuclear Rocket Fuel

To appreciate the importance of deuterium as the preferred and abundantly available nuclear rocket fuel, one must consider the secondary reactions with deuterium of the helium-3 and tritium reaction products from deuterium-deuterium fusion. Taking these reactions into account, one obtains from 6 deuterium nuclei an energy of 26.8 megaelectronvolts in charged fusion products, made up of helium-3 and hydrogen, and an energy of 16.55 MeV in neutrons. This means 62 percent of the energy is released into charged fusion products and 38 percent into neutrons — a substantial improvement over the deuterium-tritium reaction, in which only 20 percent of the energy goes into helium-4.

Of interest also is the average velocity, averaged over the momentum of the charged fusion products, because it is a measure of the maximum specific impulse, respectively the maximum exhaust velocity. For the six charged fusion reaction products given in Table 1, one obtains an average velocity of 1.5 by 10⁹ cm/s.

Table 1. The charged fusion products of a detonation in deuterium: their energy and velocity

| Fusion product | Energy (MeV) | Velocity (10⁹ cm/s) | |---|---|---| | Helium-3 | 0.8 | 1.23 | | Hydrogen | 3.0 | 2.40 | | Hydrogen | 14.7 | 5.30 | | Helium-4 | 3.6 | 1.31 | | Helium-4 | 3.7 | 1.33 | | Tritium | 1.0 | 0.80 |

Because the 6 charged fusion products are accompanied by 9 electrons, they have to share their kinetic energy with 9 electrons. This reduces the maximum specific impulse by the square root of 2.5, to 0.95 by 10⁹ cm/s.

A reduction of the specific impulse does not occur if the electrons have enough time to escape the burning plasma behind the detonation front; that is, in a time shorter than the time for them to be heated by the charged fusion products. The time needed for the electrons to be heated by the charged fusion reaction products can be computed from the range of the charged fusion products and their velocity in a plasma at temperature T; it has then to be compared with the time the electron takes to escape the burning plasma behind the detonation front, which is the radius of the burning deuterium cylinder divided by the electron velocity. Putting a number density of 10²³ per cm³, a temperature of about 10⁸ K, and velocities of about 10⁹ cm/s for both electrons and fusion products, one finds that the escape condition requires a cylinder radius below 0.4 cm.

To reach the highest specific impulse possible, one should make the deuterium cylinder as thin as possible.

Magnetic Entrapment of the Charged Fusion Products and the Stopping of the Proton Beam in Dense Deuterium

If a fission bomb is used to trigger a thermonuclear detonation, so much energy is available that almost any radiation implosion configuration is likely going to work. As an example, one may place a fission bomb and a sphere of solid deuterium in a shell of gold, in the two foci of an ellipsoidal cavity. The radiation released by the exploding fission bomb, by ablating the gold, launches a convergent shock wave into the liquid deuterium. With the temperature in the shock wave rising approximately as the inverse of the distance from the center of the deuterium sphere, the ignition temperature is reached at some distance from the center. But only if this distance is larger than the stopping length of the deuterium-deuterium fusion reaction products, typically a few cm, is a radially outward-moving detonation wave ignited. This configuration is essentially the same kind of hohlraum, or cavity, configuration used in the indirect drive mode of laser fusion for a small deuterium-tritium sphere.

A configuration of this kind can still be used to burn deuterium if the deuterium-tritium microexplosion is used to trigger a larger deuterium explosion. For a starship that will depend on deuterium as its only rocket fuel, this possibility is excluded.

But another possibility arises if the ignition is done with a 10⁷-ampere gigaelectronvolt proton, or deuterium, beam. If focused onto one end of a slender, cylindrical deuterium rod, the beam not only can be made powerful enough to ignite the deuterium, but its strong azimuthal magnetic field entraps the charged deuterium-deuterium reaction fusion products within the deuterium cylinder, launching a deuterium detonation wave propagating with supersonic speed down the cylinder. There the fusion gain and yield can in principle be made arbitrarily large, depending only on the length of the deuterium rod.

The range of the charged fusion products is determined by their Larmor radius, which is a constant depending on the particle’s mass, charge and kinetic energy divided by the magnetic field. If the magnetic field is produced by the proton beam current, one has at the surface of the deuterium cylinder an azimuthal magnetic field equal to 0.2 times the current divided by the radius. Requiring that the Larmor radius stay below the cylinder radius then gives a critical current, equal to 50 times the constant. In Table 2, the values of that constant and of the critical current are compiled for all the charged fusion products of the deuterium-deuterium reaction. For all of them, the critical current is below 3.84 by 10⁶ amperes. Therefore, with the choice of about 10⁷ amperes, all the charged fusion products are entrapped inside the deuterium cylinder.

Table 2. Critical ignition currents for thermonuclear reactions

| Reaction | Fusion product | Energy (MeV) | Constant a (G cm) | Critical current (A) | |---|---|---|---|---| | DT | Helium-4 | 3.6 | 2.7 by 10⁵ | 1.35 by 10⁶ | | DD | Helium-3 | 0.8 | 1.12 by 10⁵ | 5.6 by 10⁵ | | DD | Tritium | 1.0 | 2.5 by 10⁵ | 1.25 by 10⁶ | | DD | Hydrogen | 3.0 | 2.5 by 10⁵ | 1.25 by 10⁶ | | DHe-3 | Hydrogen | 14.65 | 5.56 by 10⁵ | 3.84 by 10⁶ | | DHe-3 | Helium-4 | 3.66 | 2.78 by 10⁵ | 1.39 by 10⁶ |

For the argon ion laser configuration proposed for the launch into Earth orbit, where a small amount of deuterium-tritium serves as a trigger for the ignition of a larger amount of deuterium, the ignition of a magnetic-field-supported detonation wave in deuterium is possible there with an auxiliary high-explosive-driven megampere current generator, setting up an axial magnetic field by an azimuthal current around the rod. The charged fusion products there are spiraling down the rod. The current needed to entrap the charged fusion products is there of the same order of magnitude; that is, about 10⁷ amperes.

For the deuterium-tritium thermonuclear reaction, the condition for a propagating burn in a sphere of radius r and density rho, heated to a temperature of 10⁸ K, is that the product of density and radius be at least 1 g/cm². This requires energy of about 1 megajoule. For the deuterium reaction, this condition is a density-radius product of at least 10 g/cm², with an ignition temperature about 10 times larger. That a thermonuclear detonation in deuterium is possible at all is due to the secondary combustion of the tritium and helium-3 fusion reaction products. The energy required would be about 10⁴ times larger, or about 10⁴ megajoules — for all practical purposes out of reach for nonfission ignition. However, if the ignition and burn are along a deuterium cylinder, where the charged fusion products are entrapped by a magnetic field within the cylinder, the sphere condition is replaced by a condition on the length of the cylinder.

If the charged fusion products are entrapped within the deuterium cylinder, and if the density-radius condition is satisfied, and finally if the beam energy is large enough that a length of the cylinder equal to 10 divided by the density in centimetres is heated to a temperature of 10⁹ K, a thermonuclear detonation wave can propagate down the cylinder. This then leads to large fusion gains.

The stopping length of single GeV protons in dense deuterium is much too large to fulfil that inequality. But this is different for an intense beam of protons, where the stopping length is determined by the electrostatic proton-deuteron two-stream instability. In the presence of a strong azimuthal magnetic field, the beam dissipation is enhanced by the formation of a collisionless shock, with the thickness of the shock by order of magnitude equal to the Larmor radius of the deuterium ions at a temperature of 10⁹ K, which for a magnetic field on the order of 10⁷ gauss is on the order of 10⁻² cm.

For the two-stream instability alone, the stopping length is set by the velocity of light, the proton ion plasma frequency and the ratio of the beam density to the target density. For a hundredfold compressed deuterium rod, one has a target density of 5 by 10²⁴ per cm³ and an ion plasma frequency of 2 by 10¹⁵ per second, and a beam proton density of 2 by 10¹⁶ per cm³. One finds a density ratio of 4 by 10⁻⁹ and a stopping length of 1.2 by 10⁻² cm. This short length, together with the formation of the collisionless magnetohydrodynamic shock, ensures the dissipation of the beam energy into a small volume at the end of the deuterium rod. For a deuterium number density of 5 by 10²⁴ per cm³, one has a density of 17 g/cm³, and to reach a density-radius product above 10 g/cm² requires a heated length of about 0.6 cm. With the stopping length shorter than that, the condition for the ignition of a thermonuclear detonation wave is satisfied.

For hundredfold compressed deuterium, the cross-sectional area is 10⁻³ cm², where initially it was 10⁻¹ cm². With that area and a length of 0.6 cm, one finds an ignition energy of about 10¹⁰ erg, or about 1 gigajoule. This energy is provided by the 10⁷-ampere GeV proton beam lasting 10⁻⁷ seconds. The time is short enough to ensure the cold compression of deuterium to high densities. For a thousandfold compression, found feasible in laser fusion experiments, the ignition energy is 10 times less.

In hitting the target, a fraction of the proton beam energy is dissipated into X-rays by entering and bombarding the high-atomic-number material cone focusing the proton beam onto the deuterium cylinder. The X-rays released fill the hohlraum surrounding the deuterium cylinder, compressing it to high densities, while the bulk of the proton beam energy heats and ignites the deuterium cylinder at its end, launching in it a detonation wave.

If the GeV, 10⁷-ampere proton beam passes through background hydrogen plasma, it induces in the plasma a return current carried by its electrons, where the electrons move in the same direction as the protons. But because the current of the proton beam and the return current of the plasma electrons are in opposite directions, they repel each other. Since the stagnation pressure of the proton beam is much larger than that of the electron return current, the return current electrons will be repelled from the proton beam toward its surface. Evaluating both pressures gives about 3 by 10¹¹ dyn/cm² for the beam against about 5 by 10² dyn/cm² for the return current — negligible even if the electron density were a thousand times larger, as in highly compressed deuterium. The assumption that the magnetic field of the proton beam is sufficiently strong to entrap the charged fusion products within the deuterium cylinder is therefore well justified.

Solution in Between Two Extremes

With chemical propulsion, manned space flight to the Moon is barely possible and only with massive multistage rockets. For manned space flight beyond the Moon, nuclear propulsion is indispensable. Nuclear thermal propulsion is really not much better than advanced chemical propulsion. Ion propulsion, using a nuclear reactor to drive an electric generator, has a much higher specific impulse but not enough thrust for short interplanetary transit times needed for manned missions. This leaves propulsion by a chain of fission bombs, or fission-triggered fusion bombs, as the only credible option. There the thrust and specific impulse are comparatively huge, but a comparatively small explosive yield is desirable. Making the yield too small, the bombs become extravagant in the sense that only a small fraction of the fission explosive is consumed.

This problem can be overcome through the nonfission ignition of small fusion explosions. A first step in this direction is the nonfission ignition of deuterium-tritium thermonuclear microexplosions, expected to be realized in the near future. This reaction was chosen for the first proposed thermonuclear microexplosion propulsion concept, with the ignition done by an intense relativistic electron beam. But because in the deuterium-tritium reaction 80 percent of the energy is released into neutrons that cannot be reflected from the spacecraft by a magnetic mirror, it was proposed to surround the microexplosion with a neutron-absorbing hydrogen propellant, increasing the thrust at the expense of the specific impulse. For this reason, in the Daedalus interstellar probe study by the British Interplanetary Society, the neutron-less helium-3-deuterium reaction was proposed, because for such a mission the specific impulse should be as high as possible. But even in a helium-3-deuterium plasma, there are some neutron-producing deuterium-deuterium reactions. There is no large source of helium-3 on Earth, though it might exist on the surface of the Moon and in the atmosphere of Jupiter. In the deuterium-deuterium reaction, much less energy goes into neutrons, but it is more difficult to ignite.

Figure 1 sets three cases side by side. Upper left: the experimentally verified ignition of a deuterium-tritium pellet with the X-rays generated in an underground test from a fission bomb — the Centurion-Halite experiment at the Nevada Test Site — requiring a few megajoules at a density-radius product of about 1 g/cm². Upper right: the 15-megaton Mike test, where with the Teller-Ulam configuration a large amount of liquid deuterium is ignited with a fission bomb, at a density-radius product of about 10 g/cm². At the bottom: the proposed hypothetical deuterium target, where a detonation wave in a thin cylindrical deuterium rod is ignited by a pulsed 10⁷-ampere GeV proton beam, utilizing the strong magnetic field of the beam current.

To estimate the order of magnitude of what is needed, we consider a spacecraft with a mass of 10³ tons, or 10⁹ g, to be accelerated at one g, requiring a thrust of about 10¹² dyne. To establish the magnitude and number of fusion explosions needed to propel the spacecraft to a velocity of 100 km/s, we use the thrust equation with an exhaust velocity of 10⁸ cm/s, equal to the expansion velocity of the fusion bomb plasma. This gives a mass flow of 10⁴ g/s, or 10 kg/s, and a propulsion power of 5 by 10¹⁹ erg/s. With 4 by 10¹⁹ erg equivalent to the explosive energy of one kiloton of TNT, this is equivalent to about one nuclear kiloton bomb per second.

From the rocket equation, setting the final mass equal to the initial mass minus the mass of all used-up bombs, and if one bomb explodes per second so that its mass is 10⁴ g: assuming the spacecraft reaches a velocity of 100 km/s, the velocity needed for fast interplanetary travel, the total bomb mass is about 10⁸ g, requiring about 10⁴ one-kiloton fusion bombs releasing 5 by 10²³ erg. By comparison, the kinetic energy of the spacecraft, 5 by 10²² erg, is 10 times less. In reality it is still smaller, because a large fraction of the energy released by the bomb explosions is dissipated into space.

One can summarize these estimates by concluding that a very large number of nuclear explosions are needed, which for fission explosions, as well as for deuterium-tritium explosions, would become very expensive. This strongly favors deuterium, which is more difficult to ignite than a mixture of deuterium with tritium but is abundantly available. The following text tries to show how bomb propulsion solely with deuterium might be possible.

The Nonfission Ignition of Small Deuterium Nuclear Explosives

With no deuterium-tritium microexplosions yet ignited, the nonfission ignition of pure deuterium fusion explosions seems to be a tall order. An indirect way to reach this goal is by staging a smaller deuterium-tritium explosion with a larger deuterium explosion. There the driver energy, but not the driver, may be rather small. A direct way requires a driver with order of magnitude larger energies.

The generation of GeV potential wells, made possible with magnetic insulation of conductors levitated in ultrahigh vacuum in a laboratory on Earth, has the potential to lead to order of magnitude larger driver energies. It is the ultrahigh vacuum of space that enables this to be achieved without levitation. Therefore, the spacecraft, acting as a capacitor, can be charged up to GeV potentials.

If the spacecraft is charged to a positive GeV potential, a gigajoule intense relativistic ion beam below the Alfvén current limit can be released from the spacecraft and directed to the deuterium explosive for its ignition. If the current needed for ignition is below the Alfvén limit for ions, the beam is stiff. The critical Alfvén current for protons is 3.1 by 10⁷ times beta times gamma amperes, with beta the proton velocity over the velocity of light and gamma the relativistic factor. For GeV protons, the Alfvén current is well in excess of the critical current to entrap the deuterium-deuterium fusion reaction products, which is the condition for detonation.

Figure 2 shows a possible bomb configuration: the liquid or solid deuterium explosive has the shape of a long cylinder, placed inside a cylindrical hohlraum; a GeV proton beam coming from the left dissipates part of its energy into a burst of X-rays compressing and igniting the deuterium cylinder, while the main portion is focused by a cone onto the rod; also marked are the magnetic field, the miniature target rocket chamber, the solid hydrogen and the laser beam that heats it. With its gigajoule energy lasting less than 10⁻⁷ seconds, the beam power is greater than 10¹⁶ watts, sufficiently large to ignite the deuterium explosive.

Because the condition for thermonuclear burn and detonation depends only on the critical current and not on the radius of the deuterium cylinder, one may wish to make the diameter of the deuterium cylinder as small as possible, because as was shown above the specific impulse can become largest, with the electrons not taking away kinetic energy from the charged fusion products. Therefore, the yield of the deuterium fusion explosions can be made much smaller, eliminating the need for Orion-type shock absorbers, but the thrust there is also much smaller. For very-deep-space missions, that would not be a disadvantage.

A problem in either case is that 38 percent of the energy is released as neutrons. In hitting the spacecraft, they lead to its heating, requiring a presumably large radiator. For a long and thin deuterium rod, this problem can likely be reduced by a boron diaphragm on the deuterium rod, because boron is a good neutron absorber. It can be enhanced by a hydrogen moderator, because the absorption cross section for neutrons is greatly increased with a reduced neutron kinetic energy. Both the boron and the hydrogen there simply become part of the propellant, reducing the specific impulse but increasing the thrust.

Figure 3 shows the screening of the spacecraft against the neutrons by a boron diaphragm, with solid hydrogen as a neutron moderator to increase the neutron absorption cross section of boron, and the neutrons released from the deuterium cylinder.

As noted earlier, in comets there is a large amount of deuterium readily available for mining. And we know comets also contain nitrogen and carbon. From this knowledge we can assume that very likely other light elements, such as boron, exist in relatively high concentrations in comets.

Although the waste heat radiator remains a problem, it favors large explosions, because most of the waste heat accompanies the propellant into space. Droplet radiators, with the droplets slowly evaporating, are unlikely to work. Placing the neutron-absorbing radiators near the shock absorber, permitting them to get red-hot, and thermally insulating the rest of the spacecraft from the radiators may solve the problem.

Delivery of a GeV Proton Beam Onto the Deuterium Fusion Explosive

The spacecraft is inductively charged against an electron cloud surrounding the craft, and with a magnetic field on the order of 10⁴ gauss, easily reached by superconducting currents flowing in an azimuthal direction around the craft, is magnetically insulated against the electron cloud up to GeV potentials. The spacecraft and its surrounding electron cloud form a virtual diode with a GeV potential difference.

To generate a proton beam, it is proposed to attach a miniature hydrogen-filled rocket chamber to the deuterium bomb target at the position where the proton beam hits the fusion explosive. A pulsed laser beam from the spacecraft is shot into the rocket chamber, vaporizing the hydrogen, which is emitted through the Laval nozzle as a supersonic plasma jet. If the nozzle is directed toward the spacecraft, a conducting bridge is established, rich in protons, between the spacecraft and the fusion explosive. Protons in this bridge are then accelerated to GeV energies, hitting the deuterium explosive. Because of the spacecraft’s large dimensions, the jet does not have to be aimed at the spacecraft very accurately.

The original idea for the electrostatic energy storage on a magnetically insulated conductor was to charge up a levitated superconducting ring to GeV potentials, with the ring magnetically insulated against breakdown by the magnetic field of a large toroidal current flowing through the ring. It is here proposed to give the spacecraft a topologically equivalent shape, using the entire spacecraft for the electrostatic energy storage. There toroidal currents flowing azimuthally around the outer shell of the spacecraft not only magnetically insulate the spacecraft against the surrounding electron cloud but also generate a magnetic mirror field that can reflect the plasma of the exploding fusion bomb. In addition, the expanding bomb plasma can induce large currents, and if these currents are directed to flow through magnetic field coils positioned on the upper side of the spacecraft, electrons from there can be emitted into space surrounding the spacecraft by thermionic emitters placed on the inner side of these coils, inductively charging the spacecraft for subsequent proton beam ignition pulses. A small high-voltage generator driven by a small onboard fission reactor can make the initial charging, ejecting from the spacecraft negatively charged pellets.

Figure 4 shows the superconducting atomic spaceship, positively charged to GeV potential, with azimuthal currents and a magnetic mirror; a fusion minibomb in position to be ignited by the intense ion beam, storage space for the bombs, a bioshield for the payload, coils pulsed by current drawn from an induction ring, and the electron flow neutralizing the space charge of the fusion explosion plasma.

With the magnetic insulation criterion that E stay below B in electrostatic units, then for a field of 10⁴ gauss and an electric field of 3 by 10³ electrostatic units, or 9 by 10⁵ V/cm, one has E about one third of B. A spacecraft with a dimension of 3 by 10³ cm can then be charged to a potential of about 3 by 10⁹ volts, with a stored electrostatic energy on the order of 1 gigajoule. The discharge time is on the order of the dimension divided by the velocity of light — in our example, about 10⁻⁷ seconds. For a proton energy pulse of 1 gigajoule, the beam power is 3 by 10¹⁶ erg/s, or 30 petawatts, large enough to ignite a pure deuterium explosion.

Lifting of Large Payloads Into Earth Orbit

To lift large payloads into Earth orbit remains the most difficult task. For a launch from the Earth’s surface, magnetic insulation inside the Earth’s atmosphere fails, and with it the proposed pure deuterium bomb configuration. A different technique is suggested here, one I had first proposed in a classified report dated January 1970, declassified in July 2007 and thereafter published. A similar idea was proposed in a classified Los Alamos report dated November 1970 and declassified in July 1979. In both cases the idea is to use an expendable laser for the ignition of each nuclear explosion, with the laser material thereafter becoming part of the propellant. The Los Alamos scientists had proposed to use an infrared carbon dioxide or chemical laser for this purpose, but this idea does not work, because the wavelength is too long and therefore unsuitable for inertial confinement fusion. I had suggested an ultraviolet argon ion laser instead.

However, since argon ion lasers driven by an electric discharge have a small efficiency, I had suggested a quite different way of pumping it. There the efficiency can be expected to be quite high. It was proposed to use a cylinder of solid argon, surrounding it by a thick cylindrical shell of high explosive. If simultaneously detonated from outside, a convergent cylindrical shockwave is launched into the argon. For the high explosive, one may choose hexogen with a detonation velocity of 8 km/s. In a convergent cylindrical shockwave, the temperature rises as the distance from the axis to the power minus 0.4. If the shock is launched from a distance of about 1 m onto an argon rod with a radius equal to 10 cm, the temperature reaches 90,000 K, just right to excite the upper laser level of argon.

Following its heating to 90,000 K, the argon cylinder radially expands and cools, with the upper laser level frozen into the argon. This is similar to a gas dynamic laser, where the upper laser level is frozen in the gas during its isentropic expansion in a Laval nozzle. To reduce depopulation of the upper laser level during the expansion by superradiance, one may dope the argon with a saturable absorber, acting as an antiknock additive. In this way, megajoule laser pulses can be released within 10 nanoseconds. A laser pulse from a small Q-switched argon ion laser placed in the spacecraft can then launch a photon avalanche in the argon rod, igniting a deuterium-tritium microexplosion.

Figure 5 shows the argon ion laser igniter, used to ignite a staged deuterium-tritium and deuterium-deuterium fusion explosion in a mini-Teller-Ulam configuration: a solid argon rod, a cylindrical shell of high explosive, detonators, and a Q-switched argon ion laser oscillator.

Employing the Teller-Ulam configuration, by replacing the fission explosive with a deuterium-tritium microexplosion, one can then ignite a much larger deuterium-deuterium explosion.

As an alternative, one may generate a high current linear pinch discharge with a high-explosive-driven magnetic flux compression generator. If the current is on the order of 10⁷ amperes, the laser can ignite a deuterium-tritium thermonuclear detonation wave propagating down the high current discharge channel, which in turn can ignite a much larger pure deuterium explosion.

If the craft is launched from the Earth’s surface, one has to take into account the mass of the air entrained in the fireball. The situation resembles a hot-gas-driven gun, albeit one of rather poor efficiency. For a bomb energy of 5 by 10¹⁹ erg, a craft mass of 10⁹ g, and setting the required velocity at the escape velocity of about 10 km/s, one finds that about 10 explosions are needed. Assuming an efficiency of 10 percent, about 100 one-kiloton explosions would therefore be needed.

Neutron Entrapment in an Autocatalytic Thermonuclear Detonation Wave — a Means to Increase the Specific Impulse and to Solve the Large Radiator Problem

The principal reason why neutrons released by thermonuclear reactions pose such a serious problem is that they cannot be repelled from the spacecraft by a magnetic field. However, choosing a neutron-absorbing target, one can reduce the flux of neutrons hitting the spacecraft. Besides inflicting material damage on the spacecraft, the neutrons release heat that must be removed by a very large radiator.

The idea of the autocatalytic thermonuclear detonation wave presents a solution which, if feasible, would very much reduce the magnitude of this problem. For its implementation, it requires very large bremsstrahlung flux densities in the burn zone behind the thermonuclear detonation front. Such large bremsstrahlung flux densities will occur in deuterium detonation burn, at the highest temperature for all the thermonuclear reactions.

In an autocatalytic thermonuclear detonation, soft X-rays generated through the burn of the thermonuclear plasma behind the detonation front compress the still unburned thermonuclear fuel ahead of the front. The increase in the fuel density, both in the Teller-Ulam configuration and in the autocatalytic thermonuclear detonation wave, is of crucial importance, with the reaction rate proportional to the square of the density.

Figure 6 shows an autocatalytic thermonuclear detonation using a soft X-ray precursor from the burn zone to precompress the thermonuclear fuel ahead of the detonation front; the soft X-rays travel through the gap between the tamp and the liner.

From the burning plasma behind the detonation front, energy flows into all spatial directions. Part is by bremsstrahlung and part by electronic heat conduction. Roughly half of the energy flows into the liner, one quarter into the still unburned fuel ahead of the wave, and one quarter into the opposite direction. For a temperature of 10⁹ K, the bremsstrahlung emission rate is about 3.2 by 10⁻²³ times the square of the number density, in erg per cm³ per second. The flux of the bremsstrahlung that goes into the liner is that rate times half the radius of the deuterium rod just behind the detonation front; about one half of this radiation runs ahead of the detonation front, where it precompresses the deuterium.

We are aiming at a density where the neutrons are absorbed in the burning plasma cylinder. If the neutron-deuteron collision cross section is about 10⁻²⁴ cm², then the neutron path length must be smaller than the radius, which requires that the number density times the radius be at least 10²⁴ per cm². If the radius is 0.01 cm, then the number density must be about 10²⁶ per cm³, that is 5 by 10³ times the particle number density of liquid deuterium. With that density one finds a precursor flux of about 3 by 10²⁷ erg per cm² per second. The flux onto the surface of a deuterium tube whose length is comparable to its radius then comes out at about 10²⁴ erg/s, or 10¹⁷ watts — 100 petawatts, certainly powerful enough to compress the deuterium to more than thousandfold density.

With the entrapment of the neutrons comes an increase of the specific impulse. With 38 percent of the energy going into the kinetic energy of the neutrons and 62 percent into charged fusion products, the specific impulse is increased by the factor 1.275. This increases the maximum exhaust velocity from 1.5 by 10⁹ cm/s to 1.9 by 10⁹ cm/s, or 0.063 c.

In the course of the thermalization in the supercompressed plasma, the neutron absorption cross section is greatly increased, both in the liner and tamp, with the liner also compressed to high densities. If the liner and tamp are made from boron, which has a large neutron-absorption cross section, the spacecraft is heated only by a greatly reduced thermal neutron flux, and only this much smaller amount of heat must be removed by a radiator.

Testing the Deuterium Microdetonation Concept

For the Orion bomb propulsion concept, testing was a serious problem. If tested on the Earth, it would have resulted in the large fallout of fission products. These tests would have been needed to study the survival of the pusher plate under the repeated exposure of kiloton fission explosions. Of course, the tests could have been carried out in space, but this would have been extremely expensive, because it would have required launch by chemical rockets of the huge Orion spaceship into space.

Fortunately, this is not necessary for the deuterium microdetonation propulsion concept, because there exists an alternative way to generate a 10⁷-ampere GeV proton beam: replacing the huge spaceship used as a large capacitor to be charged up to gigavolt potentials with a Super Marx generator. This Super Marx generator can achieve on Earth what the huge spaceship can achieve in space: the generation of gigavolt, 10⁷-ampere proton beams. Since the realization of pure deuterium burn would obviously be a breakthrough in fusion, the expenditure for the development of a Super Marx generator would be well justified.

Up until now nuclear fusion by inertial confinement has been achieved only using large fission explosives as a means, or driver, for ignition. From this experience we know that the ignition is easy with sufficiently large driver energies, difficult to duplicate with lasers or electric pulse power by an ordinary Marx generator. The problem therefore is not the configuration of the thermonuclear explosive but the driver, be it for the ignition of pure deuterium as in the Mike test or for the ignition of deuterium-tritium as in the Centurion-Halite experiment, because for sufficiently large driver energies the target configuration is of secondary importance.

Substantially larger driver energies can be reached with the Super Marx generator. It can be viewed as a two-stage Marx generator, where a bank of ordinary Marx generators assumes the role of a first stage. If the goal is the much more difficult ignition of a pure deuterium microexplosion, the Super Marx generator must in addition deliver a much larger amount of energy, compared with that of the most powerful lasers, and also generate a magnetic field in the thermonuclear target that is strong enough to entrap the charged deuterium-deuterium fusion products within the target. Only then is the condition for a propagating thermonuclear burn fulfilled.

Figure 7 shows the circuit of an ordinary Marx generator, in which n capacitors charged to a voltage v are switched into series over spark gaps, adding up to a voltage n times v. Figure 8 shows the Super Marx generator, in which N Marx generators charge up N fast capacitors to a voltage V, which switched into series add up to N times V. Figure 9 is an artist’s conception of a 1.5-km-long Super Marx generator composed of 100 fifteen-metre-long high-voltage capacitors, each designed as a magnetically insulated coaxial transmission line, placed inside a high-vacuum vessel; each is charged by two conventional Marx generators symmetrically to 10 MV, the Marx generators are then electrically decoupled, and the individual capacitors are connected in series via spark gap switches, producing a potential of 1 GV. Figures 10 to 12 give a detailed view of one section, the injection of the GeV, 10 MA proton beam into the chamber with the cylindrical deuterium target, and a schematic of a few elements of the chain.

Following their charging up of the Super Marx generator, the Marx generators are disconnected from the Super Marx. If the capacitors of the Super Marx can hold their charge long enough, this can be done by mechanical switches.

To erect the Super Marx, its capacitors are switched into series by circular spark gap switches. The capacitors of the Super Marx are magnetically levitated inside an evacuated tunnel and magnetically insulated against the wall of the tunnel by an axial magnetic field, generated by superconducting external magnetic field coils. The magnetic insulation criterion requires that B exceed E, with B in gauss and E in electrostatic cgs units. If the field is 3 by 10⁴ gauss, for example, magnetic insulation is possible up to 3 by 10⁴ electrostatic units, about 10⁷ V/cm, at the limit of electron field emission. To withstand a voltage of 10⁹ volts between the outer positively charged surface of the capacitors in series and the tunnel wall then requires a distance somewhat greater than 1 metre.

Assuming a breakdown strength of the dielectric larger than 3 by 10⁴ V/cm and a potential difference of 10⁷ volts between the inner and outer conductor, the smallest distance of separation between both conductors has to be about 3 by 10² cm. If, for example, the length is 1.6 by 10³ cm, the inner radius 8 by 10² cm and the dielectric constant about 10, one finds a capacitance of about 2 by 10⁴ cm. For these numbers, the energy stored in one capacitor at 10⁷ volts adds up, over the 100 capacitors of the Super Marx, to about 10¹⁶ erg. About 10 times more energy can be stored if the radius of the capacitor is about 3 times larger, if there is a larger dielectric constant, or if a combination of these conditions exists. This means that for about 100 capacitors, an energy of 10¹⁶ erg — 1 gigajoule — can be stored in the mile-long Super Marx.

Another idea, proposed by Fuelling, is to place the ordinary Marx generators of the first stage inside the coaxial capacitors of the Super Marx. The advantage of this configuration is that it does not require disconnection of the Marx generators from the capacitors of the Super Marx prior to its firing. Because the charging and discharging of the Super Marx can be done very fast, one can use compact water capacitors, where the dielectric constant is about 80. And instead of magnetic insulation of the capacitors of the Super Marx against the outer wall, one can perhaps use transformer oil for the insulation. Giving each inner segment of the Super Marx enough buoyancy, for example by adding air chambers, these segments can be suspended in the transformer oil. There the outer radius of the coaxial capacitors is much larger. This permits storage of gigajoule energies in the Super Marx.

Figure 13 shows the superconducting toroidal capacitor and its discharge onto the target. The last capacitor of the Super Marx is a superconducting ring with a large toroidal current. There the large azimuthal magnetic field set up by the toroidal current magnetically insulates the ring against breakdown to the wall. The load is the deuterium target, consisting of a solid deuterium rod covered with a thin ablator placed inside a cylindrical hohlraum. To the left of the hohlraum and the deuterium rod is a mini-rocket chamber filled with solid hydrogen.

The method of discharging the energy from the Blumlein transmission line to the target then goes as follows. A short laser pulse is projected into the mini-rocket chamber through a hole of an electrode at the center of the ring. By heating the hydrogen in the mini-rocket chamber to a high temperature, a supersonic hydrogen jet is emitted through the Laval nozzle toward the electrode at the center of the ring, forming a bridge to the target. A second laser pulse then traces out an ionization trail inside the hydrogen jet, facilitating an electric discharge to the target, with the space charge neutralizing plasma pinching the proton beam down to a small diameter.

The Super Marx generator therefore can accomplish on Earth what the spacecraft acting as a large capacitor can do in space.

The testing of an argon ion laser driven by high explosives can, of course, be done on Earth, and the same applies to the conjectured superexplosives.

Conclusion

If large-scale manned spaceflight has any future, a high-specific-impulse, high-thrust propulsion system is needed. The only known propulsion concept with this property is nuclear bomb propulsion. However, since large-yield nuclear explosions are for obvious reasons undesirable, the nuclear explosions should be comparatively small. But because of what Freeman Dyson described as the tyranny of the critical mass, small fission bombs or fission-triggered fusion bombs become extravagant, with only a fraction of the nuclear material consumed. The same is true for nuclear fission gas core rocket reactors, where much of the unburned fission fuel is lost in the exhaust.

In the original Orion bomb propulsion concept, the propulsive power was through the ablation of a pusher plate. There the energy is delivered to the pusher plate by the black-body radiation of the exploding bomb. The propulsion by non-fission-triggered fusion bombs not only has the advantage that it is not subject to the tyranny of the critical mass, but the propulsive power is there delivered by the kinetic energy of the expanding hot plasma fireball repelled from the spacecraft by a magnetic mirror. This is particularly true for a pure deuterium bomb, where, compared with deuterium-tritium, more energy is released into charged fusion products.

Whereas in a fission explosion most of the energy is lost into space by the undirected black-body radiation, much more propulsive energy can be drawn from the plasma of a pure deuterium fusion bomb explosion, in conjunction with a magnetic mirror.

Manned space flight requires lifting large masses into Earth orbit, where they are assembled into a large spacecraft. While this can be done with chemical rockets, it would be much more economical if it could be done with a chain of small nuclear explosions. Without radioactive fallout, this can be done with a chain of laser-ignited fusion bombs, with one laser for each bomb, where the lasers become part of the exhaust. Ignition can be done not by infrared chemical or carbon dioxide lasers, as was suggested by the Los Alamos team, but rather by an ultraviolet laser driven by high explosives, as suggested by the author.

Looking to the future, using deuterium — widely available on most planets of the solar system and in the Oort cloud outside the solar system — as the nuclear rocket fuel would make manned space flight to the Oort cloud possible, at a distance of about one-tenth of one light year.

Appendix: Conjectured Metastable Superexplosives Formed Under High Pressure for Thermonuclear Ignition

Under normal pressure, the distance of separation between two atoms in condensed matter is typically on the order of 10⁻⁸ cm, with the distance between molecules formed by the chemical binding of atoms of the same order of magnitude. The electrons of the outer electron shells of two atoms undergoing a chemical binding form a bridge between the reacting atoms. The formation of the bridge is accompanied by a lowering of the electric potential well for the outer-shell electrons of the two reacting atoms, with the electrons feeling the attractive force of both atomic nuclei. Because of the lowering of the potential well, the electrons undergo, under the emission of electronvolt photons, a transition into lower energy molecular orbits. At higher pressures, bridges between the next inner shells are formed under the emission of soft X-rays.

Going to still higher pressures, a situation can arise with the building of electron bridges between shells inside shells.

Figure 14 contrasts an ordinary explosive, in which the outer-shell electrons of the reacting atoms form electronvolt molecules accompanied by the release of heat through electronvolt photons, with a superexplosive, in which the outer-shell electrons melt into a common outer shell with inner electron shells forming kilovolt molecules accompanied by the release of keV X-ray photons. Figure 15 shows how, with increasing pressure, electron bridges are formed between shells inside shells melting into common shells.

There the explosive power would be even larger. Now consider a situation where the condensed state of many closely spaced atoms is put under high pressure making the distance of separation between the atoms much smaller, and where the electrons from the outer shells coalesce into one shell surrounding both nuclei, with the electrons from inner shells forming a bridge. Because there the change in the potential energy is much larger, the change in the electron energy levels is also much larger, potentially on the order of keV. There then a very powerful explosive is formed, releasing its energy in a burst of keV X-rays. This powerful explosive is likely to be very unstable, but it can be produced by the sudden application of a high pressure at just the moment when it is needed. Because an intense burst of X-rays is needed for the ignition of a thermonuclear microexplosion, it could be used as an alternative to the argon ion laser for the ignition of a pure fusion bomb.

The energy of an electron in the ground state of a nucleus of charge Z e is minus 13.6 Z² electronvolts. With the inclusion of all the Z electrons surrounding that nucleus, the exponent softens to 2.42, with the outer electrons less strongly bound. Now assume that two nuclei are so strongly pushed together that they act like one nucleus of charge 2 Z e onto the 2 Z electrons surrounding it. The difference of the two energies is then about 58.5 times Z to the power 2.42 electronvolts. Using the example of neon, atomic number 10, one obtains about 15 keV. Of course, it would require a very high pressure to push two neon atoms that close to each other, but this example shows it is plausible that smaller pressures exerted on heavier nuclei with many more electrons may result in a substantial lowering of the potential well for their electrons.

A pressure of about 100 megabars, that is 10¹⁴ dyn/cm², can be reached with existing technology in sufficiently large volumes, with at least three possibilities: bombardment of a solid target with an intense relativistic electron or ion beam; hypervelocity impact; or bombardment of a solid target with beams or by hypervelocity impact, followed by a convergent shock wave.

Bombardment of a Solid Target With an Intense Relativistic Electron or Ion Beam

This possibility was considered by Kidder, who computes a pressure of 50 megabars if an iron plate is bombarded with a 1-MJ, 10-MeV, 10⁶-ampere relativistic electron beam, focused down to an area of 0.1 cm². Accordingly, a 2-MJ beam would produce 100 megabars. Instead of an intense relativistic electron beam, one may use an intense ion beam. It can be produced by the same high-voltage technique, replacing the electron beam diode by a magnetically insulated diode. Using intense ion beams has the additional benefit that the stopping of the ions in a target is determined by a Bragg curve, generating the maximum pressure inside the target, not on its surface.

Hypervelocity Impact

A projectile with a density of about 20 g/cm³ accelerated to a velocity of 30 km/s would, upon impact, produce a pressure of about 100 megabars. The acceleration of the projectile to these velocities can be done by a magnetic traveling wave accelerator.

Bombardment of a Solid Target With Beams or By Hypervelocity Impact, Followed By a Convergent Shock Wave

If, upon impact of either a particle beam or a projectile, the pressure is less than 100 megabars — for example, only on the order of 10 megabars — but is acting over a larger area, a tenfold increase in the pressure over a smaller area is possible by launching a convergent shock wave from the larger area on the surface of the target onto a smaller area inside. According to Guderley, the rise in pressure in a convergent spherical shock wave goes as the radius to the power minus 0.9, which means 100 megabars could be reached by a tenfold reduction in the radius of the convergent shock wave. While it is difficult to reach 30 km/s with a traveling magnetic wave accelerator, it is easy to reach a velocity of 10 km/s with a two-stage light gas gun.

We assume an equation of state relating pressure to the cube of the number density. For a pressure of 100 megabars we may set the Fermi pressure of the solid at 10¹¹ dyn/cm². With the lattice constant related to the number density, the lattice constant scales as the pressure ratio to the power minus one ninth. Such a lowering of the interatomic distance is sufficient for the formation of molecular states.

Calculations done by Müller, Rafelski, and Greiner show that for the molecular states bromine-bromine, iodine-gold, and uranium-uranium, a twofold lowering of the distance of separation leads to a lowering of the electron orbit energy eigenvalues by about 0.35 keV and 1.4 keV respectively. At a pressure of 100 megabars, where the lattice constant is halved, the result of these calculations can be summarized by a logarithmic law: the logarithm of the energy shift in keV equals 1.3 by 10⁻² times Z minus 1.4, where Z is here the sum of the nuclear charge for both components of the molecule formed under the high pressure.

Figure 16 is a pressure against interatomic-distance diagram for the upper atomic and lower molecular adiabats. It illustrates how the molecular state is reached during the compression along the upper adiabat at the distance where the pressure attains its critical value. In passing over this pressure, the electrons fall into the potential well of the two-center molecule, releasing their potential energy as a burst of X-rays. Following its decompression, the molecule disintegrates along the lower adiabat.

If the conjectured superexplosive consists of just one element, as in the case of the bromine-bromine reaction or the uranium-uranium reaction, no special preparation for the superexplosive is needed. But as the example of the aluminium and iron oxide thermite reaction shows, reactions with different atoms can release a much larger amount of energy compared with other chemical reactions. For the conjectured superexplosives, this means they have to be prepared as homogeneous mixtures of nanoparticle powders, bringing the reacting atoms as close together as possible.

For the ignition of a thermonuclear reaction, one may consider the following scenario. A convergent shock wave launched at the outer radius into a spherical shell reaches the inner radius at a pressure of 100 megabars. After the inward-moving convergent shock wave has reached the inner radius, an outward-moving rarefaction wave is launched from the same radius, from which an intense burst of X-rays is emitted. One can then place a thermonuclear deuterium-tritium target inside the cavity of that radius, with the target bombarded, imploded, and ignited by the X-ray pulse. The ignited deuterium-tritium can there serve as a hot spot for the ignition of deuterium.

Figure 17 shows the inertial confinement fast-ignition configuration.

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