LULI 2000 laser at the École Polytechnique, Paris. Photo: Wikimedia

In this article, Jonathan Tennenbaum constructs – conceptually – a hydrogen-boron fusion reactor similar to one proposed by Australian plasma physicist Heinrich Hora.

Hora’s approach is one of many – in various stages of development – proposed for achieving nuclear fusion power. I don’t intend to endorse one idea over another but writing about Hora’s extremely promising concept is an excellent way to acquaint readers with some of today’s most exciting areas of science and technology.

Ideally, readers should be familiar with the preceding articles in this series and the following pieces of the puzzle:  

1. The reaction between a nucleus of hydrogen and one of boron yields three helium nuclei (alpha particles), which escape from the scene of the reaction at high velocities. The fact that the alpha particles are charged particles – each one carrying two units of positive charge – provides the possibility of converting their energy of motion directly into electric power. (Part 2)

2. The enormous difficulty of achieving hydrogen-boron fusion. If heat is to be used, the required temperatures lie in the range of billions of degrees; the reaction probability (the “cross-section” of the reaction) is low; extremely high densities (or very long confinement times) are required in order to ignite the hydrogen-boron fuel and obtain a sufficient degree of “burn-up.” (Part 2)

3. Use lasers to trigger “microexplosions” of tiny pellets of hydrogen-boron fuel. A hydrogen-boron power plant will work in a pulsed regime, generating one microexplosion per second (or several seconds) in an explosion chamber equipped to extract electrical energy from the resulting bursts of alpha particles by slowing them down in an electric field.

4. Lessons learned from a half-century of attempts to realize fusion power by means laser-triggered “microexplosions,” following a paradigm inherited from the development of the first hydrogen bomb. This approach involves compressing and heating a spherical fuel pellet by hitting it from all directions by simultaneous laser pulses. Unfortunately, instabilities tend to develop in the plasma created when the fuel is heated, interfere with the compression and ignition process (Part 3).

5. One approach is to “outflank” instabilities by operating on time-scales that are much shorter than the time required for bad behavior to develop.

6. Theoretical predictions and experimental indications of the existence of “ponderomotive” (accelerating) forces generated in target material under the action of intense pulses of laser light, whose effects differ radically from those caused by heating alone. The shorter and “cleaner” the laser pulses, the more these ponderomotive forces dominate the scene relative to thermal effects. Calculations predicting that under appropriate conditions, ultra-short, ultra-high-power laser pulses will accelerate macroscopic “blocks” of plasma to enormous velocities. (Part 5)

8. In 1985, the invention of chirped pulse amplification (CPA), allowed laser pulses to be amplified to enormous powers. Lasers were then developed with powers in the range of petawatts (a million billion-watts) and pulse-lengths between a picosecond and a femtosecond. (Part 4)

9. Experimental confirmation, in 1996, of the “plasma block acceleration” phenomenon in 1996, confirmed again in later experiments. (Part 5)

10. Calculations indicating that ignition of hydrogen boron fusion could be obtained far more easily with a cylindrical configuration using a single laser pulse focussed on one end of a cylindrical fuel pellet than the classical spherical implosion method. The plasma block accelerated to tremendous velocities into the fuel material, acts as a compressing piston as well as – de facto – a neutralized particle beam, with a million times the current densities achieved with conventional particle accelerators. (Part 5)   

Illustration: Courtesy Heinrich Hora

11. Successful experimental generation of large numbers (billions or more) of hydrogen-boron reactions, occurred by irradiating a fuel target with a single high-power laser pulse. (Part 5)

Borrowing from magnetic confinement fusion

There is one more essential element missing before we can go ahead with the hydrogen-boron prototype reactor.

The proposed set-up, with a cylindrical fuel pellet hit end-on by a single laser pulse, has a serious weak point: there is nothing to prevent the fuel from expanding radially outwards during the ignition process. This would cause the density of the fuel to drop, preventing an effective burn-up of the fuel. We might get a “fizzle” instead of a full microexplosion.

To solve this problem, Hora borrows a basic principle from so-called magnetic confinement fusion – the great competitor to laser fusion. A sufficiently powerful magnetic field, directed parallel along the axis of the cylinder, can counteract the tendency for the burning fuel to expand, confining it for the short instant required for the fusion burn wave to propagate all the way to the far end of the cylinder.

Magnetic confinement fusion exploits the fact that charged particles, when moving in a powerful magnetic field, experience forces that cause them to spiral around the magnetic field lines. The plasma is thereby trapped in the magnetic field.

In reality, the situation is complicated – as usual in the field of plasma physics – by the fact that plasmas generate their own magnetic fields and can defeat attempts to contain them in externally imposed “magnetic bottles.”

Faced with such misbehavior, the pursuit of magnetic confinement fusion has pushed researchers toward ever-higher magnetic field strengths. The mammoth International Thermonuclear Experimental Reactor (ITER), under construction in Cadarache, France, requires 10,000 tons of giant superconducting magnets to confine its plasma in a six-meter-radius toroidal chamber.

The ITER magnet system. Illustration: Wikimedia

ITER’s magnets are designed to generate magnetic field strengths of 10-12 Tesla – about six times the strength of the fields employed by the nuclear magnetic resonance imaging (MRI) machines used by hospitals.

By contrast, radial confinement of the burning fuel cylinder in Hora’s proposed reactor will require magnetic fields of more than 1,000 Tesla, a hundred times stronger than the ITER, albeit in an extremely tiny volume. This, at least, is what the calculations show.

How to produce super-high magnetic fields?

In 2012 the research group of Shinsuke Fujioka at the Institute of Laser Engineering in Osaka, Japan succeeded in generating fields of the even larger intensity with a simple method using laser pulses. For this purpose, they used the Gekko XII laser, built to carry out laser fusion experiments. The laser produced a short (one nanosecond) pulse with a power of approximately 10 trillion watts.

The Gekko XII laser in Osaka, Japan. Photo: Wikimedia

Fujioka’s setup consists of two parallel metal plates connected by a length of wire shaped in a loop. One of the plates has a small circular hole in it, through which the laser pulse can illuminate a small area on the opposing surface of the second plate. See the diagram below. (two loops are used instead of one, and the fuel pellet is added).

When the intense Gekko laser pulse hits the lower plate, it immediately transforms the outer layers of the metal into a plasma. The electrons are ripped away from the nuclei and rapidly accelerated to velocities near the speed of light (so-called “hot electrons”).

A huge number of these electrons fly across the gap between the capacitor plates and land on the upper plate, giving it a high negative charge. For a short moment the positively charged nuclei – which are much more massive than the electrons and much slower to respond – are left behind.

A huge electric potential difference builds up between the upper and lower plates. This drives electric current through the wire. The loop in the wire acts as a single-turn coil, generating a super-intense magnetic field pulse. The Japanese researchers measured field strengths of 1,500 Tesla, more than enough for Hora’s requirements.  

Time to ‘build’ a hydrogen-boron fusion reactor

(Again, I am talking about a conceptual design, nothing more, along the lines of Hora’s proposal as I understand it. Interested readers can consult his US patent application, granted in September 2019.)

The reactor produces energy in the form of regularly repeated microexplosions within an explosion chamber. The rate of “shots” might be about one per second for a commercial version, longer for the prototype.

Each microexplosion yields about one gigajoule of energy, equivalent to 280 kWh. At one “shot” per second, that would yield an average gross power of 1 GW. Assuming a high efficiency of conversion (see below), we would get an electric power output comparable to modern nuclear power plants. A prototype would presumably have slower pulse rates and a correspondingly lower power output.  

The fuel for the microexplosions comes in the form of long and thin cylinders, approximately 0.2 millimeters in diameter and a centimeter long, each containing approximately 14 milligrams of hydrogen and boron. The fuel cylinder is suspended in a small assembly with two capacitor plates connected by two conducting loops as shown in the diagram. Their purpose is to generate a powerful magnetic field parallel to the cylindrical axis, at the moment of ignition of the micro explosion, in the manner demonstrated by Fujioka et al.  

Hydrogen-boron fuel assembly (left). Explosion chamber for the hydrogen-boron reactor, with fuel assembly. Illustrations courtesy Heinrich Hora

Each microexplosion is generated using a pair of precisely-timed, nearly simultaneous ultra-short pulses from two lasers (presumably combined in a single system).

The pulse from Laser 1 (see diagram above) generates a powerful 1,000 Tesla magnetic field parallel to the cylinder axis. The pulse from Laser 2, focused on one end of the fuel cylinder, ignites the hydrogen-boron reactions and sets off a “burn wave” that propagates through to the opposite end. The magnetic field ensures that the plasma does not expand much until the burnup is completed.

The explosion chamber, kept at a high vacuum, is about one meter in diameter and designed to withstand the force of the microexplosions, each corresponding to about five grams of TNT. The chamber has ports for the entry of the two laser beams and for exchanging used and new fuel assemblies. It is connected to the high-voltage system used to extract the energy of the alpha particles.

Producing electric power from the hydrogen-boron microexplosions is relatively straightforward in principle. The shower of positive-charged alpha particles emitted by a microexplosion in the center of the chamber generates a powerful current pulse, which can be harvested using technology already ok developed in the context of ultra-high-voltage DC electric power transmission systems. The DC pulse is then transformed into alternating current.

How much will it cost?

Hora estimates that a working prototype of his hydrogen-boron reactor could be built for around US$100 million. Although he admits the cost almost sounds suspicious, the biggest cost would be a laser system similar to those already in operation in various laboratories. These installations already have the approximate power and pulse length required by Hora.

Japan’s Gekko XII is one such facility. Another operation suitable for fuel ignition is the PETawatt Aquitaine Laser (PETAL) in Bordeaux, France. This facility went into service in 2015 and cost about $55 million to build.

The cost of a tailor-made reactor might be considerably lower since PETAL is a one-of-a-kind facility designed to fulfill a variety of different applications.

One important problem remains to be solved: Gekko XII and PETAL need considerable time between pulses – an hour or more. Attaining higher pulse repetition rates for such laser systems is a significant technological challenge – one which is already the focus of much international research for diverse applications.   

Will it work?

At this point, prospects look good. However, as Hora stresses, a series of issues need to be resolved to ensure there are no unforeseen barriers and to obtain more precise parameters for the reactor’s design. Fortunately, the necessary experimental and computational investigations do not require investment into new facilities and know-how. Both are already available in laboratories around the world. This greatly reduces the cost and risk in the run-up to building the first prototype. A priority for Hora’s company, HB11 Energy, is to raise the required funds and to distribute tasks to suitable research groups.

If all this works out, we could be approaching a golden-age of cost-effective electricity production.

In the next, concluding installment, Australian plasma physicist Heinrich Hora will share his thoughts in an interview.

Jonathan Tennenbaum received his PhD in mathematics from the University of California in 1973 at age 22. Also a physicist, linguist and pianist, he’s a former editor of FUSION magazine. He lives in Berlin and travels frequently to Asia and elsewhere, consulting on economics, science and technology.