Laser-driven nuclear fusion doubtless has the potential to become the No. 1 energy source for mankind in the foreseeable future. Apart from an essentially unlimited resource base, the fundamental reason lies in the unparalleled energy densities and power densities that laser fusion can generate. Growth in power-density has been a characteristic of overall technological progress throughout history, correlating strongly with increases in the real physical productivity of society.

Unfortunately, it is extremely difficult to ignite a self-sustaining “fusion fire.” Temperatures of hundreds of millions of degrees are needed for the deuterium-tritium reaction, and billions of degrees for the radioactivity-free hydrogen-boron reaction (see Part 2: Nuclear power’s ray of hope: hydrogen-boron fusion). Long before reaching these temperatures, the fuel is transformed into a plasma, sometimes called “the fourth state of matter,” which is capable of extremely complicated behavior.

Strictly speaking, the temperatures mentioned above apply only to so-called thermonuclear fusion, in which the reactions are produced by random collisions of nuclei flying around in a heated medium. Fusion might in fact be achieved more easily in highly non-equilibrium states, where the concept of “temperature” no longer applies. In a certain sense Heinrich Hora’s approach to hydrogen-boron fusion, to be discussed below, goes exactly in that direction.

(As far as room-temperature, so-called “cold fusion” is concerned, I am personally convinced that some, at least, of the claimed phenomena are real, albeit quite possibly involving different nuclear processes than fusion, and not adequately explained. One might speculate about possible applications to the generation of heat. The power densities are many orders of magnitude below those of laser fusion.)

Coming back to conventional laser fusion, ignition and an efficient “burnup” of fusion fuel require not only the mentioned temperatures, but also compressing the fuel to extremely high densities.

A simple analogy is the internal combustion engine: compression by the piston creates the conditions for a rapid, efficient and complete combustion of the fuel. Otherwise it would just burn at a leisurely pace, generating little or no power. Compression also causes heating. In the diesel engine the compression is so large, that it reaches ignition temperature for the fuel-air mixture.

Diesel engines typically compress the inlet air by a factor of 15-20 times.

By comparison, the compressions required for laser fusion ignition are roughly 50 billion times larger. What kind of “piston” would be capable of creating such pressures?

Up to now a single basic scenario, known as ablative or radiation implosion, has dominated the laser fusion scene and absorbed by far the largest share of financial resources (Part 3, Nuclear power: Lessons from the hydrogen bomb). A tiny spherical fuel pellet is bombarded on all sides by simultaneous laser pulses (or by X-rays generated from the laser pulses). The outer layer of the pellet is instantly heated to huge temperatures and expands in an explosive fashion (“ablation”). This sudden expansion exerts tremendous pressure on the inner layers of the spherical pellet, causing it to implode and compressing the fuel to super-high densities. Here shock waves, generated by the compression and propagating toward the center, play a key role in the subsequent ignition process.

Unfortunately this scenario runs into many difficulties. The chief culprit is a phenomenon known as the Rayleigh-Taylor instability. At the boundary between the outer and inner layers, slight undulations appear, which rapidly grow and reach deep into the target, disrupting the compression and ignition process. Despite many clever tricks and expensive countermeasures, it has not proven possible to bring the Rayleigh-Taylor instability under control.

Rayleigh-Taylor instability in fluid flow (left). Rayleigh-Taylor instability cropping up in a laser fusion experiment. Images: Wikimedia

There must be a better way!

Working for Westinghouse as a young man in the mid-1960s, plasma physicist Heinrich Hora could examine hundreds of photographs of the plasmas generated by laser pulses impacting targets. He saw clear evidence of phenomena that did not fit into the simplified models of laser-matter interactions, used in most research at that time. Hora’s calculations for the equation of motion of laser-generated plasma revealed, in addition to the pressure force generated by the heating, a “nonthermal” force term – a force deriving from the powerful electrical and magnetic fields generated by the laser pulse.

The presence of such fields is no surprise; after all, light is itself composed of rapidly-varying electric and magnetic fields. In powerful laser pulses, however, these fields reach such intensities, that their effect can differ drastically from that of ordinary light. A very crude analogy: an ordinary water wave, causes objects to just bob up and down when it passes. By contrast, a breaker wave generates powerful horizontal motion, that can drive surfers forward. The transition from a normal wave to a breaker is a typical nonlinear effect. Another example of nonlinearity, relevant to laser fusion, is the formation of a shock wave when a medium is rapidly compressed, i.e by an aircraft crossing the so-called sound barrier. 

Hora called the additional, nonlinear force term in his equations, the “ponderomotive force.” Calculations, together with a wide variety of experimental results suggested that laser energy could be converted with high efficiency into coherent directed motion of portions of the plasma, as opposed to simply being dissipated as heat. 

Calculations in 1978 indicated that the efficiency might even reach to 99%, with thermal effects retreating into the background. 

It was natural for Hora to consider whether this effect might be exploited in order to ignite nuclear fusion, in different and much more efficient ways than the conventional scheme of ablative implosion.

This was the beginning of a long trail leading to his present concept for a hydrogen-boron reactor.

Experimental confirmation

In appears that Hora’s work on the ponderomotive force did not generate much enthusiasm in the mainline laser fusion community. One reason might be the nightmarish complexity of the calculations involved, which induces plasma physicists to simplify their equations. In that context, it is common practice to omit terms that are expected to have only a small effect on the solution. Under some physical conditions, however, the “small” effects can suddenly become very large.

Another reason was that the laser pulses utilized tended to be too long, insufficiently powerful and not “clean” enough in form to display the ponderomotive effects in a sufficiently undeniable way.

This situation began to change with advent of chirped pulse amplification and ultra-short-pulse ultra-high-power lasers (see Part 4: Fusion power enters world of ‘extreme light’).

In 1996 Hora’s calculations found startling experimental confirmation in an experiment carried out by the German laser physicist Roland Sauerbrey in Göttingen. Sauerbrey irradiated a foil target by an excimer laser pulse of less than a trillionth of a second (a picosecond). He observed the formation of two “blocks” of plasma, accelerated in opposite directions to high velocities – one toward the laser and the other one in the opposite direction. The accelerations measured by Sauerbrey were incredibly large: of the order of 100 million billion times the acceleration of gravity.

Acceleration of plasma blocks by the ponderomotive force of a laser pulse. Image courtesy of Heinrich Hora

The accelerations found by Sauerbrey are many orders of magnitude larger than those that could be produced by heat expansion alone. Here forces of a completely different nature are in play, forces which can only be explained by direct ponderomotive effects of the laser field. In his research paper, published in the journal Physics of Plasmas, Sauerbrey remarked:

“The results demonstrate that during the short subpicosecond laser pulse the plasma motion is actually dominated by acceleration rather than by a  constant expansion velocity. The measured accelerations are among the highest accelerations that have been generated in the laboratory for  macroscopic objects.”

The measurements agreed in all respects with Hora’s predictions.

Sauerbrey’s results do not stand alone. In 2000 the Hungarian laser physicist István Földes and his collaborators demonstrated similar accelerations in experiments with carefully tailored ultrashort pulses. Within a trillionth of a second portions of plasma reached velocities of a more than 100 kilometers per second. Hora’s calculations indicated that velocities 100 times higher could be reached.

Could such super-accelerated plasma blocks give us the “piston” we need to compress fusion fuel to ignition? A fascinating possibility!  

Often refered to by other names, the pondermotive force has emerged from a small corrective term in a mathematical equation into an well-established physical phenomenon, having potentially revolutionary technological applications. Apart from fusion, the nonlinear forces exerted by laser pulses can be exploited in miniaturized particle accelerators for use in medicine, science and industry. A linear accelerator or cyclotron filling a large hall or even kilometers long might soon be replaced by a table-top device.

BELLA, the Berkeley Laboratory Laser Accelerator uses nonlinear interaction with laser light to accelerate an electron beam to 10 GeV (10 billion electron volts) within a distance of approximately one meter. Photo: Wikimedia

Faster is simpler

Meanwhile, starting in the late 1990s, experimental investigations by the prominent Chinese physicist Zhang Jie and others established clarity on a key point: the interaction between a laser pulse and a target changes dramatically when the pulse length goes down from nanoseconds (billionths of a second) to picoseconds (trillionths of a second) or less.  

In a certain sense the phenomena become much simpler.

Why? As I mentioned, pursuit of laser fusion by ablation has long been plagued by instabilities in the motion of the plasma created by the laser pulse, preventing an effective compression of the fuel.

However, every process in nature operates on a certain time scale. The instabilities in question take a certain amount of time to develop. Provided we can intervene on a much shorter time-scale, we won’t have to worry about them.

Specifically, the insidious Rayleigh-Taylor instability develops on a time-scale of nanoseconds.

By contrast, the formation and acceleration of plasma blocks, demonstrated by Sauerbrey and others, occurs on a time scale of a picosecond, more than a thousand times shorter.

The ponderomotive force, evoked by the laser pulses’s electric and magnetic fields, does its work long before the heating and resulting pressure forces have time to develop. But we need picosecond or femtosecond lasers to make that happen. The nanosecond pulses, employed by the National Ignition Facility its unsuccessful attempts to achieve ignition by the heat-driven process of ablative implosion, were far too long.

It is worth quoting Hora himself on this issue:

“It took dozens of years to realize the basic difference between the thermodynamic dominated laser fusion with nanosecond pulses in contrast to the entirely different non-thermal processes with the thousand times shorter picosecond laser-plasma interaction. For nanosecond interaction … the laser energy has to be thermalized to produce… the hydrodynamic and gas-dynamic pressures for ablation, compression, heating and thermonuclear reactions… These problems can be reduced if the processes are performed within very short times such that the problematic mechanisms don’t have sufficient time to develop… During the interaction, the dominating forces are not of thermodynamic nature but of the non-thermal electrodynamics of the laser fields with the plasma.”

– German plasma physicist Heinrich Hora

Pleasant surprises

Sauerbrey’s results were the first of a series of pleasant surprises, which have brought the dream of hydrogen-boron fusion ever closer.

Hora took a bold step, to drop the spherical implosion scenario completely and try something much simpler. He assumed a cylindrical shape; and instead of illuminating a spherical target by simultaneously laser pulses from all sides, Hora proposed simply focusing a single, ultra-high-power laser pulse on one end of the cylinder. Ignition would be reached with the help of a single plasma block “piston,” propelled by the ponderomotive force into the bulk of the fuel.

Extensive calculations, published in 2009-10, showed that the conditions for ignition of a hydrogen-boron fuel are much, much easier to fulfill with the cylindrical geometry. In fact, not much more difficult than the deuterium-tritium reaction. That was a very pleasant surprise.

In the meantime, real-life experiments demonstrated the generation of hydrogen-boron reactions by ultra-short-pulse lasers. The quantity of reactions grew in leaps and bounds as the laser intensities and laser pulse qualities improved. Analysis of the results proved that the reactions were triggered by nonthermal mechanisms, rather than heat.

In 2005 the group of Belyaev in Moscow succeeded for the first time in triggering hydrogen-boron reactions by an intense picosecond laser pulse striking a boron-rich polymer target. 100,000 alpha particles were detected as products of the hydrogen-boron reaction.  

The PALS laser system in Prague, Czech Republic. At right the experimental chamber for observing laser-matter interactions. Photos: Wikimedia

In 2014 analogous experiments, carried out at the Prague Asterix Laser System (PALS) facility in the Czech Republic yielded several millions of alpha particles per shot. 

Subsequently, a sustained effort by the PALS group to optimize the target and laser pulse characteristics pushed the number up to a billion alpha particles per shot. Finally, at the beginning of this year an international scientific team from the Czech Republic and Poland put out an announcement with the title “Laser-driven proton-boron fusion: A way to radiation-free nuclear energy?” announcing a yield of 100 billion alphas and launching a call to action:

“Following a recent experiment at the Prague Asterix Laser System (PALS), Czech Republic, we report a record yield of 1011 alpha particles, achieved by focusing a sub-nanosecond, 600 J laser beam onto a boron nitride thick target. … We show that such a surprising figure is not of a thermonuclear nature. It is rather explicable in terms of a beam-driven fusion scheme… The reaction yield achieved this way is 100 times higher than that achieved at the same facility in 2014, and preludes to a further 10-time increase by straightforward optimisation of the target. Our findings, recent theoretical predictions and the advent of dramatically enhanced laser capabilities call for an urgent, systematic investigation of possible ignition schemes in laser-driven proton-boron fusion.” [link]

In the following installment, I shall describe Heinrich Hora’s design for a hydrogen-boron power plant.

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.

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