The NIF gain result, how they did it and why power plant capsules will be easier to design

We have heard a lot about what NIF did a few weeks ago, but how did they do it? This is my understanding, at least, based on the technical briefing from the announcement.

Indirect Drive

First things first, NIF uses indirect drive, a detail often skipped for a lay audience. The laser does not shine directly onto the fuel capsule. Instead, it illuminates the inside of a gold cylinder. When laser light is absorbed in a high-Z material like gold, it mainly heats it up. The inside of the gold cylinder gets so hot that it emits x-rays.

Gold is very effective at both absorbing and emitting x-ray radiation. Inside the cylinder x-ray photons are constantly being emitted, travelling across the cylinder, and being absorbed. If you paused time, so that all the photons stopped for a moment, you could look at where they are, where they are going, and the energy they have. This sea of photons is the “radiation field” inside the cavity. The constant emission and absorption bring this radiation field into thermal equilibrium with the temperature of the gold wall. What you get is a blackbody source of x-rays, with a Planckian spectrum. The gold cylinder has become a “hohlraum”.

The NIF lasers shine on the inside of a gold cylinder, heating it up and forming a bath of x-rays. It is the x-rays that hit the capsule, not the lasers, causing it to implode.

It is the x-rays that then impinge on the capsule. The capsule is made of a low-Z material, carbon, and when this kind of material absorbs radiation, it heats up, like the gold, but also expands outwards very rapidly. Every action has an equal and opposite reaction; the capsule implodes.

The trouble with this is that what you want is perfectly uniform x-ray radiation everywhere on the capsule surface. What you get is not uniform. There are ends in the gold cylinder, which have to be there to let the lasers in, but they inevitably let some x-rays out. Then there are a finite number of laser beams. This means that the inside wall of the cylinder is not uniform in temperature, it has hot spots where the lasers hit and cooler spots elsewhere. And unfortunately, the capsule itself is in the middle, right in the way of any x-ray trying to cross directly through the centre of the cylinder. Drive asymmetry is inevitable.

The pattern of laser absorption on the inside of a hohlraum from NOVA, a predecessor to NIF. The walls are not uniform in temperature, there are hot spots where the lasers hit.

The Available Energy is Fixed

There is a decade-long story of design evolution at NIF. The first megajoule shot, from Aug 2021, was the HYBRID-E design, and it is almost certain that the Dec 2022 gain shot was also HYBRID-E. The HYBRID approach (“high yield big radius implosion design”, apparently) uses bigger capsules. But the whole design was not scaled up. Proportionally, the shell of the capsule was thinner to maintain the required implosion velocity.

This brings us to one of the key trade-offs for inertial fusion – you have a fixed budget of energy; the facility is the constant. A bigger capsule will have more fuel and higher potential yield. It will also lead to longer confinement time, one of the three parameters that make up the fusion triple product. But the mass of the capsule will be larger; at fixed energy, the implosion velocity must be lower. It is the velocity which sets, more than anything else, the temperature, another part of the triple product. Fusion performance is a function of both mass and velocity.

Fusion performance is a function of both mass and velocity, with more of both best. But the facility energy is fixed, which puts a cap on kinetic energy and leads to complex trade-offs.

Unless you thin the capsule down, make it bigger but with proportionally thinner walls, exactly the HYBRID strategy. Unfortunately, that walks straight into a second key aspect of fusion, which is instability. The thinner the shell the less robust it will be to instabilities. Any particular instability will progress at a given speed, and all else being equal, with a thinner shell the perturbations will be proportionally larger. And like drive asymmetry, seeds for instability are inevitable. They can come from defects in the shell, engineering structures such as the “tent” which holds the capsule in the centre of the cylinder, or the fill tube used to introduce the fuel.

The decade-long design challenge has been to make best use of the total laser energy, whilst keeping the drive uniform, and without falling foul of instabilities.

The HYBRID-E Design

The HYBRID designs use bigger capsules with thinner walls. The HYBRID-E design, specifically, uses a capsule that is also proportionally larger when compared to the hohlraum. This leads to drive asymmetry. The “equator” of the capsule, the bit halfway along the length of the gold cylinder, gets less x-rays. If you imagine standing on that point of the capsule and looking out at the hohlraum wall, as the capsule gets larger, you see less of the wall “head on”. You see the surface at a higher angle. Like the sun hitting the Earth at high latitudes, the energy per unit area is less.

To fix this, the HYBRID-E design uses “cross-beam energy transfer” or CBET. This is a seriously complex quantum and kinetic phenomenon, the essence of which is that two laser beams overlapping with each other in a plasma environment can exchange energy. It is sort of like a gravitational slingshot but swapping energy between laser beams instead a satellite and a planet. On NIF there are beams coming in at four different angles. Some energy is borrowed from the ends of the cylinder and redirected towards the middle through control of CBET, compensating for the lack of drive at the equator.

Typical energy transfers between beam angles in the HYBRID-E design. A significant proportion of the beam energy at 44 degrees is reapportioned.

CBET is controlled by separating the wavelengths of the different lasers by a small amount. It is a very empirical science but with a database of previous shots to study, and with a shoot-then-correct approach, implosions can be tuned from oval final states back to round.

Controlling the wavelength separation of the lasers controls the cross-beam energy transfer (CBET), allowing implosions to be tuned from oblate to round to prolate.

Another important feature of HYBRID-E seems to be smaller laser entrance holes. This reduces the x-ray losses and makes the overall hohlraum more efficient. A more efficient hohlraum gives more flexibility in using that fixed total energy, allowing the pulse to be extended slightly, also a key feature of HYBRID-E.

Dec 2022 Gain Shot

So what did they do to get to gain? They said they made the shell thicker. That is going to increase the mass and therefore drop the implosion velocity. Past work shows that going to DT ice thickness of 65 um, compared to 55 um, dropped the implosion velocity from 400 to 385 km/s; small changes have large effects. The key is that the Dec 2022 shot was “matched with higher laser energy”. The laser had 8% more energy, which implies 4% more velocity, and which in principle takes you back up to 400 km/s.

They also described the thicker shell as having “more margin”, another way of saying more robustness to instabilities. They said the Aug 2021 shot was their “most pristine shell ever”, whereas the Dec 2022 shot was described as having “tungsten inclusions in large number”, i.e. lots of little specks of tungsten in the shell. Tungsten is very dense so each of these little specks locally increases the mass. Each one becomes a tiny anchor on the implosion, locally slowing the velocity and distorting the shape. A thicker shell means more of this can be tolerated.

They also said that the thicker shell “burns more fuel”. This is to do with the amount of shell left at the end of the implosion. Most of the diamond is ablated away, typically less than 10% of the total mass remains. Whatever does remain holds the fuel in place. If there is more left, it holds it a little longer, the confinement time is increased, and more fuel can be burnt.

And the last piece is the symmetry. They said that they had a shot in Sept 2022 with a 1.22 MJ yield, and that the only change between that shot the Dec one was tuning the symmetry, i.e. controlling the CBET, i.e. tuning the wavelength separation. Sept will have been their best guess at an optimised design, which they then will have observed to be slightly oval. Reaching back into the data archive and figuring out the just-so tweak to get it back to round has raised the yield from 1.22 to 3.05 MJ.

More Energy Makes Everything Easier

Bigger is easier for fusion, and now it is hopefully clear why. Overall, an 8% increase in laser energy led to 230% increase in fusion yield. With more laser energy, NIF could have just gone straight for the bigger, thicker capsule and still maintained the implosion velocity. The delicate balance played here between mass, velocity and instabilities wouldn’t have been so delicate.

And tweaking of the implosion symmetry through the very complex cross-beam energy transfer process could also have been avoided. We know, now, that that particular blob of round plasma they created in the Dec 2022 shot ignites. Now imagine an oval blob of plasma, but one where the round version fits entirely inside the oval. If the round one ignites, the bigger oval one will ignite too. But, of course, the bigger oval requires more energy.

Power plants will use higher energy drivers than NIF. More energy gives you more margin; capsules for power plants will be easier to design. And, of course, the energy of the driver itself is not really the key parameter, not for a plant, it is how much it costs that matters, and how much energy it produces. This is one of the deepest reasons why I believe First Light Fusion can succeed. We have a much cheaper driver, we can afford more energy, and we will have a more robust approach because of it.


How NIF got to gain, explainer by @FLF_Nick! #fusion

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