# Maximum theoretical $\text{D-T}$ energy output in proposed First Light Fusion (FLF) fuel pellet

I recently stumbled into Youtube videos diving into the science behind First Light Fusion's (FLF) goal of creating an inertial confinement fusion (ICF) fuel pellet by leveraging the phenomenon of cavitation, as exhibited in nature by the pistol shrimp. I began dusting off my partial differential equations and ramping up on Naiver-Stokes to model the cavitation, when I stumbled into an older FLF video which caused me to pause.

In the older video, the fuel pellet was stated as being equivalent in energy to a barrel of oil. In newer videos, the fuel pellet is stated as being able to power a UK home for 2 years. A barrel of oil is ~1700 kWh, and the average household consumption of energy in UK is on order of 8.5 - 10 kWh per day, which extrapolating biannually is 6200 - 7300 kWh, which is notably more energy than a single barrel of oil.

FLF's goal is very sensible in that their focus is the design and eventual manufacture of the ICF fuel pellets and corresponding projectile, with the idea that other companies will create and manage a power plant to consume the fuel pellets, using known proven technology. FLF proposes the use of liquid thorium in conjunction with steam power generation, all of which will obviously affect the energy gain Q factor. Not to mention the energy required to accelerate the projectile to strike the fuel pellet, or the energy to extract deuterium and tritium, etc, etc...

Without consideration for the aforementioned Q factor gains and losses, but instead focusing purely on the fusion aspect, given the size of the fuel pellet, stated in the aforementioned links as being a 15mm cube with a 1mm cavity containing a deuterium-tritium (D-T) mix, what is the maximal amount of energy possible from the fuel pellet under the following assumptions...

• the 1mm cavity is spherical
• the D-T mix is at 1 atmosphere of pressure
• the D-T fusion is 100% efficient

That all being said, what is the spectrum of truth regarding the potential energy output?

• Sep 14, 2022 at 3:57
• the energy density DT is in the introduction here epress.lib.uts.edu.au/student-journals/index.php/PAMR/article/… Sep 14, 2022 at 5:16
• @annav thanks for the background information and the energy density link, which is useful in not only confirming that the D-T reaction is the most appropriate for inertial confinement, but also provides the resulting energy density in J/kg. With this and a bit more research on the isothermic properties of D-T, I'll take a stab at an answer that can be scrutinized if no one else chimes in... Sep 18, 2022 at 15:16

I am going to say this right up front: I am a complete sceptic about FLF's concept.

I would love you to continue your collapse calculations, because frankly I think the possibility of getting the required density (100 times that of lead) is simply impossible using their concept.

And if there is anything that ever cried out "Rayleigh Taylor" it's the idea of collapsing a spherical void with a freaking plastic cube, and do so by pushing on ONE SIDE of it. How the f is that supposed to work?! Even their own simulations on YT show pretty much completely chaotic collapses.

As you have noted, the company has continued to change the concept both in what they claim it does and how they claim it will work and what they claim it will be made out of. And throughout, the entire argument for why it will work is "Pistol shrimp, cool, amiright?!"

So...

The calculation of the potential output is found in Nuckoll's original paper. The primary issue for ICF is that the fuel is disassembled at a speed that is somewhat faster than the fusion rate. So ICF systems tend to blow apart before much of the fuel has undergone fusion - this is why NIF only got Q~0.7 in spite of ignition, the propagating burn was snuffed out when the rest of the fuel flew off.

• My perspective is that the modelling of the inertial confinement based on the cavitation concept will in turn lead to a search for the appropriate materials and configuration of both the target and projectile. That is, once the optimal inertial confinement solution space is modelled taking into account material characteristics and the configuration of the target and projectile, then it's a matter of finding a combination of physical materials and associated manufacturing processes, that combined reside in the modelled solution space that predict appropriate levels of energy density... Sep 18, 2022 at 15:19
• So, concur with the skepticism concerning their "marketecture" showing a plastic cube as the target, but their business model is after all about manufacturing the targets, which of course will be a trade secret, so the plastic cube is likely just a stand-in to make the concept graspable... Per my comment to @annav, when I have a block of time I'll take a stab at answering the question I proposed, knowing full well it will be critiqued... Sep 18, 2022 at 15:20

## General Assessment

After researching NIST online resources on the isothermal properties of Deuterium (D), it became apparent that temperature is a critical factor in the density of D-T, so temperature has been included in assessing the energy equivalency of D-T in the FLF proposed projectile cavity relative to a barrel of oil.

Note the following assumptions when interpreting the table.

• Not surprisingly, scant information was readily available for the very rare T, so the D-T State and Density are estimates based on the assumption that the isothermal properties of T are approximately that of D.
• The 1 mm cavity in the fuel pellet that holds the D-T is assumed to be spherical.
• The D-T pressure in the 1 mm cavity is assumed to be 1 atm. The density of course is driven by the temperature, and the NIST WebBook on Deuterium is indispensable in providing this quantity.

• The D-T mix is assumed to be equal parts of D and T, in terms of atoms.
• The entire 17.6 MeV release from a D-T fusion event is assumed to be energy that can be converted to usable energy.
• None of these calculations consider further downstream fission processes involving thorium or lithium that can produce additional energy as a result of the initial D-T fusion process.
• The D-T mix is assumed to be 100% fused, which is very unrealistic, and likely more on the order of 25 - 50%.
• Based on the Average Operating Heat Rate for Selected Energy Sources, the kWh production of Petroleum and Nuclear are essentially equivalent in efficiency, which is not surprising if the electrical power production is steam generation in both cases. Thus when arriving at the barrel of oil equivalent of the FLF fuel pellet, the assumption is that the efficiency of the electrical energy production thereafter, whether driven by the FLF fuel pellet or oil, is also generally equivalent.

With all that in mind, the table below shows three (3) energy yields at various temperatures, again with the density of the D-T mixture being driven by the temperature.

TEMP

C
PRS

atm
D-T (est)
State

D
Density

kg/m3
D-T (est)
Density

kg/m3
DIA

mm
Volume

mm3
D-T

g
Energy

J
Oil

barrels
300 1 supercritical 0.08562 0.10979 1 0.52360 5.7485E-08 1.8897E+10 3.05
40 1 vapor 0.15667 0.20089 1 0.52360 1.0519E-07 3.4579E+10 5.58
0 1 vapor 0.17961 0.23030 1 0.52360 1.2059E-07 3.9642E+10 6.40

So, near room temperature with full fusion energy capture, the FLF fuel pellet can theoretically produce the energy equivalent of 5.58 barrels of oil or 9500 kWh, which given the statistic in the posted question of 6200 - 7300 kWh biannually for the English home, provides reasonable validation of FLF’s claims that a single fuel pellet can power a home for 2 years.

That being said, if the fusion reaction is 33% efficient (wild guess) then the FLF fuel pellet will theoretically produce 3130 kWh, which is half the claim relative to powering an English home biannually, but again, this estimate is purely from the fusion reaction only, and does not factor in any downstream energy gains from lithium or thorium fission processes which will likely contribute to the overall energy output, and therefore FLF’s claim likely still stands...

## Postscript... The Possibilities...

In researching the energy output of D-T, what's really intriguing is the D-T fuel mixture at -250 C, where it is in the liquid state at 1 atm of pressure, and hence the density greatly increases relative to the vapor state, to the point where the same assumptions lead to 3 full magnitudes of additional D-T fuel mixture in the FLF fuel pellet cavity of 1 mm diameter, resulting in an astounding equivalent in barrels of oil.

TEMP

C
PRS

atm
D-T (est)
State

D
Density

kg/m3
D-T (est)
Density

kg/m3
DIA

mm
Volume

mm3
D-T

g
Energy

J
Oil

barrels
-250 1 liquid 163.89 210.15 1 0.52360 1.1004E-04 3.6172E+13 5841
-250 1 liquid 163.89 210.15 0.1 5.2360E-04 1.1004E-07 3.6172E+10 5.84

Notwithstanding the fact that extreme low temperatures slow the interatomic interactions, which is the opposite of what is required to bring about fusion, yet does bring the atoms closer in proximity, this liquification of D-T offers the possibility of a fuel pellet cavity with a diameter 10% the stated size of 1 mm, that is, a diameter of 0.1 mm (the thickness of a human hair!) or 1/1000 the volume, with a similar energy output of a 1 mm cavity containing D-T at room temperatures. (That being said, see though ICF discussion involving solid form of D-T...)

This presents the possibility of more of the surrounding fuel pellet mass being brought to bear on the D-T fuel mixture when hit with the projectile, as the ratio of force to surface area of the fuel is greatly increased, all other factors being equal. Of course, the extreme low temperature of the fuel pellet might require it to gradually move towards the presence of the heated lithium or thorium so that the outer fuel pellet casing warms to a state that will be less brittle, thus behaving more like a fluid when hit with the projectile, in order to leverage the natural phenomena of cavitation.

But more importantly, it seems there is the possibility that while the projectile is compressing the fuel pellet, that one can near simultaneously hit the fuel pellet cavity with a high energy laser or microwave, thereby transitioning the D-T mixture from liquid to vapor, bringing to bear additional huge pressure changes in favor of the fusion process. For example, a jump from -250C to 0C brings with it a D-T pressure change from 1 atm to 2500 atm!...

In light of these possibilities, assuming the aforementioned is within the bounds of physics, the FLF claim can almost be said to be towards the low end of the spectrum of possible energy output... The primary obstacle as I see it appears to be the sheer quantity of factors involved, with a seemingly daunting effort in discovering the optimal configuration, materials, manufacturing processes, and operational processes...

So, if there is even a slim hope that the FLF ICF concept can come to fruition, it will be well worth the effort given the potential payoff of near limitless greener energy...

• You calculated the amount of energy in the fuel, but do not consider whether or not inciting fusion in that fuel is even possible? Nov 13, 2022 at 13:56
• @MauryMarkowitz yes, that's correct. The question in summary was "What is the maximal amount of energy possible from the fuel pellet?" given the physical dimensions as described by FLF in their videos, not whether ICF is possible when introducing cavitation as FLF is attempting... Nov 13, 2022 at 23:37