The Prospect of Clean Energy Production from Fusion

A Peak Behind the Curtain

Andrew Franklin

Introduction

VERBAL DISCLAIMER

"There's no miracle people. It just happens that they got interested in this thing and they learned all this stuff."

- Richard Feynman

Talk Outline

• Essential nuclear physics
• Fusion fundamentals
• Incomplete overview of current approaches
• A taste of the technical challenges
• Survey from 1,000 feet
• Example of a tokamak design
• Resource Dump

Essential Nuclear Physics

Unit of Energy

• Electron Volt ($eV$): the amount of energy gained by as single electron through a potential difference of 1 $V$ in an electric field.

\begin{equation} 1 ev = 1.6 \times 10^{-19} J \end{equation}

• An electron with 1 $eV$ of kinetic energy has a speed of about $5.93 \times 10^5 \: m / s$ (1,326,503 $mph$)
• $c \approx 3 \times 10^8 m/s$

Energy/Temperature Conversion

• Energy units are sometimes used to express the temperature of a fluid.
• $E(eV) = T(K) \left( \frac{1 \: eV}{11,600 \: K} \right)$
• Example, a room temperature fluid ($20 \: ^o C$ = $293.15 \: K$) has an energy of $0.0253 \: eV$

Unit of Mass

• The atomic mass unit ($amu)$ is defined to be exactly 1/12 the mass of a neutral $^{12}C$ atom.
• $1 \: amu = 1.6605402 \times 10^{-27} \: kg$

• $m_e \approx 5.496 \times 10^{-4} \: amu$
• $m_n \approx 1.007 \: amu$
• $m_p \approx 1.009 \: amu$

Einstein's Famous Equation

For bevity, let's skip all of special relativity...

• $E = m c^2$

where $c^2 = 931.5 \frac{MeV}{amu}$.

Nucleus Mass Defect

$Z m_p + Z m_e + N m_n > m_{^A_ZX^N}$

where did the mass go?

Binding Energy

$BE = c^2 \left( Z m_p + Z m_e + N m_n - m_{^A_ZX^N} \right)$

The amount of energy that would need to be absorbed to dismantle the nucleus. $\frac{BE}{A}$ is a stability index with stability associated with high values.

Stability Curve

Nuclear Reactions

An example of the notation for generic binary reactions

\begin{equation} x + X \rightarrow Y + y \end{equation}

or the more terse notation

\begin{equation} X(x,y)Y \end{equation}

Coulomb Barrier

\begin{equation} E_\text{repulsion} \propto \frac{e^Z}{R} \end{equation}

where $e$ is the electic charge, $R$ is the distance between the charges, $E$ is the amount of energy to bring $Z$ protons together. $R$ is on the order of $10^{-12} \: cm$.

Cross Sections

\begin{equation} \sigma \equiv \lim_{\Delta x \rightarrow 0} \frac{R}{n_b v_b N A \Delta x} \end{equation}

$\sigma$ is the microscopic cross section with units of barns ($b$). $1 \: b = 10^{-24} cm^2$.

Some Important Nuclear Reactions

Stuff not covered

• Energy distribution amoungst constituents (consequence of conservation of momentum)
• Neutron flux
• Reaction rates
• Radioactivity
• etc.

Fusion Fundamentals

Important Fusion Reactions

Probably the most interesting one for this conversation \begin{equation} D + T \rightarrow \: ^4He + n \end{equation} This reaction has a Q value of 17.59 MeV. The neutron has 14.05 MeV of kinetic energy! The Heluim has 3.54 MeV.

More on these fusion Reactions

• The $^6Li$ and $^{11}B$ reactions are classifies as "aneutronic"
• aneutronic reactions eliminate the inventory associated with neutron activation (i.e. radioactive waste)
• aneutronic fuels are an advanced fuel because they have a lower cross section for fusion that $D$-$D$ or $D$-$T$ reactions
• Tritium has a half-life of 12.3 years. It must be breed.

Back to the Coulombic Barrier

• $D$-$T$ reaction (2 protons) is repelled by a potential of 444 keV
• $D$-$^3He$ (3 protons) is repelled by a potential of 1 MeV!
• Despite the high barrier energy, tunneling allows a non-zero cross section at energies below that
• $D$-$T$ at 10 keV (cold tritium plasma) has a fusion cross section of about 2 mb
• $n$-$^{235}U$ at thermal energies (0.0253 eV) has a fission cross section of 585.1 b

Plasma Confinement

• Gravitational (e.g. stars)
• Magnetic (e.g. Tokamaks)
• Inertial Confinement (e.g. LLNL - NIF)

Incomplete overview of current approaches

Inertial Confinement

• National Ignition Facility
• First breakeven shot
• 1% thermal efficiency
• Lasers are very inefficient by modern standards
• Machining tolerances on the pellet are extremely tight
• LIFE
• 10 shots / sec
• Manufacturing on mass scale to the fine tolerances is not there, yet
• Still produces waste from the 14.1 MeV neutrons
• Machining tolerances on the pellet are extremely tight

Tokamaks

• ITER
• International mega-project
• Not expected to reach break even, but should provide valuable knowledge towards commercialization
• Machining tolerances on the pellet are extremely tight
• Commonwealth Fusion Systems
• Much smaller in scale
• Leaveraging advances in superconducting ceramics to generate a strong magnetic field

Other Startups

• General Fusion
• HB11
• Helion
• Zap

A taste of the technical challenges

Part 1

Extended Bateman Equation

\begin{equation} \frac{d\vec{N}(t)}{dt} = A \vec{N}(t) \end{equation}

• Potentially Stiff
• Can be solved using backward euler, best rational approximation, or matrix exponentials

Problem Prompt

• $FLiBe$ blanket surrounding a thermonuclear reactor
• Total neutron flux of $10^{14} \: n/cm^2 \cdot s$
• Assume 50% of the neutrons are 14.1 $MeV$ and the other half is 2.45 $MeV$
• How long will it take for the blanket to be as radioactive as a Brazil nut?

Problem Prompt

• $FLiBe$ blanket surrounding a thermonuclear reactor
• Total neutron flux of $10^{14} \: n/cm^2 \cdot s$
• Assume 50% of the neutrons are 14.1 $MeV$ and the other half is 2.45 $MeV$
• How long will it take for the blanket to be as radioactive as a Brazil nut?

Simplified $^{238}U$ Decay Chain

$^{6}Li$ and $^{7}Li$ Activation/Decay Chain

Side Note

• Dashed arrows: decays
• Red arrows: neutron interactions with 2.45 MeV neutrons
• Blue arrows: neutron interactions with 14.1 MeV neutrons

$^{9}Be$ Activation/Decay Chain

$^{19}F$ Activation/Decay Chain

Simplified $FLiBe$ Activation/Decay Chain

Atom Population Simulation

Activity Density Plots

A taste of the technical challenges

Part 2

Multiphysics Modeling

Applied AI

Machine and Deep Learning

Uncertainty Quantification

HPC

Survey from 1,000 feet

• Lots of money being poured into these projects.
• Less regulation than the fission side of the industry.
• Starting to demonstrate some results, but commercialization is still a ways off.
• Aneutronic fusion could be "clean" in most senses of the word, but harder to achieve.

• Neutronic fusion would be easier to achieve, but not "clean" in terms of radioactive waste.
• Whatever ends up being built, it's likely that the capacity could be scaled to match the local demand.
• Doesn't limiting physics of fusion reactors to be baseload power.
• Challenging to accurately predict timelines without more substantial demonstrations.

Example of a tokamak design

MIT Plasma Science and Fusion

Resources

• Nuclear Engineering Fundamentals
• Nuclear Concepts for Engineers by Mayo (2001)
• Nuclear Energy An Introduction to the Concepts, Systems, And Applications of Nuclear Processes by Murray (2009)
• Historical Inspiration
• The Los Alamos Primer by Serber (1992)
• Radiation Shielding
• Atoms, Radiation, and Radiation Protection by Turner (2007)
• Radiation Shielding by Shultis & Faw (2000)

• Work In Progress