Nuclear Energy Basics: Reactors, Fission, Fusion and Key Concepts

This class aims to provide a foundational understanding of nuclear energy for individuals without a prior nuclear background, including lawyers, undergraduates, and graduate students from other scientific disciplines. The goal is to ensure everyone is on the same page regarding the basics of nuclear reactors and energy extraction.

Energy at the Atomic Scale

Energy is defined as the measure of motive power. While the joule is a common unit in macroscopic physics, at the atomic scale, the electron volt (eV) is preferred due to the extremely small energy quantities involved. One electron volt is the energy required to move a single electron up 1 volt of potential. For context, 1 electron volt is approximately 1.6 x 10^-19 joules.

Atomic Nomenclature

Atoms consist of a nucleus made of protons (positively charged) and neutrons (neutral), collectively called nucleons. The number of protons is denoted by 'Z', which defines the element. The mass number represents the total count of protons and neutrons. For example, Uranium-238 has 92 protons (defining it as Uranium) and a total of 238 nucleons. Isotopes of an element differ in their number of neutrons.

Forces within the Nucleus

The nucleus is held together by several forces:

• Coulombic Repulsion: Protons, being positively charged, exert repulsive electrostatic forces.
• Weak Force: Involved in beta decay, but not a primary focus for this discussion.
• Strong Force: This is the primary force that glues the nucleus together, overcoming coulombic repulsion.

The strong force exhibits unique characteristics:

• It has a minimum potential energy at very short distances (around 0.8 femtometers, 10^-15 meters), indicating an attractive force.
• At even shorter distances, it becomes repulsive, preventing nucleons from being crammed too closely.
• It rapidly diminishes at longer distances (beyond 3 femtometers), explaining why nuclei don't simply absorb all available nucleons.

The attractive strong force is significantly stronger than the repulsive coulombic force (approximately 100 times stronger at typical nucleon distances), which is why nuclei remain bound. However, other factors like spin and exclusion rules dictate specific nuclear configurations, preventing the formation of arbitrary combinations of protons and neutrons.

The Table of Isotopes and Stability

The table of isotopes plots the number of protons against the number of neutrons. Stable isotopes (those that do not undergo radioactive decay) are typically found along a specific band. Isotopes outside this band are unstable and undergo radioactive decay to reach a more stable state.

Energy from Radioactive Decay

When unstable atoms decay, they release energy. For example, Plutonium-238, with a half-life of 87 years, generates significant heat through radioactive decay. This property is utilized in Radioisotope Thermoelectric Generators (RTGs) to power spacecraft like Voyager. Other isotopes like Strontium-90 and Cesium-137 were used by the Soviet Union in nuclear batteries for remote applications like Arctic lighthouses. While radioactive decay releases energy, the rate is fixed by the isotope's half-life, making it difficult to control for practical energy generation.

The Curve of Binding Energy

The curve of binding energy illustrates the stability of different isotopes. It plots the binding energy per nucleon against the number of nucleons. Nuclei that are very light or very heavy have lower binding energy per nucleon, meaning they are less tightly bound than those in the middle of the curve (e.g., iron). This explains why iron is the most stable element and why processes like fission (splitting heavy nuclei) and fusion (combining light nuclei) release energy, as they move towards more stable configurations.

Radioactive decay involves a small change in binding energy, typically in the range of 100 keV to 1 MeV per nucleon. While this is a tiny amount of energy per atom, the vast number of atoms in a macroscopic sample (Avogadro's number) allows for useful energy generation.

Stimulated Nuclear Reactions: Fusion

To control energy release, stimulated reactions are employed. Fusion involves joining two light nuclei to form a heavier, more stable nucleus, releasing a significant amount of energy. A common fusion reaction involves Deuterium (Hydrogen-2) and Tritium (Hydrogen-3):

Deuterium + Tritium → Helium-4 + Neutron + Energy

This reaction releases approximately 17.6 MeV of energy, significantly more than typical radioactive decay.

The challenge with fusion is overcoming the coulombic repulsion between the positively charged nuclei. This requires extremely high temperatures (around 10 million degrees Celsius) to give the nuclei enough kinetic energy to fuse. Confining and heating plasma to these temperatures stably is a major engineering hurdle.

Stimulated Nuclear Reactions: Fission

Fission involves splitting a heavy nucleus into lighter ones, also releasing energy. While many heavy nuclei can be induced to release neutrons (e.g., n, 2n reactions), these typically yield small energy gains. However, a few special nuclei, notably Uranium-235, undergo a unique fission reaction when struck by a neutron, splitting into two smaller fragments and releasing approximately 200 MeV of energy. This is the basis for all current nuclear fission energy.

The key to a sustained fission reaction is that each fission event releases more than one neutron, which can then trigger further fissions, leading to a chain reaction.

Criticality and Chain Reactions

A chain reaction is sustained when, on average, more than one neutron from a fission event causes another fission.

• Subcritical: If fewer than one neutron per fission causes another fission, the chain reaction dies out.
• Supercritical: If more than one neutron per fission causes another fission, the chain reaction grows exponentially. This is the principle behind nuclear weapons.
• Critical: In a nuclear reactor, the goal is to maintain a controlled critical state where, on average, exactly one neutron per fission causes another fission, leading to a stable power output.

Criticality is fundamentally a geometric consideration. The "critical mass" refers to the minimum amount of fissile material needed to sustain a chain reaction, but this value depends heavily on the geometry and presence of neutron reflectors.

Controlling Fission in Reactors: Delayed Neutrons

The time between fission events in solid uranium is extremely short (around 10 nanoseconds, known as a "shake"). If a reactor relied solely on these "prompt" neutrons, it would reach full power in a fraction of a microsecond, making control impossible.

The solution lies in delayed neutrons. A small fraction (about 0.6%) of neutrons are not released immediately during fission but are emitted later by radioactive decay products of the fission fragments. These delayed neutrons have half-lives ranging from milliseconds to minutes.

Reactor design leverages these delayed neutrons:

1. The reactor is designed to be "prompt subcritical," meaning it cannot sustain a chain reaction with only prompt neutrons.
2. The delayed neutrons then push the reactor into a "momentarily supercritical" state, allowing the chain reaction to continue.
3. The half-lives of the delayed neutron precursors effectively slow down the reactor's response time, making it controllable.

This statistical reliance on delayed neutrons means that reactors are inherently chaotic systems that require dynamic control to prevent uncontrolled power excursions and meltdowns.

Reactor Control Mechanisms

To control the fission rate, reactors utilize:

• Leakage: The geometry of the reactor core is designed to allow a certain amount of neutrons to escape, keeping it close to criticality.
• Control Rods: These are made of materials (like boron) that have a high neutron capture cross-section. By inserting or withdrawing control rods, excess neutrons can be absorbed, fine-tuning the fission rate.

Fission Reactor Types

Thermal vs. Fast Reactors

Neutrons released during fission are "fast" (high kinetic energy, around 2 MeV).

• Thermal Reactors: These reactors slow down (thermalize) the fast neutrons to "thermal" energies (around 0.02 eV). This is because the probability of fission for Uranium-235 increases significantly at lower neutron energies. Slowing down neutrons also makes reactors safer, as accidental fission is less likely with fast neutrons.
  • Moderators: Materials like water, graphite, or heavy water are used to slow down neutrons. Light atoms are effective moderators because they absorb more kinetic energy from colliding neutrons. Water is a common moderator due to its abundance of hydrogen.
• Fast Reactors: These reactors operate with fast neutrons, without significant moderation. They require higher concentrations of fissile material (e.g., highly enriched uranium or plutonium) because the fission cross-section for fast neutrons is lower. Fast reactors are more complex to design and control but offer advantages like breeding new fissile material from non-fissile isotopes.

Uranium Enrichment

Natural uranium contains only about 0.7% Uranium-235 (the fissile isotope), with the rest being Uranium-238. To be used in most reactors, the concentration of Uranium-235 must be increased through a process called uranium enrichment, which separates isotopes based on their mass.

• Low Enriched Uranium (LEU): Typically 3-5% Uranium-235, sufficient for most thermal reactors.
• High Assay Low Enriched Uranium (HALEU): Up to 20% Uranium-235, used in some advanced small reactor designs that have higher neutron leakage.
• Weapons Grade Uranium: Greater than 90% Uranium-235, used in very small reactors (e.g., submarine reactors) and nuclear weapons.

Water-Cooled Reactors

• Boiling Water Reactor (BWR): Water acts as both moderator and coolant. It boils directly in the reactor core, producing steam that drives a turbine. A drawback is that the steam loop becomes contaminated with radioactive materials due to fuel corrosion.
• Pressurized Water Reactor (PWR): Water in the reactor core is kept under high pressure to prevent boiling, even at high temperatures (around 300°C). This superheated water then transfers heat to a separate, clean water loop in a steam generator, producing steam for the turbine. This design isolates radioactive materials within the containment, enhancing safety. PWRs are the most common type of commercial reactor.

Advanced Reactor Concepts

• High-Temperature Gas-Cooled Reactor (HTGR): These reactors use fuel pebbles (uranium grains coated with graphite) and are cooled by an inert gas like helium. They can operate at very high temperatures, leading to higher thermal efficiencies and potential for industrial heat applications. Challenges include fuel abrasion, fission product diffusion, and criticality control due to changing geometry in pebble bed designs.
• Molten Salt Reactor (MSR): These reactors use a liquid salt (e.g., FLiBe – Fluorine, Lithium, Beryllium) as both fuel and coolant. They offer advantages like passive safety features and high operating temperatures. However, challenges include the corrosive nature of molten salts and the toxicity of beryllium.
• Fast Breeder Reactor (FBR): These are fast reactors designed to produce more fissile material (e.g., plutonium from uranium-238) than they consume. They offer efficient utilization of uranium resources but involve handling weapons-grade materials and complex sodium cooling systems (sodium is highly reactive with air and water).

Fusion Reactor Concepts

Fusion reactors aim to achieve controlled fusion reactions.

• Inertial Confinement Fusion (ICF): A small pellet of fuel is compressed and heated by powerful lasers, causing it to fuse. The National Ignition Facility (NIF) is a prominent example. Achieving symmetrical heating and compression is a significant challenge.
• Magnetic Confinement Fusion (MCF): Plasma is confined and heated within a magnetic field (e.g., in tokamaks) to prevent it from touching the reactor walls. Heating can be achieved through radiofrequency energy or neutral beam injection.

Both fission and fusion technologies present unique engineering challenges and safety considerations, which are continuously being researched and refined.