14.3 Nuclear fusion and stellar nucleosynthesis

Nuclear fusion powers stars and holds promise for clean energy on Earth. It combines light atomic nuclei to form heavier ones, releasing enormous energy. This process requires extreme temperatures and pressures, overcoming the repulsion between positively charged nuclei.

Stellar nucleosynthesis, driven by fusion, creates heavier elements from lighter ones. Stars progress through various fusion stages as they evolve, producing elements up to iron. Supernovae and neutron star mergers forge even heavier elements, enriching the universe with diverse atomic species.

Nuclear Fusion: Process and Conditions

Fusion Basics and Requirements

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• Nuclear fusion combines two or more atomic nuclei into heavier ones when strong nuclear force overcomes electrostatic repulsion between protons
• Requires extreme temperatures (millions of degrees Kelvin) to provide kinetic energy for nuclei collisions
• Demands high pressure to compress nuclei (provided by intense gravitational force in stars)
• Proton-proton chain converts hydrogen into helium in main sequence star cores
• Quantum tunneling allows particles to overcome Coulomb barrier without sufficient classical kinetic energy
• Mass defect in fusion reactions releases enormous energy (described by $E = mc^2$)

Fusion Reactions and Energy Release

• Most common fusion reaction in stars fuses hydrogen into helium
• Deuterium-tritium fusion produces helium and a neutron ($^2H + ^3H \rightarrow ^4He + n$)
• Carbon-nitrogen-oxygen (CNO) cycle important in more massive stars
• Helium fusion (triple-alpha process) creates carbon in older stars
• Fusion of heavier elements (carbon, oxygen, neon, silicon) occurs in massive stars
• Energy release per fusion reaction varies (deuterium-tritium releases 17.6 MeV)

Overcoming Fusion Barriers

• Coulomb barrier repels positively charged nuclei (overcome by extreme temperatures and pressures)
• Lawson criterion defines conditions for sustained fusion reactions (temperature, density, confinement time)
• Magnetic confinement fusion uses powerful magnetic fields to contain plasma (tokamak reactors)
• Inertial confinement fusion compresses fuel pellets with lasers or ion beams
• Muon-catalyzed fusion uses muons to bring nuclei closer together (limited by muon lifetime)

Nuclear Fusion in Stars

Stellar Energy Production

• Nuclear fusion powers stars by providing outward pressure against gravitational collapse
• Proton-proton chain dominates in low-mass stars (Sun)
• CNO cycle becomes more important in stars more massive than 1.3 solar masses
• Energy from core fusion transported outward by radiation and convection
• Fusion rate self-regulates to maintain hydrostatic equilibrium
• Main sequence stars fuse hydrogen into helium for majority of their lives

Stellar Evolution and Fusion Stages

• Stars evolve off main sequence as core hydrogen depletes
• Red giant phase begins with hydrogen shell burning around inert helium core
• Helium flash occurs in low-mass stars when core reaches fusion temperature
• Asymptotic giant branch (AGB) phase involves alternating hydrogen and helium shell burning
• Massive stars progress through carbon, neon, oxygen, and silicon burning stages
• Stellar evolution path determined by initial mass (white dwarf, neutron star, black hole)

Fusion in Extreme Stellar Environments

• Degenerate matter in white dwarfs can support fusion reactions (novae, Type Ia supernovae)
• Neutron star mergers create extreme conditions for rapid neutron capture process
• Supernovae provide environment for creation of heaviest elements
• Pulsational pair instability in very massive stars causes periodic fusion bursts
• Accretion-induced collapse can trigger fusion in compact stellar remnants

Stellar Nucleosynthesis and Heavy Elements

Light Element Production

• Big Bang nucleosynthesis produced primordial hydrogen, helium, and trace lithium
• Stellar nucleosynthesis creates heavier elements from lighter ones through fusion
• Main sequence stars primarily produce helium through hydrogen fusion
• Alpha process fuses helium into carbon, oxygen, and other alpha-particle nuclei
• Proton capture reactions create odd-numbered elements (sodium, aluminum)

Heavy Element Synthesis

• Iron-peak elements mark limit of exothermic fusion reactions
• S-process (slow neutron capture) occurs in AGB stars (produces half of elements heavier than iron up to bismuth)
• R-process (rapid neutron capture) happens in supernovae and neutron star mergers (creates remaining heavy elements beyond bismuth)
• P-process (proton capture) produces some rare, proton-rich isotopes
• Cosmic ray spallation creates light elements (lithium, beryllium, boron) in interstellar medium

Nucleosynthesis Impact on Universe

• Stellar nucleosynthesis crucial for chemical evolution of universe
• First generation (Population III) stars enriched early universe with heavy elements
• Supernova explosions disperse newly created elements into interstellar medium
• Galactic chemical evolution models track element production over cosmic time
• Abundance patterns in old stars provide clues about early nucleosynthesis processes

Fusion vs Fission: Energy and Sustainability

Energy Release Comparison

• Fusion releases more energy per unit mass than fission (larger mass defect in light nuclei fusion)
• Typical fusion reaction (deuterium-tritium) releases 17.6 MeV
• Fission of uranium-235 releases about 200 MeV per reaction
• Fusion fuel (hydrogen isotopes) more abundant than fission fuel (uranium, plutonium)
• Fusion energy density higher than fission (potential for more compact reactors)

Environmental and Safety Considerations

• Fusion produces primarily harmless helium as byproduct
• Fission generates radioactive waste requiring long-term storage
• Fusion fuels (deuterium, tritium) can be extracted from seawater
• Fission relies on rare heavy elements (uranium, thorium)
• Runaway fusion reactions self-limiting due to plasma dispersion
• Fission reactions can lead to meltdowns if not properly controlled

Technological Challenges

• Fusion requires extreme temperatures and pressures (millions of degrees, intense magnetic fields)
• Fission occurs at much lower temperatures (easier to initiate and control)
• Current fusion reactors not yet achieving net energy gain (Q > 1)
• Fission technology well-established with operational power plants
• Fusion plasma confinement remains a significant engineering challenge
• Materials for fusion reactors must withstand intense neutron bombardment