Clean Energy from First Principles

Nuclear Fission

Releases energy by splitting heavy atomic nuclei (uranium, plutonium), converting mass to energy via E=mc² with ~3 million times the energy density of fossil fuels.

Fundamental Principle

The Fission Reaction

Nuclear fission releases energy by splitting heavy atomic nuclei into lighter fragments. When a neutron strikes a fissile nucleus (typically uranium-235 or plutonium-239), the nucleus becomes unstable and splits into two medium-mass fragments, releasing additional neutrons and enormous energy.

A typical U-235 fission reaction:

92235U+01n→56144Ba+3690Kr+201n+∼200 MeV^{235}_{92}U + ^1_0n \rightarrow ^{144}_{56}Ba + ^{90}_{36}Kr + 2^1_0n + \sim200 \text{ MeV}

The exact fission products vary statistically, but the energy release is consistently around 200 MeV per fission event.

Energy Accounting

The ~200 MeV released per U-235 fission distributes approximately as:

Component Energy (MeV) Recovery
Kinetic energy of fission fragments 165 Captured as heat
Kinetic energy of neutrons 5 Captured as heat
Prompt gamma rays 7 Captured as heat
Beta particles from fission product decay 7 Captured as heat
Gamma rays from fission product decay 6 Captured as heat
Antineutrinos 10 Lost (escapes reactor)
Total ~200 ~190 MeV recoverable

Converting to macroscopic quantities:

Comparison with Chemical Energy

The energy density advantage of nuclear fuel over chemical fuels is extraordinary:

Fuel Energy Density Ratio to Coal
Coal 24 MJ/kg 1×
Natural gas 55 MJ/kg 2.3×
Gasoline 46 MJ/kg 1.9×
Uranium (LWR, once-through) ~500,000 MJ/kg ~20,000×
Uranium (breeder cycle) ~80,000,000 MJ/kg ~3,000,000×

A single uranium fuel pellet (about 7 grams) contains energy equivalent to approximately:

This extreme energy density is nuclear power's fundamental advantage: enormous energy from minimal fuel mass, minimal mining, and minimal waste volume (though waste toxicity remains a challenge).

The Chain Reaction

For practical energy production, fission must be self-sustaining. Each fission releases 2-3 neutrons on average. If at least one neutron from each fission causes another fission, the reaction continues.

Criticality conditions:

Power reactors operate at criticality (k = 1), with the reaction rate controlled by:

  1. Control rods: Neutron-absorbing materials (boron, cadmium, hafnium) inserted to absorb excess neutrons
  2. Moderator: Material that slows neutrons to increase fission probability
  3. Delayed neutrons: ~0.65% of fission neutrons are emitted with delay (seconds), providing time for control adjustments

Without delayed neutrons, reactor control would be impossible, as the neutron generation time is microseconds.

Neutron Moderation

Fission neutrons emerge "fast" (energies >1 MeV, velocities ~10⁷ m/s), but U-235 has a much higher fission cross-section for "thermal" neutrons (energies ~0.025 eV, velocities ~2,200 m/s).

Moderator materials slow neutrons through elastic collisions:

The moderation ratio (slowing power/absorption) determines how efficiently a moderator thermalizes neutrons without losing them.

Conversion Mechanism

Reactor Design Principles

Nuclear reactors convert fission heat to electricity through a thermodynamic cycle, typically a steam Rankine cycle:

  1. Fission releases heat in fuel
  2. Coolant (water, gas, or liquid metal) removes heat from fuel
  3. Steam generator (or direct boiling) produces steam
  4. Turbine converts steam energy to mechanical rotation
  5. Generator converts rotation to electricity
  6. Condenser rejects waste heat to environment

The thermal efficiency is limited by the Carnot efficiency and practical temperature constraints:

ηCarnot=1−TcoldThot\eta_{Carnot} = 1 - \frac{T_{cold}}{T_{hot}}

Nuclear plants typically operate at lower temperatures than fossil plants due to materials limitations, yielding lower thermal efficiencies.

Major Reactor Types

Pressurized Water Reactor (PWR) - ~70% of global fleet

Boiling Water Reactor (BWR) - ~15% of global fleet

Pressurized Heavy Water Reactor (PHWR/CANDU) - ~5% of global fleet

Advanced Gas-cooled Reactor (AGR) - UK only

Light Water Graphite Reactor (RBMK) - Russia/former USSR

Thermal Efficiency Comparison

Reactor Type Steam Temperature Thermal Efficiency
PWR 275-290°C (saturated) 32-34%
BWR 285°C (saturated) 32-33%
PHWR (CANDU) 260-310°C 29-31%
AGR 540-640°C (superheated) 40-41%
Supercritical fossil 540-620°C 42-45%
Combined cycle gas N/A 55-62%

Nuclear plants have lower thermal efficiency than modern fossil plants primarily due to:

  1. Fuel cladding temperature limits (zirconium alloys)
  2. Reactor vessel integrity requirements
  3. Safety margins for loss-of-coolant scenarios

Advanced reactor designs (Generation IV) aim for higher temperatures and efficiencies.

Capacity Factors

Nuclear plants excel at baseload operation with very high capacity factors:

Technology Typical Capacity Factor
Nuclear (US fleet 2024) 92%
Nuclear (global average) 80-82%
Coal 40-50%
Combined cycle gas 40-60%
Onshore wind 25-35%
Solar PV 10-25%
Hydropower 30-50%

The US nuclear fleet's 92% capacity factor represents decades of operational optimization. This high availability partially compensates for lower thermal efficiency in overall economics.

Fuel Cycle

Uranium Supply Chain

Mining:

- Open pit, underground, or in-situ leaching (ISL) - Ore grades: 0.1-20% U₃O₈ (most deposits <1%) - Major producers: Kazakhstan (39%), Canada (24%), Namibia (12%) - Global production (2024): ~60,000 tonnes U

Milling:

Conversion:

Enrichment:

Fuel fabrication:

Uranium Resources

Global identified recoverable uranium resources (2023):

At current consumption (~67,000 tonnes/year):

Top countries by uranium resources (2023):

Country Resources (kt U) Share
Australia 1,684 28%
Kazakhstan 906 15%
Canada 588 10%
Russia 486 8%
Namibia 470 8%
South Africa 320 5%
Brazil 277 5%
Others 1,204 20%

Spent Fuel and Waste

A typical 1 GW PWR produces annually:

- ~27 tonnes of spent fuel - Containing ~250 kg plutonium, ~1 tonne fission products

Spent fuel composition:

Waste management options:

  1. Once-through cycle (most countries):

    • Spent fuel stored in pools, then dry casks
    • Eventual deep geological disposal
    • US Yucca Mountain (canceled), Finland Onkalo (under construction)

  2. Closed cycle with reprocessing (France, Russia, UK, Japan, India):

    • Separates uranium and plutonium for recycling
    • Reduces waste volume by ~75%
    • Produces MOX fuel (mixed oxide)
    • Reduces long-lived actinides

  3. Advanced fuel cycles (future):

    • Fast reactors could "burn" transuranics
    • Thorium cycle produces less long-lived waste

Radioactive waste categories:

Nuclear produces far less waste by volume than fossil fuels, but waste toxicity and longevity remain significant challenges. A lifetime's electricity for one person from nuclear produces about 40 grams of high-level waste.

Global Status

Installed Capacity (2024-2025)

Global totals:

Top countries by nuclear capacity:

Country Reactors Capacity (GWe) Nuclear Share
United States 94 97 19%
France 57 63 65-70%
China 57 55 5%
Russia 36 27 20%
South Korea 26 26 30%
Canada 19 14 15%
Ukraine 15 13 ~55%
Japan 12 operating 10 8%
India 24 9 3%
UK 9 6 15%

Top 5 countries account for 71% of global nuclear capacity.

Construction and Pipeline

Under construction (2024-2025):

Construction starts (2024):

Countries building first reactors:

Construction times:

Nuclear electricity generation has been relatively stable:

The 2024 record reflects:

Country Trajectories

Expanding:

Stable/Declining:

Phased out:

Economics

Cost Components

Nuclear power costs divide into:

  1. Capital costs (60-75% of LCOE):

    • Reactor and containment construction
    • Site preparation and grid connection
    • Financing costs (interest during construction)

  2. Operations and maintenance (15-25%):

    • Staffing (large workforce required)
    • Maintenance and inspections
    • Regulatory compliance

  3. Fuel costs (5-15%):

    • Uranium purchase
    • Conversion, enrichment, fabrication
    • Spent fuel management

  4. Decommissioning and waste (5-10%):

    • End-of-life reactor dismantling
    • Long-term waste storage/disposal

Levelized Cost of Electricity (LCOE)

LCOE estimates vary enormously depending on assumptions and location:

New nuclear construction (2024 estimates):

Source Region LCOE ($/MWh)
Lazard USA (Vogtle-based) $142-222
IEA/NEA OECD average (7% discount) $42-102
BloombergNEF China $62
BloombergNEF USA $180+
IEA/NEA Russia $27-57

For comparison (2024):

Existing nuclear plants (operating, depreciated) have very low marginal costs: $25-40/MWh, making continued operation economically attractive.

The Cost Challenge

Nuclear construction costs have increased dramatically in Western countries:

Overnight capital costs ($/kW):

Contributing factors:

Recent Western projects:

China's advantage:

Economic Outlook

Nuclear faces a challenging economic environment:

However, nuclear offers value not captured in simple LCOE:

Many analysts argue that "system LCOE" including storage and grid integration costs would favor nuclear, but this remains debated.

Advanced Reactors

Generation III+ (Current New Builds)

Currently deployed advanced designs:

Westinghouse AP1000:

EPR (European Pressurized Reactor):

Russian VVER-1200:

APR1400 (South Korea):

Small Modular Reactors (SMRs)

SMRs are reactors under 300 MWe designed for factory fabrication and modular deployment.

Operational SMRs (as of 2024):

Reactor Country Capacity Status
Akademik Lomonosov Russia 2×35 MWe Floating, operational 2020
HTR-PM China 2×105 MWe Pebble-bed, grid 2021
RITM-200 Russia 55 MWe Icebreakers

Leading SMR designs in development:

NuScale VOYGR (USA):

GE-Hitachi BWRX-300:

Rolls-Royce SMR (UK):

Terrestrial Energy IMSR (Canada):

SMR challenges:

SMR potential advantages:

Generation IV Reactors

Six advanced reactor concepts under international development:

  1. Sodium-cooled Fast Reactor (SFR)

    • Liquid sodium coolant, fast neutron spectrum
    • Can breed fuel and burn actinides
    • TerraPower Natrium (USA) under construction
    • Russian BN-800 operational

  2. Lead-cooled Fast Reactor (LFR)

    • Liquid lead or lead-bismuth coolant
    • High temperature capability
    • Newcleo (UK/Italy) in development

  3. Molten Salt Reactor (MSR)

    • Fuel dissolved in molten salt coolant
    • Inherent safety (fuel drains to dump tank)
    • Can use thorium fuel cycle
    • Terrestrial Energy, Kairos Power developing

  4. Very High Temperature Reactor (VHTR)

    • Helium coolant, graphite moderator
    • 750-1000°C outlet temperature
    • Process heat for hydrogen production
    • China HTR-PM partially demonstrates

  5. Supercritical Water-cooled Reactor (SCWR)

    • Water above critical point (374°C, 22 MPa)
    • Higher thermal efficiency (~45%)
    • Conceptual stage

  6. Gas-cooled Fast Reactor (GFR)

    • Helium coolant, fast spectrum
    • Conceptual stage

Generation IV timeline:

Environmental Considerations

Lifecycle Emissions

Nuclear power has very low lifecycle CO₂ emissions:

Technology Lifecycle Emissions (g CO₂-eq/kWh)
Coal 820
Natural gas 490
Solar PV 41
Nuclear 12
Onshore wind 11
Hydropower 24

Nuclear's emissions come primarily from:

The fuel cycle is far less carbon-intensive than any fossil fuel.

Safety Record

Major accidents:

- **Three Mile Island (1979)**: Partial meltdown, no deaths, minimal radiation release - **Chernobyl (1986)**: Explosion and fire, ~30 immediate deaths, ~4,000 estimated excess cancer deaths (disputed) - **Fukushima (2011)**: Three meltdowns following tsunami, 1 death attributed to radiation, ~2,200 evacuation-related deaths

Deaths per TWh (all causes):

Energy Source Deaths per TWh
Coal 24.6
Oil 18.4
Natural gas 2.8
Hydropower 1.3
Wind 0.04
Nuclear 0.03
Solar 0.02

Nuclear is among the safest energy sources per unit of electricity generated, primarily because:

Land Use

Nuclear has the smallest land footprint per unit of energy:

Technology Land Use (m²/MWh/year)
Nuclear 0.3
Natural gas 0.4
Coal 1.0
Solar PV 5-10
Wind 70-100 (including spacing)
Hydropower Variable (reservoir)

A 1 GW nuclear plant occupies ~1-4 km². An equivalent solar farm requires ~15-25 km².

Water Use

Nuclear plants require significant cooling water (like all thermal plants):

This can constrain siting in water-scarce regions. Some advanced designs target air cooling or reduced water use.

Proliferation and Security

Nuclear power creates materials (enriched uranium, plutonium) with potential weapons applications:

- Power reactor fuel (3-5% enrichment) cannot be used directly for weapons - Reprocessing separates plutonium, which is weapons-usable - International safeguards (IAEA) monitor nuclear materials - Proliferation risk influences fuel cycle choices (e.g., US once-through policy)

Security concerns include:

Modern plants are designed to withstand aircraft impact and other threats.

Strategic Outlook

Role in Decarbonization

Nuclear's potential contribution to climate mitigation:

IEA Net Zero Scenario:

IPCC scenarios:

COP28 Declaration (2023):

Near-Term Prospects (2025-2035)

Likely developments:

Challenges:

Realistic capacity by 2035:

Long-Term Potential

By 2050:

Key uncertainties:

  1. Can Western countries rebuild nuclear construction capability?
  2. Will SMRs achieve cost reductions through serial production?
  3. How will nuclear compete with renewables+storage?
  4. Will public acceptance increase or decrease?
  5. Can construction timelines and costs be controlled?

Comparative Assessment

Attribute Nuclear Wind+Solar+Storage
Dispatchability Excellent Requires storage
Land use Minimal Significant
Capacity factor 80-92% 25-35% (before storage)
Construction time 5-15 years 1-3 years
Capital intensity Very high Moderate
Fuel supply security High (small volume, stockpileable) High (no fuel)
Public acceptance Contested Generally positive
Waste Long-lived, low volume Short-lived, high volume

Nuclear and renewables are often framed as competitors, but both are needed for deep decarbonization. Nuclear provides firm, dispatchable power that complements variable renewables.

Conclusion

Nuclear fission offers an extraordinarily energy-dense, low-carbon power source that has operated safely and reliably for over 60 years. Its ~400 GW global capacity generates 10% of world electricity with minimal emissions, land use, and fuel requirements.

The technology faces genuine challenges:

Yet nuclear also offers unique advantages:

The path forward likely involves:

Nuclear fission is neither the sole solution to climate change nor a technology that should be abandoned. It is a proven, scalable, low-carbon energy source whose future role will be determined by economics, policy choices, and societal preferences as much as by technical factors.