# Fusion Gain Factor (Q) — First Principles Breakdown ## 1. What is Q? **Q** is the **fusion energy gain factor**: Q = Pfus / Pinput - `Pfus` = Fusion power produced - `Pinput` = External power used to heat and sustain the plasma **Breakeven (scientific)** happens at **Q = 1**, where fusion power equals input heating power. --- ## 2. Where Does the Input Power Go? - Heating the plasma to fusion conditions - Compensating for energy losses (radiation, conduction, particle escape) --- ## 3. Where Does the Fusion Power Go? Fusion energy comes out as: - **Charged particles (e.g., alpha particles)** → Stay in plasma → contribute to **self-heating** - **Neutrons** → Escape plasma → hit external blanket → converted to heat **Key point:** Only ~20% of D-T fusion energy (from alphas) can self-heat the plasma. The rest is available for generating electricity. --- ## 4. Breakeven Types | Type | Meaning | Q Value | |-----------------------|-------------------------------------------------------|------------------| | **Scientific** | Pfus = Pinput (just plasma heating) | Q = 1 | | **Engineering** | Reactor powers its own heating systems via electricity| Q ≈ 5–8 (MCF) | | **Ignition** | No external heating needed | Q → ∞ | | **Commercial** | Reactor earns back costs (ops, fuel, capex) | Q ≥ 20–25 (varies)| | **Extrapolated** | Performance if using tritium, based on test fuel | — | --- ## 5. Why Q ≈ 5 Is Needed for Ignition (D-T Fuel) Only 20% of fusion energy stays in plasma as alpha particles. To fully self-sustain heating: Self-heating = External heating → Q = 1 / 0.2 = 5 --- ## 6. Power Conversion and Recirculation Losses Real systems have efficiency limits: - `ηheat` = Efficiency of plasma heating (~0.7) - `ηelec` = Heat-to-electric conversion (~0.4) - `frecirc` = Fraction of electricity sent back to heating (~0.2) - `fch` = Fraction of fusion energy in charged particles (~0.2 for D-T) --- ## 7. Engineering Breakeven Formula To reach **Qeng = 1**: Qeng = 1 / (ηheat × ηelec × frecirc × (1 - fch)) Using typical values: Qeng = 1 / (0.7 × 0.4 × 0.2 × 0.8) ≈ 22 So you need **Q ≈ 22** for a real power plant to sustain itself with internal electricity recirculation. --- ## 8. Summary - **Q = 1** → Scientific breakeven (proof of concept) - **Q ≥ 5** → Plasma self-heats (ignition) - **Q ≥ 10–20** → Net electricity possible - **Q ≥ 22+** → Realistic engineering breakeven with recirculation losses > Q is necessary, but not sufficient. Reactor economics depend on recirculation, conversion efficiency, fuel availability, and capex. --- ## Bonus: Terms Recap - **Scientific breakeven**: Q = 1 - **Engineering breakeven**: Enough electricity to power own heaters - **Ignition**: Self-heating replaces all external heating - **Extrapolated Q (Qext)**: Estimated Q if using tritium - **Commercial breakeven**: Reactor pays for itself economically --- ## Example (ITER-like Reactor) - Fusion output: 500 MW - Input power: 50 MW - Q = 10 - 20% (100 MW) used for self-heating - 400 MW available for extraction - With ηheat = 0.7, ηelec = 0.4 - Up to ~112 MW electricity generated - Can hit engineering breakeven if recirculation demand <112 MW