What Is the Lawson Criterion & Fusion Triple Product Calculator?
Formulated by British physicist J. D. Lawson in 1955, the Lawson criterion establishes the fundamental energy balance for net-power thermonuclear fusion.
The modern triple product combines density n, temperature T, and energy confinement time τE into a single figure of merit.
How Does the Lawson Criterion & Fusion Triple Product Calculator Work?
For self-sustaining fusion ignition (Q → ∞), alpha particle self-heating must balance core Bremsstrahlung radiation and conductive transport losses.
D-T fusion peaks around 15 keV (~170 million °C), requiring n·T·τE ≥ 3 × 10²¹ keV·s/m³.
Lawson Criterion & Fusion Triple Product Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
Evaluates the product of fuel density, thermal kinetic temperature, and energy retention timescale.
How to Use the Lawson Criterion & Fusion Triple Product Calculator
- Enter the core ion density, temperature in keV, and confinement time in seconds.
- Review the resulting percentage of the ignition threshold and estimated Q factor.
Step-by-Step Example Calculation
ITER Baseline Burning Plasma Scenario
Input Values:
Understanding Your Result
Q = 1: Scientific breakeven (fusion power output equals auxiliary heating power input).
Q ≥ 5: Burning plasma regime (self-heating dominates auxiliary heating).
Q → ∞: Ignition (reactor remains hot without any external heating).
Factors That Affect the Result
- Magnetic field strength B: Confinement time τE scales strongly with tokamak size and magnetic field (H-mode scaling).
- Impurities: High-Z impurities radiate enormous power, quenching the triple product.
When Should You Use This Calculator?
- Benchmarking magnetic (tokamak, stellarator) and inertial confinement fusion experiments.
- Evaluating progress from JET to ITER and commercial fusion startups.
Assumptions & Limitations
- Based on a 50:50 deuterium-tritium fuel mixture at optimal ~15 keV operating temperature.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard international fusion benchmark relation.