Plasma Density in Fusion Reactors Calculator

Plasma density is the number of ions or electrons per cubic meter in the fusion plasma. It directly determines the fusion reaction rate: higher density means more frequent collisions between deuterium and tritium nuclei, leading to greater fusion power output. The density is limited by stability constraints (Greenwald limit), confinement quality, and the magnetic field strength. ITER aims for a plasma density of about 10²⁰ particles/m³ to achieve Q=10 (10 times more power out than in).

The Lawson criterion defines the conditions necessary for a fusion reactor to achieve ignition (self-sustaining burn). It is expressed as the triple product: n × T × τE ≥ 3 × 10²¹ m⁻³·keV·s (for D-T fusion), where n is plasma density, T is temperature, and τE is energy confinement time. Achieving this triple product requires simultaneously high density, high temperature (∼15 keV), and long energy confinement time. ITER is designed to reach a triple product of about 1.5 × 10²¹.

The Greenwald limit is a practical operational limit on plasma density in tokamaks, given by nG = I/(πa²) × 10²⁰ m⁻³, where I is plasma current in megaamperes and a is minor radius in meters. Exceeding this limit typically leads to plasma disruptions, which can damage reactor components. Most tokamaks operate at 60-100% of the Greenwald limit. Advanced confinement modes like H-mode help achieve higher densities closer to the limit.

The toroidal magnetic field B₀ is one of the most important parameters in magnetic confinement fusion. Higher B₀ allows: (1) higher plasma density before instabilities (n ∝ B₀/R), (2) better energy confinement time (τE ∝ B₀⁰.⁸⁵), (3) higher plasma current for stability (I ∝ B₀), and (4) operation at higher beta (plasma pressure/magnetic pressure). ITER operates at 5.3 T, while future reactors like DEMO target 6-8 T. High-temperature superconductors (REBCO) may enable 10+ T in compact reactors.