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Bremsstrahlung Radiation Loss Calculator (Fusion Plasma)

Bremsstrahlung (German for "braking radiation") occurs when electrons decelerate during Coulomb collisions with ions in a hot plasma.

Core plasma electron density.

Effective charge of plasma ions (Pure D-T = 1.0; tungsten/carbon impurities raise Zeff to 1.5 - 2.5).

Core electron temperature in keV.

Plasma confinement volume in cubic meters (e.g. 840 m³ for ITER).

Calculated Result
22.24 MW

Total Bremsstrahlung Radiated Power

Volumetric Radiation Loss

27.80 kW/m³

Impurity Scaling Factor (Zeff)

1.50

Plasma Confinement Volume

800 m³

Calculation Breakdown

  1. Volumetric Bremsstrahlung LawP_br = 5.35×10⁻³⁷ · Zeff · n_e² · √T_e = 27.80 kW/m³
  2. Total Core Radiation LossP_total = P_br · V = 22.24 MW

What Is the Bremsstrahlung Radiation Loss Calculator (Fusion Plasma)?

Bremsstrahlung is the continuous X-ray radiation emitted when electrons are accelerated or deflected by the electric field of atomic nuclei.

Because hot fusion plasmas are optically thin to X-rays, all Bremsstrahlung photons escape immediately to the vessel walls, causing parasitic core cooling.

How Does the Bremsstrahlung Radiation Loss Calculator (Fusion Plasma) Work?

Volumetric power loss scales as ne² · √Te · Zeff.

Because radiation scales with Z², even tiny fractions of high-Z impurities (such as sputtered tungsten Z=74 or iron Z=26) drastically increase radiative cooling and prevent ignition.

Bremsstrahlung Radiation Loss Calculator (Fusion Plasma) Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

P_br = 5.35 × 10⁻³⁷ · Z_eff · n_e² · √T_e (W/m³), P_total = P_br · V

Models quantum electrodynamic dipole radiation emitted during electron-ion scattering.

How to Use the Bremsstrahlung Radiation Loss Calculator (Fusion Plasma)

  1. Enter electron density and temperature.
  2. Specify Zeff from spectroscopic diagnostics.
  3. Input the plasma volume to determine total Megawatts radiated.

Step-by-Step Example Calculation

ITER-Scale Plasma: 800 m³ at 12 keV

Input Values:

electronDensityM3:100000000000000000000
effectiveChargeZeff:1.5
electronTemperatureKeV:12
plasmaVolumeM3:800
Worked Steps: Predicts ~22.3 MW of continuous Bremsstrahlung power radiated to the first wall.

Understanding Your Result

Ptotal indicates the continuous X-ray heat load on plasma-facing first-wall armor.

This power must be continuously compensated by fusion alpha-particle self-heating.

Factors That Affect the Result

  • Zeff: Impurities are the most dangerous threat to fusion; clean fuel with Zeff close to 1.0 is essential.

When Should You Use This Calculator?

  • Calculating thermal loads on divertor and first-wall armor tiles.
  • Evaluating core radiative cooling limits for advanced aneutronic fuels (D-³He, p-¹¹B).

Assumptions & Limitations

  • Assumes Born approximation thermal Bremsstrahlung and ignores synchrotron/cyclotron radiation.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Standard NRL Plasma Formulary equation.

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