Bremsstrahlung Radiation
The braking radiation emitted when electrons are deflected by ions, an unavoidable energy loss from any plasma.
Braking radiation
When a free electron is deflected by the Coulomb field of an ion it accelerates, and accelerating charges radiate. This bremsstrahlung (German for braking radiation) is emitted as a continuous spectrum and is an intrinsic loss from any hot, ionized plasma. The radiated power density scales as:
P_brems ~ Z_eff n_e^2 sqrt(T_e)It grows with the square of density and, importantly, with the effective charge Z_eff, so even small amounts of high-Z impurities strongly increase radiation losses. The temperature dependence is mild (square root), so bremsstrahlung cannot be avoided by simply running hotter.
The Z-squared penalty
Because the emission from each ion scales as Z^2, heavy impurities (tungsten, iron) radiate far more than the hydrogen fuel. Keeping the plasma clean, low Z_eff, is therefore essential to the power balance, and it constrains plasma-facing-material choices.
Consequences for fusion
- Bremsstrahlung sets a minimum ignition temperature: below it, radiation beats fusion heating
- It is a hard floor for advanced (aneutronic) fuels with higher-Z reactants
- Some bremsstrahlung is reabsorbed only in extremely dense plasmas; in fusion it escapes
How it enters power balance
Bremsstrahlung is a loss term in the plasma energy balance, evaluated locally from n_e, T_e, and Z_eff and integrated over the plasma. It competes directly with fusion self-heating in the Lawson analysis.
Fuel-dependent importance
For D-T at optimal temperature, bremsstrahlung is a manageable fraction of the fusion power. For higher-temperature, higher-Z fuels like D-3He, bremsstrahlung is a larger and more limiting loss, one of the physics considerations for the Kronos burner as a D-3He design study, where operating temperature and confinement must overcome the higher radiative floor.