Bremsstrahlung Radiation

Bremsstrahlung Radiation

Bremsstrahlung (German for "braking radiation") is electromagnetic radiation emitted when a charged particle — typically an electron — is accelerated (or decelerated) by the Coulomb field of another charged particle, usually an ion.

Physics of Bremsstrahlung

In a plasma, electrons constantly encounter ions and are deflected by their electric fields. Each deflection causes the electron to radiate. This is also called free-free emission because the electron is unbound before and after the encounter.

Power Emitted Per Unit Volume

The total bremsstrahlung power radiated per unit volume is:

$P_{brem} = C_{brem} \cdot n_e^2 \cdot Z^2 \cdot \sqrt{T}$

where:

• (C_{brem} = 1.69 \times 10^{-38}) W m³ K(^{-1/2})
• (n_e) is the electron number density (m(^{-3}))
• (Z) is the ion charge number
• (T) is the plasma temperature (K)

The (\sqrt{T}) dependence arises because higher temperatures mean higher electron velocities, but shorter interaction times — the net effect scales as (v \propto T^{1/2}).

Cooling Time

The energy density of the plasma is (U = \frac{3}{2} n k_B T). The radiative cooling time is:

$t_{cool} = \frac{\frac{3}{2} n k_B T}{P_{brem}}$

This tells us how long it takes for bremsstrahlung to radiate away the plasma's thermal energy.

Significance for Fusion

Bremsstrahlung is a major energy loss mechanism in fusion plasmas. For a reactor to achieve ignition, the fusion power must exceed bremsstrahlung losses. This sets a minimum temperature requirement for the fuel.

For a deuterium-tritium plasma, the crossover occurs near 5 keV ((\sim 58) million K), which is why fusion reactors must operate at extremely high temperatures.