Engineering & Science
Thermal Bremsstrahlung Plasma Radiation Loss & Z_eff Impurity Scaling
Calculate free-free thermal bremsstrahlung volumetric power loss P_br = 1.42e-40 * g_ff * Z_eff^2 * n_e^2 * SQRT(T_K) (in kW/m^3) for magnetic fusion plasmas and X-ray galaxy clusters.
Why high-Z tungsten or carbon wall impurities quench tokamak fusion plasmas via Z^2 bremsstrahlung!
Whenever hot plasma electrons decelerate around positively charged ions of charge number Z, they radiate continuous free-free X-ray photons ("Bremsstrahlung" = braking radiation). Integrating over a Maxwellian electron distribution yields the SI volumetric bremsstrahlung emission density across both magnetic-confinement fusion plasmas and intracluster X-ray gas: P_br (W/m^3) = 1.42e-40 * g_ff * Z^2 * n_e * n_i * SQRT(T_K)!
Look at the punishing Z^2 sensitivity in a magnetic-confinement plasma at electron density n_e = 1.0e20 m^-3, ion density n_i = 1.0e20 m^-3, temperature T = 1.0e8 K (~8.62 keV), and quantum Gaunt factor g_ff = 1.20: pure hydrogenic D-T fuel (Z = 1) radiates 17.04 kW/m^3, whereas a Z = 3 lithium plasma at the same densities radiates 9x more—153.36 kW/m^3!
| Plasma Species Scenario (ne = ni = 10^20 m^-3, T = 10^8 K, gff = 1.2) | Ion Charge Z | Bremsstrahlung Loss (kW/m^3) | Fusion Energy Balance Impact |
|---|---|---|---|
| Clean Hydrogenic D-T Plasma | Z = 1 | 17.04 kW/m^3 | Manageable below alpha-heating power |
| Triply Charged Low-Z Plasma | Z = 3 | 153.36 kW/m^3 (9x Higher!) | Quadratic Z^2 radiative cooling surge |
| Zero or Negative Density / Temp | Guarded Input | "Invalid Plasma Inputs" | Requires T > 0, ne > 0, ni > 0, Z >= 1 |
Volumetric Thermal Bremsstrahlung Power Density P_br (kW/m^3)
Evaluates 1.42e-40 * g_ff * Z^2 * n_e * n_i * SQRT(T_K) / 1000 using densities in units of 10^20 m^-3 (so 1.0 = 10^20 m^-3, avoiding 40-digit manual entry errors!).
=IF(OR(B2 <= 0, B3 <= 0, B4 < 1, B5 <= 0, B6 <= 0), "Invalid Plasma Inputs", ROUND(1.42 * B6 * (B4 ^ 2) * B2 * B3 * SQRT(B5) / 1000, 2))Equivalent Electron Thermal Energy k_B * T in keV
Converts Kelvin plasma temperature B5 into fusion kiloelectronvolts via k_B / (1000 * e) = 8.617333e-8 keV/K.
=IF(B5 <= 0, "Invalid Plasma Inputs", ROUND(B5 * 0.0000000861733, 2))Try the example
Use the original values or change them to test your understanding.