Past exam of the physics B course of the University of Cambridge / 2018 / Paper 1 / Section A / A4 / Solution

The conventional electron plasma frequency isUse $n_e=10^{25}{\mathrm{m}}^{-3}$, $e=1.602\times 10^{-19}\mathrm{C}$, $m_e=9.109\times 10^{-31}\mathrm{kg}$ and ${\epsilon }_0=8.854\times 10^{-12}\mathrm{F}{\mathrm{m}}^{-1}$. ThenThe equal proton density ensures charge neutrality; it does not double the electron density in this formula. Protons have their own plasma frequency,If both cold species are allowed to move in the relative charge-separation oscillation, its squared frequency is ${\omega }_{pe}^2+{\omega }_{pi}^2$. This gives $1.7843\times 10^{14}\mathrm{rad}{\mathrm{s}}^{-1}$, only about $0.027\%$ above the electron-only answer, because $m_p\gg m_e$.