= Solution
Propagation through an already formed cold <plasma (physics)>[plasma] requires $\omega_L>\omega_p$, hence $\boxed{\lambda_L<\lambda_p=2\pi c/\omega_p}$. For the illustrative <density> above, that is a cutoff near 126 micrometres. It is a propagation ceiling, not a sufficient condition for producing ionization.
\b[TODO — the unique cutoff inherits the unspecified <density>, and a literal maximum wavelength for gas ionization also needs gas species, laser intensity and the ionization mechanism.] A single-photon threshold would impose $hc/\lambda\geq I_{\mathrm{ion}}$; strong-field or multiphoton ionization is a different criterion. None of those data is supplied. The density-dependent propagation condition is the part determined symbolically.
Back to article page
