Question

A sounding of dilute plasma by radiowaves of various frequencies reveals that rediowaves with wavelength exceeding `lambda_(0) = 0.75m` experience total internal reflection. Find the free electron concentration in that plasma.

Answer 1

In the plasma radio waves with wavelength exceeding `lambda_(0)` are not propagated. We interpret this to mean thet the permittively become negative for such waves. Thus
`0 =1 - (n_(0)e^(2))/(epsilon_(0)m omega^(2))` if `omega = (2pi c)/(lambda_(0))`
Hence `(n_(0)e^(2)lambda_(0)^(2))/(4pi^(2)epsilon_(0)mc^(2)) = 1`
or `n_(0) = (4pi^(2) epsilon_(0) mc^(2))/(e^(2)lambda_(0)^(2)) = 1.984 xx 10^(9) per c.c`