  It is demonstrated that in high temperature collisionless plasmas the
propagation of high-frequency electromagnetic waves is naturally subject to a
classical Higgs mechanism which in some cases generates a very small though
finite mass on the otherwise massless photons. Though this has no further
obvious consequence for any plasma processes, it is very satisfactory because
it explains the retardation and cut-off of electromagnetic waves when
encountering plasmas. Interestingly, low frequency electromagnetic plasma waves
(Alfv\'en waves and whistlers) remain carried by confined massless photons.
These just experience the increase in the dielectric constant provided by the
plasma in the low frequency range below the cyclotron frequency.
