  The radiation formation length for relativistic particles, $l_c \sim \gamma^2
\lambda$ ($\gamma$ is the Lorentz factor, $\lambda$ is the emitted wavelength),
is much lager than the inter-particle distances in many astrophysical
applications. This leads to the importance of plasma effects even for the high
energy emission. The consequences are nontrivial: (i) averaging of the phases
of the emitting particles reduces the power (a.k.a., a circle current does not
emit); (ii) density fluctuations may lead to the sporadic production of
coherent emission; (iii) plasma effects during assembly of a photon may lead to
the suppression of the emission (Razin-Tsytovich effect for the superluminal
modes), or, in the opposite limit of subluminous normal modes, to the newly
discussed synchrotron super-radiance. For synchrotron emission the radiation
formation length is the same for all emitted waves, $\sim c/\omega_B$
(non-relativistic Larmor length); for curvature emission it is $R/\gamma$ -
macroscopically long in pulsar magnetospheres (e.g., kilometers for radio). The
popular model of coherent curvature emission by bunches", with kilometers-long
radiation formation length, particles swinging-out in a rotating magnetospheres
before they finish emitting a wave, extreme requirements on the momentum
spreads, and demands on the electric energy needed to keep the
electrostatically repulsing charges together, all make that model internally
inconsistent. Long radiation formation lengths affect how emission from PIC
simulations should be interpreted: phases of the emitted wave should be added
over the radiation formation length, not just the powers from the instantaneous
acceleration of each particle.
