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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 astrophysicalapplications. This leads to the importance of plasma effects even for the highenergy emission. The consequences are nontrivial: (i) averaging of the phasesof the emitting particles reduces the power (a.k.a., a circle current does notemit); (ii) density fluctuations may lead to the sporadic production ofcoherent emission; (iii) plasma effects during assembly of a photon may lead tothe suppression of the emission (Razin-Tsytovich effect for the superluminalmodes), or, in the opposite limit of subluminous normal modes, to the newlydiscussed synchrotron super-radiance. For synchrotron emission the radiationformation 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). Thepopular model of coherent curvature emission by bunches", with kilometers-longradiation formation length, particles swinging-out in a rotating magnetospheresbefore they finish emitting a wave, extreme requirements on the momentumspreads, and demands on the electric energy needed to keep theelectrostatically repulsing charges together, all make that model internallyinconsistent. Long radiation formation lengths affect how emission from PICsimulations should be interpreted: phases of the emitted wave should be addedover the radiation formation length, not just the powers from the instantaneousacceleration of each particle.

Radiation formation length in astrophysical high brightness sources