A system of equations is provided that may be used in the study of relativistic charged particle beams. The equations are based upon the equations of the kinetic theory for first, second and third order moments and the system is closed by letting the third order moment depend on the lower order ones. The form of that dependence is formally equal to the explicit constitutive function given by extended thermodynamics. However, here the contributions to the third order moment can be classed as being different in order of magnitude, because there is a smallness parameter characterizing the small dispersion of the particle beam. The resulting system of equations is quite specific, it is fully covariant and it is equivalent to a symmetric hyperbolic system thus ensuring existence and uniqueness of solutions.
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