  A model for the dynamics of a classical point charged particle interacting
with higher order jet fields is introduced. In this model, the dynamics of the
charged particle is described by an implicit ordinary second order differential
equation. Such equation is free of run-away and pre-accelerated solutions of
Dirac's type. The theory is Lorentz invariant, compatible with the first law of
Newton and Larmor's power radiation formula. Few implications of the new
equation in the phenomenology of non-neutral plasmas is considered.
