We consider the general problem of charged particle motion in a strong electromagnetic field of arbitrary configuration and find a universal behaviour: for sufficiently high field strengths, the radiation losses lead to a general tendency of the charge to move along the direction that locally yields zero lateral acceleration. The relativistic motion along such a direction results in no radiation losses, according to both classical and quantum descriptions of radiation reaction. We show that such a radiation-free direction (RFD) exists at each point of an arbitrary electromagnetic field, while the time-scale of approaching this direction decreases with the increase of field strength. Thus, in the case of a sufficiently strong electromagnetic field, at each point of space, the charges mainly move and form currents along local RFD, while the deviation of their motion from RFD can be calculated in order to account for their incoherent emission. This forms a general description of particle, and therefore plasma, dynamics in strong electromagnetic fields, the latter can be generated by state-of-the-art lasers or in astrophysical environments.
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