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To study the transport phenomena of energetic particles in plasmas, a new type of mesh-free plasma simulation model is introduced. The model is implemented within the parallel tree code Pretty Efficient Parallel Coulomb-solver, which uses an O (N log N) Barnes-Hut tree algorithm to speed up the force calculation. In this paper, we present an extension of this approach to include magnetic fields within the so-called Darwin or magnetoinductive approximation, which neglects the transverse part of the displacement current in Ampère's law. This effectively omits radiation, which means that the timestep is no longer limited by the Courant condition, as in the fully electromagnetic case. The ability of the model to give a valid description of an N-body system with self-consistently evolving E- and B-fields is demonstrated by preliminary tests.