On the possibility of chaotic motion and acceleration of ions in oscillating plasma structures

Self-consistent, electronic space charge structures of the type of BGK (Bernstein-Greene-Kruskal) solutions, formed over regions of constant background density, may oscillate in time coherently as a rigid system, with given characteristic frequencies. The equation of motion of a test particle in the electric field of the oscillating electrons is considered. It is noted that when the BGK solution is periodic in space, the test particle equation is formally equivalent to that of a nonlinear oscillator excited periodically, and that the motion may show chaotic dynamic behaviour. On the other hand, if the electron structure is quasi-periodic in space with a weakly varying wavelength, the test particle energy may increase as in a beat wave accelerator. It follows that MeV ions can be produced over small distances in dense plasmas auxiliary. (Author)