Abstract
An axial magnetic field of sufficient strength strength is imposed in the electron cooling devices on charged-particle beams, such that the mean cyclotron radius of electrons is much smaller than the average distance among electrons themselves. In this paper it is shown that this project condition implies an ordered evolution of system, without allowing thermal equilibrium between transversal and longitudinal degrees of freedom. This result has been obtained using a Lyapunov exponents technique in a simplified beam model.
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