Direct electron acceleration by a propagating laser pulse of circular polarization in an ion-channel guiding is studied by developing a relativistic three-dimensional single particle code. The electron chaotic dynamic is also studied using time series, power spectrum, and Liapunov exponent. It is found that the electron motion is regular (non-chaotic) for laser pulse with short time duration, while for long enough time duration, the electron motion may be chaotic. In the case of non-chaotic motion, the electron can gain and retain very high energy in the presence of ion-channel before reaching the steady-state, whereas in the case of chaotic motion, the electron gains energy and then loses it very rapidly in an unpredictable manner.
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