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The energy loss of a fast parton scattering elastically in a weakly coupled quark-gluon plasma is formulated as an initial value problem. The approach is designed to study an unstable plasma, but it also reproduces the well known result of energy loss in an equilibrium plasma. A two-stream system, which is unstable due to longitudinal chromoelectric modes, is discussed here some detail. In particular, a strong time and directional dependence of the energy loss is demonstrated.

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