  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.
