  Quark-gluon plasma produced at the early stage of ultrarelativistic heavy ion
collisions is unstable, if weakly coupled, due to the anisotropy of its
momentum distribution. Chromomagnetic fields are spontaneously generated and
can reach magnitudes much exceeding typical values of the fields in
equilibrated plasma. We consider a high energy test parton traversing an
unstable plasma that is populated with strong fields. We study the momentum
broadening parameter $\hat q$ which determines the radiative energy loss of the
test parton. We develop a formalism which gives $\hat q$ as the solution of an
initial value problem, and we focus on extremely oblate plasmas which are
physically relevant for relativistic heavy ion collisions. The parameter $\hat
q$ is found to be strongly dependent on time. For short times it is of the
order of the equilibrium value, but at later times $\hat q$ grows exponentially
due to the interaction of the test parton with unstable modes and becomes much
bigger than the value in equilibrium. The momentum broadening is also strongly
directionally dependent and is largest when the test parton velocity is
transverse to the beam axis. Consequences of our findings for the phenomenology
of jet quenching in relativistic heavy ion collisions are briefly discussed.
