  In supernova remnants, the nonlinear amplification of magnetic fields
upstream of collisionless shocks is essential for the acceleration of cosmic
rays to the energy of the "knee" at 10^{15.5}eV. A nonresonant instability
driven by the cosmic ray current is thought to be responsible for this effect.
We perform two-dimensional, particle-in-cell simulations of this instability.
We observe an initial growth of circularly polarized non-propagating magnetic
waves as predicted in linear theory. It is demonstrated that in some cases the
magnetic energy density in the growing waves, can grow to at least 10 times its
initial value. We find no evidence of competing modes, nor of significant
modification by thermal effects. At late times we observe saturation of the
instability in the simulation, but the mechanism responsible is an artefact of
the periodic boundary conditions and has no counterpart in the supernova-shock
scenario.
