THE ROLE OF UPSTREAM WAVES IN SUPERCRITICAL QUASI-PARALLEL SHOCK RE-FORMATION

It has been demonstrated by hybrid simulations of collisionless shocks that the shock itself is not stationary but exhibits a cyclic behavior. We have performed a number of one-dimensional hybrid simulations of collisionless shocks and of the interaction of two plasma streams in order to assess the role of upstream waves in the re-formation process. We found that when upstream waves and reflected ions are present, the waves inevitably steepen up and lead to shock re-formation. To investigate the interaction of the reflected ions with upstream waves, the hybrid code is then used in two stages. In the first stage a shock together with upstream diffuse particles and waves is generated. In the second stage, upstream wave trains are isolated, and their subsequent interaction with a finite length ion beam as well as with ions emitted from a moving point source is investigated. The results show that the original wave amplitude grows and the wave steepens. This is due to a deceleration and deflection of the beam ions once they encounter a wave crest with a large local value of the angle-THETA(Bn) between the magnetic field and the direction of beam propagation: the deflection leads to a local density increase and due to the compressibility to a corresponding magnetic field increase. This sets up a positive feedback loop during which the background ions are also decelerated and can even get reflected. It is concluded that shock re-formation can be caused by the interaction of reflected ions with low-frequency upstream waves.