Firehose and Mirror Instabilities

In this two-dimensional test problem for the CGL-MHD code we simulated a model of the firehose instability. Initially we set uniform magnetic field with the strength equal 1 and uniform density equal 1 as well. Initial velocity is set to zero. To initiate the firehose instability we set the ratio of parallel to perpendicular pressures according to the criterion $\beta_\parallel - \beta_\perp > 2$.

Figure 1: Texture maps of the magnetic field at different stages of the evolution of firehose instability for times 0, 0.5, 1.0, and 5.0 from left to right, respectively.

In Figure 1 we show the subsequent stages of the evolution of magnetic field during the development of the firehose instability. The images show textures of magnetic field for times 0.1, 0.5, 1.0 and 5.0 of Alfvenic time. The initially larger pressure component parallel to magnetic lines causes the line bending and in consequence continuous growth of the instability. The development of magnetic field structure, starting from the smallest to larger scales, is clearly visible.