Firehose and Mirror Instabilities

The firehose instability is driven by an anisotropy of pressure in a magnetized plasma when the condition $\beta_\parallel - \beta_\perp > 2$ is fulfilled noerdlinger68. In its linear stage it is manifested in Alfvén waves of near-zero frequency in which the ambient magnetic field veers sinusoidally in direction. In its nonlinear stage, the instability leads to a tangling and mixing of the magnetic field lines in the plasma, possibly accompanied by plasma compressions.

Magnetic mirror instability is the slow magnetosonic wave driven unstable by the anisotropic pressure in collisionless plasmas with the criterion $\beta_\parallel< \beta_\perp^2 / (1 + \beta_\perp)$. It plays an important role in low frequency magnetic turbulence in high-$\beta$ space plasmas, e.g., the Earth's magnetosheath, and also potentially in high-$\beta$ laboratory mirror or dipole plasmas with large fraction of trapped particles. A quasi-hydrodynamic analysis of kinetic mirror instability in non-Maxwellian plasmas recently found that the maximum growth rate increases with perpendicular wave number until the perpendicular wavelength becomes comparable to the ion gyroradius[1]. Therefore, the finite Larmor radius effects are important in determining the threshold and the wavelength of the kinetic mirror instability.