Linear theory of low frequency magnetosonic instabilities in counterstreaming bi-Maxwellian plasmas

An effect of the bi-Maxwellian counterstreaming distribution function is analyzed with regard to the linear low frequency instabilities in magnetized homogeneous collisionless plasmas. New analytical marginal instability conditions for the firehose and the mirror modes have been obtained. Presence of counterstreams along the ambient magnetic field causes a huge effect on the instability conditions of those modes. The instability conditions very sensitively depend on the functional dependence of the counterstreaming parameter P. The theoretically predicted results might give a full potential explanation for the observed solar wind temperature anisotropy diagram in A-β∥ plane [S. D. Bale et al., Phys. Rev. Lett. 103, 211101 (2009)].