The preacceleration of electrons through reflection and shock drift acceleration ( SDA ) is essential for the diffusive shock acceleration ( DSA ) of nonthermal electrons in collisionless shocks .
Previous studies suggested that , in weak quasi-perpendicular ( Q _ { \perp } ) shocks in the high- \beta ( \beta = P _ { gas } / P _ { B } ) intracluster medium ( ICM ) , the temperature anisotropy due to SDA-reflected electrons can drive the electron firehose instability , which excites oblique nonpropagating waves in the shock foot .
In this paper , we investigate , through a linear analysis and particle-in-cell ( PIC ) simulations , the firehose instabilities driven by an electron temperature anisotropy ( ETAFI ) and also by a drifting electron beam ( EBFI ) in \beta \sim 100 ICM plasmas .
The EBFI should be more relevant in describing the self-excitation of upstream waves in Q _ { \perp } -shocks , since backstreaming electrons in the shock foot behave more like an electron beam rather than an anisotropic bi-Maxwellian population .
We find that the basic properties of the two instabilities , such as the growth rate , \gamma , and the wavenumber of fast-growing oblique modes are similar in the ICM environment , with one exception ; while the waves excited by the ETAFI are nonpropagating ( \omega _ { r } = 0 ) , those excited by the EBFI have a non-zero frequency ( \omega _ { r } \neq 0 ) .
However , the frequency is small with \omega _ { r } < \gamma .
Thus , we conclude that the interpretation of previous studies for the nature of upstream waves based on the ETAFI remains valid in Q _ { \perp } -shocks in the ICM .