Many factors are considered in instability analysis, such as self-gravity, differential rotation, and magnetic field. Cosmic rays (CRs) are another factor that have been recently considered and shown to play a dynamic role. However, the effect of CRs on the stability of hot dilute plasma systems has not yet been considered. This type of plasma is believed to be found in the intracluster medium of galaxy clusters and inefficient radiation accretion flows around black holes. Here, we study the dynamic effects of CRs on instability modes in such systems. We discuss analytically some special cases and work out general cases numerically. We show that the growth rate of some unstable modes such as magnetothermal instability (MTI), gyroviscous magnetorotational instability, and convective instability which depend on the ratio of CR pressure to gas pressure (βcr), the ratio of the radial gradient of CR pressure to the radial gradient of gas pressure (), and CR diffusion coefficient. CRs can alter MTI criterion. In this paper, we show that a plasma which is stable in ideal MTI criterion, i.e. dT/dR > 0, such as cooling flow clusters, can be unstable in the presence of CRs if || > 1.
