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Recently, cosmic rays (CRs) have emerged as a leading candidate for drivinggalactic winds. Small-scale processes can dramatically affect global windproperties. We run two-moment simulations of CR streaming to study how soundwaves are driven unstable by phase-shifted CR forces and CR heating. We verifylinear theory growth rates. As the sound waves grow non-linear, they steepeninto a quasi-periodic series of propagating shocks; the density jumps at shockscreate CR bottlenecks. The depth of a propagating bottleneck depends on boththe density jump and its velocity; {\Delta}P_c is smaller for rapidly movingbottlenecks. A series of bottlenecks creates a CR staircase structure, whichcan be understood from a convex hull construction. The system reaches a steadystate between growth of new perturbations, and stair mergers. CRs are decoupledat plateaus, but exert intense forces and heating at stair jumps. The absenceof CR heating at plateaus leads to cooling, strong gas pressure gradients andfurther shocks. If bottlenecks are stationary, they can drastically modifyglobal flows; if their propagation times are comparable to dynamical times,their effects on global momentum and energy transfer are modest. The CRacoustic instability is likely relevant in thermal interfaces between cold andhot gas, as well as galactic winds. Similar to increased opacity in radiativeflows, the build-up of CR pressure due to bottlenecks can significantlyincrease mass outflow rates, by up to an order of magnitude. It seeds unusualforms of thermal instability, and the shocks could have distinct observationalsignatures.

The Cosmic Ray Staircase: the Outcome of the Cosmic Ray Acoustic Instability