Spatial structure of the flow velocity (blue line) in the reference frame of the shock, which is located at x = 0. The diffusion length of a particle with momentum p is x_p1 upstream and x_p2 downstream. These are the largest distances the particle can diffuse and return to the shock to be further accelerated. The shock compression factor σ = u₁/u₂ is the ratio of the immediate pre- to post-shock velocities. Instead, σ_p(p) = u_p1(p)/u_p2(p) is an effective compression factor “seen” by a relativistic particle with momentum p; it varies with momentum. The shock here is not CR-modified, and therefore u_p1(p) = u₁ upstream, for any momentum. For the downstream region, one may use an approximation u_p2(p) ≈ u₂(x_p2) (see Sect. 3.4).