  Despite being studied for many years, the structure of collisionless shocks
is still not fully determined. Such shocks are known to be accelerators of
cosmic rays, which, in turn, modify the shock structure. The shock width
$\lambda$ is known to be connected to the cosmic rays (CRs) spectral index,
$a$. Here, we use an instability analysis to derive the shock width in the
presence of CRs. We obtain an analytical expression connecting the shock width
to the CRs index and to the fraction of upstream particles that are
accelerated. We find that when this fraction becomes larger than $\sim$~30\%, a
new instability becomes dominant. The shock undergoes a transition where its
width increases by a factor $\sim 8- 10$, and the CRs acceleration effectively
ends. Our analysis is valid for strong, non-relativistic and unmagnetized
shocks. We discuss the implication of these results to the expected range of
CRs spectra and flux observed, and on the structure of non-relativistic
collisionless shocks.
