  Constraints on the diffusion and acceleration parameters in five young
supernova remnants (SNRs) are derived from the observed thickness of their
X-ray rims, as limited by the synchrotron losses of the highest energy
electrons, assuming uniform and isotropic turbulence. It is shown that the
magnetic field must be amplified up to values between 250 and 500 microGauss in
the case of Cas A, Kepler, and Tycho, or ~ 100 microGauss in the case of SN
1006 and G347.3-0.5. The diffusion coefficient at the highest electron energy
can also be derived from the data, by relating the X-ray energy cutoff to the
acceleration timescale. Values typically between 1 and 10 times the Bohm
diffusion coefficient are found to be required. We also find interesting
constraints on the energy dependence of the diffusion coefficient. This favours
diffusion regimes between the Kraichnan and the Bohm regime, and rejects
turbulence spectrum indices larger than ~ 3/2. Finally, the maximum energy of
the accelerated particles is found to lay between 10^13 and 5 10^13 eV for
electrons, and around Z \times 8 10^14 eV at most for nuclei (or ~ 2.5 times
less if a Bohm diffusion regime is assumed), roughly independently of the
compression ratio assumed at the shock. Even by taking advantage of the
uncertainties on the measured parameters, it appears very difficult for the
considered SNRs in their current stage of evolution to produce protons up to
the knee of the cosmic-ray spectrum, at ~ 3 10^15 eV, and essentially
impossible to accelerate Fe nuclei up to either the ankle at ~ 3 10^18 eV or
the second knee at ~ 5 10^17 eV.
