  Evidence is accumulating suggesting that collisionless shocks in supernova
remnants (SNRs) can amplify the interstellar magnetic field to hundreds of
microgauss or even milli-gauss levels, as recently claimed for SNR RX
J1713.7-3946. If these fields exist, they are almost certainly created by
magnetic field amplification (MFA) associated with the efficient production of
cosmic rays by diffusive shock acceleration (DSA) and their existence
strengthens the case for SNRs being the primary source of galactic cosmic ray
ions to the `knee' and beyond. However, the high magnetic field values in SNRs
are obtained exclusively from the interpretation of observations of radiation
from relativistic electrons and if MFA via nonlinear DSA produces these fields
the magnetic field that determines the maximum ion energy will be substantially
less than the field that determines the maximum electron energy. We use results
of a steady-state Monte Carlo simulation to show how nonlinear effects from
efficient cosmic ray production and MFA reduce the maximum energy of protons
relative to what would be expected from test-particle acceleration.
