  We suggest a physical mechanism whereby the acceleration time of cosmic rays
by shock waves can be significantly reduced. This creates the possibility of
particle acceleration beyond the knee energy at ~10^15eV. The acceleration
results from a nonlinear modification of the flow ahead of the shock supported
by particles already accelerated to the knee momentum at p ~ p_*. The particles
gain energy by bouncing off converging magnetic irregularities frozen into the
flow in the shock precursor and not so much by re-crossing the shock itself.
The acceleration rate is thus determined by the gradient of the flow velocity
and turns out to be formally independent of the particle mean free path
(m.f.p.). The velocity gradient is, in turn, set by the knee-particles at p ~
p_* as having the dominant contribution to the CR pressure. Since it is
independent of the m.f.p., the acceleration rate of particles above the knee
does not decrease with energy, unlike in the linear acceleration regime. The
reason for the knee formation at p ~ p_* is that particles with $p > p_*$ are
effectively confined to the shock precursor only while they are within limited
domains in the momentum space, while other particles fall into
``loss-islands'', similar to the ``loss-cone'' of magnetic traps. This
structure of the momentum space is due to the character of the scattering
magnetic irregularities. They are formed by a train of shock waves that
naturally emerge from unstably growing and steepening magnetosonic waves or as
a result of acoustic instability of the CR precursor. These losses steepen the
spectrum above the knee, which also prevents the shock width from increasing
with the maximum particle energy.
