  Supernova remnants (SNRs) have long been assumed to be the source of cosmic
rays (CRs) up to the "knee" of the CR spectrum at 10^15 eV, accelerating
particles to relativistic energies in their blast waves by the process of
diffusive shock acceleration (DSA). Since cosmic ray nuclei do not radiate
efficiently, their presence must be inferred indirectly. Previous theoretical
calculations and X-ray observations show that CR acceleration modifies
significantly the structure of the SNR and greatly amplifies the interstellar
magnetic field. We present new, deep X-ray observations of the remnant of
Tycho's supernova (SN 1572, henceforth Tycho), which reveal a previously
unknown, strikingly ordered pattern of non-thermal high-emissivity stripes in
the projected interior of the remnant, with spacing that corresponds to the
gyroradii of 10^14 - 10^15 eV} protons. Spectroscopy of the stripes shows the
plasma to be highly turbulent on the (smaller) scale of the Larmor radii of TeV
energy electrons. Models of the shock amplification of magnetic fields produce
structure on the scale of the gyroradius of the highest energy CRs present, but
they do not predict the highly-ordered pattern we observe. We interpret the
stripes as evidence for acceleration of particles to near the knee of the CR
spectrum in regions of enhanced magnetic turbulence, while the observed highly
ordered pattern of these features provides a new challenge to models of DSA.
