Young supernova remnants such as Tycho generally exhibit a bright circ
ular clumpy shell in both radio and X-ray emission. For several young
remnants, various arguments suggest that the magnetic held is larger t
han can be explained by compression of a few microgauss ambient magnet
ic field by the shock wave. Radio polarization studies reveal a net ra
dial orientation of magnetic fields in the shell which cannot be expla
ined by the simple compression either. We model Rayleigh-Taylor instab
ility at the interface of the ejecta and the shocked ambient medium to
explain these observations. We have performed multidimensional MHD si
mulations of the instability in the shell of a Type I supernova remnan
t for the first time utilizing a moving grid technique which allows us
to follow the growth of the instability and its effect on the local m
agnetic held in detail. We find that the evolution of the instability
is very sensitive to the deceleration of the ejecta and the evolutiona
ry stage of the remnant. As the reverse shock enters the inner uniform
density region, Chevalier's self-similar stage ends and the thickness
of radio shell increases and the instability weakens. Our simulation
shows that Rayleigh-Taylor and Kelvin-Helmholtz instabilities amplify
ambient magnetic fields locally by as much as a factor of 60 around de
nse figures due to stretching, winding, and compression. Globally, the
amount of magnetic held amplification is low and the magnetic energy
density reaches only about 0.3% of the turbulent energy density at the
end of simulation. Strong magnetic held lines draped around the finge
rs produce the radial B vector polarization, whereas thermal bremsstra
hlung from the dense fingers themselves produces the clumpy X-ray emis
sion. As a result, the X-ray emission peaks inside of the radio emissi
on. The surface brightness profile shows no detailed correspondence be
tween radio and X-ray emission. The major part of radio and X-ray lumi
nosity comes from the mixing region.