  The synchrotron X-ray "stripes" discovered in Tycho's supernova remnant (SNR)
have been attracting attention since they may be evidence for proton
acceleration up to PeV. We analyzed Chandra data taken in 2003, 2007, 2009, and
2015 for imaging and spectroscopy of the stripes in the southwestern region of
the SNR. Comparing images obtained at different epochs, we find that time
variability of synchrotron X-rays is not limited to two structures previously
reported but is more common in the region. Spectral analysis of nine bright
stripes reveals not only their time variabilities but also a strong
anti-correlation between the surface brightness and photon indices. The spectra
of the nine stripes have photon indices of \Gamma = 2.1--2.6 and are
significantly harder than those of the outer rim of the SNR in the same region
with \Gamma = 2.7--2.9. Based on these findings, we indicate that the magnetic
field is substantially amplified, and suggest that particle acceleration
through a stochastic process may be at work in the stripes.
