  We study the asymptotic behaviour of tame harmonic bundles. First of all, we
prove a local freeness of the prolongation by an increasing order. Then we
obtain the polarized mixed twistor structure. As one of the applications, we
obtain the norm estimate of holomorphic or flat sections by weight filtrations
of the monodromies.
  As other application, we establish the correspondence of semisimple regular
holonomic $D$-modules and polarizable pure imaginary pure twistor $D$-modules
through a tame pure imaginary harmonic bundles, which is a conjecture of
Sabbah. Then the regular holonomic version of Kashiwara's conjecture follows
from the results of Sabbah and us.
  Keywords: Higgs fields, harmonic bundle, variation of Hodge structure, mixed
twistor structure, $D$-module.
