  In this work we investigate the quench dynamics in the Kondo model on the
Toulouse line in presence of a local magnetic field. It is shown that this
setup can be realized by either applying the local magnetic field directly or
by preparing the system in a macroscopically spin-polarized initial state. In
the latter case, the magnetic field results from a subtlety in applying the
bosonization technique where terms that are usually referred to as finite-size
corrections become important in the present non-equilibrium setting. The
transient dynamics is studied by analyzing exact analytical results for the
local spin dynamics. The time scale for the relaxation of the local dynamical
quantities turns out to be exclusively determined by the Kondo scale. In the
transient regime, one observes damped oscillations in the local correlation
functions with a frequency set by the magnetic field.
