  We give detailed description of the transport spin current in the chiral
helimagnet. Under the static magnetic field applied perpendicular to the
helical axis, the magnetic kink crystal (chiral soliton lattice) is formed.
Once the kink crystal begins to move under the Galilean boost, the spin-density
accumulation occurs inside each kink and there emerges periodic arrays of the
induced magnetic dipoles carrying the transport spin current. The coherent
motion of the kink crystal dynamically generates the spontaneous
demagnetization field. This mechanism is analogous to the
D\"{o}ring-Becker-Kittel mechanism of the domain wall motion in ferromagnets.
To describe the kink crystal motion, we took account of not only the tangential
$\phi$-fluctuations but the longitudinal $\theta$-fluctuations around the
helimagnetic configuration. Based on the collective coordinate method and the
Dirac's canonical formulation for the singular Lagrangian system, we derived
the closed formulae for the mass, spin current and induced magnetic dipole
moment accompanied with the kink crystal motion. To materialize the theoretical
model presented here, symmetry-adapted material synthesis would be required,
where the interplay of crystallographic and magnetic chirality plays a key role
there.

Strongly Correlated Electrons;Materials Science