  We perform a many-body investigation of the spin dephasing in $n$-typed InAs
quantum wells under moderate magnetic fields in the Voigt configuration by
constructing and numerically solving the kinetic Bloch equations. We obtain the
spin dephasing time due to the Rashba effect together with the spin conserving
scattering such as the electron-phonon, the electron-nonmagnetic impurity as
well as the electron-electron Coulomb scattering. By varying the initial spin
polarization, temperature, impurity density, applied magnetic field and the
interface electric field, we are able to study the spin dephasing time under
various conditions. For the electron density and quantum well width we study,
the many-body effect dominates the spin dephasing. Moreover, we find an
anomalous resonance peak in the spin dephasing time for high initial spin
polarization under moderate magnetic fields.
