  We study the Kitaev spin liquid (KSL) in a [001] magnetic field employing the
mean field theory (MFT/MF) in the Majorana fermion representation. The MF
Hamiltonian of the system has the Bogoliubov de-Gennes (BdG) form of a 2D Weyl
superconductor. We discover a robust gapless regime in intermediate magnetic
field for both gapless and gapped AFM KSL with Jx = Jy before the system is
polarized in high magnetic field. A topological phase transition (PT)
connecting two gapless phases with nodal lines takes place at a critical
magnetic field hc1 in this regime. While the nodal lines at hc1 is protected by
the mirror symmetry with Jx = Jy and disappear at Jx 6= Jy with a gap opening
near the critical field, the nodal points at E = 0 can exist at intermediate
fields even without mirror symmetry. We reveal that the phase evolution of the
KSL in the magnetic field is driven by the competition between the magnetic
field and the particle-hole (p-h) asymmetry of the normal state of the BdG
Hamiltonian, which results in the robust intermediate gapless phase for AFM
KSL. For FM KSL, there is no intermediate PT before polarization. The above
phase diagrams are confirmed by dynamical MFT (DMFT) results.
