Bloch Equations in Laboratory (stationary) Frame of Reference
Let M(t) = (Mx(t), My(t), Mz(t)) be the nuclear magnetization. Then the Bloch equations read:
where γ is the gyromagnetic ratio and B(t) = (Bx(t), By(t), B0 + ΔBz(t)) is the magnetic field experienced by the nuclei. The z component of the magnetic field B is sometimes composed of two terms:
- one, B0, is constant in time,
- the other one, ΔBz(t), may be time dependent. It is present in magnetic resonance imaging and helps with the spatial decoding of the NMR signal.
M(t) × B(t) is the cross product of these two vectors. M0 is the steady state nuclear magnetization (that is, for example, when t → ∞); it is in the z direction.
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