Query about a protons magnetic moment precession during excitation in MRI

If you consider B0 acting along the z axis then we know the there will be precession about this axis due to the component of the magnetic moment in the x y plane. This precession occurs at the larmor frequency.

If you apply a B1 field that acts orthogonal to B0 and rotates at the same rate w about the z axis, then the component of the magnetic moment along the z axis will give rise to a torque that causes precession about B1. This is why there is a downwards spiral motion.

There is a precession about X-Y due to B0 and there is precession about B0 due to the fact the torque is coming from the longitudinal component of the magnetic moment.

We're are dealing with magnetic fields which are vector quantities so you have to consider also the direction and not only the module. The excitation field, $B_1$, must be orthogonal to the direction of the $mathbf{B_1} × mathbf{μ} ne 0$, to generate transitions of the nuclear spin state.

To convince you that a small magnetic field is able to excite the spins consider the system in a rotating frame. In this frame the axes rotate with an angular velocity $omega_{rot}$. The apparent frequency of the Larmor precession in such a frame will be

$omega_0 - ω_{rot} = Omega$.

Seen by this rotating frame the original external field $B_0$ is reduced to $B_{red}$

$B_{red} = -frac{Omega}{gamma}$

If we take an $omega_{rot} = omega_{tx}$, (tx= transmitter) $B_1$ appears to be stationary.

We've to consider both fields. The vector sum of $B_{red}$ and $B_1$ is called effective field $B_{eff}$

$B_{eff} = sqrt{B_1 + B_{red}}$

The key fact is that, although $B_0$ is very much larger than $B_1$, we can eliminate the effect of the $B_0$ field by setting the transmitter frequency close to the Larmor frequency i.e. by making the offset small. With this condition the reduced field $B_{red}$ is small and it is then possible for the small $B_1$ field to begin to exert an influence. In the limit that the offset is zero ($Omega = 0$), $B_{red}$ disappears and the $B_1$ field is the only one left in the rotating frame.

2. What is depicted in the animation seems to be the decay of the magnetization vector after a 180° pulse with $B_0$ oriented along the negative $z$. The spiral is caused by the decay of the $M_{xy}$ component of the magnetization with a time constant $T_2$ and the $M_z$ component with a time constant $T_1$