Rotating reference frame magnetic moment

Figure 1. Precessing magnetic moment in (a) the laboratory reference frame and in (b-d) the rotating reference frame.

Figure 2. Magnetic moment precessing about the rf field in the rotating reference frame.

Fig. 2 (A) Macroscopic equilibrium magnetization Mq from the vector sum of the individual nuclear moments fi (B) magnetization interacting with Bi rf field in the laboratory reference frame and (C) magnetization interacting with Bi field in the rotating reference frame.

Frequently in this book we will want to depict nuclear spin orientations like those shown in Figure 2.7. More often than not, we will focus our attention on the net nuclear magnetic moment (M) rather than on the individual nuclear spins. Because M will sometimes precess around B0 (i.e., the z axis), we need a more convenient way than the dashed ellipses used so far to depict M as it precesses and changes orientation. Henceforth we will use another convention to represent this precessional motion of M, the rotating frame of reference, which is designed to show the effects of B on M. 

The torque /t x Bj will cause each magnetic moment /i, which is stationary in the rotating frame, to process around the direction of the field B]". This direction is fixed in the rotating fl-ame (let us call it the x -direction) and rotates around the z-axis with the Larmor frequency in the laboratory reference frame. If the tfequency of the RF field S2 is not equal to col, i e., in the off-resonance case, the precession of the magnetic moments in the rotating frame is around an axis defined by an effective magnetic field given by ... 

As shown in Fig. 2.1 (b), the nuclear moments still precess with Larmor frequency v0 about the z axis in the xy plane, as does the resultant transverse magnetization (Figs. 2.1(b) and 2.2(b)). In the rotating frame (Section 1.7.3), the transverse magnetization with reference frequency v0 stands while faster or slower components with v( > v0 or v, < v0 will rotate clockwise or counterclockwise, respectively, as shown in Fig. 2.3. 

In general, the motion of M in the rotating frame follows from the classical torque exerted on it by Beff. The effect of an rf pulse is then to tip M away from the z axis and to generate a component in the x y plane. As viewed from the laboratory frame of reference, this component precesses in the xy plane and induces an electrical signal at frequency w in a coil placed in this plane. As the nuclear moments that make up M precess, they lose phase coherence as a result of interactions among them and magnetic field inhomogeneity effects, as described in Section 2.7. Thus Mxy decreases toward its equilibrium value of zero, and the... 

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