Spin Ensembles & the Net Magnetisation

What this figure is for

An imaging voxel holds something like 10¹⁹ protons. This figure shows a handful of them, arranged on a lattice so you can see where each one sits in the sample, and asks the only question that matters for signal: do they agree on the phase?

• Thermal equilibrium. Every moment precesses about B₀, but the azimuths are random. The transverse parts cancel exactly and the sum lies along z. A stationary vector along B₀ induces no voltage, which is why a magnet full of polarised protons is silent until you excite it.
• Coherent. After a 90° pulse every moment points the same way in the transverse plane. Now the sum is as large as it can be and it rotates, so the coil sees a signal.
• Spread of fields. Give each location a slightly different field and the phases fan out. The individual moments are undiminished, but their sum shrinks. Nothing has been lost yet, only scrambled, which is exactly why a 180° pulse can bring it back.

Turn on Shade spheres by field offset to see the field map itself: warm spheres sit in a higher field and run ahead, cool spheres lag. Then watch the phase colours sort themselves along that same gradient.

Try this in class: set the inhomogeneity to zero, apply a 90°, and note the flat signal. Now raise the inhomogeneity slider while it runs. The decay you create is T₂*, and the dashed envelope shows how much slower the true T₂ decay is underneath it.