Presets
Playback
Sample and pulses
A field gradient spreads the precession frequencies (T2* decay); the 180-degree pulse reverses the dephasing, leaving only true T2 loss.
Sequence
Model checks
The science
What is modelled
A cloud of isochromats (spin packets) along the sample axis precesses in the rotating frame. A resonant RF field B1 rotates them about the x axis; field inhomogeneity (a gradient) gives each packet a different offset frequency; T1 and T2 relax them. The exact precession-plus-relaxation step is the same module as on the 3D page.
Equations
- Pulse duration:
tp = (θ/360) / (γ B1), γ/2π = 42.577 MHz/T. - Free precession of each packet at its offset,
Mxy → Mxy e-t/T2,Mz → 1 + (Mz - 1) e-t/T1. - Hahn echo at 2τ with amplitude
e-2τ/T2.
Checks run in the page
- A 90-degree pulse gives |Mxy| = 1 and Mz = 0.
- Homogeneous free decay follows exp(-t/T2).
- The Hahn echo amplitude follows the T2 prediction.
Classical macroscopic-spin model; uniform B1; not a quantum density-matrix solver. The sample is a finite set of spin packets, so the signal shows small periodic revivals that a continuous distribution would not have.
What to try
- Press FID with a large gradient: the signal dies in a few milliseconds (T2*), but the Hahn echo recovers it.
- Detune the RF by 40 Hz and watch the pulse stop being a clean 90 degrees.
- Shorten T2 to 60 ms and compare the echo curve with exp(-2 tau/T2).