A p/2 pulse is applied at t = 0, sending the longitudinal magnetization of a sample into the…

A _/2 pulse is applied at t = 0, sending the
longitudinal magnetization of a sample into the transverse plane in the
direction of the x-axis. At that instant a spatially-varying (but temporally
constant) magnetic field B(r) oriented in the z direction is added to the
static field B0. The spatiallyvarying Larmor frequency is then given by

and the phase of the precessing sample is given by

A _ pulse is then applied at time _ .

(a) What is the phase _(

A _/2 pulse is applied at t = 0, sending the
longitudinal magnetization of a sample into the transverse plane in the
direction of the x-axis. At that instant a spatially-varying (but temporally
constant) magnetic field B(r) oriented in the z direction is added to the
static field B0. The spatiallyvarying Larmor frequency is then given by

and the phase of the precessing sample is given by

A _ pulse is then applied at time _ .

(a) What is the phase _(r,t) immediately before and
immediately after the _ pulse?

(b) What is the phase _(r,t) at time TE = 2_ ?

(c) Make a conclusive statement about the use of spin echoes
when there are spatially-varying gradients in use.

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