What is the origin of the nuclear magnetic dipole moment (m) and how is it oriented relative to an external magnetic field B0? 24-Nov-18

From Quantum Mechanics (I = ½-particle; 1H, 13C,31P,…) z m q y f x 24-Nov-18

Characterizing the motion of m in B0 11/24/2018 Characterizing the motion of m in B0 m = gL L; angular momentum (spin) = m x B ; torque Exercise 1.1: Derive the above equation (qualitatively) 24-Nov-18 EWH

Solution Larmor Equation - the basic NMR equation w = -gB 24-Nov-18

11/24/2018 Conclusion THE LARMOR EQUATION (w = -gB) IS DERIVED FROM A CLASSICAL MECHANICAL APPROACH THE SPIN MOTION IS WITHIN THE MHz-RANGE (Radio-frequencies) 24-Nov-18 EWH

MOTION OF m IN A ROTATING FRAME OF REFERENCE w; rotation frequency of the reference frame relative to the static frame 24-Nov-18

mU  cos(w-w0)t mV  sin(w-w0)t Exercise 1.4. Find the solution of the above equation in the rotating frame, (Note w0= -gB0) mU  cos(w-w0)t mV  sin(w-w0)t 24-Nov-18

One dipole (mi) → Many dipoles ( ) Mxy = 0 !!!!! 24-Nov-18

LINEAR POLARIZED FIELD [B1= B1cos(wt)] 11/24/2018 LINEAR POLARIZED FIELD [B1= B1cos(wt)] Rf-irradiation Conclusion: A LPF is composed of two opposite rotating fields 24-Nov-18 EWH

RFR Application of an rf-pulse along the u-direction (Why and what effect ?) 24-Nov-18

Excersize 1.5: What effect will B1have on the magnetization when on resonance (w0 = w) ? Discuss 24-Nov-18

a B1 The magnetization is rotated an angle a during the duration t of the rf-pulse Show experiment ! 24-Nov-18

Decaying FID? – show experiment 24-Nov-18

Including (phenomenologicaly) relaxation terms in the Bloch equation (RFR): 24-Nov-18

Bloch Equation (on resonance, after magnetization is rotated onto the v-axis) Solution (after the magnetization is rotated into the uv-plane (w1 = 0); Exercise 2.2) 24-Nov-18

Water Confined between Solid Glass beads - Experiment 24-Nov-18

Effect of various types of magnetic field inhonogeneities on the FID decay Let N(B) represent the number of spins experiencing a magnetic field B. Since w = gB, we may write dN = N(w)dw What is the observable signal intensity M if ? 24-Nov-18

What if N(B) = 24-Nov-18

Why doesn’t the FID decay exponentially with time as expected from theory? (Perform a CPMG pulse sequence) 24-Nov-18

Why does the FID decay faster (1/T2 Why does the FID decay faster (1/T2*) than what is predicted by the true spin-spin relaxation rate 1/T2? FID Homogeneous field lnM Inhomogeneous field Time 24-Nov-18

Principles for Measuring T2 Spin gymnastics: Controlled sequence of rf-pulses Hahn spin-echo: p/2-t-p-t-deteksjon (p/2)-puls 24-Nov-18

The basic (p/2)x – p-x spin-echo experiment 24-Nov-18

Magnetization in the rotating frame “100 meter” 24-Nov-18

24-Nov-18

EKKO 24-Nov-18

SPIN-ECHO-EKSPERIMENT 1/T2+1/T2INH 24-Nov-18

p/2-t-(p-t-deteksjon)n CPMG-pulse sequence p/2-t-(p-t-deteksjon)n 24-Nov-18

T1-experiment 24-Nov-18