1. Lecture 2: Magnetic Statics
Jeff Perez and Dwight Chambers
3/15/

2. Important Points from Last Time:
Magnetism -> moving charges
Nuclear spin
3 Kinds of Magnetism:
Ferromagnetism (a metal bar magnet)
Diamagnetic materials (pair electrons)
!Paramagnetic materials (unpaired electrons)!
Magnetic-Magnetic Interactions:
dM/dt = MxB

3. Brief History of NMR
NMR is discovered by Purcell and Bloch who being their work at MIT in the RadLab
Bloch (a quantum physicist) develops classical picture
Purcell (an classical physicist) develops quantum picture
Share the 1952 Nobel Prize in Physics for NMR

4. Magnetic Interactions
A magnetic spin in a static magnetic field will PRECESS!
If a spin is aligned or anti-aligned with the field - there’s no torque - no spin.
The energy of magnetic interactions is from Zeeman interactions - Aligned - lowest energy; anti-aligned - highest energy!

5. Bloch Equations!!!
Bloch develops a simple set of rules to describe the behavior of spins in a magnetic field: the Bloch Equations!!!
Three aspects
Precession
Relaxation
Nutation
Image credit:

6. Precession - Spinning
Why: MAGNETIC-MAGNETIC INTERACTION IS A TORQUE - A TWIST or a SPIN!
dMx/dt = Mx X B
RIGHT HAND RULE
IF SPIN IS ALIGNED - NO PRECESSION!
- image credit

7. Precession - PT 2: LAMOR How fast would a spin spin? Lamor Freq, 
dMx/dt = Mx X B
Could compute cross product and then use an energy - angular momentum relationship to find angular velocity OR
To SIMPFLY:  = *B
Example: for protons -  = 2*PI*4250 Hz/G, lets assume B = 7T, then 1.86 GHz (1.86 Billions revolutions a seconds)

8. Relaxation
Why: SPINS WANT TO MINIMIZE THEIR ENERGY - WANT TO ALIGN WITH MAGNETIC FIELD
How: All exponential decay
X and Y - T2
Z - T1
T1>T2

9. Relaxation - PT 2!
In order to get to a lower energy state, the magnetic spins must RADIATE!!!
Thankfully, they radiate radiowaves
Why? Wavelength of radiation ~ c/(spin rate)
Example: c/(300 MHz) ~ 6 meters - RADIO Waves
We detect these radio waves - they are the SIGNAL!

10. NUTATION
Exactly like Precession - but arises from field other than Bo static field
Can be hard to think about unless you use the rotating frame!

11. Rotating Frame How does it work: How does it help us?
If you have a spin, rotating at 2 GHz - it can be difficult to think about its behavior
What if the axes spun at that same speed - the spin appears STATIONARY!
How does it work:
If the spins aren’t precessing - they must see no NET static magnetic field
The UNDERLYING idea here is RESONANCE!
The resonant frequency is the LAMOR frequency!!!

12. Rotating Frame and Resonance
Resonance is like a kid swinging on a playground swing set:
If the kid doesn’t pump his/her legs at all, (s)he won’t move at all!
If the kid pumps them at too high a rate, NO MOVEMENT EITHER!
If they pump just right - they will swing!

13. Rotating Frame and Resonance PT 2!
SWING ANALOGY:
Pretend you are standing on the x-axis and there is a spin, starting at the x-axis, going around the z axis (x-y plane)
When should you push to accelerate the spin? When it’s on the x-axis!
If its spinning at a rate of 10 revolutions a second, you should push every 1/10th of a second - because that’s when the spins are next to you!
If its spinning at a rate of 2 GHz, you should “push” every 2 nanoseconds!
“Pushing” = frequency of radio wave you should use to excite the magnetic spins

14. Bloch Equations and Rotating Frame - Bottom Line
Relaxation, Precession, Nutation
Spins will inter act via a torque (precession / nutation)
Spins always behave to minimize energy (relaxation)
Rotating Frame:
Not physically true, but useful way to think about problems
Rotating Frame is accomplished when your excitation radio waves are at the right - resonant - frequency!

15. Using Bloch Equations! Exciting Magnetization
You turn on a magnet - the spins will align with that magnetic field. Now you want to see them - we need them to RADIATE!
Radiation happens in the TRANSVERSE (X-Y) plane!

16. NUTATION -> Excitation!
If we turn on a magnetic field, quickly, and perpendicular to the static one - we can rotate the magnetization into the transverse plane via Bloch equations (nutation)!!!
How long do we need to apply our “rotating field” - called B1?
How strong does B1 need to be?
 = *B1*tp
Max rotation to transverse plane -  = pi/2

17. Questions? Next Time - LAB!!! Next Time - Lecture!
Exciting Spins, Spectrometer Basics, Finding Pi, Pi/2 pulses for H2O
Next Time - Lecture!
Famous Experiments, Gradients, Profiles and MORE!