Magnetic Resonance and Bloch Equations
Magnetic Resonance and Bloch Equations
This Demonstration visualizes the dynamics in the process of magnetic resonance in which the macroscopic magnetization of an ensemble of paramagnetic particles is exposed to the common action of a static magnetic field and a weak magnetic field () that rotates with a frequency around . The motion of is governed by the Bloch equations. The effect of on is maximized when the rotational frequency is equal to the Larmor free precession frequency =γ (i.e. detuning ).
M
B
0
B
1
=/γ
B
1
Ω
R
ω
B
0
M
B
1
M
ω
ω
0
B
0
ω≈0
ω
0
Many interesting cases are registered as bookmarks, which you can activate by clicking the small cross at the upperright corner. For example:
• Free Larmor precession, which occurs for =0, so that magnetization precesses around at the Larmor frequency.
B
1
B
0
• A pulse, for which rotates at the Larmor frequency (detuning = 0) and for which is switched on for a time duration , such that =π/2. As a result, the magnetization is flipped by into the  plane.
π/2
B
1
B
1
τ
π/2
Ω
R
τ
π/2
π/2
x
y
• A pulse, for which rotates at the Larmor frequency (detuning = 0) and for which is switched on for a time duration , such that =π. As a result, the magnetization is flipped by to the direction.
π
B
1
B
1
τ
π
Ω
R
τ
π
π

z
• Magnetic resonance with relaxation, for which the magnetization reaches a steady state. You can play with the value of the frequency detuning . If or , the effect of is small and the steady state is close to the equilibrium magnetization along . However, when , the effect of is important and the steady state is reached far from the axis.
ω
ω
0
ω≪
ω
0
ω≫
ω
0
B
1
z
ω≈
ω
0
B
1
z
• Adiabatic following occurs for , in which case the magnetization precesses rapidly around the magnetic field and therefore follows the direction of adiabatically.
ω≪
ω
0
B