Master's Thesis - Studierstube Augmented Reality Project - Graz ...

3.2 Excitation of Magnetized Matter
strive for thermo-dynamic equilibrium and the first one as an annoyance (in example
an additional excitation of a coincidentally with ω 1 precessing magnetic moment) of
surrounding fields. [Abragam1989] provides an insight into the complete quantum mechanical
processes and their classical interpretation on these relaxation processes. The
upcoming considerations are based on these assumptions, because a detailed derivation
of these coherences would go beyond the scope of this thesis.
The description of the relaxational movement of the magnetization vector and hence
the amount of detectable magnetization after an excitation pulse can be approximated
with a first order process in the rotation coordinate frame
∂M x ′ y ′
∂t
= − M x ′ y ′
T 2
(3.17)
for transversal relaxation during time T 2 and
∂M z ′
∂t
= − M z ′ − M 0 z ′
T 1
z ′ = z (3.18)
for longitudinal relaxation processes during a longer time T 1 . M 0 z ′ describes the available
rotatable magnetization in z ′ -direction before any RF-pulse.
The solution of this system of differential equations leads to
M xy = M xy (0 + ) · e −t/T2 · e −iω 0t
and (3.19)
M z = M 0 z (1 − e −t/T 1
) + M z (0 + ) · e −t/T 2
(3.20)
in the laboratory system at a time t after RF-excitation. Figure 3.2.1 illustrates these
coherences explicitly.
3.2.2 Nuclear Magnetic Resonance Signal
As a result of inevitable inhomogeneities of the magnetic field B 0 the purly material
specific reachable time for T 2 is actually not the relevant time for transversal relaxation.
Instead the transversal relaxation happens much faster than T 2 during the so called
time T ∗ 2 where 1
T ∗ 2
= 1 T 2
+ γ∆B 0 . (3.21)
This circumstance is not necessarily unfavorable since the dephasing caused by field
inhomogeneities can be compensated - in contrast to the irreversible T 2 decay. Two
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