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Radiation damping (NMR)
Radiation damping is a dynamical process that occurs in all NMR and MRI experiments. Once the magnetization is excited, an electromotive force (EMF) is generated in the detection coil, producing an AC current known as the free-induction-decay (FID) current. The FID current is always accompanied by an alternating magnetic field, which can act back on the magnetization. This back-action causes the magnetization to rotate toward its equilibrium position, which is known as radiation damping [1].

Radiation damping is a mechanism that works in parallel with relaxation to bring the excited magnetization back to thermal equilibrium. Radiation damping not only accelerates the decay of the transverse component of the magnetization, but also speeds up the buildup of the longitudinal magnetization. Radiation damping effects are not always easily observable. They can be seen only in NMR experiments where the magnetization is very strong, such as when the sample concentration is high or when the magnetic field is very high. They are not observable in MRI experiments, because the spin echo signals in MRI are acquired in the presence of gradient and the gradient rapidly destroys the coherence of the transverse magnetization.

During the relaxation process, the magnitude of the magnetization vector changes, and the transverse and longitudinal component develop independently. In contrast, during radiation damping, the magnitude value of the magnetization vector keeps unchanged, and the transverse and longitudinal components are coupled by a rotation equation. The concept of radiation damping was first introduced to NMR by an Indian Physicist G. Suryan [2] in 1949, who noted radiation damping would act as a line-broadening mechanism in addition to T2 relaxation. Later in 1954, the US Physicists N. Bloembergen and R. V. Pound [3] proposed a theory to explain how radiation damping affects the dynamics of both longitudinal and transverse magnetizations. They introduced a time constant TRD to quantitatively describe the dynamics and developed a theory known as the radiation-damping-modified Bloch equations. This theory has become an essential tool for understanding the behavior of the magnetization in NMR and MRI experiments.

Theory
In rotating frame when on resonance, the radiation-damping-modified Bloch equations take the form:

dMz/dt=-(Mz-M0)/T1+Mxy2/(M0TRD)

dMxy/dt=-Mxy/T2-MxyMz/(M0TRD)

where Mz and Mxy are respectively the longitudinal and transverse components of the magnetization vector, and M0 is the equilibrium magnetization, and

TRD=2(μ0γηQM0)-1

with μ0 being the vacuum susceptibility, γ the nuclear gyromagnetic ratio, η the coil filling factor, and Q the quality factor of the receiver circuit. With the radiation-damping-modified Bloch equations, all radiation damping related problems can be solved.

Effects
In most NMR and all MRI experiments, radiation damping is not considered, i.e. it is assumed that Trd→∞, and the radiation damping terms are missing. As a result, the solutions of the Bloch equations show exponential decay of the transverse magnetization and exponential growth of the longitudinal magnetization. However, as long as M0≠0, TRD cannot be infinite, the exponential dynamics of the magnetization components are modified with hyperbolical behavior. Specifically, when TRD is very short, the transverse magnetization decays following a hyperbolic secant curve and the longitudinal magnetization grows following a hyperbolic tangent curve.

With some approximations, the radiation-damping-modified Bloch equations can have analytical solutions that reveals why radiation damping effects are not always observable [4]. The solutions show that, under any experimental conditions, no matter how weak the magnetization is, there always exist competitions between radiation damping and relaxation. When radiation damping takes a minute to finish while relaxation takes less than 1 second to finish, radiation damping will not show appreciable effects. In MRI, the presence of gradient causes the spin echo signal to completely die away in just a millisecond. Then radiation damping and even relaxation effects are hardly seen in the spin echo decays.

See also

References

1. X.A. Mao, C.H. Ye, Understanding radiation damping in a simple way, Conc. Magn. Reson. 9 (1997) 173–187. 2. G. Suryan, Nuclear magnetic resonance and the effect of the methods of observation, Curr. Sci. 6 (1949) 203–204

3. N. Bloembergen, R.V. Pound, Radiation damping in magnetic resonance experiments, Phys. Rev. 95 (1954) 8–12

4. X.A. Mao, J.X. Guo, C.H. Ye, NMR line-shape theory in the presence of radiation damping, Phys. Rev. B 49 (1994) 15702–15711