Dynamics of radiation damping in nuclear magnetic resonance

Abstract

The time evolution of spins-1/2 subject to radiation damping, which is commonly encountered for solvent peaks at high field, is examined in detail. The well-known analytic results for rectangular pulses on undamped spin-1/2 systems are extended to the radiation damped case, and reveal surprisingly complex dynamics. Explanations in terms of Bloch vectors are also presented, and composite pulse sequences which would also be insensitive to radiation damping are proposed. In addition, gradient optimization programs were developed to find shaped π and π/2 pulses insensitive to radiation damping. The optimized pulses compensate for radiation damping effects even when the characteristic damping time is shorter than the pulse length.

Improving MRI differentiation of gray and white matter in epileptogenic lesions based on nonlinear feedback

“…Figure 5h illustrates the limitations of frequency selective excitation or saturation methods, which are highly susceptible to poor field homogeneity (29) and exhibit unexpectedly complex dynamics in the presence of radiation damping (13). To correct for field inhomogeneity effects, multiple point separation methods have been developed to distinguish water and fat (28 -30); however, such methods require acquisition of multiple images to estimate the field inhomogeneity, and may not provide sufficiently separated phase information from components with very similar resonance frequencies.…”

“…Radiation damping is a macroscopic field that acts back on the spins through the induced current in the receiver coil, as dictated by Lenz's law (11)(12)(13). It exerts a torque to nutate the magnetization back to the asymptotically stable ϩz-axis at a rate proportional to the magnitude of the average transverse magnetization ͗m ϩ ͘, where m ϩ ϵ m x ϩ im y .…”

“…For a sample onresonance in a well-tuned probe, the radiation damping field B rd (t) can be approximated in S.I. units as (13):…”

Radiation damping diagnostics

“…4 can be obtained only if either radiation damping or relax-Ž . ation can be ignored 19,20 . Therefore, to keep our treatment of the effects of radiation damping general, we resort to the numerical integration of w x Ž .…”

N = 2 supersymmetric radiation damping problem on a noncommutative plane

“…The analysis of dissipative systems in quantum theory has a great interest and relevance either because of fundamental reasons [4] or because of its applications in our real world [5][6][7][8][9]. The explicit time dependence of the Lagrangian and Hamiltonian operators introduces a major difficulty in this study since the canonical commutation relations are not preserved in time.…”