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Complete solution for rotating frame relaxation functions during adiabatic pulses.

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  • 1Center for Magnetic Resonance Research, University of Minnesota, Minneapolis, MN, USA.

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Summary

This study introduces a new framework, the Tilting Triply Rotating Frame (TTRF), to accurately describe relaxation during adiabatic radiofrequency pulses. This accounts for fictitious magnetic fields, improving accuracy in high-resolution NMR experiments.

Keywords:
Adiabatic pulsesDipolar relaxationsFictitious fieldRotating frameT(1ρ)T(2ρ)

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Area of Science:

  • * Magnetic Resonance Spectroscopy
  • * Quantum Control and Coherence

Background:

  • * Conventional descriptions of adiabatic radiofrequency (RF) pulses use the Tilting Doubly Rotating Frame (TDRF) or second rotating frame (SRF).
  • * These models are adequate when magnetization aligns perfectly with the effective magnetic field or evolves on a perpendicular plane.
  • * They neglect fictitious magnetic fields arising from the time evolution of the effective magnetic field, which can be significant when the adiabatic condition is not strictly met.

Purpose of the Study:

  • * To develop a general treatment for relaxation functions during adiabatic RF pulses that accounts for non-negligible fictitious magnetic fields.
  • * To derive solutions for relaxation functions within the Tilting Triply Rotating Frame (TTRF).
  • * To analyze relaxation during Hyperbolic Secant (HSn) pulses (HS1 and HS4).

Main Methods:

  • * Derivation of relaxation function solutions in the Tilting Triply Rotating Frame (TTRF).
  • * Application of the TTRF framework to Hyperbolic Secant (HSn) pulses, specifically HS1 and HS4.
  • * Analysis of the influence of pulse modulation functions and parameters on relaxation contributions.

Main Results:

  • * Obtained general solutions for relaxation functions in the TTRF for HSn pulses.
  • * Demonstrated that fictitious field contributions to relaxation depend on pulse modulation and parameters.
  • * Provided corrections to relaxation descriptions accounting for the fictitious field.

Conclusions:

  • * The TTRF provides a more accurate description of relaxation during adiabatic RF pulses when fictitious fields are significant.
  • * The derived corrections are relevant for specific experimental setups, particularly in high-resolution NMR.
  • * This work offers a generalized treatment for relaxation phenomena in advanced RF pulse sequences.