Early NMR spectra were obtained with continuous wave (CW) techniques by slowly sweeping the frequency of the RF field1. Although these techniques were largely replaced by pulsed methods, there is a resurgent interest in CW techniques for imaging samples with very short T2 times2. In this work, we provide an experimental proof-of-concept study of the steady state behaviour for amplitude modulated CW excitation.
We extend our previous analysis of the Bloch equation in a novel excitation-dependent rotating frame of reference and derive an analytical solution using a periodic averaging approximation3. Experiments on a spherical phantom of Gad-doped water (T1=139ms, T2=342ms) were performed on a Bruker 4.7T scanner. To track the evolution of the bulk magnetisation, 600 FID signals were acquired each after the application of an amplitude modulated CW pulse with incremented timing. This proof-of-concept technique, although slow, avoids the need for additional hardware. Acquisition was repeated for 21 amplitude modulation factors between 0 and 1 with a modulation frequency of 100Hz. A second experiment tested 41 amplitude values between 0 and 120Hz with a modulation frequency of 50Hz and modulation factor of 1.
Experimental results are in excellent agreement with our theoretical analysis. A secondary resonance condition is established when the amplitude of the RF field equals the modulation frequency, as has been demonstrated for optical resonance with similar excitation4. Under this condition, the steady state signal is substantial, approximately 40% of the equilibrium magnetisation. The signal also has 59% of its energy at higher-order harmonics of the modulation frequency.
We anticipate that large amplitude signals at this secondary resonance condition will lead to novel NMR spectroscopy and imaging applications.