Local measure of the electromagnetic field in magnetic resonance coils: How do simulations help to disentangle the contributions of the electric and magnetic fields?

The development of probes for Nuclear Magnetic Resonance (NMR) spectroscopy of metabolites, biomolecules or materials requires the accurate determination of the radio-frequency (RF) magnetic field strength, B, at the position of the sample since this RF-field strength is related to the signal sensitivity and the excitation bandwidth. The Ball Shift (BS) technique is a commonly employed test bench method to measure the B value. Nevertheless, the influence of the RF electric field, E, on BS is often overlooked. Herein, we derive, from Maxwell equations, an analytical expression of the BS, which shows the contribution of both the electric and magnetic energies to the BS value. This equation shows that the BS allows quantifying the B field strength only in regions where the electric energy is small with respect to the magnetic one. The numerical simulations of electromagnetic (EM) field and energy prove that this condition is fulfilled at 100.5MHz inside the electrically balanced coil of a double-resonance H/X 4mm Magic Angle Spinning (MAS) probe since for that circuit, the center of the coil is an antinode for the B standing wave and a node for the E one. We also show that the simulated BS values agree well with the experimental ones. Conversely, NMR experiments show that the contribution of the electric energy to BS becomes significant when the X channel of this probe is connected to a frequency splitter. In that case, the use of BS method to estimate the B value is compromised.