A Thermal-Frequency Locking Method for Permanent Magnet Magnetic Resonance Systems

Temperature-induced magnetic field drift is a dominant source of slow magnetic field variations in permanent magnet magnetic resonance (PMR) systems, resulting in line broadening, spectral distortion, and imaging artifacts. Conventional methods, such as field-frequency locking or software-based correction, require complicated additional hardware chains or suffer from limited performance. In this work, we propose a thermal-frequency locking (TFL) method to achieve long-term sub-ppm field stability. This method monitors the thermal state of the magnet array and employs a temperature-frequency prediction model to estimate the frequency drift caused by temperature-induced magnetic field variations. A corresponding compensation current is then applied through the Z0 coil to dynamically lock the resonance frequency. Experimental results show that under TFL, the maximum frequency drift over 72 h is reduced from approximately 1950 Hz to 12 Hz. From 12 to 72 h, the frequency drift is further constrained to 3 Hz, corresponding to an average drift rate of 2.3 ppb/h. In continuous ethanol monitoring, the worst-case peak frequency deviation decreases from 99.7 to 2.0 Hz, and the mean spectral correlation coefficient increases from 0.92 to 0.997. Moreover, restart-based shimming experiments demonstrate that the final line width decreases from 12.53 ± 0.96 Hz to 6.44 ± 0.33 Hz. These results confirm that the proposed TFL method effectively improves magnetic field stability, spectral reproducibility, and shimming robustness, providing a practical route for reliable long-term operation of compact PMR systems.