Modeling and Experimental Validation of Frequency Instability Induced by Magnetic-Field-Noise in Rb–129Xe NMR Angular Velocity Sensor

Nuclear magnetic resonance (NMR) angular velocity sensors are promising high-precision inertial devices whose frequency stability can be significantly degraded by stochastic triaxial magnetic field disturbances. For sensor design and performance optimization, a quantitative relationship is required between magnetic field noise, nuclear spin phase fluctuations, and Allan variance-based frequency stability metrics. In this study, we develop an analytical model that maps triaxial magnetic field noise to the absolute frequency stability of the nuclear spin resonance signal by combining Bloch spin dynamics with the impulse sensitivity function (ISF) framework from oscillator phase noise theory. The white noise and 1/f noise contributions along the longitudinal (z) and transverse (x/y) axes are treated separately. The model predicts direct baseband conversion of longitudinal magnetic noise, frequency translation of transverse wideband noise through the periodic ISF term, and amplification of transverse low frequency noise by residual DC transverse fields. To validate the model, controlled magnetic noise is injected through the three-axis coils of an Rb–129Xe NMR angular velocity sensor, and the resulting overlapping Allan deviations are compared with the analytical predictions. The injection measurements show that increasing longitudinal white magnetic noise raises the WFN contribution, while longitudinal flicker-noise injection increases the fitted frequency-stability plateau. The transverse-noise and RF-amplitude measurements are discussed within the validity range of the magnetic-noise model. The proposed model therefore provides a quantitative basis for triaxial magnetic noise budgeting, transverse bias control, and stability optimization in high precision NMR angular velocity sensors but does not constitute a complete angular-rate error budget.