Radiation damping and reciprocity in nuclear magnetic resonance: the replacement of the filling factor

The basic equation describing radiation damping in nuclear magnetic resonance (NMR) is rewritten by means of the reciprocity principle, to remove the dependence of the damping constant upon filling factor - a parameter which is neither uniquely defined for easily measured. The new equation uses instead the transceive efficiency, i.e. the peak amplitude of the radiofrequency B field in laboratory coordinates, divided by the square root of the resistance of the detection coil, for which a simple and direct means of measurement exists. We use the efficiency to define the intrinsic damping constant, i.e. that which obtains when both probe and preamplifier are perfectly matched to the system impedance. For imperfect matching of the preamp, it is shown that the damping constant varies with electrical distance to the probe, and equations are given and simulations performed, to predict the distance dependence, which (for lossless lines) is periodic modulo a half wavelength. Experimental measurements of the radiation-damped free induction NMR signal of protons in neat water are performed at a static B field strength of 14.1T; and an intrinsic damping constant measured using the variable line method. For a sample of 5mm diameter, in an inverse detection probe we measure an intrinsic damping constant of 204 s(-1), corresponding to a damping linewidth of 65 Hz for small tip angles. The predicted intrinsic linewidth, based upon three separate measurements of the efficiency, is 52.3 Hz, or 80% of the measured value.