A theory is presented for radiation damping (RD) in the toroid cavity nuclear magnetic resonance detector, a cylindrically symmetric inhomogeneous-rf field detector in which the magnitude of B-1 is inversely proportional to the distance from the cylindrical symmetry axis. The equations of motion of the magnetization components are obtained and discussed. Numerical simulations of conventional- and composite-pulse experiments are presented, along with a discussion of the effects of RD on the evolution of magnetization. Preliminary simulations of RD in the presence of inhomogeneous line broadening are also presented. The signature effect of radiation damping in the TCD is the winding or unwinding of magnetization gratings that has recently been observed by other researchers. The observed magnitude of the effect is linked to the effective filling factor, which currently appears to be limited by the stray inductance of the detection circuit. The results are of interest in connection with recent findings regarding the interaction of RD with the dipolar demagnetizing field.