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This is the second in a series of papers aimed at developing a practicaltime-domain method for self-force calculations in Kerr spacetime. The keyelements of the method are (i) removal of a singular part of the perturbationfield with a suitable analytic "puncture" based on the Detweiler--Whitingdecomposition, (ii) decomposition of the perturbation equations in azimuthal($m$-)modes, taking advantage of the axial symmetry of the Kerr background,(iii) numerical evolution of the individual $m$-modes in 2+1-dimensions with afinite difference scheme, and (iv) reconstruction of the physical self-forcefrom the mode sum. Here we report an implementation of the method to computethe scalar-field self-force along circular equatorial geodesic orbits around aKerr black hole. This constitutes a first time-domain computation of the selfforce in Kerr geometry. Our time-domain code reproduces the results of a recentfrequency-domain calculation by Warburton and Barack, but has the addedadvantage of being readily adaptable to include the back-reaction from the selfforce in a self-consistent manner. In a forthcoming paper---the third in theseries---we apply our method to the gravitational self-force (in the Lorenzgauge).

Self force via $m$-mode regularization and 2+1D evolution: II. Scalar-field implementation on Kerr spacetime