  We report a detailed investigation on near-ground state cooling of one and
two trapped atomic ions. We introduce a simple sideband cooling method for
confined atoms and ions, using RF radiation applied to bare ionic states in a
static magnetic field gradient, and demonstrate its application to ions
confined at secular trap frequencies, $\omega_z \approx 2\pi\times 117 $kHz.
For a single \ybplus ion, the sideband cooling cycle reduces the average phonon
number, $\left\langle\,n\,\right\rangle$ from the Doppler limit to
$\left\langle\,n\,\right\rangle =$ 0.30(12). This is in agreement with the
theoretically estimated lowest achievable phonon number in this experiment. We
extend this method of RF sideband cooling to a system of two \ybplus ions,
resulting in a phonon number of $\left\langle\,n\,\right\rangle =$ 1.1(7) in
the center-of-mass mode. Furthermore, we demonstrate the first realisation of
sympathetic RF sideband cooling of an ion crystal consisting of two
individually addressable identical isotopes of the same species.
