  We present an ion trap with an integrated fiber cavity, designed for strong
coupling at the level of single ions and photons. The cavity is aligned to the
axis of a miniature linear Paul trap, enabling simultaneous coupling of
multiple ions to the cavity field. We simulate how charges on the fiber mirrors
affect the trap potential, and we test these predictions with an ion trapped in
the cavity. Furthermore, we measure micromotion and heating rates in the setup.
