  We demonstrate photodissociation of BeH$^+$ ions within a Coulomb crystal of
thousands of $^9$Be$^+$ ions confined in a Penning trap. Because BeH$^+$ ions
are created via exothermic reactions between trapped, laser-cooled
Be$^+$($^2\text{P}_{3/2}$) and background H$_2$ within the vacuum chamber, they
represent a major contaminant species responsible for infidelities in
large-scale trapped-ion quantum information experiments. The
rotational-state-insensitive dissociation scheme described here makes use of
157 nm photons to produce Be$^+$ and H as products, thereby restoring Be$^+$
ions without the need for reloading. This technique facilitates longer
experiment runtimes at a given background H$_2$ pressure, and may be adapted
for removal of MgH$^+$ and AlH$^+$ impurities.
