A special ion trap was initially built up to perform β-ν correlation experiments with radioactive ions. The trap geometry is also well suited to perform experiments with laser-cooled ions, serving for the development of a new type of Penning trap, in the framework of the project TRAPSENSOR at the University of Granada. The goal of this project is to use a single (40)Ca(+) ion as detector for single-ion mass spectrometry. Within this project and without any modification to the initial electrode configuration, it was possible to perform Doppler cooling on (40)Ca(+) ions, starting from large clouds and reaching single ion sensitivity. This new feature of the trap might be important also for other experiments with ions produced at radioactive ion beam facilities. In this publication, the trap and the laser system will be described, together with their performance with respect to laser cooling applied to large ion clouds down to a single ion.