A lithographic apparatus includes an illumination system configured to condition a radiation beam, a projection system configured to project the radiation beam onto a substrate, and a filter system for filtering debris particles out of the radiation beam. The filter system includes a plurality of foils for trapping the debris particles, a support for holding the plurality of foils, and a cooling system having a surface that is arranged to be cooled. The cooling system and the support are positioned with respect to each other such that a gap is formed between the surface of the cooling system and the support. The cooling system is further arranged to inject gas into the gap.