Method for operating pressure wave charger and pressure wave charger

The pressure wave supercharger (1) for compressing fresh air (2a) for an internal combustion engine comprises a cold gas housing (6), a hot gas housing (7), and a rotor housing (11) arranged therebetween, wherein a rotatable cell rotor (8) is arranged within the rotor housing (11), and wherein the hot gas housing (7) comprises a high-pressure exhaust gas passage (4) and a low-pressure exhaust gas passage (5), and wherein the cold gas housing (6) comprises a fresh air passage (2) and a charge air passage (3), and wherein the high-pressure exhaust gas passage (4), the low-pressure exhaust gas passage (5), the fresh air passage (2) and the charge air passage (3) are fluidly connected to the cell rotor (8), wherein the hot gas housing (7) comprises a first bearing (13) and the cold gas housing (6) comprises a second bearing (14), and wherein the cell rotor (8) comprises a rotor shaft (12) which is mounted in the first and in the second bearing (13, 14), and wherein the hot gas housing (7) comprises a heat exchanger (7c) which is configured such that at least the first bearing (13) can be cooled.