Capacitor manufacturers offer capacitor series that are specifically targeted on camera flash applications. For example, Rubycon has the FW series, and NCC has the PH series. These have working voltages of about 300V to 330V and a typical capacitance of 100μF to 150μF, so at first glance these seem to be standard high-voltage electrolytic capacitors. Nevertheless, they are designated for camera flash applications.
What makes these capacitors particularly suitable in terms of ESR, construction, etc. ?