We have slapped together several strobelights before on breadboards, usually of the simple "relaxation oscillator" type based on neon bulbs firing at around 95V or so. The flash frequency with these type of circuits is somewhat limited, and we were looking for a strobelight that would flash at a very wide range of frequency: .1Hz to an almost continuous source of light at 50Hz or so. Compared to most off-the-shelf strobelights, this one uses a slightly different technique which makes things a little more challenging, but also makes for a very interesting and original end design.
One problem with 120V line-powered strobelights is the fact that there is only 120V to work with, and most flash tubes work best at voltages almost twice that. The problem was fixed by adding a voltage multiplier circuit consisting of two large capacitors and two 1N4007 diodes. The end result is 300VDC (120V * 1.414 * 2) used to charge the main energy discharge capacitors, which are connected directly across the terminals of the flash tube. The core of the strobelight uses the very common NE555 IC in astable multivibrator mode to generate a 50% duty cycle square wave that is variable in frequency from .1Hz to around 40Hz. The output of the 555 controls a high voltage MOSFET via its gate pin. When the 555 output is LO and the MOSFET is turned off, a small value capacitor is charged through a resistor to 300VDC. When the 555 output goes HI, this saturates the MOSFET and the small capacitor (charged to 300V) shorts into the primary of a trigger transformer. This generates a quick 6,000V pulse which ionizes the xenon gas inside the flash tube. As soon as the gas is ionized, a very strong current pulse flows through the xenon, and this in turn generates a relatively short-lived burst of white light. So this strobelight design uses a 555 and MOSFET instead of a neon bulb and SCR to switch the trigger capacitor.