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Here is a variable flashing strobe light circuit. The question is if we connect 3 more capacitors in parallel with C2 same value so total will be 88uf instead of 22 uf ...Will this affect the xenon tube or cause it to burst ?
C1 is nothing more than a storage capacitor; increasing its value will decrease the frequency, since it will take longer to charge between flashes. There are two time constants at play here: R1/C2 and R2R3/C3. I'm too lazy to figure out the relationship.
R1 is not going to limit the current into the tube; the current is supplied by C2.
The peak and ave power to the tube as well as peak current are of importance - if C2 ( 88uF ) is allowed to charge to peak mains ( actually 2x ) then the peak current and power will be significantly higher - limiting the service life of the tube.
Notably C1 should have a diode across it to prevent excessive charge in the reverse direction - with C2 = 88uF, C1 will likely fail earlier than for a smaller C2
Xenon tubes run with several 100 uF in photo flashes, in so far the tube should stand the pulse energy. Lifetime will be reduced nevertheless due to electrode sputtering. But as stated, a higher capacitance value would limit the pulse rate below the usual range of a strobe light.
To drive my xenon timing light I hooked up a bridge voltage doubler with two 4uF capacitors rated 600 V (200V would be adequate). Plus 2 diodes. It worked.
Engine idle speed 600 rpm means a flash every 1/5 second (cylinder fires every other engine spin). To my eyes the bulb flashed every time. My cap values seemed low yet the voltage apparently stayed high enough (above 220 VDC).
Possibly a faster flash rate needs greater uF. It's hard to predict the effect of the 1k input resistor in your schematic. (According to my simulation it admits current bursts of 54mA).
Your schematic has a Villard doubler. C2 must be rated to endure 340 VDC. C1 can be rated for 170 V. If it were a bridge doubler then both caps endure 170V peak.)