Spanning high voltage between capacitors in series
You should use balancing resistors across the capacitors, assuming it's a simple series connection of electrolytic capacitors. 

The appropriate resistor to use across each capacitor is 

R = \$ \frac {n V_M - V_b}{0.0015C V_b}\$

R is in M ohms

n is the number of capacitors

C in uF is the capacitance of each capacitor

\$V_M\$ is the voltage allowed on each capacitor 

\$V_b\$ is the total voltage across the string

If we allow 400V across each cap and total voltage will not exceed 15kV 
then we have a balancing resistor value of 555K ohms. 

Each one needs a power rating suitable for the highest possible voltage, 
so 

\$P_R = \frac {V_M^2}{R} \$ = 0.29W  for this example

The balancing resistors will suck 0.54mA in this example, which is 8.1W total,
a significant power loss, so you may not be able to get full voltage from your coil. 

Reference: Cornell-Dublier Aluminum Electrolytic Capacitor Application Guide