Capacitor Energy per Bang

E_CAP = 0.5 C_o (V_P / N_LINE)²

Where:
E_CAP = Energy Stored in Single Capacitor per Bang (Joules)
C_o = Capacitance of a Single Capacitor (Farads)
V_P = Gap Firing Voltage (Volts)
N_LINE = Number of Capacitors per String

 
Internal Resistance of a Single Capacitor

R_CAP = TANd / (2 p C_o F)

Where:
R_CAP = Internal Real Resistance of a Single Capacitor (Ohms)
TANd = Dissipation Factor
C_o = Capacitance of a Single Capacitor (Farads)
F = Fundamental Frequency of Primary Circuit (Hz)

F (kHz)    TANd
10            0.0004
50            0.0008
100          0.0010
200          0.0016
300          0.0024
400          0.0040
 

Power Dissipation per Small Capacitor

W_o = K_SYNC BPS E_CAP R_CAP / (R_CAP + R_PRI)

Where:
W_o = Power Dissipation per Small Capacitor (Watts)
K_SYNC = 1 for Synchronous Gap or 0.5 for Non-Synchronous Gap
BPS = Bangs per Second
E_CAP = Energy Stored in Single Capacitor per Bang (Joules)
R_CAP = Internal Real Resistance of a Single Capacitor (Ohms)
R_PRI = Primary Circuit Equivalent Resistance (~3 Ohms)

 
Temperature Rise of Small Capacitor

T_o = W_o K_o

Where:
T_o = Temperature Rise of Small Capacitor (° C)
W_o = Power Dissipation per Small Capacitor (Watts)
K_o = Small Capacitor Thermal Dissipation Factor (° C / Watt)

Lead Spacing (mm)       K_o
5                                    250
7.5                                 167
10                                  133
15                                  83
22.5                               67
27.5                               40
37.5                               33
 

Reliability

T_o (° C)     Reliability
0 - 5          Very Good
5 - 10        Good
10 -15       ?
> 15           Bad
 

Life Expectancy

L_LIFE = 10⁶ ((V_ACcap N_LINE) / V_AC)¹⁵

Where:
L_LIFE = Life Expectancy of Capacitor (Hours)
V_ACcap = AC Voltage Rating of a Single Capacitor (VAC)
N_LINE = Number of Capacitors per String
V_AC = RMS Voltage of Primary Charging Transformer (VAC)
 

Example:

Total Primary Capacitance = 28nF
Fundamental Frequency = 100 kHz
Firing Voltage = 21000 Volts (15000 VAC)
BPS = 120
Gap = Non-Synchronous
Primary Capacitor = 7 strings of 14 x 56nF small caps whose lead spacing is 27.5 mm and the AC voltage rating is 630 VAC.

How reliable would this be and how long should it last?

E_CAP = 0.5 C_o (V_P / N_LINE)²
E_CAP = (0.5) (56 x 10^-9) (21000 / 14)²
E_CAP = 0.063 Joule

R_CAP = TANd / (2 p C_o F)
R_CAP = 0.0010 / (2 p (56 x 10^-9) 100000)
R_CAP = 0.02842 Ohm

W_o = K_SYNC BPS E_CAP R_CAP / (R_CAP + R_PRI)
W_o = (0.5) (120) (0.063) (0.02842) / (0.02842 + 3)
W_o = 0.0355 Watt

T_o = K_o W_o
T_o = 40 x 0.0355
T_o = 1.42 ° C

L_LIFE = 10⁶ ((V_ACcap N_LINE) / V_AC)¹⁵
L_LIFE = 10⁶ ((630 x 14) / 15000)¹⁵
L_LIFE = 347 Hours

 
The reliability should be "Very Good".

The Life Expectancy is 347 Hours.