Here is a list of capacitors tested by the high voltage community to be known to withhold the use as primary capacitor in Tesla coils.
Capacitor specifications are taken from data sheets at 100kHz and some values for peak current, rms current, ESR and dv/dt are estimates(* marked) from similar capacitors and graph read outs.
Capacitive reactance Xc = 1 / ( 2 * π * f * C)
ESR can be calculated from the tangent of loss angle given as TANδ in the data sheets. ESR is frequency dependant. Capacitance is given in Farad, frequency in Hertz. ESR = (1 / (2 * π * f * C)) * TANδ = TANδ * Xc.
Thermal resistance (Rth) when given in data sheets are either Watt needed to raise the temperature by one Kelvin or degree Celsius the temperature raises by one Watt dissipation. Conversion from W/K to °C/W is to divide one by W/K dissipation factor. °C/W = 1 / (W/K).
Ipeak is calculated from the dV/dT rating times the capacitance of the capacitor. Capacitance given in micro Farad times pulse rise time given in micro seconds will give a result in Ampere. Ipeak or Ipulse = C * dV/dT.
As a rule of thumb ESL is about 1.6 nH per millimetre of lead distance between the capacitor itself and the rest of the circuit. This also includes the leads of the capacitor itself. This only applies to well designed capacitors.