What is the self-healing in MPP type capacitors how it heals, whether it is metals deposition which heals, how it self heal when puncturing in the film due to short circuit.
Clearing in a metallized film capacitor is possible only because of the thin amount of metal present from the metallizing process. When a fault occurs in the capacitor, the energy creates a plasma, vaporizes the metallization and leaves an insulating layer only. As long as the fault is not too large, thus blowing a hole through the insulation, then the capacitor remains good and loses a miniscule amount of capacitance.
We had difficulty using MPP caps in our last high voltage pulse application, but were ultimately successful. Our problem was due to their "self-healing" resulting in gradual deterioration and wear-out of the capacitor. Over time, depending on the application, small holes can form in the dielectric. This causes small portions of the thin metallized regions to short together, resulting in high current that vaporizes the metal at the short. This reduces the capacitance a small amount. Eventually, so many holes and shorts can occur that the capacitance value is no longer within specification. Several of our candidate capacitors exhibited premature wear-out in life-testing due to this effect. I would recommend rigorous life-testing if using MPP capacitors in a pulse application, I don't believe DC applications are nearly as stressful.
If the capacitors cleared during pulsing leading to failure, then I would believe that they were not properly designed for your application. As a film capacitor manufacturer, we have special designs and films for pulsing applications and have pulse test equipment we use to check parts before they are shipped. Failures of pulsing capacitors are usually associated with voltages being higher than what the film capacitor can really handle, voltage spikes that exceed the rated voltage have been problems in the past. The pulsing being very slow and almost like a DC application can also present a problem. Pulsing capacitors may not work long under a steady state condition with the same voltages as the pulses they are rated for.