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When a breakdown of the thermally insulating vacuum occurs in an energized high power coil system (e.g. a leakage of the He-cooling system or to the surrounding air) the coils warm up and have to be discharged fast to avoid destruction. Due to the coil inductance and the necessary discharge time, a high voltage is produced in the coil and the feeder system. Therefore an unspecified pressure coincides with the occurrence of a high voltage at the coil and feeder system. It is well known that under these conditions arcing can occur at a magnet when it is not perfectly insulated even for voltages 1 kV (Paschen-effect). The gas dependent breakdown voltage minimum occurs typically in the range of some 100 V at a pressure value that depends from geometry and temperature. For lower and higher pressures the breakdown voltage is increasing. For a high power magnet system an insulation is necessary that can withstand high voltage in the 10 kV range although any possible pressure is applied to the system. Usually a pressure independent solid insulation is used to solve this requirement. In order to test the reliability of this electrical insulation under all pressure conditions, a so-called Paschen test has to be performed. This Paschen test is a high voltage test with pressures varying between good vacuum and ambient pressure. In this paper examples for insulation failures on large coils found with Paschen testing are given. In a series of experiments with samples that have been prepared with intended insulation faults the necessity of Paschen testing is demonstrated to identify insulation problems that are not visible under good vacuum or ambient pressure. Therefore, a Paschen-test is also a useful high voltage diagnostic tool to localize insulation faults in solid insulated magnets.