For proper thermal insulation, superconducting magnets have to be operated in a vacuum. The coolant of the magnet is helium at a temperature of approximately 4 to 5 K. Accidents can suddenly change the pressure, which then passes the pressure of the Paschen minimum. Here, the breakdown voltage for He is approximately 160 V. The nominal operating condition for the insulation can change drastically. The breakdown of He between plane electrodes was investigated under conditions similar to those of the operation of superconducting magnets at room temperature and 4 K. It was found that the breakdown voltage in the Paschen minimum was higher than expected at room temperature, which was explained by the impurity. An additional effect observed especially at low pressures is that the measured pressure in the vacuum vessel does not seem to agree with the pressure of the electrode gap. Furthermore a helium leak of 1 Pa l/s was introduced between the electrodes. No measurable influence of this leak was found within the measuring accuracy at low temperatures.