The atmospheric pressure dielectric barrier discharge in helium is a pulsed discharge in nature. If during the electrical current pulse a glow discharge is reached, then this pulse will last only a few microseconds in operating periods of sinusoidal voltage with lengths of about 10 to 100 µs. In this paper we demonstrate that right before a glow discharge is reached, the discharge very closely resembles the commonly assumed Townsend discharge structure, but actually contains some significant differing features and hence should not be considered as a Townsend discharge. In order to clarify this, we present calculation results of high time and space resolution of the pulse formation. The results indicate that indeed a maximum of ionization is formed at the anode, but that the level of ionization remains high and that the electric field at that time is significantly disturbed. Our results also show where this intermediate structure comes from.