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The puzzling behavior of space charge inside solid dielectrics has been revealed by space charge measurement techniques. In particular, positive and negative “charge packets” propagating through the bulk with a repetitive character are thought to be related to prebreakdown mechanisms. Here, we investigated the space charge distribution in a lateral direction by using our recently developed two-dimensional pulsed electroacoustic setup and discovered that the structure of the charge packets is not homogeneous in the lateral direction. This could change drastically the common view as regards their generation and propagation mechanisms as well as their relationship to breakdown.