Several techniques have been proposed to explore hypervolumetric datasets but most of them fail to be efficient when very large fields are to be processed. This report describes an interactive visualization technique designed to explore at real-time framerates very large hypervolumetric 4-D+t scalarfields (with up to 16GB raw data per time step). We introduce a new out-of-core scheme aiming at generalizing to hypervolumes, brick-based techniques, already standartly used for large volumetric (e. g. 3D) datasets. For a given time step, we visualize the entire 4-D space by displaying directly 2-D arrays of height fields, each height field representing a 2-D hyperslice of the 4-D space. The contribution of this work consists in introducing an efficient partitionning scheme, that we called hyper-bricks, in such a way that it overcomes all hardware bottlenecks, namely the progressive load from disk, the decompression time (CPU) and the display time (GPU). We show that our technique, further using a cache system and a level of detail representation allows users to explore the full hypervolume at real-time framerates even on low-end PCs with basic graphics cards. We mainly apply our technique to the interactive exploration of plasma behaviors resulting from large numerical semi-Lagrangian simulations.