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The effect on space charge accumulation of the introduction of nano-filler into polyethylene is usually studied using thin 100 μm samples in electric fields reaching 100 kV/mm. However, the insulation thickness in an actual HVDC cable is usually some centimeters. Thus there is a great thickness difference between the experiment sample and the insulation application. Here we investigate the thickness dependence of space charge accumulation in unfilled and LDPE doped with nano-SiO2 over a range of temperatures in a field of 50 kV/mm. It is found that the space charge in LDPE/SiO2 nanocomposites exhibits marked thickness dependence whereas in the unfilled LDPE it shows very little thickness dependence. A simulation based on the bipolar injection model and Takada's trapping potential model has been carried out in order to explain the differences. It is found that when the simulation included the effects of charge injection, extraction, trapping, recombination, mobility and diffusion, it is able to explain the heterocharge formation in the unfilled LDPE, and the thickness dependence in the two kinds of materials.