Plerionic supernova remnants exhibit radio emission with remarkably flat spectral indices ranging from \alpha = 0.0 to \alpha = -0.3 .
The origin of very hard particle energy distributions still awaits an explanation , since shock waves generate particle distributions with synchrotron spectra characterized by \alpha \leq - 0.5 .
Acceleration of high energy leptons in magnetohydrodynamic turbulence instead may be responsible for the observed hard spectra .
This process is studied by means of relativistic test particle calculations using electromagnetic fields produced by three-dimensional simulations of resistive magnetohydrodynamical turbulence .
The particles receive power-law energy spectra N ( \gamma ) \propto \gamma ^ { - s } with s 
ranging from 1.2 to 1.6 , i.e .
particle spectra that are required to explain the radio emission of plerions .