  A general reformulation of the exchange energy of $5f$-shell is applied in
the analysis of the magnetic structure of various actinides compounds in the
framework of LDA+U method. The calculations are performed in an efficient
scheme with essentially only one free parameter, the screening length. The
results are analysed in terms of different polarisation channels, due to
different multipoles. Generally it is found that the spin-orbital polarisation
is dominating. This can be viewed as a strong enhancement of the spin-orbit
coupling in these systems. This leads to a drastic decrease in spin
polarisation, in accordance with experiments. The calculations are able to
correctly differentiate magnetic and non-magnetic Pu system. Finally, in all
magnetic systems a new multipolar order is observed, whose polarisation energy
is often larger in magnitude than that of spin polarisation.
