The first wind nebula around a magnetar was recently discovered in X-rays around Swift J1834.9 - 0846 .
We study this magnetar ’ s global energetics and the properties of its particle wind or outflows .
At a distance of \sim 4 kpc , Swift J1834.9 - 0846 is located at the center of the supernova remnant ( SNR ) W41 whose radius is \sim 19 pc , an order of magnitude larger than that of the X-ray nebula ( \sim 2 pc ) .
The association with SNR W41 suggests a common age of \sim 5 - 100 kyr , while its spin-down age is 4.9 kyr .
A small natal kick velocity may partly explain why a wind nebula was detected around this magnetar but not around other magnetars , most of which appear to have larger kick velocities and may have exited their birth SNR .
We find that the GeV and TeV source detected by Fermi/LAT and H.E.S.S. , respectively , of radius \sim 11 pc is most likely of hadronic origin .
The dynamics and internal structure of the nebula are examined analytically to explain the nebula ’ s current properties .
Its size may naturally correspond to the diffusion-dominated cooling length of the X-ray emitting e ^ { + } e ^ { - } pairs .
This may also account for the spectral softening of the X-ray emission from the nebula ’ s inner to outer parts .
Analysis of the X-ray synchrotron nebula implies that ( i ) the nebular magnetic field is \gtrsim 11 \mu G ( and likely \lesssim 30 \mu G ) , and ( ii ) the nebula is not powered predominantly by the magnetar ’ s quiescent spin-down-powered MHD wind , but by other outflows that contribute most of its energy .
The latter are most likely associated with the magnetar ’ s bursting activity , and possibly dominated by outflows associated with its past giant flares .
The energy source for the required outflows can not be the decay of the magnetar ’ s dipole field alone , and is most likely the decay of its much stronger internal magnetic field .