PSR J1833-1034 and its associated Pulsar Wind Nebula (PWN) has been investigated in depth through X-ray observations ranging from 0.1 to 200 keV. The low energy X-ray data from Chandra reveal a complex morphology that is characterised by a bright central plerion, no thermal shell and an extended diffuse halo. The spectral emission from the central plerion softens with radial distance from the pulsar, with the spectral index ranging from $Gamma $ = 1.61 in the central region to $Gamma $ =2.36 at the edge of the PWN. At higher energy INTEGRAL detected the source in the 17--200 keV range. The data analysis clearly shows that the main contribution to the spectral emission in the hard X-ray energy range is originated from the PWN, while the pulsar is dominant above 200 keV. Recent HESS observations in the high energy gamma-ray domain show that PSR J1833-1034 is a bright TeV emitter, with a flux corresponding to $sim$2 per cent of the Crab in 1--10 TeV range. In addition the spectral shape in the TeV energy region matches well with that in the hard X-rays observed by INTEGRAL. Based on these findings, we conclude that the emission from the pulsar and its associated PWN can be described in a scenario where hard X-rays are produced through synchrotron light of electrons with Lorentz factor $gammasim10^{9}$ in a magnetic field of $sim$10 micro Gauss. In this hypothesis the TeV emission is due to Inverse Compton interaction of the cooled electrons off the Cosmic Microwave Background photons. Search for PSR J1833-1034 X-ray pulsed emission, via RXTE and Swift X-ray observations, resulted in an upper limit that is about 50 per cent.
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