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The observed radio jets in the Galactic Center $\gamma$-ray source 1E 1740.7$-$2942 and its apparent association with a high density molecular cloud (though there is not yet enough observational evidence to substantiate a physical association) provide important clues to the physical properties of the central source, presumably a mass-accreting black hole. We present a detailed analysis of the energetics, morphology and radiation properties of the radio jets. We calculate the $e^+-e^-$ pair luminosity injected into the jets from the central source inferred from the observed radio flux and compare it with the constraints from $\gamma$-ray observations. We found that (1) the jets cannot be made of pure pairs unless the jets are highly relativistic, and (2) the jets cannot be made of pure normal plasma if the radio emitting particles in the jets are not dominated by those from the surrounding ISM. Therefore we argue that the jets are most probably mixed and then estimate the optimal proton/positron ratio in the jets. From the observed morphology of the jet-lobe structure, we estimate the advancing velocity of the jet in the ISM, and the velocity of the central source relative to its surrounding medium. The constraints of these estimates on the physical parameters of the central engine in 1E1740 are discussed.
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