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We apply a new method to determine the magnetic field in coronal loops usingobservations of coronal loop oscillations. We analyze seven Doppler shiftoscillation events detected by SUMER in the hot flare line Fe XIX to obtainoscillation periods of these events. The geometry, temperature, and electrondensity of the oscillating loops are measured from coordinated multi-channelsoft X-ray imaging observations from SXT. All the oscillations are consistentwith standing slow waves in their fundamental mode. The parameters are used tocalculate the magnetic field of coronal loops based on MHD wave theory. For theseven events, the plasma $\beta$ is in the range 0.15-0.91 with a mean of0.33$\pm$0.26, and the estimated magnetic field varies between 21-61 G with amean of 34$\pm$14 G. With background emission subtracted, the estimatedmagnetic field is reduced by 9%-35%. The maximum backgroud subtraction gives amean of 22$\pm$13 G in the range 12-51 G. We discuss measurement uncertaintiesand the prospect of determining coronal loop magnetic fields from futureobservations of coronal loops and Doppler shift oscillations.Comment: 26 pages, 7 figures and 5 tables, Accepted for publication in the  Astrophysical Journal (2007, 656, in press

Determination of the Coronal Magnetic Field from Hot‐Loop Oscillations Observed by SUMER and SXT