We present the first far ultraviolet (FUV) spectra of the four known Balmer-dominated supernova remnants (SNRs) in the Large Magellanic Cloud, acquired with the Far Ultraviolet Spectroscopic Explorer. The remnants DEM L 71 (0505-67.9), 0509-67.5, 0519-69.0 and 0548-70.4 are all in the non-radiative stages of evolution and exhibit expansion speeds ranging from ~ 500 km/s to ~ 5000 km/s. We have detected broad emission lines of Ly beta, Ly gamma, C III and O VI in DEM L 71 (V(FWHM) ~ 1000 km/s) and have detected broad Ly beta and O VI emission in 0519-69.0, (V(FWHM) ~ 3000 km/s). In addition, broad Ly beta emission (V(FWHM) ~ 3700 km/s) has been observed in 0509-67.5, the first detection of broad line emission from this SNR. No emission was detected in our FUSE spectrum of 0548-70.4, allowing us to place only upper limits on the FUV line fluxes. The spectra of these SNRs are unaffected by postshock cooling, and provide valuable probes of collisionless heating efficiency in high Mach number shocks. We have used the Ly beta / O VI flux ratio and relative widths of the broad Ly beta and O VI lines to estimate the degree of electron-proton and proton-oxygen ion equilibration in DEM L 71, 0509-67.5, and 0519-69.0. Although our equilibration estimates are subject to considerable uncertainty due to the faintness of the FUV lines and contributions from bulk Doppler broadening, our results are consistent with a declining efficiency of electron- proton and proton-oxygen ion equilibration with increasing shock speed. From our shock velocity estimates we obtain ages of 295-585 years for 0509-67.5 and 520-900 years for 0519-69.0, respectively, in good agreement with the ages obtained from SN light echo studies.
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