We present results from an optical study of two young Balmer-dominated remnants of SNIa in the Large Magellanic Cloud, 0509$-$67.5 and 0519$-$69.0, in an attempt to search for signatures of efficient cosmic-ray (CR) acceleration. We combine proper motion measurements from HST with corresponding optical spectroscopic measurements of the H$alpha$ line at multiple rim positions from VLT/FORS2 and SALT/RSS and compare our results to published Balmer shock models. Analysis of the optical spectra result in broad H$alpha$ widths in the range of 1800-4000 km s$^{-1}$ for twelve separate Balmer-dominated filaments that show no evidence for forbidden line emission, the corresponding shock speeds from proper motion measurements span a range of 1700-8500 km s$^{-1}$. Our measured values of shock speeds and broad H$alpha$ widths in 0509$-$67.5 and 0519$-$69.0 are fit well with a Balmer shock model that does not include effects of efficient CR acceleration. We determine an upper limit of 7%/$chi$ (95% confidence) on the CR acceleration efficiency for our ensemble of data points, where $chi$ is the ionization fraction of the pre-shock gas. The upper limits on the individual remnants are 6%/$chi$ (0509$-$67.5) and 11%/$chi$ (0519$-$69.0). These upper limits are below the integrated CR acceleration efficiency in the Tycho supernova remnant, where the shocks predominantly show little H$alpha$ emission, indicating that Balmer-dominated shocks are not efficient CR accelerators.
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