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We describe the construction and operation of an x-ray beam size monitor(xBSM), a device measuring $e^+$ and $e^-$ beam sizes in the CESR-TA storagering using synchrotron radiation. The device can measure vertical beam sizes of$10-100~\mu$m on a turn-by-turn, bunch-by-bunch basis at $e^\pm$ beam energiesof $\sim2~$GeV. At such beam energies the xBSM images x-rays of$\epsilon\approx$1-10$~$keV ($\lambda\approx 0.1-1$ nm) that emerge from ahard-bend magnet through a single- or multiple-slit (coded aperture) opticalelement onto an array of 32 InGaAs photodiodes with 50$~\mu$m pitch. Beamlinesand detectors are entirely in-vacuum, enabling single-shot beam sizemeasurement down to below 0.1$~$mA ($2.5\times10^9$ particles) per bunch andinter-bunch spacing of as little as 4$~$ns. At $E_{\rm b}=2.1 $GeV, systematicprecision of $\sim 1~\mu$m is achieved for a beam size of $\sim12~\mu$m; thisis expected to scale as $\propto 1/\sigma_{\rm b}$ and $\propto 1/E_{\rm b}$.Achieving this precision requires comprehensive alignment and calibration ofthe detector, optical elements, and x-ray beam. Data from the xBSM have beenused to extract characteristics of beam oscillations on long and shorttimescales, and to make detailed studies of low-emittance tuning, intra-beamscattering, electron cloud effects, and multi-bunch instabilities.

Vertical beam size measurement in the CESR-TA $e^+e^-$ storage ring using x-rays from synchrotron radiation