Multiple-reflection time-of-flight mass spectrometry is an emerging technique that meets the challenges of mass spectrometry at current and future accelerator facilities for the research with exotic nuclei. Moreover, many new applications in analytical mass spectrometry appear on the horizon. In a multiple-reflection time-of-flight mass spectrometer (MR-TOF-MS) the analyzer is traversed many times by the ions, extending the flight path by several orders of magnitude over conventional time-of-flight mass spectrometers (TOF-MS). MR-TOF-MS thus allow to achieve a very high mass resolving power (>100,000) in a compact device. They combine the advantages of conventional TOF-MS, viz. extremely short measurement times (∼ ms), a large mass range, very high sensitivity and non-scanning operation, with very high mass resolving power and accuracy. MR-TOF-MS can serve as devices for high-accuracy mass measurements of very short-lived nuclei, as high-resolution mass separators, and as broadband mass spectrometers for diagnostic purposes. In this article, an overview of MR-TOF-MS developments for the research with short-lived nuclei is given. Different instrumental implementations are reviewed. Despite the same operation principle, different instrumental solutions exist, which give rise to significant differences in applicability and performance. A novel performance criterion for mass spectrometers for the research with exotic nuclei is presented, and a performance increase for MR-TOF-MS of at least one order of magnitude compared to the established technique of TOF-ICR is found. The MR-TOF-MS for the Low-Energy Branch of the Super-FRS at the Facility for Antiproton and Ion Research (FAIR), which has recently been commissioned at the FRS Ion Catcher at GSI, is presented in some detail. Applications of MR-TOF-MS at accelerator facilities as well as their scientific potential outside the field of nuclear physics are discussed.
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