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Spectroscopy of soft X-rays is an extremely powerful tool to understand the physics of hot plasmas in the universe, but in many cases, such as kinematic properties of stellar emission lines or weak absorption features, we have reached the limits of current instrumentation. Critical-angle transmission (CAT) gratings blaze the dispersed spectra into high orders and also offer high throughput. We present detailed ray-traces for the Arcus mission, which promises an effective area > 300 cm2 in the soft X-ray band. It uses four petals of Athena-like silicon pore optics. Each petal spans an azimuth of about 30 degrees and thus offers a point-spread function that is significantly narrower in one dimension than a full mirror would provide. Each of these channels has its own optical axis. For each channel, CAT gratings are arranged on a tilted Rowland torus, and the four separate tori are positioned to overlap in such a way that the dispersed spectra from both pairs can be imaged onto a common set of CCD detectors, while at the same time keeping the requirement of the spectroscopic focus. Our ray-traces show that a set of 16 CCDs is sufficient to cover both zeroth orders and most of the dispersed signal. We study the impact of misalignment, finite size of components, and spacecraft jitter on the spectral resolution and effective area and prove that the design achieves R > 3000 even in the presence of these non-ideal effects. In 2017, we presented the ray-traces for the initial Arcus proposal. Since then, Arcus was accepted for a phase A study and we have spent a lot of additional effort to tweak the optical design (for example, we originally intended to have two petals each share an optical axis, but decided against it to avoid alignment constraints) and to link it back to practical mechanical engineering tolerances. In the process, parameters that were only roughly known in the initial proposal have been set to much better than a millimeter, and effects that seemed not important initially have now been studied in much more detail. This contribution presents those detailed studies and tells the story how we used ray-traces to make a better instrument with a more robust design.
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