{'fraction_non_alphanumeric': 0.015483182060864922, 'fraction_numerical': 0.0, 'mean_word_length': 4.949206349206349, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Study of zero-chromaticity in FFAG accelerators

Interest on fixed field alternating gradient (FFAG) accelerators has been subject to a great revival in the last decade, because of new needs and thanks to new available technologies, as indicates the increasing number of FFAGs built or under commissioning around the world. Most of them are built so that the chromaticity is suppressed, i.e. the number of betatron oscillations is invariant with the particle energy. Chromaticity is indeed an essential feature in particle accelerators, since it creates issues of betatron resonance crossing, and limits the momentum range available in the machine. In FFAG rings, an analytical solution of the magnetic field configuration called “scaling” condition is usually used to suppress the chromaticity. It is indeed possible to keep independent of momentum the transverse linearized equations of motion if two conditions are fulfilled. The first one is that the di↵erent momentum closed orbits should be photographic enlargements from each other in the median plane. The second one is that the vertical magnetic field in the median plane follows a law in machine radius to the power of k, constant geometrical field index. But this law implies to use circular machines with only one type of cell and constrains the shape of the accelerator. To overcome this constraint, the application of the scaling condition on a straight FFAG beam line has been considered in this study. It is indeed possible to keep independent of momentum the transverse linearized equations of motion if two equivalent conditions as in the circular case are fulfilled. The first one is the orbit similarity, that is to say the di↵erent momentum reference trajectories are a translation of each other in the median plane. The second one is the vertical magnetic field B z in the median plane should follow B