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Long bunches with a uniform longitudinal line density held by barrier buckets are considered for a future luminosity upgrade of the Large Hadron Collider (LHC). With such bunches, the luminosity is maximised for a fixed number of particles. Instead of conventional barrier buckets, periodic barriers are proposed. These are generated with multiple RF harmonics (e.g. multiples of 40 MHz). A possible scheme to create and hold long flat bunches in the LHC is described, and the resulting gain in luminosity is estimated.
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