Circular Mode Optics for High Brightness Beams and High Luminosity Colliders
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Abstract: Beam brightness—and, for colliders, luminosity—scale with intensity and with how densely the beam occupies phase space (emittance). Flat beams can increase brightness and luminosity by having a smaller emittance in one transverse plane. However, at low energy and high intensity, they are difficult to preserve because space-charge forces act directly in real (x, y) space and tend to blow up the smaller emittance plane. We show how circular-mode beams provide a practical route: they remain round in physical space while carrying strongly unequal eigen-emittances (intrinsic flatness). The intrinsic flatness also helps with nonlinear effects such as space-charge-induced tune spread and resonances. Circular modes allow the beam to traverse the space-charge-dominated region at low energy while preserving intrinsic flatness, after which a controlled decoupling transforms the circular-mode beam into a conventional flat beam for high-brightness/high-luminosity operation.