Analytic Derivation of Vertical Chromaticity in Fermilab Muon g-2 Storage Ring
Researchers have derived a closed-form analytic expression for the vertical chromaticity of the Fermilab Muon g-2 storage ring by expanding the Hamiltonian and integrating equations of motion order by order. Vertical chromaticity is a key parameter in particle accelerator design that describes how particle trajectories depend on momentum. The result achieves agreement with computational simulations at the 10^-11 level, providing a precise theoretical tool for understanding and optimizing the muon g-2 experiment.
A new theoretical analysis provides an analytic derivation of vertical chromaticity (ξ_y) for the Fermilab Muon g-2 storage ring, extending previous work on horizontal chromaticity. The researchers used Hamiltonian mechanics, expanding the system as a Taylor polynomial in dynamical variables and integrating the equations of motion systematically to obtain second-order aberrations for the magnetic dipole and combined-function dipole-quadrupole elements used in the ring. The resulting closed-form expression for the continuous-ring model shows remarkable agreement with independent COSY INFINITY differential-algebra computations across a range of electrostatic-quadrupole voltages (10-26 kV), with discrepancies at only the 10^-11 level. This work contributes to the theoretical understanding of the muon g-2 experiment's storage ring dynamics and was submitted to the International Journal of Modern Physics A.
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Analytic Derivation of Vertical Chromaticity in the Fermilab Muon $g{-}2$ Storage Ring
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