Abstract
Generating a multidimensional crystalline beam in a storage ring has been known to be difficult without a special cooling force, i.e., tapered cooling, because of the momentum dispersion induced by bending magnets. It is, however, possible to eliminate the dispersion all around the ring by adding an electric dipole field in each magnetic bending region. A storage ring with such unique deflectors should enable us to reach multidimensional crystalline states with an ordinary untapered cooling force. In order to verify this expectation, molecular dynamics simulations are performed to study beam crystallization in several dispersion-free storage rings including the S-LSR at Kyoto University. The present results show that various crystalline states can be established without relying on the tapered force.
Highlights
In the ultimate low temperature state of an ion beam, the perfect balance is achieved between the external focusing force and internal Coulomb repulsive force
Where pz is the scaled longitudinal momentum of a particle in the beam rest frame, is the radius of curvature in the bending regions, the left-hand side represents the change in pz at the cooling section, fz is the strength of the cooling force, and Cxs is the tapering factor dependent on the lattice structure of the storage ring
We numerically explore the beam behavior in dispersion-free rings, applying the molecular dynamics (MD) technique
Summary
In the ultimate low temperature state of an ion beam, the perfect balance is achieved between the external focusing force and internal Coulomb repulsive force. Where pz is the scaled longitudinal momentum of a particle in the beam rest frame, is the radius of curvature in the bending regions, the left-hand side represents the change in pz at the cooling section, fz is the strength of the cooling force, and Cxs is the tapering factor dependent on the lattice structure of the storage ring. Since the scalar potential of the electrostatic field accelerates or decelerates particles at the edges of the deflection element, the particles can have the same angular velocity in the bending section and receive no shear force This device has been known as a dispersion-free deflector for mass spectrometry [18,19]. The MD code CRYSTAL [21] is employed in Sec. IV to show that multidimensional crystalline beams can be generated in dispersion-free rings without tapering the cooling force.
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