3 research outputs found
Nonlinear Integrable Ion Traps
Quadrupole ion traps can be transformed into nonlinear traps with integrable
motion by adding special electrostatic potentials. This can be done with both
stationary potentials (electrostatic plus a uniform magnetic field) and with
time-dependent electric potentials. These potentials are chosen such that the
single particle Hamilton-Jacobi equations of motion are separable in some
coordinate systems. The electrostatic potentials have several free adjustable
parameters allowing for a quadrupole trap to be transformed into, for example,
a double-well or a toroidal-well system. The particle motion remains regular,
non-chaotic, integrable in quadratures, and stable for a wide range of
parameters. We present two examples of how to realize such a system in case of
a time-independent (the Penning trap) as well as a time-dependent (the Paul
trap) configuration
Ring for test of nonlinear integrable optics
Nonlinear optics is a promising idea potentially opening the path towards
achieving super high beam intensities in circular accelerators. Creation of a
tune spread reaching 50% of the betatron tune would provide strong Landau
damping and make the beam immune to instabilities. Recent theoretical work has
identified a possible way to implement stable nonlinear optics by incorporating
nonlinear focusing elements into a specially designed machine lattice. In this
report we propose the design of a test accelerator for a proof-of-principle
experiment. We discuss possible studies at the machine, requirements on the
optics stability and sensitivity to imperfections.Comment: 3 pp. Particle Accelerator, 24th Conference (PAC'11) 28 Mar - 1 Apr
2011: New York, US
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A search for integrable four-dimensional nonlinear accelerator lattices
Integrable nonlinear motion in accelerators has the potential to introduce a large betatron tune spread to suppress instabilities and to mitigate the effects of space charge and magnetic field errors. To create such an accelerator lattice one has to find magnetic and/or electric field combinations leading to a stable integrable motion. This paper presents families of lattices with one invariant where bounded motion can be easily created in large volumes of the phase space. In addition, it presents two examples of integrable nonlinear accelerator lattices, realizable with longitudinal-coordinate-dependent magnetic or electric fields with the stable nonlinear motion, which can be solved in terms of separable variables