Integrable systems appeared in physics long ago at the onset of classical dynamics with examples being Kepler's and other famous problems. Unfortunately, the majority of nonlinear problems turned out to be nonintegrable. In accelerator terms, any 2D nonlinear nonintegrable mapping produces chaotic motion and a complex network of stable and unstable resonances. Nevertheless, in the proximity of an integrable system the full volume of such a chaotic network is small. Thus, the 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 electrtic 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 3 families 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.

The beam-beam interaction in the Tevatron collider sets limits on bunch intensity and luminosity. These limits are caused by a tune spread in each bunch which is mostly due to head-on collisions, but there is also a bunch-to-bunch tune spread due to parasitic collisions in multibunch operation. We propose to compensate these effects with the use of a countertraveling electron beam, and we present general considerations and physics limitations of this technique.

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The wake forces produced by a beam bunch can be reduced by making the vacuum chamber cross section axially asymmetric. Furthermore, the asymmetry results in a betatron tune shift for particles in the tail of the bunch. As a result, transverse instabilities of the bunch should be significantly suppressed for an asymmetric vacuum chamber. [S0031-9007(99)08709-8] PACS numbers: 29.27.Bd, 29.20.Dh An ultrarelativistic charged particle generates electromagnetic fields behind it in the vacuum chamber. The net effect of these fields on a following charge is determined by integrating the force over a structure period of the vacuum chamber L. The integrated transverse force F caused by a slight offset r 0 of the leading particle from the axis of a round chamber is conventionally expressed in terms of the wake function [1]: Z L

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This paper presents a scheme for three-step laser-based stripping of an H ÿ beam for charge exchange injection into a high-intensity proton ring. First, H ÿ atoms are converted to H 0 by Lorentz stripping in a strong magnetic field, then neutral hydrogen atoms are excited from the ground state to upper levels by a laser, and the remaining electron, now more weakly bound, is stripped in a strong magnetic field. The energy spread of the beam particles gives rise to a Doppler broadened absorption linewidth, which makes for an inefficient population of the upper state by a narrow-band laser. We propose to overcome this limitation with a ''frequency sweeping'' arrangement, which populates the upper state with almost 100% efficiency. We present estimates of peak laser power and describe a method to reduce the power by tailoring the dispersion function at the laser-particle beam interaction point. We present a scheme for reducing the average power requirements by using an optical ring resonator. Finally, we discuss an experimental setup to demonstrate this approach in a proof-of-principle experiment.

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Thin carbon foils are used as strippers for charge exchange injection into high intensity proton rings. However, the stripping foils become radioactive and produce uncontrolled beam loss, which is one of the main factors limiting beam power in high intensity proton rings. Recently, we presented a scheme for laser stripping an H ÿ beam for the Spallation Neutron Source (SNS) ring. First, H ÿ atoms are converted to H 0 by a magnetic field, then H 0 atoms are excited from the ground state to the upper levels by a laser, and the excited states are converted to protons by a magnetic field. In this paper we report on the proof-ofprinciple demonstration of this scheme to give high efficiency (around 90%) conversion of H ÿ beam into protons at SNS in Oak Ridge. The experimental setup is described, and comparison of the experimental data with simulations is presented.