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This paper describes the design and simulation of a proof-of-concept quasi-integrable octupole lattice at the University of Maryland Electron Ring (UMER). This experiment tests the feasibility of nonlinear integrable optics, a novel technique that is expected to mitigate resonant beam loss and enable low-loss high-intensity beam transport in rings. Integrable lattices with large amplitude-dependent tune spreads, created by nonlinear focusing elements, are proposed to damp beam response to resonant driving perturbations while maintaining large dynamic aperture [Danilov and Nagaitsev PRSTAB 2010]. At UMER, a lattice with a single octupole insert is designed to test the predictions of this theory. The planned experiment employs a low-current high-emittance beam with low space charge tune shift (~0.005) to probe the dynamics of a lattice with large externally-induced tune spread. Design studies show that a lattice composed of a 25-cm octupole insert and existing UMER optics can induce a tune spread of sim 0.13. Stable transport is observed in PIC simulation for many turns at space charge tune spread 0.008. A maximum spread of dnu = 0.11 (RMS 0.015) is observed for modest octupole strength (peak 50 T/m^3). A simplified model of the system explores beam sensitivity to steering and focusing errors. Results suggest that control of orbit distortion to <0.2 mm within the insert region is essential. However, we see only weak dependence on deviations of lattice phase advance (<=0.1 rad.) from the invariant-conserving condition.
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Recently, the study of integrable Hamiltonian systems has led to nonlinear accelerator lattices with one or two transverse invariants and wide stable tune spreads. These lattices may drastically improve the performance of high-intensity machines, providing Landau damping to protect the beam from instabilities, while preserving dynamic aperture. The Integrable Optics Test Accelerator (IOTA) is being built at Fermilab to study these concepts with 150-MeV pencil electron beams (single-particle dynamics) and 2.5-MeV protons (dynamics with self fields). One way to obtain a nonlinear integrable lattice is by using the fields generated by a magnetically confined electron beam (electron lens) overlapping with the circulating beam. The required parameters are similar to the ones of existing devices. In addition, the electron lens will be used in cooling mode to control the brightness of the proton beam and to measure transverse profiles through recombination. More generally, it is of great interest to investigate whether nonlinear integrable optics allows electron coolers to exceed limitations set by both coherent or incoherent instabilities excited by space charge.
We present the results of experimental studies on the transverse and longitudinal dynamics of a single electron in the IOTA storage ring. IOTA is a flexible machine dedicated to beam physics experiments with electrons and protons. A method was developed to reliably inject and circulate a controlled number of electrons in the ring. A key beam diagnostic system is the set of sensitive high-resolution digital cameras for the detection of synchrotron light emitted by the electrons. With 60--130 electrons in the machine, we measured beam lifetime and derived an absolute calibration of the optical system. At exposure times of 0.5~s, the cameras were sensitive to individual electrons. Camera images were used to reconstruct the time evolution of oscillation amplitudes of a single electron in all 3~degrees of freedom. The evolution of amplitudes directly showed the interplay between synchrotron-radiation damping, quantum excitations, and scattering with the residual gas. From the distribution of measured single-electron oscillation amplitudes, we deduced transverse emittances, momentum spread, damping times, and beam energy. Estimates of residual-gas density and composition were calculated from the measured distributions of vertical scattering angles. Combining scattering and lifetime data, we also provide an estimate of the aperture of the ring. To our knowledge, this is the first time that the dynamics of a single electron is tracked in all three dimensions with digital cameras in a storage ring.
The use of nonlinear lattices with large betatron tune spreads can increase instability and space charge thresholds due to improved Landau damping. Unfortunately, the majority of nonlinear accelerator lattices turn out to be nonintegrable, producing chaotic motion and a complex network of stable and unstable resonances. Recent advances in finding the integrable nonlinear accelerator lattices have led to a proposal to construct at Fermilab a test accelerator with strong nonlinear focusing which avoids resonances and chaotic particle motion. This presentation will outline the main challenges, theoretical design solutions and construction status of the Integrable Optics Test Accelerator underway at Fermilab.
We outline the design of beam experiments for the electron linac at the Fermilab Accelerator Science and Technology (FAST) facility and for the Integrable Optics Test Accelerator (IOTA), based on synchrotron light emitted by the electrons in bend dipoles, detected with gated microchannel-plate photomultipliers (MCP-PMTs). The system can be used both for beam diagnostics (e.g., beam intensity with full dynamic range, turn-by-turn beam vibrations, etc.) and for scientific experiments, such as the direct observation of the time structure of the radiation emitted by single electrons in a storage ring. The similarity between photon pulses and spectrum at the downstream end of the electron linac and in the IOTA ring allows one to test the apparatus during commissioning of the linac.
Quasi-achromat lattices (small dispersion is allowed in their straight sections, between their cells) are considered; in a cell, there are bending magnets of two kinds, of unequal magnetic field. Minimization of the effective emittance is carried out by the following algorithm (which follows Teng, and partly Lee). (1) Every inner dipoles contribution to the natural emittance is minimized with respect to all optics parameters (relating to dispersion and beta-function), except for the shift parameter, s_0, which specifies the interval between the beta-function minimum and the center of a magnet; for a side bending magnet, its contribution to an integral relating to the effective emittance (the relation uses the fact that the arithmetic mean majorizes the geometric mean) is minimized. (2) The other parameters of dipoles (fields, lengths or angles ratios, shifts) are restricted with the boundary conditions: the equality of Courant-Snyder invariants on the exit from a magnet and on the entrance to the following one. (3) The minimum of effective emittance and the last free parameters (two or three) can be found by computation. The accuracy of this method falls with decreasing of the number of internal dipoles in a cell, and still the isomagnetic Tanaka-Ando minimum (for the modified DBA*-lattice which has no inner dipoles) is reproduced with accuracy better than half a percent. If the number of dipoles per cell does not exceed four, the smallest effective emittance (14% lower than TA-limit) is achieved for QBA**-lattice where all dipoles have nonzero shifts.
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