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It is discovered that, for a high intensity beam, the 4 ¼ 360 (or 4 ¼ 1) resonance of a linear accelerator is manifested through the octupolar term of space charge potential when the depressed phase advance per cell is close to and below 90 but no resonance effect is observed when is just above 90 . To verify that this is a resonance, a frequency analysis is performed and a study of resonance crossing from above and from below the resonance is conducted. It is observed that this fourth order resonance is dominating over the better known envelope instability and practically replacing it. The simulation study shows a clear emittance growth by this resonance and its stop band. A proposal to GSI was made to perform an experiment to measure the stop band of this resonance using the UNILAC. The experiment confirmed this resonance and will be published in a separate paper.

In a particle accelerator with a periodic structure beam space charge force may excite resonant beam emittance growth if the particle's transverse phase advance approaches 90 degrees . A recent simulation study with the PARMILA code [D. Jeon, Phys. Rev. ST Accel. Beams 12, 054204 (2009)]10.1103/PhysRevSTAB.12.054204 has shown the feasibility of measuring the stop band of this fourth order resonance in the GSI Universal Linear Accelerator UNILAC and proposed its experimental verification, which is reported here. Measurements of transverse phase space distributions behind a periodically focusing structure reveal a fourfold symmetry characteristic of fourth order resonances as well as a resonance stop band above sigma_{0}=90 degrees per focusing cell. These experimental findings agree with results from three different beam dynamics simulation codes, i.e., DYNAMION, PARMILA, and TRACEWIN.

We investigate effects of quantum fluctuation, potential well distortion, quantum lifetime, and Touschek lifetime of the quasi-isochronous ͑QI͒ dynamical system. The Fokker-Planck equation is employed to study the equilibrium bunch distribution. The quantum lifetime in the moderate damping regime is compared with analytical formulae. The effects of harmonic radio-frequency phase modulation on equilibrium distribution function, quantum lifetime reduction, and the occurrence of stochastic resonance are studied. The formula for the Touschek lifetime for the QI dynamical system is derived and studied.

A new type of spin depolarization resonance has been observed at the Brookhaven Alternating Gradient Synchrotron (AGS). This spin resonance is identified as a strong closed-orbit sideband around the dominant intrinsic spin resonance. The strength of the resonance was proportional to the 9th harmonic component of the horizontal closed orbit and proportional to the vertical betatron oscillation amplitude. This "hybrid" spin resonance cannot be overcome by the partial snake at the AGS, but it can be corrected by the harmonic orbit correctors.

ORBIT (Objective Ring Beam Injection and Tracking) is a new particle tracking code for rings. Modelling capabilities include H -foil injection mechanisms, longitudinal and transverse space charge effects, and second order matrix transport. Additional code features include a programmable interactive driver shell, and interactive plotting.

Transverse emittance growth along the Alvarez drift tube linac (DTL) section is a major concern with respect to the preservation of beam quality of high current beams at the GSI UNILAC. In order to define measures to reduce this growth, appropriate tools to simulate the beam dynamics are indispensable. This paper is about the benchmarking of three beam dynamics simulation codes, i.e. DYNAMION, PARMILA, and PARTRAN against systematic measurements of beam emittances for different transverse phase advances along the DTL. Special emphasis is put on the modeling of the initial distribution for the simulations. The concept of rms equivalence is expanded from full intensity to fractions of less than 100% of the beam. The experimental setup, data reduction, preparation of the simulations, and the evaluation of the simulations are described. In the experiments and in the simulations, a minimum of the rms-emittance growth was observed at zero current phase advances of about 60. In general, good agreement was found between simulations and experiment for the mean values of horizontal and vertical emittances at the DTL exit.

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