Dynamic aperture (DA) is one of the key nonlinear properties for a storage ring. Although there have been both analytical and numerical methods to find the aperture, the reverse problem of how to optimize it is still a challenging problem. A general and flexible way of optimizing the DA is highly demanded in accelerator design and operation. In this paper, we discuss the use of multiobjective optimization for DA. First we consider using objective functions based only on numerical tracking results. Data mining of these results demonstrated a correlation between DA and low-order nonlinear driving terms. Next we considered using objective functions which included both numerical tracking results and analytical estimates of low-order nonlinear driving terms. This resulted in faster convergence. The National Synchrotron Light Source II (NSLS-II) lattice was taken as an example to illustrate this method. This multiobjective approach is not limited by particular linear or nonlinear lattice settings, and can also be applied for optimizing other properties of a storage ring.
In this paper, we explore a method to manipulate low energy electron bunches in a space charge dominated regime, and we use this method to design low energy linac bunch compressors to compress electron bunches in a space charge dominated regime. In the method, we use the space charge effects instead of avoiding them; i.e., we use the space charge forces to generate the required energy chirp instead of the ordinary method which uses the rf accelerating system to generate the chirp. We redefine the concepts of the dispersion function and beta functions in a space charge dominated regime to guide the optimization. Using this method, we study the low energy (5-22 MeV) linac bunch compressor design to produce short (∼150 fs) and small size (∼30 μm) bunches for the electron beam slicing project. The low energy linac bunch compressors work in a space charge dominated regime, and the bunches at the downstream of the gun have a negative energy chirp due to the space charge effects. To provide compression for the negative energy chirped bunch, we design a positive R 56 dispersive section using a four-dipole chicane with several quadrupole magnets. We have designed low energy linac bunch compressors with different photocathode rf guns. For example, one linac bunch compressor with the BNL photocathode electron rf gun has achieved a low energy bunch with the 166 fs rms bunch length, 28 and 31 μm rms beam size in the vertical and horizontal directions, respectively, at 5 MeV with 50 pC charge. Another example with LBNL's very-high frequency gun has achieved a low energy bunch with the 128 fs rms bunch length, 42 and 25 μm rms beam size in the vertical and horizontal directions, respectively, at 22 MeV with 200 pC charge.
Shadows of black holes surrounded by an optically thin emitting medium have been extensively discussed in the literature. The Hioki-Maeda algorithm is a simple recipe to characterize the shape of these shadows and determine the parameters of the system. Here we extend their idea to the case of a dressed black hole, namely a black hole surrounded by a geometrically thin and optically thick accretion disk. While the boundary of the shadow of black holes surrounded by an optically thin emitting medium corresponds to the apparent photon capture sphere, that of dressed black holes corresponds to the apparent image of the innermost stable circular orbit. Even in this case, we can characterize the shape of the shadow and infer the black hole spin and viewing angle. The shape and the size of the shadow of a dressed black hole are strongly affected by the black hole spin and inclination angle. Despite that, it seems that we cannot extract any additional information from it. Here we study the possibility of testing the Kerr metric. Even with the full knowledge of the boundary of the shadow, those of Kerr and non-Kerr black holes are very similar and it is eventually very difficult to distinguish the two cases.
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