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Dynamic Aperture (accelerator Physics)
The dynamic aperture is the stability region of phase space in a circular accelerator. For hadrons In the case of protons or heavy ion accelerators, (or synchrotrons, or storage rings), there is minimal radiation, and hence the dynamics is symplectic. For long term stability, tiny dynamical diffusion (or Arnold diffusion In applied mathematics, Arnold diffusion is the phenomenon of instability of integrable Hamiltonian systems. The phenomenon is named after Vladimir Arnold who was the first to publish a result in the field in 1964. More precisely, Arnold diffusio ...) can lead an initially stable orbit slowly into an unstable region. This makes the dynamic aperture problem particularly challenging. One may be considering stability over billions of turns. A scaling law for Dynamic aperture vs. number of turns has been proposed by Giovannozzi. For electrons For the case of electrons, the electrons will radiate which causes a damping effect. This means that one typically only ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Synchrotron
A synchrotron is a particular type of cyclic particle accelerator, descended from the cyclotron, in which the accelerating particle beam travels around a fixed closed-loop path. The magnetic field which bends the particle beam into its closed path increases with time during the accelerating process, being ''synchronized'' to the increasing kinetic energy of the particles. The synchrotron is one of the first accelerator concepts to enable the construction of large-scale facilities, since bending, beam focusing and acceleration can be separated into different components. The most powerful modern particle accelerators use versions of the synchrotron design. The largest synchrotron-type accelerator, also the largest particle accelerator in the world, is the Large Hadron Collider (LHC) near Geneva, Switzerland, built in 2008 by the European Organization for Nuclear Research (CERN). It can accelerate beams of protons to an energy of 6.5 tera electronvolts (TeV or 1012 eV). Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Storage Ring
A storage ring is a type of circular particle accelerator in which a continuous or pulsed particle beam may be kept circulating typically for many hours. Storage of a particular particle depends upon the mass, momentum and usually the charge of the particle to be stored. Storage rings most commonly store electrons, positrons, or protons. Storage rings are most often used to store electrons that radiate synchrotron radiation. Over 50 facilities based on electron storage rings exist and are used for a variety of studies in chemistry and biology. Storage rings can also be used to produce polarized high-energy electron beams through the Sokolov-Ternov effect. The best-known application of storage rings is their use in particle accelerators and in particle colliders, where two counter-rotating beams of stored particles are brought into collision at discrete locations. The resulting subatomic interactions are then studied in a surrounding particle detector. Examples of such facilities ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radiation
In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or through a material medium. This includes: * ''electromagnetic radiation'', such as radio waves, microwaves, infrared, visible light, ultraviolet, x-rays, and gamma radiation (γ) * ''particle radiation'', such as alpha radiation (α), beta radiation (β), proton radiation and neutron radiation (particles of non-zero rest energy) * '' acoustic radiation'', such as ultrasound, sound, and seismic waves (dependent on a physical transmission medium) * ''gravitational wave, gravitational radiation'', that takes the form of gravitational waves, or ripples in the curvature of spacetime Radiation is often categorized as either ''ionizing radiation, ionizing'' or ''non-ionizing radiation, non-ionizing'' depending on the energy of the radiated particles. Ionizing radiation carries more than 10 electron volt, eV, which is enough to ionize atoms and molecules and break ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symplectic Manifold
In differential geometry, a subject of mathematics, a symplectic manifold is a smooth manifold, M , equipped with a closed nondegenerate differential 2-form \omega , called the symplectic form. The study of symplectic manifolds is called symplectic geometry or symplectic topology. Symplectic manifolds arise naturally in abstract formulations of classical mechanics and analytical mechanics as the cotangent bundles of manifolds. For example, in the Hamiltonian formulation of classical mechanics, which provides one of the major motivations for the field, the set of all possible configurations of a system is modeled as a manifold, and this manifold's cotangent bundle describes the phase space of the system. Motivation Symplectic manifolds arise from classical mechanics; in particular, they are a generalization of the phase space of a closed system. In the same way the Hamilton equations allow one to derive the time evolution of a system from a set of differential equations, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arnold Diffusion
In applied mathematics, Arnold diffusion is the phenomenon of instability of integrable Hamiltonian systems. The phenomenon is named after Vladimir Arnold who was the first to publish a result in the field in 1964. More precisely, Arnold diffusion refers to results asserting the existence of solutions to nearly integrable Hamiltonian systems that exhibit a significant change in the action variables. Arnold diffusion describes the diffusion of trajectories due to the ergodic theorem in a portion of phase space unbound by any constraints (''i.e.'' unbounded by Lagrangian tori arising from constants of motion) in Hamiltonian systems. It occurs in systems with more than ''N''=2 degrees of freedom, since the ''N''-dimensional invariant tori do not separate the 2''N''-1 dimensional phase space any more. Thus, an arbitrarily small perturbation may cause a number of trajectories to wander pseudo-randomly through the whole portion of phase space left by the destroyed tori. Background and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tune Shift With Amplitude
The tune shift with amplitude is an important concept in circular accelerators or synchrotrons. The machine may be described via a symplectic one turn map at each position, which may be thought of as the Poincaire section of the dynamics. A simple harmonic oscillator has a constant tune for all initial positions in phase space. Adding some non-linearity results in a variation of the tune with amplitude. Amplitude may refer to either the initial position, or more formally, the initial action of the particle. Definition Consider dynamics in phase space. These dynamics are assumed to be determined by a Hamiltonian, or a symplectic map. For each initial position, we follow the particle as it traces out its orbit. After transformation into action-angle coordinates, one compute the tune \nu and the action J. The tune shift with amplitude is then given by \frac. The transformation to action-angle variables out of which the tune may be derived may be considered as a transformatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Accelerator Physics
Accelerator physics is a branch of applied physics, concerned with designing, building and operating particle accelerators. As such, it can be described as the study of motion, manipulation and observation of relativistic charged particle beams and their interaction with accelerator structures by electromagnetic fields. It is also related to other fields: *Microwave engineering (for acceleration/deflection structures in the radio frequency range). *Optics with an emphasis on geometrical optics (beam focusing and bending) and laser physics (laser-particle interaction). *Computer technology with an emphasis on digital signal processing; e.g., for automated manipulation of the particle beam. *Plasma physics, for the description of intense beams. The experiments conducted with particle accelerators are not regarded as part of accelerator physics, but belong (according to the objectives of the experiments) to, e.g., particle physics, nuclear physics, condensed matter physics or m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
