scholarly journals Detection of gravitational waves in circular particle accelerators

2020 ◽  
Vol 102 (12) ◽  
Author(s):  
Suvrat Rao ◽  
Marcus Brüggen ◽  
Jochen Liske
Keyword(s):  
Gravitational Waves ◽  
Particle Accelerators ◽  
Circular Particle

Structure and Breakdown of Invariant Tori in a 4-D Mapping Model of Accelerator Dynamics

1997 ◽  
Vol 07 (12) ◽  
pp. 2707-2722 ◽  
Author(s):  
M. N. Vrahatis ◽  
H. Isliker ◽  
T. C. Bountis
Keyword(s):  
Periodic Orbits ◽  
Invariant Tori ◽  
Small Scale ◽  
Particle Accelerators ◽  
Chaotic Motions ◽  
Small Perturbations ◽  
Rotation Numbers ◽  
Circular Particle ◽  
Beam Stability ◽  
Space Dynamics

We study sequences of periodic orbits and the associated phase space dynamics in a 4-D symplectic map of interest to the problem of beam stability in circular particle accelerators. The increasing period of these orbits is taken from a sequence of rational approximants to an incommensurate pair of irrational rotation numbers of an invariant torus. We find stable (elliptic–elliptic) periodic orbits of very high period and show that smooth rotational tori exist in their neighborhood, on which the motion is regular and bounded at large distances away from the origin. Perturbing these tori in parameter and/or initial condition space, we find either chains of smaller rotational tori or certain twisted tube-like tori of remarkable morphology. These tube-tori and tori chains have small scale chaotic motions in their surrounding vicinity and are formed about invariant curves of the 4-D map, which are either single loops or are composed of several disconnected loops, respectively. These smaller chaotic regions as well as the non-smoothness properties of large rotational tori under small perturbations, leading to eventual escape of orbits to infinity, are studied here by the computation of correlation dimension and Lyapunov exponents.

NONLINEAR PHENOMENA IN CIRCULAR PARTICLE ACCELERATORS I: SEXTUPOLAR NONLINEARITIES

1993 ◽  
Vol 03 (05) ◽  
pp. 1083-1102
Author(s):  
RUI DILÃO
Keyword(s):  
Relative Error ◽  
Transverse Motion ◽  
Particle Accelerators ◽  
Nonlinear Phenomena ◽  
Maximum Relative Error ◽  
Design And Optimization ◽  
Aperture Problem ◽  
Circular Particle ◽  
Dynamic Aperture ◽  
The Stability

In this paper we relate the methods of the theory of dynamical systems to problems of accelerator design and optimization. It is written in review article style and any prior knowledge of accelerator physics is not required. We derive the Poincaré map for the equation of horizontal transverse motion of a test particle in a circular accelerator in the presence of any number of sextupolar nonlinearities. This map is studied within the framework of nonlinear dynamics and we identify several optimization strategies for the design of an accelerator magnet lattice. The dynamic aperture problem is analysed and we obtain, for a beam line with two sextupoles, the dependence of the dynamic aperture on the line parameters. The mechanisms of aperture reduction near rational values of the tune, ν0 = p/q ≠ 1/3, are due to the creation of heteroclinic tangles and do not affect the stability of the design orbit. For a machine with an arbitrary number of localized sextupolar fields, we obtain the dependence of the nonlinear tune on the amplitude of the particles and the parameters of the accelerator. The predictions for the nonlinear tune agree with the numerical simulations within the maximum relative error of 6% at large amplitudes (~ dynamic aperture) and within the relative error range 1%–2% at intermediate amplitudes (~ half dynamic aperture).

NONLINEAR PHENOMENA IN CIRCULAR PARTICLE ACCELERATORS II: BEAM-BEAM INTERACTION

1993 ◽  
Vol 03 (06) ◽  
pp. 1411-1422
Author(s):  
RUI ALVES-PIRES ◽  
RUI DILÃO
Keyword(s):  
Phase Space ◽  
Chaotic Behavior ◽  
Transverse Motion ◽  
Particle Accelerators ◽  
Nonlinear Phenomena ◽  
Maximum Relative Error ◽  
Beam Position ◽  
Circular Particle ◽  
Beam Interaction ◽  
Amplitude Growth

We calculate the Poincaré map for the equation of horizontal transverse motion of a test particle in an accelerator under the action of generic nonlinear forces. We particularize to beam-beam type interactions and we study the dynamics of the map. Beam instabilities due to beam-beam interaction are caused by chaotic behavior and not by amplitude growth, as is the case of other nonlinearities due to special purpose machine magnets. There exists a closed region in phase space where the motion is chaotic, even if the central design orbit is unstable. For large amplitudes in phase space the motion is regular and no chaotic behavior or amplitude growth exists. The beam-beam tune as a function of the beam position x is calculated and predictions agree with the numerical values within the maximum relative error of 10%, for beam positions |x| ≤ σ, where σ is the r.m.s. size of the beam. When beams cross at high distances the variation in the tune due to beam-beam effect disappears and the tune value approaches the betatron tune.

Specimen Preparation of Near Surface Ion Irradiated Samples

1985 ◽  
Vol 43 ◽  
pp. 170-171
Author(s):  
K. F. Russell ◽  
L. L. Horton
Keyword(s):  
Radiation Damage ◽  
Heavy Ions ◽  
Target Material ◽  
Metal Alloys ◽  
Specimen Surface ◽  
Specimen Preparation ◽  
Particle Accelerators ◽  
Near Surface ◽  
Graaff Accelerator ◽  
Van De Graaff

Beams of heavy ions from particle accelerators are used to produce radiation damage in metal alloys. The damaged layer extends several microns below the surface of the specimen with the maximum damage and depth dependent upon the energy of the ions, type of ions, and target material. Using 4 MeV heavy ions from a Van de Graaff accelerator causes peak damage approximately 1 μm below the specimen surface. To study this area, it is necessary to remove a thickness of approximately 1 μm of damaged metal from the surface (referred to as “sectioning“) and to electropolish this region to electron transparency from the unirradiated surface (referred to as “backthinning“). We have developed electropolishing techniques to obtain electron transparent regions at any depth below the surface of a standard TEM disk. These techniques may be applied wherever TEM information is needed at a specific subsurface position.

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