Simulation of the Particle Dynamics in Storage Rings with Coupled Transverse Motion

Meshkov, I. N.; Sidorin, A. O.; Smirnov, Alexander V.; Syresin, E. M.; Trubnikov, G.

doi:10.1007/s10512-005-0208-4

Cited by 3 publications

(9 citation statements)

References 2 publications

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“…In any event the condition (3) can hardly be broken in the cases of interest to us here because of a very large d; as can be concluded from Table 1 of Ref. [12] where ⌫ 1 is shown to be of the order of 10 −3 -10 −5 for the present experiments.…”

Section: Previous Modelssupporting

confidence: 53%

“…[12] somewhat different from the approach of Hasse. Linking the ESR event to beam crystallization, they pointed out the very small ⌫ ʈ at the transition density.…”

Section: Previous Modelsmentioning

confidence: 87%

“…To our knowledge, there are two separate theories developed for the 1D ordering effect [5,6,12]. As mentioned already, Hasse performed Monte Carlo simulations based on a "two-particle model," successfully reproducing the ESR outputs [5].…”

Section: Previous Modelsmentioning

confidence: 98%

“…To explain this discrepancy, they investigated a binary Coulomb collision and concluded two criteria. Their first criterion can be expressed as [12] …”

Section: Previous Modelsmentioning

confidence: 99%

“…On the other hand, by requiring that two colliding particles move longitudinally, during half a betatron period, by less than the maximum impact parameter still leading to reflection, a second criterion was derived [12]:…”

Section: Previous Modelsmentioning

confidence: 99%

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One-dimensional ordering of ultra-low-density ion beams in a storage ring

et al. 2004

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The two-particle model, first introduced by Hasse, is employed to predict the beam temperature at which a one-dimensional ordered state of ions will be established in a cooler storage ring. The proposed state does not have the ions (in the beam frame) at rest, but simply has them not passing each other; i.e., remaining in the same (ordered) sequence. The model is applicable to an ultra-low-density beam where collective Coulomb interactions are negligible. It is pointed out that the nature of the anomalous beam behavior observed in electron-cooling experiments at GSI (Darmstadt) and MSL (Stockholm) is approximately free from such parameters as the lattice design, ion species, beam density, and energy. On the basis of the model, which is put in Hamiltonian form, scaled, and numerically studied, a universal criterion of one-dimensional beam ordering at low line density is derived. Analytic work is employed to explain the numerical results and derives an approximate criterion.

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Section: Previous Modelssupporting

confidence: 53%

“…[12] somewhat different from the approach of Hasse. Linking the ESR event to beam crystallization, they pointed out the very small ⌫ ʈ at the transition density.…”

Section: Previous Modelsmentioning

confidence: 87%

Section: Previous Modelsmentioning

confidence: 98%

“…To explain this discrepancy, they investigated a binary Coulomb collision and concluded two criteria. Their first criterion can be expressed as [12] …”

Section: Previous Modelsmentioning

confidence: 99%

Section: Previous Modelsmentioning

confidence: 99%

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One-dimensional ordering of ultra-low-density ion beams in a storage ring

et al. 2004

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Physical Startup of the LEPTA Accumulator

et al. 2005

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The LEPTA setup (Low Energy Particle Torroidal Accumulator) is being constructed at the Joint Institute of Nuclear Research. The main purpose of this setup is to generate intense fluxes of positronium ions and perform experiments in positronium physics. The main component of the setup is the low-energy positron accumulator with a electronic cooling system. A special feature of the accumulator is that it uses a longitudinal magnetic field to focus a circulating beam. The physical startup of the accumulator was performed in September 2004. The results of the adjustment of the main components of the accumulator, the method for obtaining a circulating beam, and the first results of measurements of its parameters are presented.The LEPTA setup (Low Energy Particle Toroidal Accumulator), whose purpose is to generate intense fluxes of positronium ions and performing experimental research on positronium, is under construction at the Joint Institute of Nuclear Research [1-4] (Fig. 1). It consists of a positron injector, an accumulator and system for detecting the positron flux. The injector includes a β + -emitting source based on 22 Na and a Penning-type trap for preliminary accumulation of positrons and subsequently injecting them, in one revolution, into the accumulator. A low-activity test source of positrons for adjusting the setup has been fabricated; its parameters are being measured.The key component of the setup is the accumulator with a 17.2 m perimeter. The purpose of the accumulator is to accumulate ~10 keV positrons and to cool them electronically. The positronium atoms are formed when electrons and positrons recombine in the cooling section. The principle of operation and the construction of the main components of the accumulator were proposed in [2], where a similar accumulator was proposed for generating atoms of antihydrogen. As a result of the low positron energy, it was proposed at the circulating beam be focused by a longitudinal magnetic field in combination with an additional spiral quadrapole field. Such a field geometry is characteristic for a modified betatron and its modifications -the stomatron [5]. But, in contrast to the stomatrons, developed and studied in the USA [6,7], the structure of the LEPTA accumulator does not possess azimuthal symmetry, and the spiral quadrapole field is present only on a short part of the orbit in the rectilinear section. In addition, in [2] an innovative injection scheme was proposed, making it possible to solve the main problem of stomatrons -introducing the beam into a longitudinal magnetic field without substantial perturbation of the beam parameters.The physical startup of the accumulator with circulating electron beam was conducted in September 2004. The main components of the accumulator were tested beforehand with a pulsed electron beam. In the present paper, the methods used to adjust the components of the accumulator and to obtain a circulating beam are presented.

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Static Criteria for the Existence of Coulomb Strings in Storage Rings

Hasse

2003

Phys. Rev. Lett.

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We derive four rigorous conditions for the stability of Coulomb strings in circular storage rings. These criteria are well met by the existing data from experiments in SIS, ESR, and CRYring but not by the NAP-M experiment. We calculate the potential of the joint transverse zigzag excitation and the longitudinal motion against each other of a string of charged particles as a function of their amplitudes and with the linear density as parameter. This potential exhibits a saddle point in amplitude space which, if overcome, destroys the order of the string. The conditions of stability are derived from the position and height of the saddle point which are fairly independent of the linear density. Our findings confirm the supposition that only the Coulomb interaction in the immediate vicinity of very close encounters of particles is important for the existence of strings.

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Simulation of the Particle Dynamics in Storage Rings with Coupled Transverse Motion

Cited by 3 publications

References 2 publications

One-dimensional ordering of ultra-low-density ion beams in a storage ring

One-dimensional ordering of ultra-low-density ion beams in a storage ring

Physical Startup of the LEPTA Accumulator

Static Criteria for the Existence of Coulomb Strings in Storage Rings

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