132 research outputs found
Isochronicity Correction in the CR Storage Ring
A challenge for nuclear physics is to measure masses of exotic nuclei up to
the limits of nuclear existence which are characterized by low production cross
sections and short half-lives. The large acceptance Collector Ring (CR) at FAIR
tuned in the isochronous ion-optical mode offers unique possibilities for
measuring short-lived and very exotic nuclides. However, in a ring designed for
maximal acceptance, many factors limit the resolution. One point is a limit in
time resolution inversely proportional to the transverse emittance. But most of
the time aberrations can be corrected and others become small for large number
of turns. We show the relations of the time correction to the corresponding
transverse focusing and that the main correction for large emittance
corresponds directly to the chromaticity correction for transverse focusing of
the beam. With the help of Monte-Carlo simulations for the full acceptance we
demonstrate how to correct the revolution times so that in principle
resolutions of dm/m=1E-6 can be achieved. In these calculations the influence
of magnet inhomogeneities and extended fringe fields are considered and a
calibration scheme also for ions with different mass-to-charge ratio is
presented.Comment: 6 figures, recised version May 201
Generalized Faddeev equations in the AGS form for deuteron stripping with explicit inclusion of target excitations and Coulomb interaction
Theoretical description of reactions in general, and the theory for
reactions, in particular, needs to advance into the new century. Here deuteron
stripping processes off a target nucleus consisting of nucleons are
treated within the framework of the few-body integral equations theory. The
generalized Faddeev equations in the AGS form, which take into account the
target excitations, with realistic optical potentials provide the most advanced
and complete description of the deuteron stripping. The main problem in
practical application of such equations is the screening of the Coulomb
potential, which works only for light nuclei. In this paper we present a new
formulation of the Faddeev equations in the AGS form taking into account the
target excitations with explicit inclusion of the Coulomb interaction. By
projecting the -body operators onto target states, matrix three-body
integral equations are derived which allow for the incorporation of the excited
states of the target nucleons. Using the explicit equations for the partial
Coulomb scattering wave functions in the momentum space we present the AGS
equations in the Coulomb distorted wave representation without screening
procedure. We also use the explicit expression for the off-shell two-body
Coulomb scattering -matrix which is needed to calculate the effective
potentials in the AGS equations. The integrals containing the off-shell Coulomb
T-matrix are regularized to make the obtained equations suitable for
calculations. For and nucleon-target nuclear interactions we assume the
separable potentials what significantly simplifies solution of the AGS
equations.Comment: 34 pages, 13 figure
Transfer matrix for a high energy cooling system
A transfer matrix for a high-energy electron cooling system, which describes the linear incoherent effects, is derived. Knowing this matrix we can treat an electron cooling section in the ring as an additional focusing element deforming the beam optic functions due to space charge forces This matrix can be implemented in different codes
(MAD, MIRKO, SixTrack et al.) for precise calculation of the beam optic and dynamic aperture in storage rings,
where a high energy electron cooling system is planed to install. As an example, an optic of the high-energy storage
ring [6] calculated by MAD code with derived matrix is given.Виводиться матриця переходу для високоенергетичної системи електронного охолодження, яка описує
лiнiйнi некогерентнi ефекти. Така матриця дозволяє розглядати секцію електронного охолодження у кiльцi,
як додатковий фокусуючий елемент, який спотворює оптичнi функцii внаслiдок сил просторового заряду.
Отримана матриця може використовуватися у рiзних програмах (MAD, MIRKO, SixTrac та iнших) для
проведення прецизiйних розрахункiв оптики пучка та динамiчної апертури нагромаджувальних кiлець, де
планується планується установка высокоенергетичних систем электронного охлаждения. Як приклад наведено розрахунок оптики високоенергетичного нагромаджувального кiльця [6], виконаний за допомогою
програми MAD та виведеної матрицi.Выводится матрица перехода для высокоэнергетической системы электронного охлаждения, которая
описывает линейные некогерентные эффекты. Такая матрица позволяет рассматривать секцию электронного
охлаждения в кольце, как дополнительный фокусирующий элемент, искажающий оптические функции
вследствие сил пространственного заряда. Полученная матрица может использоваться в различных программах (MAD, MIRKO, SixTrac и др.) для проведения прецизионных расчетов оптики пучка и динамической
апертуры в накопительных кольцах, где планируется установка высокоэнергетических систем электронного
охлаждения. В качестве примера приведен расчет оптики высокоэнергетического накопительного кольца
[6], выполненный с помощью программы MAD и выведенной матрицы
Influence of second oder aberrations on mass-separation with 270° analyzing magnet
In this paper we study nonlinear characteristics of the wide aperture dipole magnet CP-17, which is utilized as an analyzing magnet in the stable isotope separator of the INR (Institute for Nuclear Research) in Kiev. A brief theory of the second order aberration of the magnetic field is outlined. Based on this theory numerical calculations have been performed to study the achievable power resolution depending on nonlinear magnetic field and on beam parameters.Досліджуються характеристики широко-апертурного магніту СП-17, який планується використовувати як аналізуючий магніт мас-сепаратора ІЯД (Інститут ядерних досліджень) у Києві. Наведена коротка теорія аберацій другого порядку. На основі описаної теорії проведено цілий ряд чисельних розрахунків для дослідження розподільної здатності сепаратора в залежності від нелінійності магнітного поля, а також від параметрів пучка.Исследуются характеристики широко-апертурного дипольного магнита СП-17, который планируется использовать в качестве анализирующего магнита масс-сепаратора ИЯИ (Институт ядерных исследований) в Киеве. Приведена краткая теория аберраций второго порядка. На основе описанной теории проведена серия численных расчетов для исследования разрешающей способности сепаратора в зависимости от нелинейности магнитного поля, а также от параметров пучка
Momentum Space Integral Equations for Three Charged Particles: Diagonal Kernels
It has been a long-standing question whether momentum space integral
equations of the Faddeev type are applicable to reactions of three charged
particles, in particular above the three-body threshold. For, the presence of
long-range Coulomb forces has been thought to give rise to such severe
singularities in their kernels that the latter may lack the compactness
property known to exist in the case of purely short-range interactions.
Employing the rigorously equivalent formulation in terms of an
effective-two-body theory we have proved in a preceding paper [Phys. Rev. C
{\bf 61}, 064006 (2000)] that, for all energies, the nondiagonal kernels
occurring in the integral equations which determine the transition amplitudes
for all binary collision processes, possess on and off the energy shell only
integrable singularities, provided all three particles have charges of the same
sign, i.e., all Coulomb interactions are repulsive. In the present paper we
prove that, for particles with charges of equal sign, the diagonal kernels, in
contrast, possess one, but only one, nonintegrable singularity. The latter can,
however, be isolated explicitly and dealt with in a well-defined manner. Taken
together these results imply that modified integral equations can be
formulated, with kernels that become compact after a few iterations. This
concludes the proof that standard solution methods can be used for the
calculation of all binary (i.e., (in-)elastic and rearrangement) amplitudes by
means of momentum space integral equations of the effective-two-body type.Comment: 36 pages, 2 figures, accepted for publication in Phys. Rev.
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