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 $(d,p)$ reactions, in particular, needs to advance into the new century. Here deuteron stripping processes off a target nucleus consisting of ${A}$ 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 $(A+2)$-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 $T$-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 $NN$ 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

Smoothing of the time structure of slowly extracted beam from synchrotron by RF-knock-out method

Results of the study are presented in work on smoothing of the time structure of the bunch, slowly extracted from synchrotron. The numerical algorithm has been designed for study of the influence of the radio-frequency field of the resonator on time structure of the bunch. The numerical algorithm is based on method Monte-Carlo, where particles in the beam have been extracted by means a slow moving to the third-order resonance conditions. Characteristics of the time structure are vastly smoothed when synchrotron oscillations have been used as first experiments showed. Theoretical motivation of the reasons, influencing upon time structure of the slowly extracted beam, is explained in given work.Подано результати дослідження по згладжуванню часової структури пучка, повільно виведеного з синхротрону. Розроблено числовий алгоритм для вивчення впливу високочастотного поля резонатора на характеристики часової структури пучка. Числовий алгоритм базується на методі Монте-Карло, де бетатронні коливання частинок в прискорювачі розглядаються з урахуванням того, що повільний вивід пучка відбувається за резонансним методом третього порядку. Як показують перші експерименти з повільним виводом пучка, часова структура значно згладжується завдяки виникненню повздовжніх синхротронних коливань. Теоретичне обґрунтування причин, що впливають на часову структуру повільно виведеного пучка, наведено в даній роботі.Представлены результаты исследования по сглаживанию временной структуры пучка, медленно выводимого из синхротрона. Разработан численный алгоритм для изучения влияния высокочастотного поля резонатора на временную структуру пучка. Численный алгоритм основан на методе Монте-Карло, где бетатронные колебания частиц в ускорителе рассматриваются с учетом того, что пучок медленно выводится резонансным методом третьего порядка. Как показывают первые эксперименты по медленному выводу пучка, подверженному синхротронным колебаниям, временная структура значительно сглаживается. Теоретическое обоснование причин, влияющих на временную структуру медленно выводимого пучка, приведено в данной работе

The reaction pd→(pp)npd\to(pp)n at high momentum transfer and short-range NN properties

A recent cross section measurement of the deuteron breakup reaction $pd\to (pp)(0^\circ)+n(180^\circ)$, in the GeV region in a kinematics similar to backward $pd$ elastic scattering, strongly contradicts predictions of a $pd \to dp$ model based on the one-nucleon exchange, single pN scattering and $\Delta$ excitation mechanisms, and on the wave functions of the Reid soft core and Paris $NN$ potentials. We show within the same model that for the CD Bonn $NN$ potential there is qualitative agreement with the data. It is attributed to a reduction of the one-nucleon exchange at energies above 1 GeV and an increase of the $\Delta(1232)$-isobar contribution, both related to the short-range properties of the wave functions generated by this potential.Comment: 14 pages, Latex, 4 modified figure

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.