N. Nešković

Method for Fine Magnet Shaping in Cyclotrons

The fine shaping of a cyclotron magnet is usually conducted through an iterative procedure by matching the obtained and the required pre-calculated magnetic field. The quality of the obtained magnetic field is then evaluated by the closeness of the resulting ion gyration frequency to its required value. The method we propose is based directly on the gyration frequency adjustment; therefore, the pre-calculated magnetic field criterion and the empirical weight factors often needed for the corresponding shape estimate are avoided. The method is applicable to the angular width as well as the thickness of the magnet elements used in fine shaping.

Comparative Analysis of Methods for Isochronous Magnetic-Field Calculation

Accurate magnetic fields are needed for defining the operation of a multipurpose cyclotron as well as for designing other parts of the machine, as an input parameter. The quality of an isochronous magnetic field is evaluated by the closeness of the obtained ion gyration frequency to its required value. The commonly used method of isochronous field calculation for sector focused cyclotrons was Gordons procedure. The incorporation of the gyration frequency criterion in isochronous field calculation has grown with the increase of the computer speed. We suggest a highly accurate method for the isochronous magnetic field calculation based on the gyration frequency adjustment.

Optimal Acceleration in Isochronous Straight Sector Cyclotrons

During the design of a cyclotron the time and attention dedicated to the injection and extraction of a beam usually overcome those devoted to the acceleration. However, the efficiency of the accelerating process largely contributes to the overall efficiency of the machine because the beam spends the most time in the accelerating region. A thorough and systematic study of the influence of beam parameters on the overall quality of acceleration is performed. The conditions for the optimal acceleration are determined and the method for defining the complete continuous sets of input parameters providing such acceleration is proposed.

Influence of Cyclotron Magnet Gap Size on Stripping Extraction

The stripping extraction system of a cyclotron is prized by the range and quality of beams it delivers. The gap size of a cyclotron magnet is one of the parameters which significantly influence the design as well as the output characteristics of the stripping extraction system. The vertical dimension of the beam as well as of the extraction system elements placed inside a vacuum chamber is limited by the magnet gap size. Beside this direct influence, the indirect effect of the magnet gap size on stripping extraction occurs through the magnetic field and its impact on the beam dynamics in the extraction region. The performance of the extraction system is optimized by the proper placement of the point of beam exit from the cyclotron. It is shown that the optimal position of the exit point strongly depends on the magnet gap size. The performance of the optimized stripping extraction system for a smaller gap size is found to be somewhat better.

Analytical Prediction of Ion Stripping Extraction From Isochronous Cyclotrons

Accelerated ion beams are often extracted from a cyclotron by stripping some of ions electrons at the end of the acceleration process. Stripping extraction system is commonly designed and optimized using computer simulations of beam dynamics at a later stage of a cyclotron project. However, minor changes in the distance between the magnet poles are proven to cause large displacements of the optimal position of high-energy transport line. It is shown that simple analytical formulas give good prediction of the position and direction of beam exit after stripping extraction and are useful tool for preliminary facility layout planning.

Angular distributions of relativistic ions channeled in the bent Si crystals

Abstract The angular distributions of relativistic protons channeled in the bent 〈1 0 0〉 Si crystals are considered. The ion energy is 7 TeV, the radius of curvature of the crystal is 49.8 m and the crystal thickness is varied from 0.1 to 0.5 cm (before bending), corresponding to the bending angle range from 0.02 to 0.1 mrad. The crystal thickness range under consideration corresponds to the reduced crystal thickness range from 2.1 to 10.35. The angular distributions of transmitted protons were generated by the computer simulation method using the numerical solution of the ion equations of motion, with the Lindhards expression for the continuum interaction potential of the ion and the crystal. The results of the analysis show that the angular distribution has a periodic behavior for the reduced crystal thickness, Λ, smaller than about 5. For variable Λ larger than 5 the angular distribution is “frozen”, i.e. its shape does not change, and this is accompanied by a slow decrease of the number of transmitted ions as Λ increases.

Enhancement of Ion Beam Acceleration Efficiency in Isochronous Cyclotrons

A novel method for efficient analysis of ion beam acceleration in an isochronous cyclotron is proposed. Numerical simulation is used to perform multiple beam dynamics analyses on the conveniently chosen subsets of data; consequently, the total quantity of studied data is significantly reduced. The obtained results provide direct insight into beam behavior and quality of acceleration. Therefore, the analysis is not only efficient, but detailed and systematic as well. It is used to assess the impact of the accelerated orbit optimization to the enhancement of acceleration efficiency when study is extended from a single test ion to the complete ion beam consideration.

Application of ECR ion sources for surface modification of materials

Electron cyclotron resonance ion sources (ECRIS) have been used primarily as injectors for cyclotrons and linear accelerators. Significant improvement of their performance in the last two decades and substantial reduction of their price and running cost have opened the new fields of their application. In this paper we describe the applications of ECRIS in the field of surface modification of materials, which represent a relatively novel approach. The major advantages of these sources when compared to other sources applied in this field are: production of multiply charged ions, wide range of ion species obtained from gaseous and solid substances, and uninterrupted stable operation in a long period of time. New types of low power consumption ECR ion sources, with the magnetic structure made entirely of permanent magnets, are well suited for the applications using high voltage platforms, e.g., for ion implantation.

Rainbows with Positrons and Carbon Nanotubes

This chapter is devoted to the rainbows occurring in channeling of positrons of incident kinetic energy of E0 = 1 MeV in (11, 9) chiral single-wall carbon nanotubes. As it has been said and explained in Subsect. 2.3.1, the process will be treated using quantum mechanics. In this case, the mass of the projectiles is sufficiently small and their incident kinetic energy sufficiently low that they clearly exhibit their wave properties. As it has been demonstrated in Chap. 1, in such a case, each rainbow is composed of a principal rainbow and one or more supernumerary rainbows. The principal rainbow is the primary, secondary, or a higher order rainbow.

Rainbows in Proton Channeling in Silicon Crystals

In this chapter, some of the high-resolution proton channeling measurements with a very thin (100) Si crystal conducted by the Singapore group [45–48] will be thoroughly analyzed. Those extraordinary measurements have proven to be crucial for verification of the theory of crystal rainbows as the proper theory of ion channeling in crystals. We shall present the results of three experimental and theoretical studies that were induced by those measurements and performed jointly by us and the Singapore group. The first study leads to the very accurate ion-atom interaction potentials [133]. As a continuation, we shall additionally explore the process that is inverse to the transmission process under consideration, and, thus, fully answer the question of its multiplicity, which is directly connected to the essence of the crystal rainbow effect, being the ion focusing along a line reflecting the symmetry of the illuminated crystal. The second study is devoted to the effect of superfocusing of channeled ions, which is the effect of spatial focusing occurring in the middle of each rainbow cycle [134]. The third study contains the proof that the doughnut effect in ion channeling, occurring with tilted crystals, which has been seen and measured many times, is in fact a crystal rainbow effect [130]. Before presenting the results of the second and third studies, we shall describe in detail the superfocusing and doughnut effects, respectively.