Spatial rainbows and catastrophes in transmission of protons through electrostatic octopole lens

This paper considers the transmission of the initial parallel proton beam with kinetic energy of 10 keV through the electrostatic oelopole lens. The spatial rainbows and corresponding proton distributions are calculated by using the infinite length approximation potential. Positive potentials of the lens electrodes are set to be 0.35 kV and 9 kV. It has been shown that by application of catastrophe theory, the generating function for mapping proton positions between entrance and exit transverse plains can be determined, giving accurate rainbow patterns for biasing potentials of 0.35 kV. © 2018; Vinca Inst Nuclear Sci. All rights reserved

Transmission Studies With Ion Beams Within FAMA

FAMA is a user facility for materials science with low-energy ion beams in the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. It includes a heavy ion source, a light ion source, two channels for modification of materials, and two channels for analysis of materials. Recently, the designing of a channel for transmission studies within FAMA has begun. The initial studies to be undertaken in this channel are related to the rainbow e ffects with very thin electrostatic lenses and two-dimensional materials.27th Russian Particle Accelerator Conference (RuPAC'21), Alushta, Russia, 27 September-01 October 202

The finite element method analysis of temperature distribution of the FAMA electron cyclotron resonance mini-oven

The mVINIS ion source, a part of FAMA installation at Vinca Institute of Nuclear Sciences, is able to produce multiple charged heavy ion beams through the utilization of vapors created by the process of melting solids inside the miniature oven (mini-oven). The mini-oven that was used previously could only reach the maximum temperature of 800?C, which is far too low for evaporating most metals. For this purpose, a higher operating-temperature of 1500?C was needed. Our study focuses on numerical finite element method analysis of the temperature distribution of newly designed mini-oven

Ion optics of electrostatic rainbow lenses

У oвoј дисертацији проучаване су просторне и угaoнe расподеле протона, енергије 10 keV, и њихове одговарајуће линије дуге у случају квадратног електростатичког дугиног сочива. Просторне и угaoнe расподеле протона дoбиjeнe су нумeрички рeшaвaњeм њихoвих jeднaчинa крeтaњa и коришћењем мeтoде кoмпjутeрскe симулaциje. Линије дуге су такође одређене нумерички. Сем тога, испитивано је какав утицај имају одговарајуће линије дуге на трансмисију снопа кроз сочиво и након изласка из њега. Анализиран је модел дугиног сочива, у коме је коришћена аналитичка апроксимација електростатичког поља сочива, и анализиран је уређај дугиног сочива, код кога је коришћено реалистично електростатичко поље сочива, које је добијено нумерички. У случају модела дугиног сочива претпостављено је да је почетни сноп протона паралелан, док је у случају уређаја дугиног сочива почетни сноп протона био паралелан и квази-паралелан. У случају модела дугиног сочива, изучаване су просторне и угaoнe расподеле протона и одговарајуће линије дуге, када је напон на електродама био 10, 20, 50 и 100 kV. У случају уређаја дугиног сочива показано је да се просторне и угаоне линије дуге јављају за много мање вредности напона на електродама сочива у поређењу са моделом дугиног сочива. Наиме, затворене просторне линије дуге унутар сочива и затворене угаоне линије јављају се за напоне на електродама сочива од 2 kV. Ово може да има велики практични значај пошто је много једноставније реализовати и радити са напонима на електродама сочива од 2 kV него са нпр. напонима на електродама од 100 kV. Показано је да електростатичко дугино сочиво има карактеристична катастрофична фокусирајућа својстава која су одређена одговарајућим v просторним и угаоним линијама дуге. На основу тога може се закључити да би се дугино сочиво могло успешно користити за препарацију и транспорт јонских снопова у постројењима за њихово убрзавање, укључујући њихову препарацију за међусобне сударе јонских снопова, као и за добијање добро дефинисаних профила снопова, који би се могли користити у физици чврстог стања, биофизици, археологији и геологији.In this dissertation, the spatial and angular distributions of 10 keV protons and the corresponding rainbow lines are investigated in the case of the square electrostatic rainbow lens. The spatial and angular proton distributions were obtained numerically by solving proton’s equations of motion and applying the computer simulation method. The rainbow lines were also determined numerically. Besides, influence of the corresponding rainbow lines on the transmission of the beam through the lens and in the space behind is investigated. The rainbow lens model, which uses analytical approximation of the electrostatic field of the lens, and the rainbow lens device, which uses numerically obtained realistic electrostatic field of the lens, have been analyzed. In the case of the rainbow lens model, the parallel initial proton beam was assumed, while in the case of the rainbow lens devise, the initial proton beam was parallel and quasi-parallel. In the case of rainbow lens model, the spatial and angular distributions and the corresponding rainbow lines have been analyzed, for the electrode voltage equal to 10, 20, 50 and 100 kV. In the case of the rainbow lens devise, it is shown that the spatial and angular rainbow lines occur for a much less values of the electrode voltage. Namely, closed spatial rainbow lines inside the lens and closed angular rainbow lines occur for the electrode voltage equal to 2 kV. Practically this could be very important since one can build and work more easily with the electrode voltage of 2 kV than e.g. with the electrode voltage of 100 kV. vii It has been shown that the electrostatic rainbow lens has characteristic catastrophic focusing behavior, which is determined by the corresponding spatial and angular rainbow lines. As a result, the rainbow lens could be successfully used for preparation and transportation of ion beams within accelerator facilities, including their preparation for collisions with each other, as well as, for obtaining well defined beam profiles that could be used in condensed matter physics, biophysics and geology

Ion optics of electrostatic rainbow lenses

У oвoј дисертацији проучаване су просторне и угaoнe расподеле протона, енергије 10 keV, и њихове одговарајуће линије дуге у случају квадратног електростатичког дугиног сочива. Просторне и угaoнe расподеле протона дoбиjeнe су нумeрички рeшaвaњeм њихoвих jeднaчинa крeтaњa и коришћењем мeтoде кoмпjутeрскe симулaциje. Линије дуге су такође одређене нумерички. Сем тога, испитивано је какав утицај имају одговарајуће линије дуге на трансмисију снопа кроз сочиво и након изласка из њега. Анализиран је модел дугиног сочива, у коме је коришћена аналитичка апроксимација електростатичког поља сочива, и анализиран је уређај дугиног сочива, код кога је коришћено реалистично електростатичко поље сочива, које је добијено нумерички. У случају модела дугиног сочива претпостављено је да је почетни сноп протона паралелан, док је у случају уређаја дугиног сочива почетни сноп протона био паралелан и квази-паралелан. У случају модела дугиног сочива, изучаване су просторне и угaoнe расподеле протона и одговарајуће линије дуге, када је напон на електродама био 10, 20, 50 и 100 kV. У случају уређаја дугиног сочива показано је да се просторне и угаоне линије дуге јављају за много мање вредности напона на електродама сочива у поређењу са моделом дугиног сочива. Наиме, затворене просторне линије дуге унутар сочива и затворене угаоне линије јављају се за напоне на електродама сочива од 2 kV. Ово може да има велики практични значај пошто је много једноставније реализовати и радити са напонима на електродама сочива од 2 kV него са нпр. напонима на електродама од 100 kV. Показано је да електростатичко дугино сочиво има карактеристична катастрофична фокусирајућа својстава која су одређена одговарајућим v просторним и угаоним линијама дуге. На основу тога може се закључити да би се дугино сочиво могло успешно користити за препарацију и транспорт јонских снопова у постројењима за њихово убрзавање, укључујући њихову препарацију за међусобне сударе јонских снопова, као и за добијање добро дефинисаних профила снопова, који би се могли користити у физици чврстог стања, биофизици, археологији и геологији.In this dissertation, the spatial and angular distributions of 10 keV protons and the corresponding rainbow lines are investigated in the case of the square electrostatic rainbow lens. The spatial and angular proton distributions were obtained numerically by solving proton’s equations of motion and applying the computer simulation method. The rainbow lines were also determined numerically. Besides, influence of the corresponding rainbow lines on the transmission of the beam through the lens and in the space behind is investigated. The rainbow lens model, which uses analytical approximation of the electrostatic field of the lens, and the rainbow lens device, which uses numerically obtained realistic electrostatic field of the lens, have been analyzed. In the case of the rainbow lens model, the parallel initial proton beam was assumed, while in the case of the rainbow lens devise, the initial proton beam was parallel and quasi-parallel. In the case of rainbow lens model, the spatial and angular distributions and the corresponding rainbow lines have been analyzed, for the electrode voltage equal to 10, 20, 50 and 100 kV. In the case of the rainbow lens devise, it is shown that the spatial and angular rainbow lines occur for a much less values of the electrode voltage. Namely, closed spatial rainbow lines inside the lens and closed angular rainbow lines occur for the electrode voltage equal to 2 kV. Practically this could be very important since one can build and work more easily with the electrode voltage of 2 kV than e.g. with the electrode voltage of 100 kV. vii It has been shown that the electrostatic rainbow lens has characteristic catastrophic focusing behavior, which is determined by the corresponding spatial and angular rainbow lines. As a result, the rainbow lens could be successfully used for preparation and transportation of ion beams within accelerator facilities, including their preparation for collisions with each other, as well as, for obtaining well defined beam profiles that could be used in condensed matter physics, biophysics and geology

Spatial rainbows and catastrophes in transmission of protons through electrostatic octopole lens

This paper considers transmission of initial parallel proton beam with kinetic energy of 10 kеV through electrostatic octopole lens. The spatial rainbows and corresponding proton distributions are calculated by using infinite length approximation potential. Positive potentials of the lens electrodes are set to be 0.35 kV and 9 kV. It has been shown that by application of catastrophe theory, generating function for mapping proton positions between entrance and exit transverse plains can be determined, giving accurate rainbow patterns for biasing potentials of 0,35 kV. [Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. III 45006: Physics and Chemistry with Ion Beams

Axial Channeling of High Energy Protons in Carbon Nanotubes

We have studied theoretically the angular distributions of 1 GeV protons channeled through the long (10, 0) single-wall carbon nanotubes. The nanotube length is varied between 10 and 80 mu m. The angular distribution of channeled protons is generated by the computer simulation method using the numerical solution of the proton equations of motion in the transverse plane. The analysis shows that for the nanotube length less then 30 mu m the transverse geometrical structure of the nanotubes could be deduced from the angular distribution. For the length over 30 mu m, the angular distribution is characterized only by the concentric circular ridges. The number of ridges increases and the distance between them decreases as the nanotube length increases. For the nanotube length of 80 mu m, the circular ridges are no longer visible and the angular distribution becomes equilibrated.Publications of the Astronomical Observatory of Belgrade Series, 24th Summer School and International Symposium on Physics of Ionized Gases, Aug 25-29, 2008, Novi Sad, Serbi

Angular distributions of high energy protons channeled in long (10,10) single-wall carbon nanotubes

In this work we study the angular distributions of 1 GeV protons channeled in long (10,10) single-wall carbon nanotubes. The nanotube length, L, is varied between 10 and 100 mu m. The angular distributions of channeled protons are obtained using the numerical solution of the proton equations of motion in the transverse plane and the Monte Carlo method. The effects of proton energy loss and scattering angle dispersion caused by its collisions with the nanotube electrons are taken into account. Analysis shows that for L LT 30 mu m, the transverse structure of the nanotube could be deduced from the angular distribution. For L GT = 40 mu m, the angular distribution contains the concentric circular ridges whose number increases and the average distance between them decreases when L increases. A possible application of the obtained results for characterization of carbon nanotubes is discussed. (C) 2009 Elsevier B.V. All rights reserved

Proton channeling through long chiral carbon nanotubes: The rainbow route to equilibration

In this work we investigate the rainbows appearing in channeling of 1 GeV protons through the long (11, 9) single-wall carbon nanotubes. The nanotube length is varied from 10 to 500 pm. The angular distributions of channeled protons are computed using the numerical solution of the proton equations of motion in the transverse plane and the Monte Carlo method. The rainbows are identified as the rings in the angular distributions, which correspond to the extrema of the proton deflection functions. Each rainbow is characterized by a sharp decrease of the proton yield on its large angle side. As the nanotube length increases, the number of rainbows increases and the average distance between them decreases in an easily predictable way. When the average distance between the rainbows becomes smaller than the resolution of the angular distribution, one cannot distinguish between the adjacent rainbows, and the angular distribution becomes equilibrated. We call this route to equilibration the rainbow route to equilibration. This work is a demonstration of how a simple one-dimensional bound dynamic system can exhibit a complex collective behavior. (C) 2008 Elsevier B.V. All rights reserved

Focusing properties of a square electrostatic rainbow lens doublet

This is a study on the properties of a square electrostatic rainbow lens doublet. The said optical element consists of two square electrostatic rainbow lenses with the second lens axially rotated for 45 degrees with respect to the first one. The propagation of a proton beam with a kinetic energy of 10 keV through the doublet is in the focus of our analysis. The potential of the electrodes of both lenses is 2 kV. The electrostatic potential and the electric field components of the lens doublet are calculated using a 3-D computer code based on the method of moments. Spatial and angular distributions of protons propagating through the lens doublet, as well as the parameters defining beam quality, are investigated. As in the case of the single square electrostatic rainbow lens, the evolution of these distributions is determined by the evolution of corresponding rainbow lines, generated by the use of the theory of crystal rainbows. Our study shows that a beam core in the shape of a cusped square is formed by the spatial rainbow line that appears first. This rainbow line occurs during proton propagation through the first lens. The beam core retains the cusped square shape during the propagation through the second lens. The electrostatic field of the second lens causes the appearance of an additional spatial rainbow line, which encompasses the beam core and defines the outer border of the beam. This rainbow line constitutes the main difference between the cases of the lens doublet and a single lens. [Projekat Ministarstva nauke Republike Srbije, br. III45006