Microsoft Word - 291-299 291 | Physics 2014) عام 3العدد ( 27مجلة إبن الھيثم للعلوم الصرفة و التطبيقية المجلد Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (3) 2014 Ion Beam Focusing in Solenoid Magnetic Field Bushra J. Hussein Dept. of Physics/ College of Education for Pure Science (Ibn Al-Haitham)/ University of Baghdad Intesar H. Hashim Dept. of Physics/ College of Educatiocgn/ University of Al-Mustansiriyah Dheyaa A. Nasrallah Nuclear Applecation Department/Ministry of Science and Technology E-mail: dr.bushrahussam@yahoo.com Received in:15 April 2014 Accepted in :29 September 2014 Abstract The present study investigates the main parameters effect on the solenoid design as converging lens of charged particle beam passing through it. These parameters are solenoid magnetic field (B), solenoid radius (Ro) and the solenoid total length (L). The result indicates that the solenoid system is very sensitive to the change of these parameters. The solenoid acts as converge lens but may convert to diverging lens at some conditions. The best design obtained at (L=1100 mm, B=5000 gauss and Ro=150 mm). Key words: plasma source, focusing Devices, ions beam, solenoid magnet 292 | Physics 2014) عام 3العدد ( 27مجلة إبن الھيثم للعلوم الصرفة و التطبيقية المجلد Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (3) 2014 Introduction The beam means a set of particles have about the same kinetic energy and move in about the same direction [1]. In addition, the particle beams can be defined as an ensemble of charged particles moving in a direction approximately parallel to the axis of the motion, which is represented by central trajectory. This axis may be curved if the beam passes through a transverse electric or magnetic field [2]. The behavior of beams can be studied by tracing a large number of individual particles or by studying the transfer properties of curve, which assumed to be bound to the particles contained in the beam [3]. The behavior of many beam transport elements can be obtained to high degree of accuracy by considering, the first order terms in the dynamic. This yields differential equations with linear solutions. This means that the displacement and angular divergence of a particle leaving an element are given in terms of the corresponding input conditions by linear simultaneous equations in which, the coefficients depend on the length and nature of the element [4,5]. Charged particle beams have continually expanding applications in many branches of research and technology, like [1,2]: 1. Thin-Film technology (Ion implantation system). 2. Production of short-lived medical isotopes. 3. Radiation processing of food. 4. Synchrotron light sources. 5. Beam lithography. 6. Recent active areas include flat-screen cathode-ray tubes. 7. Free electron lasers. To design particle beam transport systems, we therefore adopt some organizing and simplifying requirements on the characteristics of electromagnetic fields used. The general task in beam optics is to transport charged particles from point A to point B along a desired path. We call the collection of bending and focusing magnets installed along this ideal path the magnet lattice and the complete optical system including the bending and focusing parameters a beam transport system [6]. Plasma Ion Source The ions are extracted from the plasma of gas discharge and then accelerate this ion beam when passes through the extraction electrodes into the vacuum drift tube like figure (1) [7]. That means, the ion source is the tool that produced ion beam by ionized feed material [8,9]. The emitting plasma surface area has a concave shape, which depends on the plasma density and the strength of the accelerating electric field at the plasma surface. The concave shape of the meniscus and the aperture in the source electrode produce a transverse electric field component that results in a converging beam. There are many different types of sources for the various particle species, such as light ions, heavy ions or negative ions. Most of the sources employ magnetic fields to confine the plasma. Some have several electrodes at different potentials to better control the ion beam formation and acceleration process [7] Beam Guiding and Focusing Devices Charged particle transport systems are typically designed to guide an input charged particle beam to the exit of the transport system with minimal particle loss and without degradation in beam quality [10].The passage of a trajectory (ray) across an individual element is given by a transformation which yields the output ray directly from the input ray [11]. A different type of focusing device like quadrupole magnets that focus only in one plane and defocus in the other and solenoid magnets that focus in two planes. Guiding particles through appropriate electric or magnetic fields is called particle beam optics or beam dynamics [6]. Particle optical systems are usually comprised of electric and magnetic bending elements like (dipole for magnet), focusing element like (quadrupole and solenoid magnet) and high- 293 | Physics 2014) عام 3العدد ( 27مجلة إبن الھيثم للعلوم الصرفة و التطبيقية المجلد Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (3) 2014 order multipoles for correction of aberrations. However, various modern systems for the transport require the detailed treatment of more advanced optical elements [5]. Solenoid Magnet A solenoid magnet is a cylindrically coiled electromagnet. When current is flowing through the coil, the resulting magnetic field inside the term solenoid to refer to coiled magnets that are long in the axial direction (length >> width), so that the fringe fields at their ends are small compared to the long axial field inside the coil. That means, in a solenoid, the longitudinal magnetic field on the axis is peaked at the center of the solenoid, decreases toward the ends, and approaches zero far away from the solenoid [12], see figure (2) [13]. In contrast, the radial magnetic field is peaked near the ends of the solenoid. In a simple model, the longitudinal magnetic field can be assumed to be zero outside the solenoid and uniforms inside it. A solenoid is often used to focus charged particle beams in the low energy section of accelerators and other devices such as in cathode ray tubes, image intensifiers, electron microscopes, ion microprobes and ion beam induced inertial fusion [12]. The solenoid lens is the only possible magnetic lens geometry consistent with cylindrical paraxial beams. Since the magnetic field is static, there is no change of particle energy passing through the lens; therefore, it is possible to perform relativistic derivations without complex mathematics [13]. There are three optically important regions in a solenoid magnet. At the entrance and exit regions the magnetic field has a radial and axial component, except on the magnet axis [10]. The matrices method is best to study these three regions which transfer matrices describe changes in the transverse position and angle of a particle relative to the main beam axis. The transfer matrix description of beam transport in near optical elements facilitates the study of periodic focusing. The matrix description is a mathematical method to organize information about the transverse motions of particles about the main beam axis [16]. Therefore, the transfer matrix (M) of the whole solenoid is the product of three different matrices M1, M2 and M3 corresponding to the entrance fringe field, the constant axial magnetic field and the output fringe field respectively [14,15]. Ms= M1. M2 . M3 (1) Ms=              100 0100 010 0001                      cos00sin sin)2/1(1)cos1)(2/1(0 sin0cos0 )cos1)(2/1(0sin)2/1(1              100 0100 010 0001   (2) Ms=                  22 22 22 22 // // CCSCSS CSCSCS CSSCCS SCSCSC     (3) Where: S=sinθ/2 , C=cosθ/2 and α=√k θ=2Lα k=(B/(2B0Ro))2 BoRo= the magnetic rigidity (in Gauss.mm). Bo=magnetic field in body magnet region (in Gauss). 294 | Physics 2014) عام 3العدد ( 27مجلة إبن الھيثم للعلوم الصرفة و التطبيقية المجلد Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (3) 2014 Ro = the radius of curvature of the central trajectory (in mm). B= magnetic field strength (in Gauss). L=the total length of the solenoid (in mm). The thin lens approximation is done by making the (kL) small and by keeping the first term of Taylor series for the cosine and sine. The matrix then takes the form [15]: Ms=               1/100 0100 001/1 0001 f f (4) Where f is the focal length given by: 1/f=kL= (B/2B0Ro) 2 L (5) Results and Discussion The main parameters effect on the behavior of charged particles beam passing through a system of solenoid can be fixed, these parameters are solenoid magnetic field (B), solenoid radius (Ro) and the solenoid total length (L). So any changing in the one of these parameters gives different lens which means new beam profile. The present system consists of two drift space regions before and after the solenoid and the solenoid ranging in length between 500 and 1500 mm, in magnetic field between 1000 and 6000 Gauss and in radius 150 and 300 mm. Table (1) shows the maximum width obtain at the end of the system for different values of (L, B and Ro). Figure (3) indicates the relation of maximum width obtained at the end of the system versus solenoid magnetic field as function of solenoid radius with constant total length of solenoid (L=700 mm), one could note the reduction of beam width with increasing the solenoid magnetic field for all values of Ro. The best width occurs for low values of Ro which means good focusing properties of solenoid as thin lens. Figure (4). indicates the relation of maximum width obtained at the end of the system versus solenoid magnetic field as function of solenoid total length with constant radius of solenoid (Ro=150 mm), one could note the reduction of beam width with the increase of the solenoid magnetic field for all values of Ro. But this reduction does not continue for all values of B, there is specific value of B break down this reduction in the beam width and cause increasing of beam width. This behavior appears clearly for high values of L, that means the result lens became diverge lens, in other words for each value of B there are optimum values of L to produce converge lens, which means that the solenoid may be behave as diverge lens in some conditions. Conclusions Conclusions of the present study can be summarized as follows. 1. The solenoid lens are very sensitive to the change of (L, B and Ro). 2. The solenoid acts as converge lens but may convert to diverging lens at some conditions. 3. The best design obtained at (L=1100 mm, B=5000 gauss and Ro=150 mm). References 1. Humphries,S. (2002). Charged particle Beams. Albuquerque, New Mexico, department of electrical and computer engineering university of New Mexico. 295 | Physics 2014) عام 3العدد ( 27مجلة إبن الھيثم للعلوم الصرفة و التطبيقية المجلد Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (3) 2014 2. Lawson, J.D. (1988). The physics of charged particle beams. 2nd ed., Clarendon press, Oxford. 3. Brown , K.L. & Servranckx, R.V. (1985). First and second order charged particle optics. AIP conference proceedings No.127, American institute of physics. 4. Banford, A.P. (1966). The transport of charged particle beam. E.and F.N.Spon limited, London, 5. Makino, K., Berz, M., Johnstone, C.J., & Errde, D., (2004). High-order map treatment of superimposed cavities, absorbers and magnetic multipole and solenoid fields. Nuclear Instruments and Methods in Physics Research A519 , 162-174. 6. Wiedemann, H. (2007). Particle Accelerator Physics. Third Edition Springer- Verlag Berlin Heidelberg. 7. Reiser, M. (2004). Theory and Design of Charged Particle Beams. WILEY-VCH Veriag Gmbh and Co. KGaA, Weinheim, Printed in the Federal Republic of Germany. 8. Keller, J.H. (1981). Beam Optics Design for Ion Implantation . Nuclear Instruments and Methods, 189 , 7-14. 9. Freeman, J.H.; Beanl, D.G.; Chivers, D.J, & Gard, G.A. (1978). An Electrostatics Lens for the Acceleration and Deceleration of High Intensity Ion Beams. Nuclear Instruments and Methods, 155, 29-37 10. Dehnel, K. and Dehnel, M. (2002). Using Beamline Simulator V1.3. published by accelso Inc.,Del Mar,California (1998),U.S. printing, June. 11. Carey, D.C. and Brown, K.L. (1982). A Computer Program for simulating charged particle beam transport systems, including decay calculations. printed in the U.S. of America, March. 12. Kumar, V. (2009). Understanding the Focusing of Charged Particle Beam in a Solenoid Magnetic Field. Am.,J. Phys. 77 , 737-741 13. Humphries, S. (1999). Principles of Charged Particle Acceleration. Published by Jon Wiley and Sons. Copyright (1999) University of New Mexico 14. Lombardi, A.M. (2006). Beam Lines. CERN Accelerator School, CERN-320 Copies Print September. 15. Royer, Ph. (1999). Solenoidal Optics. European Organization for Nuclear Research, CERN- PS Division Geneva, Switzerland. 16. Regenstreif, E., (1967). Focusing with Quadrupoles, Doblets, and Triplets. in Focusing of Charged Particles, edited by: A.Septier. 1, Academic Press INC., 353-410. 296 | Physics 2014) عام 3العدد ( 27مجلة إبن الھيثم للعلوم الصرفة و التطبيقية المجلد Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (3) 2014 Table (1): Maximum width obtain at the end of the system for different values of (L, B and Ro) Total Length L mm Magnet field B (Gauss) RO= 150 mm RO= 200 mm RO= 250 mm RO= 300 mm X mm Mag. (Xout/Xin) X mm Mag. (Xout/Xin) X mm Mag. (Xout/Xin) X mm Mag. (Xout/Xin) 500 1000 2000 3000 4000 5000 6000 16.481 15.639 14.243 12.312 9.893 7.132 3.296 3.127 2.848 2.462 1.978 1.426 16.604 16.130 15.341 14.243 12.843 11.158 3.320 3.226 3.068 2.848 2.568 2.231 16.661 16.357 15.852 15.146 14.243 13.146 3.332 3.271 3.170 3.029 2.848 2.629 16.692 16.481 16.130 15.639 15.009 14.243 3.338 3.296 3.226 3.127 3.001 2.848 700 1000 2000 3000 4000 5000 6000 16.369 15.191 13.246 10.582 7.369 4.512 3.273 3.038 2.649 2.116 1.473 0.902 16.541 15.877 14.775 13.246 11.310 9.021 3.308 3.175 2.955 2.649 2.262 1.804 16.621 16.195 15.488 14.503 13.246 11.728 3.324 3.239 3.097 2.900 2.649 2.345 16.664 16.369 15.877 15.191 14.312 13.246 3.332 3.273 3.175 3.038 2.862 2.649 900 1000 2000 3000 4000 5000 6000 16.256 14.744 12.257 8.906 5.261 5.000 3.251 2.948 2.451 1.781 1.052 1.000 16.478 15.625 14.211 12.257 9.811 7.027 3.295 3.125 2.842 2.451 1.962 1.405 16.580 16.034 15.126 13.863 12.257 10.335 3.316 3.206 3.025 2.772 2.451 2.067 16.636 16.256 15.625 14.744 13.619 12.257 3.327 3.251 3.125 2.948 2.723 2.451 1100 1000 2000 3000 4000 5000 6000 16.144 14.298 11.280 7.321 4.244 8.050 3.228 2.859 2.256 1.464 0.849 1.610 16.414 15.372 13.650 11.280 8.364 5.340 3.282 3.075 2.730 2.256 1.672 1.068 16.540 15.872 14.764 13.226 11.280 8.980 3.308 3.174 2.952 2.645 2.256 1.796 16.608 16.145 15.370 14.296 12.929 11.282 3.321 3.228 3.074 2.859 2.585 2.256 1300 1000 2000 3000 4000 5000 6000 16.031 13.854 10.316 5.901 5.031 11.822 3.206 2.770 2.063 1.180 1.006 2.364 16.351 15.121 13.091 10.316 7.001 4.331 3.270 3.024 2.618 2.063 1.400 0.866 16.499 15.710 14.403 12.592 10.316 7.682 3.299 3.142 2.880 2.518 2.063 1.536 16.580 16.031 15.121 13.854 12.244 10.316 3.316 3.206 3.024 2.770 2.448 2.063 1500 1000 2000 3000 4000 5000 6000 15.919 13.411 9.370 4.796 7.040 15.807 3.183 2.682 1.874 0.959 1.408 3.161 16.288 14.869 12.534 9.370 5.784 4.487 3.257 2.974 2.506 1.874 1.156 0.897 16.459 15.549 14.043 11.963 9.370 6.477 3.291 3.109 2.808 2.392 1.874 1.295 16.551 15.919 14.869 13.411 11.563 9.370 3.310 3.183 2.974 2.682 2.312 1.874 297 | Physics 2014) عام 3العدد ( 27مجلة إبن الھيثم للعلوم الصرفة و التطبيقية المجلد Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (3) 2014 Figure No.(1): Schematic of a plasma ion source [7]. Figure No.(2):Solenoid magnetic (a) Magnetic field lines in a solenoid (b) Geometry and field lines (c) Variation of longitudinal magnetic field on Bz(0,z) [13] Extraction electrodes Ion beam + -V0 Plasma Drift Tube Emitting Surface Plasma Meniscus (b) (c) (a) 298 | Physics 2014) عام 3العدد ( 27مجلة إبن الھيثم للعلوم الصرفة و التطبيقية المجلد Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (3) 2014 1000 2000 3000 4000 5000 6000 4 6 8 10 12 14 16 18 B (Gauss) X (m m ) Ro=150 mm Ro=200 mm Ro=250 mm Ro=300 mm 1000 2000 3000 4000 5000 6000 4 6 8 10 12 14 16 18 B (Gauss) X (m m ) L=500 mm L=700 mm L=900 mm L=1100 mm L=1300 mm L=1500 mm Figure No.( 3): The relation of maximum width obtained at the end of the system versus B as function Ro with (L=700 mm) Figure No. (4): The relation of maximum width obtained at the end of the system versus B as function L with (Ro =150 mm) 299 | Physics 2014) عام 3العدد ( 27مجلة إبن الھيثم للعلوم الصرفة و التطبيقية المجلد Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (3) 2014 لولبي يتبئير حزمة ايونات في مجال مغناطيس بشرى جودة حسين قسم الفيزياء/ كلية التربية للعلوم الصرفة ( ابن الھيثم )/ جامعة بغداد أنتصار ھاتو ھاشم الجامعة المستنصرية/ لتربيةا كلية/ ءلفيزياا معلو قسم ضياء عبد المنعم نصر هللا وزارة العلوم والتكنلوجيا /قسم التطبيقات النووية 2014: ايلول 29قبل البحث 2014نيسان 15استلم البحث : الخالصة مة لحزمة اللولبي الحلزوني بوصفھا عدسة ال الملفالدراسة الحالية تفسر تأثير المعلمات االساسية في تصميم ف ) ونصBالجسيمات المشحونة المارة خاللھا. ھذه المعلمات تتمثل في شدة المجال المغناطيسي للملف اللولبي ( القطر )R) والطول الكلي للملف (Lكما معلمات.). بينت النتائج أن منظومة المغناطيس اللولبي تكون حساسة جدا لتغيير ھذه ال يعمل الملف اللولبي عدسة المة، لكن يتحول الى عدسة مفرقة عند بعض الشروط. أنسب تصميم (L=1100 mm, B=5000 gauss and Ro=150 mm) نحصل عليه عندما يكون : مصدر البالزما، نبائط التبئير، حزمة ايونات، المغناطيس اللولبيالكلمات المفتاحية