Microsoft Word - 309-317 309 | Physics 2014) عام 3(العدد 27المجلد مجلة إبن الھيثم للعلوم الصرفة و التطبيقية Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (3) 2014 the Optical Properties of Electrostatic Design and Study Mirror By using Bimurzaev Technique Intehaa A. Mohammed Dept.of Physics/College of Education for Pure Science(Ibn -Al Haitham)/University of Baghdad Received in :17April 2014, Accepted in :28 October 2014 Abstract In this research a computational simulation has been carried out on the design and properties of the electrostatic mirror and a mathematical expression has been suggested to represent the axial potential of an electrostatic mirror. The electron beam path using the Bimurzaev technique had been investigated as mirror trajectory with the aid of Runge – Kutta method. The spherical and chromatic aberration coefficients of mirror has computed and normalized in terms of the focal length. The choice of the mirror depends on the operational requirements. The Electrode shape of mirror two electrodes has been determined by using package SIMION computer program. Computations have shown that the suggested potentials give good result for low value spherical and chromatic aberration Cs/Fr= - 8.05, Cc/Fr=- 9.1, L=8mm, A=500volt, which give a good indicator for designing the mirrors Key words: electrostatic mirror, Bimurzaev technique, chromatic aberration, spherical aberration, SIMION computer program 310 | Physics 2014) عام 3(العدد 27المجلد مجلة إبن الھيثم للعلوم الصرفة و التطبيقية Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (3) 2014 Introduction Electron mirror is used to correct the chromatic and spherical aberration of lenses, this idea are back to the middle of twentieth century [1]. An electron mirror is creating when an electrode with sufficiently high negative potential is placed in the path of an electron beam. The negative electrode forms a potential hill that decelerates the incident electrons. The electrons lose their kinetic energy before reaching the electrode and are back to re– accelerated in the reverse direction. [2]. An electron mirror are capable of introducing chromatic and spherical aberrations of arbitrary sign . hence, we can utilize mirrors to compensate for the corresponding aberrations of round lenses [3] Unlike a light optics mirror, where the reflection occurs at the physical surface, the electron mirror represents a "soft" mirror, which allows the electrons to penetrate into the inhomogeneous reflection medium formed by the electrostatic potential[4] by introducing a reflection in the electron path using an electron mirror, the electron beam direction reverses and the electron velocity changes sign , thus the Scherzer theorem no longer applies [5]. The mirror field is usually confined between two electrodes a negative (mirror) electrode and a positive electrode (anode) which may be aground potential. The electrode can be shaped to provide the desired focusing effects along with reversing effect.[6] In ion mirror there is one hard reflecting point, this surface does not necessarily coincide with either the physical location of the turn around point of the ion mirror or a physical electrode surface [7]. The field inside a parabolic mirror (reflection) is curved along the axis and according to the Laplace equation it also has a curvature in a radial (or transverse) direction [8]. Electron mirror is made in various geometries according to their function in an electron optical instrument . They can be made in the form of two or three concentric cylindrical electrodes at different potentials for reducing aberration [9]. Theoretical consideration The inverse problem is important method in the design of electrostatic mirror by suggesting an axial electrostatic potential distribution using potential function.      zACzU tanh ---------------------------------(1) Where U(z) is the axial potential along the optical axis z. the constant C,A are affects the properties of this suggested potential. The equation of motion of charge particle in the electrostatic field or paraxial ray equation is given by [10] 0 422 2      R U U dz dR U U dz Rd ----------------(2) Where U' and U'' are the first and second derivatives of the axial potential U respectively. R represents the radial displacement of the beam form the axis z and the primes denote a derivative with respect to z. This research with The aid of Bimurzaev Technique and modified on it for solving electrostatic mirror trajectory by applying this trajectory equation twice at the first one applied is zero magnification condition representing the incident beam on the mirror before reflecting and the second one is applied infinite magnification condition representing the reflecting beam from the mirror. The second condition is very important because the optical properties are computed from it. The most important aberrations in an electron-optical system are spherical and chromatic aberration The spherical aberration coefficient Cs and chromatic aberration cofficient Cc referred to the image side are calculated from the following equations [11]. 311 | Physics 2014) عام 3(العدد 27المجلد مجلة إبن الھيثم للعلوم الصرفة و التطبيقية Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (3) 2014 )3( 2 3 3 14 24 5 4 5 16 4 2 22342 4 2 1                                            dzRU R R U U R R U U U U U U R U C Zi Zo S )4( 42 2 1 2 1 2 2              dzURU U RR U U R U C Zi Zo C The shape of the electrodes forming a specific electrostatic mirror has been determind by following equation [11] (5) --------------      2 4 , r zUzUzrU  The electrode shape by using SIMION computer program ,this program used to simulate electrostatic and static magnetic device for accelerating, transporting and otherwise manipulating beams of charged particles. Results and Discussion A potential distribution function has been suggested to represent an electrostatic mirror by equation 1, Figure (1) shows the axial potential U(z) and its corresponding the first and second derivatives respectively based on the proposed expression given in this equation at the above value of the constant ( C, A ) the length of mirror in the case is L= 8mm From figure (1) also we note that there is one inflection point in the second derivative of the potential distribution,( i.e. two electrode mirror have been used or chosen) The beam path along the electrostatic mirror field using Bimurzaev technique under the accelerating mode of operation has been considered represented by equation (2), and trajectories of the electrostatic mirror along various lengths L=8mm, 12mm.16mm, 20mm, as shown in figure (2) Figure (3) shows the electrostatic mirror focal length Fr is inversely proportional with (A) for all mirror length where the increase of the values of (A) causes to decrease the values of the mirror focal length , the mirror focal length can be determined from the reflect beam trajectory where the focal length of reflect beam trajectory represents the mirror focal length , from the result it is noted that the mirror focal length has a positive sign that is means the mirror type is convergence. Figure (4) noted that the electrostatic mirror spherical and chromatic aberration Cs and Cc is directly proportional with (A) for all mirror length It is noted from this figure that the value of mirror aberration (Cs,Cc) inversely with value (A) where the increase of the value of (A) causes to decrease the value of the mirror spherical and chromatic aberration at the mirror length L=(8,12,16,20)mm. Figure (5) noted that the increasing of the values of the (A) causes decreases the values of both Cs/Fr and Cc/Fr for all mirror length, these values are listed in table (1) 312 | Physics 2014) عام 3(العدد 27المجلد مجلة إبن الھيثم للعلوم الصرفة و التطبيقية Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (3) 2014 Figure (6) showed the relative spherical Cs/Fr and chromatic Cc/Fr aberration coefficient have been computed as a function of the relative mirror length L/Fr at mirror length L=8 mm where A=(500,300,275,220,175)volt. dimension of the two electrode s electrostatic -Figure (7) showed three mirror using Bimurzaev technique when the A=500 volt at the mirror length L=8mm using Simion computer program Conclusion The electrostatic mirror achieved in present investigation are useful for studying surfaces of specimens using Bimurzeav technique are considered as mirror trajectories .In this research, good results have been got using the mathematical expression for excel potential and the electron beam to produce the trajectories which are successful. from results ,The obtained negative sign of spherical and chromatic aberration Cs and Cc can be used to correct the aberration References 1.Barnett, M. E., and Nixon, W. C. (1966). A mirror electron microscope using magnetic lenses, Sci. Instrum., 44: 893-898. 2.Kuehler, J. D. (1960). A new electron mirror design, J. IBM, 4: 202-204. 3.Preikszas , D. and Rose , H. (1997), correction properties of electron mirrors, J.Electron Microsc., 46,1-9. 4.Rose, H. and Wan, W.( 2005), Aberration correction in electron microscopy, Proc. IEEE, Particle Accel. Conf., Knoxville, Tennessee., 5: 44-48. 5. Feng, J.;Forest, E.; Macdowell, A.A.; Marcus, M.; Padmore, H.; Raoux, S.; Robin, D.; Scholl, A.; Schlueter, R.; Schmid, P.; Stohr, J.; Wan, W.; Wei, D. H. and Wu, Y.(2005). An x-ray photoemission electron microscope using an electron mirror aberration corrector for the study of complex materials", J. Phys: Condens. Matter., 17: 1339- 1350. 6. Rempfer,G. F., Desloge, D. M., Skoczylas, W. P., and Griffith,O. H.(1997), Simultaneuos correction of spherical and chromatic aberration with an electron mirror: an electron optical achromat, Microsc. Microanal.3, 14-27 7.Rockwood, A. L. (1999). Stability conditions for multiply reflection electrostatic ion trap, J. Am. Soc. Mass Spectrum. 10: 241-245. 8.Doroshenko, V. M.and Cotter, R. J., 1999. Ideal velocity focusing in a reflection time – of – flight mass spectrometer, J. Am. Soc. Mass Spectrum., 10: 992-999. 9.Berger,C. and Baril , M.(1982), Studies of three cylinder electrostatic mirror and lenses, J. Appl. Phys, 53, 3950-3956 10.Grivent, P.( 1972) Electron optics, Pergamon: Oxfords and New York, 1, 174. 11.Szilagyi, M., and Szep, J.(1987). A systematic analysis of symmetric three – electrode electrostatic lenses, IEEE Trans. 34: 2634-2642. 313 | Physics 2014) عام 3(العدد 27المجلد مجلة إبن الھيثم للعلوم الصرفة و التطبيقية Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (3) 2014 Table No. (1) The optical properties of electrostatic mirror L(Mirror length) (mm) A(volt) Cs/Fr Cc/Fr 8 500 -8.05 -9.1 12 300 -9.08 -10.19 16 230 -8.71 -9.8 20 100 -6.59 -7.01 Figure No. (1) The axial potential distribution U(z) and its first and second derivatives U`(z) and U``(z) respectively of the electrostatic mirror when c=5 volt, a=300 volt and mirror length L=8mm 314 | Physics 2014) عام 3(العدد 27المجلد مجلة إبن الھيثم للعلوم الصرفة و التطبيقية Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (3) 2014 100 200 300 400 500 A (VOLT) 0.28 0.32 0.36 0.40 0.44 F r( m m ) Figure No.(3) The changeability between values of the mirror focal length (Fr)mm and (A)volt when L=8,12,16,20 mm 315 | Physics 2014) عام 3(العدد 27المجلد مجلة إبن الھيثم للعلوم الصرفة و التطبيقية Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (3) 2014 100 200 300 400 500 A(volt) -3.4 -3.2 -3.0 -2.8 -2.6 C s a n d C c CS CC 0.28 0.32 0.36 0.40 0.44 Fr(mm) -11 -10 -9 -8 -7 -6 C s /F r a n d C c /F r Cs/Fr Cc/Fr FigureNo. (5) The changeability between Cs/Fr and Cc/Fr as a function of mirror focal length Fr (mm) for different values of (A) 316 | Physics 2014) عام 3(العدد 27المجلد مجلة إبن الھيثم للعلوم الصرفة و التطبيقية Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (3) 2014 Figure No. (7) The shape of electrodes for electrostatic mirror in three- dimensions by using Simion computer program 317 | Physics 2014) عام 3(العدد 27المجلد مجلة إبن الھيثم للعلوم الصرفة و التطبيقية Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (3) 2014 تصميم ودراسة الخواص البصرية لمراة كھروستاتيكية باستعمال تقانه بمرزايف انتھاء احمد محمد التربية للعلوم الصرفة ابن الھيثم/جامعة بغدادقسم الفيزياء/كلية 2014تشرين االول 28، قبل البحث : 2014نيسان 17استلم البحث: الخالصة تم في ھذا البحث إجراء بحث حاسوبي عن تصميم وخواص المرايا الكھروستاتيكية واقتراح صيغة رياضية لتمثيل و تمت دراسة مسار الحزمة االلكترونية باستعمال تقانه بمرزايف على انھا الجھد المحوري لھذه المرأة الكھروستاتيكية .كوتا–مسار مراتي باالستعانه بطريقة رنج وتم تعييرھا بداللة البعد البؤري ان تم حساب الخواص البصرية للمرايا من معامالت الزيوغ الكروية واللونية التشغيل. تم ايجاد شكل اقطاب المراة ثنائية االقطاب ورسمھا من خالل يعتمد على طريقة ومستلزمات اختيار المراة استخدام برنامج سيميون بينت الحسابات ان الجھود المقترحة اعطت نتائج جيدة قيم قليلة للزيغين الكروي واللوني فلقد حصلنا على Cs/Fr= - 8.05 Cc/Fr=- 9.1 L=8mm A=500volt والذي يعطي مؤشر جيد لتصميم المرايا :المرا يا الكھروستاتيكية ، تقنية بمرزايف، الزيوغ الكروية، الزيوغ اللونية ، برنامج سيميونالكلمات المفتاحية