About me
http://scholar.google.com/citations?user=hZvL5eYAAAAJ
Contact Info
Address
Assistant Professor
Department of Mathematics and Sciences
College of Arts and Applied Sciences (CAAS)
Dhofar University
Post Box No. 2509
Postal Code: 211
Salalah
Sultanate of OMAN
Thesis title
Quantum theory of charged-particle beam optics
Education
Ph.D (Mathematical Physics) 1997, The Institute of Mathematical Sciences (IMSc/Matscience)<br>Chennai (Madras), India.<br><br>M.Sc. (Physics) 1990, Indian Institute of Technology (IIT), Kanpur, India.
Research
Research Interests
The quantum theory of charged-particle beam dynamics is being developed essentially using an algebraic approach. On the basis of this theory, optics of the transport of nonrelativistic and relativistic charged-particle beams through electromagnetic systems (of importance for charged-particle beam devices, like electron microscopy, microelectron-beam lithography, etc., and accelerator design) is being analyzed systematically. The machinery of Lie algebraic methods is used primarily and this facilitates an easy passage from the quantum theory to the traditional classical theory (geometrical optics). Our results include the modifications of the paraxial properties and the aberration coefficients, with —dependent contributions, for the various optical elements, like the magnetic round lenses, quadrupoles, etc., using the Schrödinger (nonrelativistic), Klein-Gordon and Dirac equations. For charged spin-half particles, the Dirac equation leads to spinor contributions to the beam dynamics. We do hope that these quantum corrections, albeit small, would be of some practical significance in certain situations; it should, however, be emphasized that, in any case, it is certainly satisfying to understand the working of the traditional classical theory as an approximation of a proper quantum theory since after all any physical system is quantum mechanical at the fundamental level.<br><br>The application of the Wigner phase-space distribution for studying the quantum mechanics of charged-particle beam transport through electromagnetic optical systems provides a natural link between the classical and the quantum descriptions. In this context, the relation between the transformation of the Wigner function of a charged-particle optical system, corresponding to the associated scalar wave function, and the transformation of the classical phase-space of the system has been studied.<br><br>The application of the spinor beam optical formalism has been shown to lead to a fully quantum mechanical understanding of the dynamics of a spin-half particle with anomalous magnetic moment, including the spin evolution, at the level of single-particle dynamics. The general theory, developed for any magnetic optical element with straight axis, describes the quantum mechanics of the orbital dynamics, the Stern-Gerlach kicks and the Thomas-Bargmann-Michel-Telegdi (Thomas-BMT) spin evolution.<br><br>In the paraxial régime of 3-dim optics, two evolution Hamiltonians are equivalent when one can be transformed to the other modulo scale by similarity through an optical system. To determine the equivalence sets of paraxial optical Hamiltonians one requires the orbit analysis of the algebra sp (4,R) of 4×4 real Hamiltonian matrices. Our strategy uses instead the isomorphic algebra so (3,2) of 5×5 matrices with metric (+1,+1,+1,−1,−1) to find 4 orbit regions (strata), 6 isolated orbits at their boundaries, and 6 degenerate orbits at their common point. We thus resolve the degeneracies of the eigenvalue classification.<br><br>RESEARCH PLANS<br><br>Portions of my work would be concerned with the applications of the above formalism and related ideas to various problems such as developing a complete quantum mechanical treatment of high energy polarized beams of Dirac particles (electrons, protons, muons, ...), including polarization, radiation effects etc., studying the quantum mechanics of beam optical aberrations relevant for electron microscopy (from low voltage to high voltage regions) and microelectron-beam device technology, ..., etc.<br><br>Using the analogy of the Helmholtz equation with the Klein-Gordon equation and the Pauli-Villars approach to the Klein-Gordon equation a formalism utilizing the powerful techniques of quantum mechanics has been developed for scalar optics including aberrations. This provides an alternative to the traditional square-root approach and gives rise to wavelength-dependent contributions modifying the aberration coefficients.<br><br>Dirac-like form of the Maxwell equations is well known in literature. Starting with the Dirac-like form of the Maxwell equations we build a formalism, which provides a unified treatment of light beam optics and polarization. The traditional results (including aberrations) of the scalar optics are modified by the wavelength-dependent contributions. Some of the well-known results in polarization studies are realized as the leading-order limit of a more general framework of our formalism.<br><br>We are also studying the Beam Halo Problem and building a diffraction-based model for the beam losses. In the proposed model we use the powerful machinery of the Quantum-like approaches. I am also currently trying to analyze the bulk characteristics of the beams using the powerful techniques of Statistical Mechanics.<br><br>Expected Outcome of the Proposed Research Plan<br><br>Any physical system is quantum mechanical at the fundamental level. So, the proposed research would lead, first of all, to a better understanding of the quantum physics of beam dynamics. Besides this, of course, the results should lead to some insight into the solutions of some of the practical problems of beam dynamics; in the polarization analysis, for example. One immediate result shall be the generalization of the beam-optical form of the Thomas-BMT equation to all orders. In our earlier paper the leading order approximation leads to the paraxial beam-optical form of the Thomas-BMT equation. The preliminary results of the proposed halo model are encouraging and further work is in progress. This will enable us to arrive at the bulk characteristics of the beams using a microscopic theory.<br>
Publications
Total
25
Journal Papers
1. S. A. Khan and R. Jagannathan, On the quantum mechanics of charged particle beam transport through magnetic lenses, Physical Review E 51, 2510-2515 (March 1995).<br><br>2. M. Conte, R. Jagannathan, S. A. Khan and M. Pusterla, Beam optics of the Dirac particle with anomalous magnetic moment, Particle Accelerators, 56, 99-126 (1996); (Preprint: IMSc/96/03/07, INFN/AE-96/08).<br><br>3. S. A. Khan and M. Pusterla, Quantum-like approach to the transversal and longitudinal beam dynamics. The halo problem, European Physical Journal A 7 No. 4, 583-587 (2000).<br><br>4. Sameen Ahmed Khan and Modesto Pusterla, Quantum approach to the halo formation in high current beams, Nuclear. Instruments and Methods in Physics Research (NIMS) A 464, Issue 1-3, 461-464 (May 2001). Refereed Proceedings of the 13th International Symposium on Heavy Ion Inertial Fusion (HIF2000). (13-17 March 2000, San Diego, USA).<br><br>5. Sameen Ahmed Khan and Kurt Bernardo Wolf, Hamiltonian orbit structure of the set of paraxial optical systems, Journal of the Optical Society of America (JOSA). A 19 (12), 2436-2444 (December 2002).<br><br>6. Sameen Ahmed Khan, Wavelength-dependent modifications in Helmholtz Optics, International Journal of Theoretical Physics, 44 (1), 95-125 (January 2005). (Kluwer Academic Publishers, 2005, https://www.editorialmanager.com/ijtp/).<br><br>7. Sameen Ahmed Khan, An Exact Matrix Representation of the Maxwell’s Equations, Physica Scripta, 71 (5), 440-442 (2005). (http://www.physica.org/).<br><br>Sameen Ahmed Khan, The Foldy-Wouthuysen Transformation Technique in Optics, Optik - International Journal for Light and Electron Optics, 117, Issue 10, pp. 481-488 (October 2006) (Elsevier, http://www.elsevier-deutschland.de/ijleo/). (Digital Object Identifier (DOI), http://dx.doi.org/10.1016/j.ijleo.2005.11.010). <br><br>8. Sameen Ahmed Khan, Maxwell Optics of Quasiparaxial Beams, Optik - International Journal for Light and Electron Optics, 121, Issue 5, pp. 408-416 (March 2010) (Elsevier, http://www.elsevier-deutschland.de/ijleo/). <br>(Digital Object Identifier (DOI), http://dx.doi.org/10.1016/j.ijleo.2008.07.027). <br><br>
Patent
Quadricmeter,<br><br>• Sameen Ahmed Khan,<br>Quadricmeter, <br>Official Journal of the Patent Office, Issue No. 43/2008, Part-I, pp. 25296 (24 October 2008).<br>Application No.: 2126/MUM/2008 A, International Classification: B69G1/36,<br>Controller General of Patents Designs and Trade Marks, Government of India.<br>http://ipindia.nic.in/ipr/patent/journal_archieve/journal_2008/patent_journal_2008.htm<br>http://ipindia.nic.in/ipr/patent/journal_archieve/journal_2008/pat_arch_102008/official_journal_24102008_part_i.pdf<br>http://www.patentoffice.nic.in/, http://www.ipindia.nic.in/<br>(patent in process, http://sameenahmedkhan.webs.com/quadricmeter.html).<br>
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Development of quantum mechanical treatment for the study of transport of charged-particle beams through electromagnetic systems.
Complete Thesis is available... moreDevelopment of quantum mechanical treatment for the study of transport of charged-particle beams through electromagnetic systems.