Monte Carlo methods in radiative transfer and electron-beam processing
|
|
- Osborn Young
- 5 years ago
- Views:
Transcription
1 Journal of Quantitative Spectroscopy & Radiative Transfer 84 (2004) Monte Carlo methods in radiative transfer and electron-beam processing Basil T. Wong, M. Pnar Menguc Radiative Transfer Laboratory, Department of Mechanical Engineering, University of Kentucky, 322 RGAN Building, Lexington, KY 40506, USA Received 6 March 2003 Abstract Monte Carlo methods (MCMs) are the most versatile approaches in solving the integro-dierential equations. They are statistical in nature and can be easily adapted for simulation of the propagation of ensembles of quantum particles within absorbing, emitting, and scattering media. In this paper, we use MCM for the solution of the Boltzmann transport equation, which is the governing equation for both radiative transfer and electron-beam processing. We briey outline the methodology for the solution of MCMs, and discuss the similarities and dierences between the two dierent application areas. The focus of this paper is primarily on the treatment of dierent scattering phase functions.? 2003 Elsevier Ltd. All rights reserved. Keywords: Monte Carlo; Radiative transfer; Electron-beam processing 1. Introduction Monte Carlo methods (MCMs) are quite versatile in handling the transient and steady particle transport phenomena within participating media. Even though they were once considered dicult to implement and computationally inecient, with the rapid development of fast and powerful computers they have become more ecient and accurate. Consequently, MC approaches have been used extensively in the last decade for photon, electron, phonon, neutron transport problems. Two of the important research areas for our interest where the MCMs have been fully exploited to study the transport phenomena are the radiative transfer [1 11] and the electron-beam processing [12 17]. Radiative transfer applications of MCM are well-documented in the literature [1,2]. The algorithms developed for radiative transfer can easily be adapted for modeling of electron transfer phenomena. Corresponding author. Tel.: /ext ; fax: address: menguc@engr.uky.edu (M.P. Menguc) /$ - see front matter? 2003 Elsevier Ltd. All rights reserved. doi: /s (03)
2 438 B.T. Wong, M.P. Menguc / Journal of Quantitative Spectroscopy & Radiative Transfer 84 (2004) Nomenclature A atomic weight (kg/mol) C scattering cross-section (m 2 ) d diameter of scatterer (m) E electron energy (kev) f particle distribution function (dimensionless) g average direction cosine in s-direction (dimensionless) h Planck constant (J-s) k wave number (m 1 ) p polarization branch (dimensionless) R cumulative probability distribution function (dimensionless) Ran A random number (dimensionless) s axis of propagation (dimensionless) W scattering rates (s 1 ) x size parameter (=d=) (dimensionless) Z atomic number (dimensionless) Greek symbols extinction coecient (= + ) (m 1 ) absorption coecient (m 1 ) direction cosine (dimensionless) photon frequency (1/s)! single scattering albedo (==) phase function (sr 1 ) scattering coecient (m 1 ) optical thickness (=Z cr ) scattering polar angle measured from s-axis (rad) azimuthal angle measured from an axis normal to s-axis (rad) wavelength (m) Subscripts e for electrons wavelength dependent for photons Superscripts scattered el elastic inel inelastic In the context of the electron transport inside solids, analytical solutions are virtually impossible to obtain due to the complicated electronic band structures [18 20] and the scattering probabilities
3 B.T. Wong, M.P. Menguc / Journal of Quantitative Spectroscopy & Radiative Transfer 84 (2004) [19,20]. With the introduction of MCMs, realistic simulations of propagating electrons are therefore easily carried out to better understand the electron transport in such systems. Indeed, electron beam scattering phenomena inside solids have been routinely analyzed via MCMs, leading to high resolution recognition and visualization of nanostructures as done by scanning electron microscopy (SEM), transmission electron microscopy (TEM), and electron energy loss spectroscopy (EELS). In this paper, our objective is to show the similarities between the MC simulations for the radiative transfer equation and the electron transport equation. The main reason responsible for the striking similarities between the MCMs used in the two mentioned research areas is the fact that the governing equations are derived from the Boltzmann Transport Equation (BTE) [18 21], which asserts the balance between the rate of change of the particle distribution and the scattering rates. Here, we will introduce the BTE. After that we outline the application of MCMs to the solution of the BTE for both photon and electron transport. The similarity and dierences between these approaches, particularly the corresponding scattering phase functions are discussed. 2. Boltzmann transport equation (BTE) The propagation of quantum particles or energy carriers such as electrons, photons, phonons, neutrons, obeys the BTE, which describes the evolution of a particle distribution (say, f) over time and space as particles undergo a number of scattering events. The general form of the BTE is written as [18 r; + ṽ f( r; k;t)= ( ; col where the collision term on the right-hand side is given as ( = r W ( k ; k)f( r ; k ;t) k W ( k; k )f( r; k;t): ; k col At the right hand side of Eq. (2), W denotes the scattering rate, the rst summation is the rate of change of f due to the in-scattering of particles while the second is the rate of change of f caused by the out-scattering of particles. Note that the particle distribution f in general depends on its location in space r, its wave vector k, and time t. In its general form, the BTE is virtually intractable owing to the seven independent variables and its integro-dierential form. Often, it is desirable to recast the BTE in terms of intensity as the solution of particle distributions in space and time may not be required Radiative transfer equation (RTE) In radiative transfer, the quantum particles are photons, each having energy of h for a given frequency (or wavelength = c=). To derive the RTE, the radiative intensity is dened in terms of the photon distribution f, the photon energy h, the density of states D, and the speed of
4 440 B.T. Wong, M.P. Menguc / Journal of Quantitative Spectroscopy & Radiative Transfer 84 (2004) light c: I ( r; ; ; t)= p f ( r; p; ; ; t)hd (p; ; )c: (3) The subscript is used to indicate that the equation is for a given specic frequency. The summation in Eq. (3) is to be performed over all polarization branches, which implies that the change of polarization of photons is ignored in this case. 1 Multiplying Eq. (1) by the photon energy, the density of states, and the speed of light, and then performing the summation over all the polarization branches, we cast the BTE in terms of the + ṽ I = ; W ( ; ; ; )I ( ; ;t) ; W (; ; ; )I ( r; ; ; t): (4) To further simplify the BTE we rewrite the in-scattering term as W ( ; ; ; )I ( ; ;t)= ( ; ; ; )I 4 ( ; ;t)d ; (5) ; where is the scattering coecient and the phase function of the medium. The in-scattering term contains all the contributions from the entire spherical solid angle. The out-scattering term is given as W (; ; ; )I ( r; ; ; t)=( + )I ( r; ; ; t); (6) ; with being the absorption coecient. After rearranging we obtain the familiar form of the RTE + ṽ I = I + ( ; ; ; 4 ( ; ;t)d : (7) Note that is the extinction coecient, which is the sum of and. Since we deal with mostly cold media in this paper, the emission term is dropped. The out-scattering term includes the absorptions and elastic out-scatterings of photons. One important thing to note for the radiative transfer is that the number of photons does not conserve; in other words, photons can be created and destroyed during inelastic scattering processes. Inelastic scatterings in general mean that the ensemble of photons is attenuated in terms of the population of photons (but not the frequency of the photons) which in turn reduces the energy of the entire ensemble Electron transport equation (ETE) In the eld of the electron-beam processing, free electrons are the energy carriers. The energy of an electron is always characterized by its wave number k (k =1=) instead of its frequency or 1 Note that polarization can be considered in the radiative transfer formulation as discussed in the paper by Vaillon et al. (see this issue of the JQSRT; Eurotherm 73 paper #26).
5 B.T. Wong, M.P. Menguc / Journal of Quantitative Spectroscopy & Radiative Transfer 84 (2004) wavelength. Unlike photons, free (propagating) electrons do not undergo absorption by other particles, which implies that inelastic scatterings change the energy of these carriers but do not attenuate the number of carriers. Therefore the wave number or the wavelength of the electrons changes as they undergo inelastic scatterings [18 21]. From the computational standpoint, the scattering cross section changes once the energy of a propagating electron ensemble is altered [15] (see Eq. (20)). To derive the ETE, we rst dene intensity for electrons similar to that of Eq. (3): I e ( r; E; ; ; t)=f e ( r; E; ; ; t)e e D e (E; ; )v e (E): (8) After casting the BTE in terms of electron intensity, the ETE is given + ṽ e I e = [e inel (E)+e el (E)]I e + el e (E) 4 E e (E ; ; ; E; ; )I e(e; ; ;t)d : (9) The ETE resembles the RTE except that the scattering coecients e s, as well as the phase function e, depend on the energy (i.e., wave number k) of the electron beam. It is not dicult to convert a MCM developed for radiative transfer into a MCM in electron-beam processing with correct implementations of the electronic scattering properties. However, computations of the ETE are usually more involved than those of the RTE. 3. MCM in radiative transfer Before attempting to derive the scattering probabilities and the distance of interactions for photons and electrons, it is informative to have an overview of the problem description and the list of assumptions. To better compare MCMs in radiative transfer and in electron-beam processing, we consider a simple homogeneous, absorbing and scattering medium. In this case, we assume that the geometry of the problem can be in any conguration. The procedures of the simulation remain unaltered for any given geometry except the denition of exiting boundaries for the particles (i.e., the exibility of a MCM). The boundaries are assumed to be transparent, i.e. non-emitting, non-absorbing or non-reecting. A monochromatic laser beam is incident on the boundary as shown in Fig. 1. The particle beam transparent boundary quantum particles participating medium Fig. 1. 2D-representation of the geometry considered in MC simulations.
6 442 B.T. Wong, M.P. Menguc / Journal of Quantitative Spectroscopy & Radiative Transfer 84 (2004) Φ ν (Θ) (sr -1 ) 10 2 Mie HG x = 1 g = x = 2 g = 0.5 x = 3 g = 0.5 x = 4 g = Θ (degrees) Fig. 2. Typical photon scattering phase functions for dierent size parameters (x = d=) in the Lorenz Mie (LM) theory and for various asymmetry factors (g) in the Henyey Greenstein (HG) phase function. medium is considered to be at zero temperature, which helps to eliminate the emission contribution to the radiant energy distribution. The general procedures of constructing a MCM can be found in Refs. [5,6,10,11,15]; therefore, they are not repeated here. Below, we discuss only the most pertaining details Directions of propagation The direction of photon scattering determines the complexity of the problem. For the isotropic scattering phase function, the probability that a photon is scattered in any given direction is uniform. The direction of scattering is sampled from the expression of all possible solid angles. The scattering polar and azimuthal angles in the simulations can be determined using random numbers (Ran and Ran )[10,11]: =2Ran ; (10) = cos 1 (1 2Ran ); where Ran and Ran may vary from 0 to 1. For spherical particles, the Lorenz Mie Theory predicts the scattering phase function at a given scattering polar angle. The phase function obtained from the Lorenz Mie theory is often expressed as a series in terms of orthogonal functions. The most common representation involves the Legendre polynomials; a typical phase function assuming azimuthal symmetry is expressed as [2,24] ()= a n P n (); (12) n=0 where P n are the Legendre polynomials of the nth order. Typical phase functions as obtained from the Lorenz Mie theory are plotted in Fig. 2 where x is the size parameter dened as d=. Here, d (11)
7 B.T. Wong, M.P. Menguc / Journal of Quantitative Spectroscopy & Radiative Transfer 84 (2004) refers to the diameter of the scatterers inside the medium. Use of the Legendre Polynomials in Monte Carlo techniques is quite involved as it is not easy to invert such a phase function to obtain. In order to overcome this setback, we build a table containing all the scattering data and interpolate as required during the simulation [25]. The Henyey Greenstein (HG) phase function can be used to simplify the anisotropic scattering phase function. The scattering polar angle as a function of random number is obtained as [10] { [ ( ) = cos g 2 1 g 2 2 ]} ; (13) 2g 1 g +2gRan where g is the asymmetry factor (i.e., the average value of the direction cosine in the propagating direction). When g 1 highly forward scattering is implied, while g 1 means highly backward scattering. Determination of the scattering azimuthal angle will follow that of the isotropic scattering as given in Eq. (10). Although the implementation of the HG phase function in a MCM is straightforward and convenient, it often compromises the correct physics representation of the complete prole Distance of interaction The interaction distance governs the distance a bundle travels without being scattered. Generally, there are three dierent approaches for determining the distance of interaction, which have been examined and reported before [11]. Here, we consider only one of them (referred to as M2 in Ref. [11]) where the distance of interaction between elastic scattering events S is sampled as S = 1 ln(ran ); and the random number, Ran is between 0 and 1 (i.e. 0 Ran 1). Note that the inverse of the scattering coecient is actually the mean free path of the photons between elastic scattering events Attenuation of photons The attenuation of photons for a given distance S depends on the absorption coecient. The fraction of photons in an ensemble recovered after travelling a distance S is given as e S while (1 e S ) is the fraction absorbed. Note that this is not the only method for treating the attenuation of photons. Other approaches can be found in Ref. [11]. (14) 4. MCM in electron-beam processing In describing the MCM in the electron-beam processing, we will consider the same geometrical details as stated in Section 3. However, instead of impinging a laser beam upon a participating medium, an electron beam is assumed incident on a solid material. The medium is considered homogeneous and free of defects and cracks and it is not subjected to any other external forces imposed by the electric eld. The probability distributions needed for the MC simulations for the electron-beam processing are discussed below.
8 444 B.T. Wong, M.P. Menguc / Journal of Quantitative Spectroscopy & Radiative Transfer 84 (2004) Directions of propagation The HG and the Lorenz Mie theories provide the scattering phase functions for photons; counterparts for electrons are the screened Rutherford and the Mott scattering cross-sections, respectively [15,26]. The screened Rutherford dierential cross section for a given solid (or an atomic number Z) has the following form [15]: where dce el (; E) =5: Z 2 d E 2 ( ) E ( ( ) 2 sin 2 + ) ; (15) E :67 3 Z =3:4 10 E : Therefore, the phase function e for the electron scattering can be written as where e (; E)= 4 Ce; el total(e)= =4 dcel Ce;total el (E) (16) e (; E) ; (17) d dce el (; E) d: (18) d The scattering polar angle can be obtained as [15] ( = cos 1 1 2Ran ) ; (19) 1+ Ran where Ran is a random number. Note that depends the energy of the electron ensemble. Such an explicit expression for the scattering polar angle has a limitation. Similar to the HG phase function which is typically inaccurate in representing the backscattering, the screened Rutherford cross section is inaccurate when it comes to low-energy (i.e., 10 kev) electron beams. In order to correctly represent the scattering phase functions for both the low- and high-energy electron beams, the Mott scattering cross section should be employed. The Mott scattering cross section for an unpolarized electron beam is typically given as [26] dce el (; E) = ; (20) d where 1 (; E)= 2i {(n + 1)[exp(2i n 1 ) 1] + n[exp(2i n ) 1]}P n (cos ); (21) E 2 1 n=0 1 (; E)= 2i ( exp(2i n 1 ) + exp(2i n ))P E 2 n (cos ): (22) 1 n=1 Here, n s are the Dirac phase shifts, P n s and P n s are the ordinary Legendre polynomials and the associated Legendre polynomials, respectively. Details of the Mott scattering cross section are
9 B.T. Wong, M.P. Menguc / Journal of Quantitative Spectroscopy & Radiative Transfer 84 (2004) Φ e (Θ) (sr -1 ) 10 3 Mott 0.02 kev 0.60 kev kev kev Rutherford 0.02 kev 0.60 kev 5.00 kev kev Θ (degrees) Fig. 3. The Rutherford and the Mott scattering phase functions for electron in gold for various electron energies; adapted from Refs. [15,26]. reported in Ref. [26]. Since azimuthal symmetry is always assumed, the azimuthal angle for scattering is obtained as in Eq. (10). The Rutherford and the Mott scattering phase functions in gold for several selected electron energies are illustrated in Fig Distance of interaction Using the same arguments given in Section 3.2, the interaction distance between elastic scattering events for electrons is determined as S = 1 ln(ran e el s ); (23) where e el = N ace; el total ; (24) A here e el is the elastic scattering coecient, which depends on the atomic number Z, the atomic weight A, the density of the solid target, and the electron energy E. Note that N a is the Avogadro number Inelastic scatterings In the electron-beam processing, the electron stopping power de=ds is used to determine the attenuation of the electron energy along the distance of interaction. The stopping power is basically the amount of electron energy lost per unit traveled distance and is dened based on the total inelastic scattering cross section as [27] de ds = ( ) Na A E inel e Ce; inel total; (25)
10 446 B.T. Wong, M.P. Menguc / Journal of Quantitative Spectroscopy & Radiative Transfer 84 (2004) where E inel e coecient can be obtained by rearranging the above equation as is the average energy loss per inelastic scattering event. Therefore, the inelastic scattering ( Na ) C inel e; total: (26) e inel = 1 de E inel e ds = A In principle, accounting the amount of energy lost in the MCM for electron-beam processing as the ensemble of electrons propagates through a distance of interaction follows the same procedures as those in Section 3.2; except, is to be replaced by e inel. However, the attenuation calculation is often performed by rst determining the stopping power and then multiplying it by the distance of interaction to determine the amount of electron energy lost within the interval. One of the commonly used expressions for the stopping power is given by the modied Bethe relationship, which is expressed as [15] de ds = 78; 500 Z AE log e ( 1:166(E +0:85J ) J ) : (27) Here J, the mean ionization potential, is assumed to be available from the experiments [15]. The shortcoming of the Bethe relationship is that it incorrectly represents the stopping power at low electron energies (i.e., 1 kev). Recently, a compilation of the experimental data containing the stopping powers for most of the elements in the periodic table including compounds was presented by Joy [28]. These experimental data demonstrate a wider range of application in various electron energies, and they can be easily incorporated in a MCM which further improve the accuracy of MCM results. 5. Sample results from MCMs In the following sections a series of results obtained using MCMs are presented for plane-parallel media with a normal incident particle beam; all other assumptions are as stated in Section 3. The coordinate system is chosen such that the point of incidence of the beam is at the origin. The geometry is dened as a rectangular volume with X cr being the width and Y cr being the length. The upper boundary is considered to be at z = 0 while the lower boundary is located at z = Z cr, and r is dened as the radial distance from the origin. During the simulation, we assumed that X cr and Y cr approach innity MCM in radiative transfer The following results are for dierent incident beam proles and for a highly scattering medium (! =0:99) with an optical thickness of 2. The rst incident beam prole considered is an impulse function. The second one is a at beam prole with a radius of 1 mm (see [5,10]). The third case is a Gaussian beam prole with a 1=e 2 -radius of 1 mm (see [5,10]). Comparisons for these three cases reveal that their eects are primarily on the radial distributions of photons. (Note that several similar parametric study results can be presented; however, because of the space requirements we limit the discussion to only the phase function eects.) Absorptions of photons within media subject to three dierent beam proles are depicted in Fig. 4. The results are normalized with the total energy (or power) of the incident beam. The radiant energy
11 B.T. Wong, M.P. Menguc / Journal of Quantitative Spectroscopy & Radiative Transfer 84 (2004) Absorption x 10 3 (mm -3 ) (a) r (mm) z (mm) Absorption x 10 3 (mm -3 ) (b) 0 1 r (mm) z (mm) Absorption x 10 3 (mm -3 ) (c) 0 1 r (mm) z (mm) Fig. 4. Normalized absorption contours (with the total energy or power of the incident beam) in units of ( 10 3 =mm 3 ) for dierent incident beam proles: (a) impulse incident beam at r = 0, (b) at incident beam with a radius of 1 mm, and (c) Gaussian incident beam with a 1=e 2 radius of 1 mm, in isotropic scattering media with! =0:99, = 2, and Z cr = 2 mm.
12 448 B.T. Wong, M.P. Menguc / Journal of Quantitative Spectroscopy & Radiative Transfer 84 (2004) Deposition x 10 9 (nm -3 ) (a) r (nm) z (nm) Deposition x 10 9 (nm -3 ) (b) r (nm) z (nm) Fig. 5. The normalized deposition (with the total energy or power of the incident beam) of electron energies within gold in units of ( 10 9 =nm 3 ) for an applied voltage of 20 kv. An incident Gaussian beam of a 1=e 2 -radius of 25nm is considered in the MCM simulations. (a) Rutherford, and (b) Mott scattering cross sections. The solid in each case is innite in thickness. absorbed is in much concentrated area when impulse beam prole is considered. On the other hand, the at beam case has the largest diusion of the energy absorbed. Note that the energy absorbed as a function of z (i.e., after integrating over r) is the same for all three cases. If we were to evaluate the absorption in terms of temperature, the impulse case would have the highest temperature at the upper boundary, followed by the Gaussian case, and nally the at beam case MCM in electron-beam processing Fig. 5 depicts the depositions of electron energies due to the electron bombardments between propagating electrons and lattices of solid, as obtained using the Rutherford and the Mott scattering
13 B.T. Wong, M.P. Menguc / Journal of Quantitative Spectroscopy & Radiative Transfer 84 (2004) cross sections (see Section 4.1). The voltage applied in these cases is 20 kv. Both gures have the same level of contour divisions, indicating that the grey shadings have the same values, correspondingly. The energies of the incident electrons are 20 kev, which is considered to be suciently high for using the Rutherford cross section without signicant errors. This is evident from the gures as one can observe that the deposition contours in both cases are similar. An increase in the applied voltage denitely increases the validity of using the Rutherford cross section while a decrease certainly requires the use of the Mott cross section in the MC simulation. 6. Conclusions The use of the laser and electron beams as diagnostic tools has been the focal point in many research areas. Due to the in-scattering nature of the particle transport, obtaining analytical solutions to the transport equation is considered to be extremely dicult; therefore, statistical methods such as Monte Carlo methods (MCM) are generally used. In this paper, the MCMs for the radiative transfer equation (RTE) and the electron transport equation (ETE) have been discussed. Since both governing equations are derived from the Boltzmann transport equation (BTE) they share the common simulation procedures except that each needs dierent scattering probabilities and properties. Details on how to obtain these scattering probabilities and properties are presented. The problem considered here is relatively simple where the boundaries are transparent and the medium is homogeneous. The treatment of the mismatched boundaries for the radiative transfer, i.e. dierent refractive indices between the surroundings and the medium, is not discussed in this context. However, they can be found in Refs. [6,10]. Also, the electron scatterings at the interface between two dierent solids are not considered here. It should be noted that MCMs generally assume the wavelengths of the particles are small compared to the characteristic length of the object of interest. Should this condition be violated the problem is to be solved using wave theories. Acknowledgements This work is supported by an NSF Nanoscale Interdisciplinary Research Team (NIRT) award from the Nano Manufacturing program in Design, Manufacturing, and Industrial Innovation (DMI ). In addition, Basil T. Wong is supported by a TVA fellowship during this study. References [1] Howell JR. Application of Monte Carlo to heat transfer problems. In: Hartnett JP, Irvine TF, editors. Advances in heat transfer. vol. 5. New York: Academic Press; [2] Modest MF. Radiative heat transfer, 2nd ed. New York: Academic Press; [3] Flock ST, Patterson MS, Wilson BC, Wyman DR. Monte Carlo modeling of light propagation in highly scattering tissues I: model predictions and comparison with diusion theory. IEEE Trans Med Eng 1989;36: [4] Hasegawa Y, Yamada Y, Tamura M, Nomura Y. Monte Carlo simulation of light transmission through living tissues. Appl Opt 1991;30:4515. [5] Jacques SL, Wang L. Monte Carlo modeling of light transport in tissues. In: Welch Gemert V, editor. Optical-thermal response of laser-irradiated tissue. New York: Plenum Press; p
14 450 B.T. Wong, M.P. Menguc / Journal of Quantitative Spectroscopy & Radiative Transfer 84 (2004) [6] Wang L, Jacques SL, Zheng L. Mcml-Monte Carlo modeling of light transport in multi-layered tissues. Comput Method Programs Biomed 1995;47: [7] Yamada Y. Light-tissue interaction and optical imaging in biomedicine. In: Tien CL, editor. Annual review of uid mechanics and heat transfer. New York: Begell House; p [8] Fowler A, Menguc MP. Propagation of focussed and multibeam laser energy in biological tissues. ASME J Biomech Eng 2000;122: [9] Walters DV, Buckius RO. Monte Carlo methods for radiative heat transfer in scattering media. In: Annual review of heat transfer. vol p [10] Wong BT. Monte Carlo techniques for the solution of the transient and steady radiative transfer equation. Master s thesis, Mechanical Engineering, University of Kentucky, Lexington, [11] Wong BT, Menguc MP. Comparison of Monte Carlo techniques to predict the propagation of a collimated beam in participating media. Numer Heat Transfer, Part B 2002;42: [12] Kotera M. A Monte Carlo simulation of primary and secondary electron trajectories in a specimen. J Appl Phys 1989;65(10): [13] Shimizu R, Ikuta T, Murata K. The Monte Carlo technique as applied to the fundamentals of Epma and Sem. J Appl Phys 1972;43: [14] Martinez JD, Mayol R, Salvat F. Monte Carlo simulation of kilovolt electron transport in solids. J Appl Phys 1990;67(6): [15] Joy DC. Monte Carlo modeling for electron microscopy and microanalysis. New York: Oxford University Press; [16] Yasuda M, Tamura K, Kawata H, Murata K, Kotera M. A Monte Carlo study of spin-polarized electron backscattering from gold thin lms. Nucl Instrum Methods Phys Res B 2001;183: [17] Kim SH, Ham YM, Lee WY, Chun KJ. New approach of Monte Carlo simulation for low energy electron lithography. Microelectron Eng 1998;41/42: [18] Ashcroft NW, Mermin ND. Solid state physics. Philadelphia: Saunders Company; [19] Ziman JM. Electrons and phonons. London: Oxford University Press; [20] Ziman JM. Principles of the theory of solids. Cambridge: Cambridge University Press; [21] Ferry DK, Goodnick SM. Transport in nanostructures. New York: Cambridge University Press; [22] Siegel R, Howell JR. Thermal radiation heat transfer. New York: Taylor & Francis; [23] Brewster MQ. Thermal radiative transfer and properties. New York: Wiley-Interscience; [24] Menguc MP, Viskanta R. Comparison of radiative transfer approximations for a highly forward scattering planar medium. JQSRT 1983;29(5): [25] Barkstorm BR. An ecient algorithm for choosing scattering directions in Monte Carlo work with arbitrary phase functions. JQSRT 1995;53(1): [26] Czyzewski Z, MacCalium DON, Romig A, Joy DC. Calculations of Mott scattering cross section. J Appl Phys 1990;68(7): [27] Egerton RF. Electron energy loss spectrometry in the electron microscope. New York: Plenum Press; [28] Joy DC. A database of electron-solid interactions srcutk/.
Equivalent isotropic scattering formulation for transient
Equivalent isotropic scattering formulation for transient short-pulse radiative transfer in anisotropic scattering planar media Zhixiong Guo and Sunil Kumar An isotropic scaling formulation is evaluated
More informationMultiple-source optical diffusion approximation for a multilayer scattering medium
Multiple-source optical diffusion approximation for a multilayer scattering medium Joseph. Hollmann 1 and ihong V. Wang 1,2, * 1 Optical Imaging aboratory, Department of Biomedical Engineering, Texas A&M
More informationDiscrete-ordinates solution of short-pulsed laser transport in two-dimensional turbid media
Discrete-ordinates solution of short-pulsed laser transport in two-dimensional turbid media Zhixiong Guo and Sunil Kumar The discrete-ordinates method is formulated to solve transient radiative transfer
More informationULTRAFAST LASER PULSE TRAIN RADIATION TRANSFER IN A SCATTERING-ABSORBING 3D MEDIUM WITH AN INHOMOGENEITY
Heat Transfer Research 46(9), 861 879 (2015) ULTRAFAST LASER PULSE TRAIN RADIATION TRANSFER IN A SCATTERING-ABSORBING 3D MEDIUM WITH AN INHOMOGENEITY Masato Akamatsu 1,* & Zhixiong Guo 2 1 Graduate School
More informationMonte Carlo study of medium-energy electron penetration in aluminium and silver
NUKLEONIKA 015;60():361366 doi: 10.1515/nuka-015-0035 ORIGINAL PAPER Monte Carlo study of medium-energy electron penetration in aluminium and silver Asuman Aydın, Ali Peker Abstract. Monte Carlo simulations
More informationLeonid A. Dombrovsky. Institute for High Temperatures of the Russian Academy of Sciences, Krasnokazarmennaya 17A, Moscow , Russia
Journal of Quantitative Spectroscopy & Radiative Transfer 7 ) 4 44 www.elsevier.com/locate/jqsrt A modied dierential approximation for thermal radiation of semitransparent nonisothermal particles: application
More informationMCRT L10: Scattering and clarification of astronomy/medical terminology
MCRT L10: Scattering and clarification of astronomy/medical terminology What does the scattering? Shape of scattering Sampling from scattering phase functions Co-ordinate frames Refractive index changes
More informationobject objective lens eyepiece lens
Advancing Physics G495 June 2015 SET #1 ANSWERS Field and Particle Pictures Seeing with electrons The compound optical microscope Q1. Before attempting this question it may be helpful to review ray diagram
More informationLaser Beam Interactions with Solids In absorbing materials photons deposit energy hc λ. h λ. p =
Laser Beam Interactions with Solids In absorbing materials photons deposit energy E = hv = hc λ where h = Plank's constant = 6.63 x 10-34 J s c = speed of light Also photons also transfer momentum p p
More informationImprovement of computational time in radiative heat transfer of three-dimensional participating media using the radiation element method
Journal of Quantitative Spectroscopy & Radiative Transfer 73 (2002) 239 248 www.elsevier.com/locate/jqsrt Improvement of computational time in radiative heat transfer of three-dimensional participating
More informationMT Electron microscopy Scanning electron microscopy and electron probe microanalysis
MT-0.6026 Electron microscopy Scanning electron microscopy and electron probe microanalysis Eero Haimi Research Manager Outline 1. Introduction Basics of scanning electron microscopy (SEM) and electron
More informationRadiation in the atmosphere
Radiation in the atmosphere Flux and intensity Blackbody radiation in a nutshell Solar constant Interaction of radiation with matter Absorption of solar radiation Scattering Radiative transfer Irradiance
More informationDepth Distribution Functions of Secondary Electron Production and Emission
Depth Distribution Functions of Secondary Electron Production and Emission Z.J. Ding*, Y.G. Li, R.G. Zeng, S.F. Mao, P. Zhang and Z.M. Zhang Hefei National Laboratory for Physical Sciences at Microscale
More informationIntroduction to modeling of thermal radiation in participating gases
Project Report 2008 MVK 160 Heat and Mass Transfer May 07, 2008, Lund, Sweden Introduction to modeling of thermal radiation in participating gases Eric Månsson Dept. of Energy Sciences, Faculty of Engineering,
More informationFundamentals on light scattering, absorption and thermal radiation, and its relation to the vector radiative transfer equation
Fundamentals on light scattering, absorption and thermal radiation, and its relation to the vector radiative transfer equation Klaus Jockers November 11, 2014 Max-Planck-Institut für Sonnensystemforschung
More informationAnalysis of Scattering of Radiation in a Plane-Parallel Atmosphere. Stephanie M. Carney ES 299r May 23, 2007
Analysis of Scattering of Radiation in a Plane-Parallel Atmosphere Stephanie M. Carney ES 299r May 23, 27 TABLE OF CONTENTS. INTRODUCTION... 2. DEFINITION OF PHYSICAL QUANTITIES... 3. DERIVATION OF EQUATION
More informationThe Monte Carlo Simulation of Secondary Electrons Excitation in the Resist PMMA
Applied Physics Research; Vol. 6, No. 3; 204 ISSN 96-9639 E-ISSN 96-9647 Published by Canadian Center of Science and Education The Monte Carlo Simulation of Secondary Electrons Excitation in the Resist
More informationp(θ,φ,θ,φ) = we have: Thus:
1. Scattering RT Calculations We come spinning out of nothingness, scattering stars like dust. - Jalal ad-din Rumi (Persian Poet, 1207-1273) We ve considered solutions to the radiative transfer equation
More informationAdaptability analysis of radiative transport diffusion approximation in planar-graded-index media
Research Article Adaptability analysis of radiative transport diffusion approximation in planar-graded-index media Advances in Mechanical Engineering 2018, ol. 10(11) 1 6 Ó The Author(s) 2018 DOI: 10.1177/1687814018809613
More informationLecture 20 Optical Characterization 2
Lecture 20 Optical Characterization 2 Schroder: Chapters 2, 7, 10 1/68 Announcements Homework 5/6: Is online now. Due Wednesday May 30th at 10:00am. I will return it the following Wednesday (6 th June).
More informationSTOCHASTIC & DETERMINISTIC SOLVERS
STOCHASTIC & DETERMINISTIC SOLVERS Outline Spatial Scales of Optical Technologies & Mathematical Models Prototype RTE Problems 1-D Transport in Slab Geometry: Exact Solution Stochastic Models: Monte Carlo
More informationMonte Carlo Sampling
Monte Carlo Sampling Sampling from PDFs: given F(x) in analytic or tabulated form, generate a random number ξ in the range (0,1) and solve the equation to get the randomly sampled value X X ξ = F(x)dx
More informationTheoretical Analysis of Thermal Damage in Biological Tissues Caused by Laser Irradiation
Copyright c 007 Tech Science Press MCB, vol.4, no., pp.7-39, 007 Theoretical Analysis of Thermal Damage in Biological Tissues Caused by Laser Irradiation Jianhua Zhou,J.K.Chen and Yuwen Zhang Abstract:
More informationLichtausbreitung in streuenden Medien: Prinzip und Anwendungsbeispiele
Lichtausbreitung in streuenden Medien: Prinzip und Anwendungsbeispiele Alwin Kienle 06.12.2013 Institut für Lasertechnologien in der Medizin und Meßtechnik an der Universität Ulm Overview 1) Theory of
More informationA model of the optical properties of a non-absorbing media with application to thermotropic materials for overheat protection
Available online at wwwsciencedirectcom Energy Procedia 30 (2012 ) 116 124 SHC 2012 A model of the optical properties of a non-absorbing media with application to thermotropic materials for overheat protection
More informationEXPERIMENTAL AND NUMERICAL STUDIES OF SHORT PULSE PROPAGATION IN MODEL SYSTEMS
Proceedings of 22 ASME International Mechanical Engineering Congress and Exposition November 17 22, 22, New Orleans, Louisiana IMECE22-3393 EXPERIMENTAL AND NUMERICAL STUDIES OF SHORT PULSE PROPAGATION
More informationThermal Effect Behavior of Materials under Scanning Electron Microscopy. Monte Carlo and Molecular Dynamics Hybrid Model.
RESEARCH AND REVIEWS: JOURNAL OF MATERIAL SCIENCES Thermal Effect Behavior of Materials under Scanning Electron Microscopy. Monte Carlo and Molecular Dynamics Hybrid Model. Abdelkader Nouiri* Material
More information22.54 Neutron Interactions and Applications (Spring 2004) Chapter 1 (2/3/04) Overview -- Interactions, Distributions, Cross Sections, Applications
.54 Neutron Interactions and Applications (Spring 004) Chapter 1 (/3/04) Overview -- Interactions, Distributions, Cross Sections, Applications There are many references in the vast literature on nuclear
More informationMonte Carlo Methods:
Short Course on Computational Monte Carlo Methods: Fundamentals Shuang Zhao Assistant Professor Computer Science Department University of California, Irvine Shuang Zhao 1 Teaching Objective Introducing
More informationMaximum time-resolved hemispherical reflectance of absorbing and isotropically scattering media
Journal of Quantitative Spectroscopy & Radiative Transfer 14 (27) 384 399 www.elsevier.com/locate/jqsrt Maximum time-resolved hemispherical reflectance of absorbing and isotropically scattering media Kyle
More informationMultiple scattering of light by water cloud droplets with external and internal mixing of black carbon aerosols
Chin. Phys. B Vol. 21, No. 5 (212) 5424 Multiple scattering of light by water cloud droplets with external and internal mixing of black carbon aerosols Wang Hai-Hua( 王海华 ) and Sun Xian-Ming( 孙贤明 ) School
More informationPhD Thesis. Nuclear processes in intense laser eld. Dániel Péter Kis. PhD Thesis summary
PhD Thesis Nuclear processes in intense laser eld PhD Thesis summary Dániel Péter Kis BME Budapest, 2013 1 Background Since the creation of the rst laser light, there has been a massive progress in the
More information5. LIGHT MICROSCOPY Abbe s theory of imaging
5. LIGHT MICROSCOPY. We use Fourier optics to describe coherent image formation, imaging obtained by illuminating the specimen with spatially coherent light. We define resolution, contrast, and phase-sensitive
More informationUsing BATSE to Measure. Gamma-Ray Burst Polarization. M. McConnell, D. Forrest, W.T. Vestrand and M. Finger y
Using BATSE to Measure Gamma-Ray Burst Polarization M. McConnell, D. Forrest, W.T. Vestrand and M. Finger y University of New Hampshire, Durham, New Hampshire 03824 y Marshall Space Flight Center, Huntsville,
More informationPreface to the Second Edition. Preface to the First Edition
Contents Preface to the Second Edition Preface to the First Edition iii v 1 Introduction 1 1.1 Relevance for Climate and Weather........... 1 1.1.1 Solar Radiation.................. 2 1.1.2 Thermal Infrared
More informationDynamics that trigger/inhibit cluster formation in a one-dimensional granular gas
Physica A 342 (24) 62 68 www.elsevier.com/locate/physa Dynamics that trigger/inhibit cluster formation in a one-dimensional granular gas Jose Miguel Pasini a;1, Patricio Cordero b; ;2 a Department of Theoretical
More informationRidge analysis of mixture response surfaces
Statistics & Probability Letters 48 (2000) 3 40 Ridge analysis of mixture response surfaces Norman R. Draper a;, Friedrich Pukelsheim b a Department of Statistics, University of Wisconsin, 20 West Dayton
More informationAnalytical Chemistry II
Analytical Chemistry II L4: Signal processing (selected slides) Computers in analytical chemistry Data acquisition Printing final results Data processing Data storage Graphical display https://www.creativecontrast.com/formal-revolution-of-computer.html
More informationPhysics of Radiotherapy. Lecture II: Interaction of Ionizing Radiation With Matter
Physics of Radiotherapy Lecture II: Interaction of Ionizing Radiation With Matter Charge Particle Interaction Energetic charged particles interact with matter by electrical forces and lose kinetic energy
More information= 6 (1/ nm) So what is probability of finding electron tunneled into a barrier 3 ev high?
STM STM With a scanning tunneling microscope, images of surfaces with atomic resolution can be readily obtained. An STM uses quantum tunneling of electrons to map the density of electrons on the surface
More informationBasic structure of SEM
Table of contents Basis structure of SEM SEM imaging modes Comparison of ordinary SEM and FESEM Electron behavior Electron matter interaction o Elastic interaction o Inelastic interaction o Interaction
More informationHIGH ENERGY ASTROPHYSICS - Lecture 7. PD Frank Rieger ITA & MPIK Heidelberg Wednesday
HIGH ENERGY ASTROPHYSICS - Lecture 7 PD Frank Rieger ITA & MPIK Heidelberg Wednesday 1 (Inverse) Compton Scattering 1 Overview Compton Scattering, polarised and unpolarised light Di erential cross-section
More informationMCSHAPE: A MONTE CARLO CODE FOR SIMULATION OF POLARIZED PHOTON TRANSPORT
Copyright JCPDS - International Centre for Diffraction Data 2003, Advances in X-ray Analysis, Volume 46. 363 MCSHAPE: A MONTE CARLO CODE FOR SIMULATION OF POLARIZED PHOTON TRANSPORT J.E. Fernández, V.
More informationAnalysis of second-harmonic generation microscopy under refractive index mismatch
Vol 16 No 11, November 27 c 27 Chin. Phys. Soc. 19-1963/27/16(11/3285-5 Chinese Physics and IOP Publishing Ltd Analysis of second-harmonic generation microscopy under refractive index mismatch Wang Xiang-Hui(
More informationLecture 06. Fundamentals of Lidar Remote Sensing (4) Physical Processes in Lidar
Lecture 06. Fundamentals of Lidar Remote Sensing (4) Physical Processes in Lidar Physical processes in lidar (continued) Doppler effect (Doppler shift and broadening) Boltzmann distribution Reflection
More informationA successive order of scattering model for solving vector radiative transfer in the atmosphere
Journal of Quantitative Spectroscopy & Radiative Transfer 87 (2004) 243 259 www.elsevier.com/locate/jqsrt A successive order of scattering model for solving vector radiative transfer in the atmosphere
More informationApplied Nuclear Physics (Fall 2006) Lecture 19 (11/22/06) Gamma Interactions: Compton Scattering
.101 Applied Nuclear Physics (Fall 006) Lecture 19 (11//06) Gamma Interactions: Compton Scattering References: R. D. Evans, Atomic Nucleus (McGraw-Hill New York, 1955), Chaps 3 5.. W. E. Meyerhof, Elements
More informationSince the beam from the JNC linac is a very high current, low energy beam, energy loss induced in the material irradiated by the beam becomes very lar
Proceedings of the Second International Workshop on EGS, 8.-12. August 2000, Tsukuba, Japan KEK Proceedings 200-20, pp.255-263 Beam Dump for High Current Electron Beam at JNC H. Takei and Y. Takeda 1 Japan
More informationLecture 6 Scattering theory Partial Wave Analysis. SS2011: Introduction to Nuclear and Particle Physics, Part 2 2
Lecture 6 Scattering theory Partial Wave Analysis SS2011: Introduction to Nuclear and Particle Physics, Part 2 2 1 The Born approximation for the differential cross section is valid if the interaction
More informationChapter V: Interactions of neutrons with matter
Chapter V: Interactions of neutrons with matter 1 Content of the chapter Introduction Interaction processes Interaction cross sections Moderation and neutrons path For more details see «Physique des Réacteurs
More informationCHARGED PARTICLE INTERACTIONS
CHARGED PARTICLE INTERACTIONS Background Charged Particles Heavy charged particles Charged particles with Mass > m e α, proton, deuteron, heavy ion (e.g., C +, Fe + ), fission fragment, muon, etc. α is
More informationIndo-German Winter Academy
Indo-German Winter Academy - 2007 Radiation in Non-Participating and Participating Media Tutor Prof. S. C. Mishra Technology Guwahati Chemical Engineering Technology Guwahati 1 Outline Importance of thermal
More informationSimulation of Plume-Spacecraft Interaction
Simulation of Plume-Spacecraft Interaction MATÍAS WARTELSKI Master of Science Thesis in Space Physics Examiner: Prof. Lars Blomberg Space and Plasma Physics School of Electrical Engineering Royal Institute
More informationHigh-Resolution. Transmission. Electron Microscopy
Part 4 High-Resolution Transmission Electron Microscopy 186 Significance high-resolution transmission electron microscopy (HRTEM): resolve object details smaller than 1nm (10 9 m) image the interior of
More informationFemtosecond laser-tissue interactions. G. Fibich. University of California, Los Angeles, Department of Mathematics ABSTRACT
Femtosecond laser-tissue interactions G. Fibich University of California, Los Angeles, Department of Mathematics Los-Angeles, CA 90095 ABSTRACT Time dispersion plays an important role in the propagation
More informationSecondary Ion Mass Spectrometry (SIMS)
CHEM53200: Lecture 10 Secondary Ion Mass Spectrometry (SIMS) Major reference: Surface Analysis Edited by J. C. Vickerman (1997). 1 Primary particles may be: Secondary particles can be e s, neutral species
More informationψ( ) k (r) which take the asymtotic form far away from the scattering center: k (r) = E kψ (±) φ k (r) = e ikr
Scattering Theory Consider scattering of two particles in the center of mass frame, or equivalently scattering of a single particle from a potential V (r), which becomes zero suciently fast as r. The initial
More informationHT NORMALIZATION FOR ULTRAFAST RADIATIVE TRANSFER ANALYSIS WITH COLLIMATED IRRADIATION
Proceedings of the ASME 2012 Summer Heat Transfer Conference HT2012 July 8-12, 2012, Rio Grande, Puerto Rico HT2012-58307 NORMALIZATION FOR ULTRAFAST RADIATIVE TRANSFER ANALYSIS WITH COLLIMATED IRRADIATION
More informationA general theory of discrete ltering. for LES in complex geometry. By Oleg V. Vasilyev AND Thomas S. Lund
Center for Turbulence Research Annual Research Briefs 997 67 A general theory of discrete ltering for ES in complex geometry By Oleg V. Vasilyev AND Thomas S. und. Motivation and objectives In large eddy
More informationMonte Carlo simulation of Secondary Electron Yield for Noble metals Martina Azzolini, Nicola M. Pugno, Simone Taioli, Maurizio Dapor
Monte Carlo simulation of Secondary Electron Yield for Noble metals Martina Azzolini, Nicola M. Pugno, Simone Taioli, Maurizio Dapor ECLOUD 18 - Elba Island- 3-7 June 2018 OUTLINE Description of the Monte
More informationPhysics sources of noise in ring imaging Cherenkov detectors
Nuclear Instruments and Methods in Physics Research A 433 (1999) 235}239 Physics sources of noise in ring imaging Cherenkov detectors For the ALICE HMPID Group Andreas Morsch EP Division, CERN, CH-1211
More informationMonte Carlo Based Calculation of Electron Transport Properties in Bulk InAs, AlAs and InAlAs
Bulg. J. Phys. 37 (2010) 215 222 Monte Carlo Based Calculation of Electron Transport Properties in Bulk InAs, AlAs and InAlAs H. Arabshahi 1, S. Golafrooz 2 1 Department of Physics, Ferdowsi University
More informationFrequency domain photon migration in the -P 1 approximation: Analysis of ballistic, transport, and diffuse regimes
Frequency domain photon migration in the -P 1 approximation: Analysis of ballistic, transport, and diffuse regimes J. S. You, 1,2 C. K. Hayakawa, 2 and V. Venugopalan 1,2,3, * 1 Department of Biomedical
More informationAuger Electron Spectroscopy
Auger Electron Spectroscopy Auger Electron Spectroscopy is an analytical technique that provides compositional information on the top few monolayers of material. Detect all elements above He Detection
More informationExperimental confirmation of the negentropic character of the diffraction polarization of diffuse radiation
Experimental confirmation of the negentropic character of the diffraction polarization of diffuse radiation V. V. Savukov In the course of analyzing the axiomatic principles on which statistical physics
More informationToday, I will present the first of two lectures on neutron interactions.
Today, I will present the first of two lectures on neutron interactions. I first need to acknowledge that these two lectures were based on lectures presented previously in Med Phys I by Dr Howell. 1 Before
More information(a) Mono-absorber. (b) 4-segmented absorbers. (c) 64-segmented absorbers
Proceedings of the Ninth EGS4 Users' Meeting in Japan, KEK Proceedings 2001-22, p.37-42 EVALUATION OF ABSORPTION EFFICIENCY FOR NIS TUNNEL JUNCTION DETECTOR WITH SEGMENTED ABSORBERS R. Nouchi, I. Yamada,
More informationTHEORY OF FIELD-ALTERED NUCLEAR BETA DECAY
Paul Scherrer Institute 12 March 2012 THEORY OF FIELD-ALTERED NUCLEAR BETA DECAY H. R. Reiss 1 OUTLINE Intent of the investigation Subject of the investigation Qualitative requirements Continuous operation
More informationElectromagnetic fields and waves
Electromagnetic fields and waves Maxwell s rainbow Outline Maxwell s equations Plane waves Pulses and group velocity Polarization of light Transmission and reflection at an interface Macroscopic Maxwell
More informationX-ray uorescence, X-ray powder diraction and Raman spectrosopy
X-ray uorescence, X-ray powder diraction and Raman spectrosopy Wubulikasimu Yibulayin, Lovro Pavleti, Kuerbannisa Muhetaer 12.05.2016. Abstract In this report we report about the experiments that were
More informationMie theory for light scattering by a spherical particle in an absorbing medium
Mie theory for light scattering by a spherical particle in an absorbing medium Qiang Fu and Wenbo Sun Analytic equations are developed for the single-scattering properties of a spherical particle embedded
More informationh p λ = mν Back to de Broglie and the electron as a wave you will learn more about this Equation in CHEM* 2060
Back to de Broglie and the electron as a wave λ = mν h = h p you will learn more about this Equation in CHEM* 2060 We will soon see that the energies (speed for now if you like) of the electrons in the
More informationEDS User School. Principles of Electron Beam Microanalysis
EDS User School Principles of Electron Beam Microanalysis Outline 1.) Beam-specimen interactions 2.) EDS spectra: Origin of Bremsstrahlung and characteristic peaks 3.) Moseley s law 4.) Characteristic
More informationInteractions with Matter
Manetic Lenses Manetic fields can displace electrons Manetic field can be produced by passin an electrical current throuh coils of wire Manetic field strenth can be increased by usin a soft ferromanetic
More information4. Inelastic Scattering
1 4. Inelastic Scattering Some inelastic scattering processes A vast range of inelastic scattering processes can occur during illumination of a specimen with a highenergy electron beam. In principle, many
More informationThe interaction of radiation with matter
Basic Detection Techniques 2009-2010 http://www.astro.rug.nl/~peletier/detectiontechniques.html Detection of energetic particles and gamma rays The interaction of radiation with matter Peter Dendooven
More informationA small object is placed a distance 2.0 cm from a thin convex lens. The focal length of the lens is 5.0 cm.
TC [66 marks] This question is about a converging (convex) lens. A small object is placed a distance 2.0 cm from a thin convex lens. The focal length of the lens is 5.0 cm. (i) Deduce the magnification
More informationNeutron Interactions Part I. Rebecca M. Howell, Ph.D. Radiation Physics Y2.5321
Neutron Interactions Part I Rebecca M. Howell, Ph.D. Radiation Physics rhowell@mdanderson.org Y2.5321 Why do we as Medical Physicists care about neutrons? Neutrons in Radiation Therapy Neutron Therapy
More informationWhat Makes a Laser Light Amplification by Stimulated Emission of Radiation Main Requirements of the Laser Laser Gain Medium (provides the light
What Makes a Laser Light Amplification by Stimulated Emission of Radiation Main Requirements of the Laser Laser Gain Medium (provides the light amplification) Optical Resonator Cavity (greatly increase
More informationStudy of absorption and re-emission processes in a ternary liquid scintillation system *
CPC(HEP & NP), 2010, 34(11): 1724 1728 Chinese Physics C Vol. 34, No. 11, Nov., 2010 Study of absorption and re-emission processes in a ternary liquid scintillation system * XIAO Hua-Lin( ) 1;1) LI Xiao-Bo(
More informationM.Dapor, R.C.Masters, I.Ross, D.Lidzey, A.Pearson, I.Abril, R.Garcia-Molina, J.Sharp, M.Unčovský, T.Vystavel, C.Rodenburg
Comparison between Experimental Measurement and Monte Carlo Simulation of the Secondary Electron Energy Spectrum of Poly methylmethacrylate (PMMA) and Poly(3- hexylthiophene-2,5-diyl) M.Dapor, R.C.Masters,
More informationName : Roll No. :.. Invigilator s Signature :.. CS/B.Tech/SEM-2/PH-201/2010 2010 ENGINEERING PHYSICS Time Allotted : 3 Hours Full Marks : 70 The figures in the margin indicate full marks. Candidates are
More informationX-ray Interaction with Matter
X-ray Interaction with Matter 10-526-197 Rhodes Module 2 Interaction with Matter kv & mas Peak kilovoltage (kvp) controls Quality, or penetrating power, Limited effects on quantity or number of photons
More informationESSENTIAL QUANTUM PHYSICS PETER LANDSHOFF. University of Cambridge ALLEN METHERELL. University of Central Florida GARETH REES. University of Cambridge
ESSENTIAL QUANTUM PHYSICS PETER LANDSHOFF University of Cambridge ALLEN METHERELL University of Central Florida GARETH REES University of Cambridge CAMBRIDGE UNIVERSITY PRESS Constants of quantum physics
More informationProblem Set 3: Solutions
PH 53 / LeClair Spring 013 Problem Set 3: Solutions 1. In an experiment to find the value of h, light at wavelengths 18 and 431 nm were shone on a clean sodium surface. The potentials that stopped the
More informationLaser Optics-II. ME 677: Laser Material Processing Instructor: Ramesh Singh 1
Laser Optics-II 1 Outline Absorption Modes Irradiance Reflectivity/Absorption Absorption coefficient will vary with the same effects as the reflectivity For opaque materials: reflectivity = 1 - absorptivity
More informationA FEM STUDY ON THE INFLUENCE OF THE GEOMETRIC CHARACTERISTICS OF METALLIC FILMS IRRADIATED BY NANOSECOND LASER PULSES
8 th GRACM International Congress on Computational Mechanics Volos, 12 July 15 July 2015 A FEM STUDY ON THE INFLUENCE OF THE GEOMETRIC CHARACTERISTICS OF METALLIC FILMS IRRADIATED BY NANOSECOND LASER PULSES
More information2. Passage of Radiation Through Matter
2. Passage of Radiation Through Matter Passage of Radiation Through Matter: Contents Energy Loss of Heavy Charged Particles by Atomic Collision (addendum) Cherenkov Radiation Energy loss of Electrons and
More informationPhase-function normalization for accurate analysis of ultrafast collimated radiative transfer
Phase-function normalization for accurate analysis of ultrafast collimated radiative transfer Brian Hunter and hixiong Guo* Department of Mechanical and Aerospace Engineering, Rutgers, the State University
More informationvan Quantum tot Molecuul
10 HC10: Molecular and vibrational spectroscopy van Quantum tot Molecuul Dr Juan Rojo VU Amsterdam and Nikhef Theory Group http://www.juanrojo.com/ j.rojo@vu.nl Molecular and Vibrational Spectroscopy Based
More informationInteraction of Particles and Matter
MORE CHAPTER 11, #7 Interaction of Particles and Matter In this More section we will discuss briefly the main interactions of charged particles, neutrons, and photons with matter. Understanding these interactions
More informationROINN NA FISICE Department of Physics
ROINN NA FISICE Department of 1.1 Astrophysics Telescopes Profs Gabuzda & Callanan 1.2 Astrophysics Faraday Rotation Prof. Gabuzda 1.3 Laser Spectroscopy Cavity Enhanced Absorption Spectroscopy Prof. Ruth
More informationThe Compton Effect. Martha Buckley MIT Department of Physics, Cambridge, MA (Dated: November 26, 2002)
The Compton Effect Martha Buckley MIT Department of Physics, Cambridge, MA 02139 marthab@mit.edu (Dated: November 26, 2002) We measured the angular dependence of the energies of 661.6 kev photons scattered
More information1 Fundamentals of laser energy absorption
1 Fundamentals of laser energy absorption 1.1 Classical electromagnetic-theory concepts 1.1.1 Electric and magnetic properties of materials Electric and magnetic fields can exert forces directly on atoms
More informationBasic physics Questions
Chapter1 Basic physics Questions S. Ilyas 1. Which of the following statements regarding protons are correct? a. They have a negative charge b. They are equal to the number of electrons in a non-ionized
More informationExact radiation trapping force calculation based on vectorial diffraction theory
Exact radiation trapping force calculation based on vectorial diffraction theory Djenan Ganic, Xiaosong Gan, and Min Gu Centre for Micro-Photonics, School of Biophysical Sciences and Electrical Engineering
More informationWe have seen how the Brems and Characteristic interactions work when electrons are accelerated by kilovolts and the electrons impact on the target
We have seen how the Brems and Characteristic interactions work when electrons are accelerated by kilovolts and the electrons impact on the target focal spot. This discussion will center over how x-ray
More informationElectron Microscopy I
Characterization of Catalysts and Surfaces Characterization Techniques in Heterogeneous Catalysis Electron Microscopy I Introduction Properties of electrons Electron-matter interactions and their applications
More informationThe Wave Nature of Matter *
OpenStax-CNX module: m42576 1 The Wave Nature of Matter * OpenStax This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 3.0 Abstract Describe the Davisson-Germer
More informationHOW TO APPROACH SCANNING ELECTRON MICROSCOPY AND ENERGY DISPERSIVE SPECTROSCOPY ANALYSIS. SCSAM Short Course Amir Avishai
HOW TO APPROACH SCANNING ELECTRON MICROSCOPY AND ENERGY DISPERSIVE SPECTROSCOPY ANALYSIS SCSAM Short Course Amir Avishai RESEARCH QUESTIONS Sea Shell Cast Iron EDS+SE Fe Cr C Objective Ability to ask the
More information