scholarly journals Effective Angle of Synchrotron Radiation

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1095
Author(s):  
Vladislav Bagrov ◽  
Anna Kasatkina ◽  
Alexey Pecheritsyn
Keyword(s):  
Synchrotron Radiation ◽  
Symmetric Distribution ◽  
Classical Electrodynamics ◽  
Exact Asymptotics ◽  
Exact Analytical Expression ◽  
Instantaneous Power ◽  
Effective Angle ◽  
Ultrarelativistic Limit ◽  
Analytical Expressions ◽  
Arbitrary Energy

An exact analytical expression for the effective angle is determined for an arbitrary energy value of a radiating particle. An effective angle of instantaneous power is defined for synchrotron radiation in the framework of classical electrodynamics. This definition explicitly contains the most symmetric distribution of half the total of the instantaneous power of synchrotron radiation. Two exact analytical expressions for the effective angle are considered for the arbitrary energy values of a radiating particle, and the second expression brings to light the exact asymptotics of the effective angle in the ultrarelativistic limit.

scholarly journals Exact quasi-relativistic wavefunctions of Hydrogen-like atoms

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Luis Grave de Peralta
Keyword(s):  
Bound States ◽  
Relativistic Quantum ◽  
Quantum Mechanical ◽  
Solid State Physics ◽  
Mechanical Wave ◽  
Atomic Orbitals ◽  
Exact Analytical Expression ◽  
Quantum Particles ◽  
Software Packages ◽  
Analytical Expressions

Abstract Exact solutions of a novel quasi-relativistic quantum mechanical wave equation are found for Hydrogen-like atoms. This includes both, an exact analytical expression for the energies of the bound states, and exact analytical expressions for the wavefunctions, which successfully describe quantum particles with mass and spin-0 up to energies comparable to the energy associated to the mass of the particle. These quasi-relativistic atomic orbitals may be used for improving ab-initio software packages dedicated to numerical simulations in physical-chemistry and atomic and solid-state physics.

scholarly journals The influence of a thermal plasma on synchrotron radiation

1988 ◽  
Vol 6 (3) ◽  
pp. 421-436 ◽  
Author(s):  
A. Crusius
Keyword(s):  
Synchrotron Radiation ◽  
Energy Loss ◽  
Total Energy ◽  
Thermal Plasma ◽  
Large Scale ◽  
Lorentz Factor ◽  
Physical Parameters ◽  
Relativistic Electrons ◽  
Physical Conditions ◽  
Analytical Expressions

The synchrotron emission from relativistic electrons in a thermal plasma with large-scale random magnetic fields is considered. In this case, the spectral synchrotron power of a single electron can be given in closed form allowing exact analytical expressions for the synchrotron emissivity, absorption coefficient, intensity and total energy loss of particles to be derived. The influence of various physical parameters such as gas density, magnetic field strength, particle's Lorentz factor on the resulting emissivities, intensities and energy loss is discussed in detail. Below the Razin– Tsytovich frequency vR = 20 Hz (ne/l cm−3) (B/l Gauss)−1, the spectral appearance of synchrotron radiation both in the optically thin and thick case is quite different than the vacuum behaviour. Since in the quasar broad line regions, vR is of the order 1011 Hz the suppression of synchrotron radiation may explain why most quasars are radio quiet. Likewise, the necessary physical conditions for the occurrence of synchrotron masering in the optically thick case are given. We obtain optical depth |τ|>1 for compact nonthermal sources. The total energy loss of a single particle is shown to be exponentially reduced at Lorentz factors less than γR = 2·1. 10−3 (ne/1 cm−3)½ (B/1 Gauss)−1.

Analysis of instantaneous power components of electric circuit with a semiconductor element

2013 ◽  
Vol 62 (3) ◽  
pp. 473-486 ◽  
Author(s):  
M. Zagirnyak ◽  
A. Kalinov ◽  
M. Maliakova
Keyword(s):  
Electric Circuit ◽  
Analyze Power ◽  
Power Method ◽  
Electric Circuits ◽  
Instantaneous Power ◽  
Automated Method ◽  
Semiconductor Converter ◽  
Orthogonal Components ◽  
Harmonic Components ◽  
Analytical Expressions

Abstract Both a classical instantaneous power method and a method based on equations of instantaneous power orthogonal components balance have been used to analyze power processes in electric circuits with semiconductor elements. Automated method of forming instantaneous power harmonic components was used to obtain analytical expressions and numerical values of instantaneous power components of analyzed electric circuits. A coefficient for estimation of a semiconductor converter nonlinearity degree has been offered.

MULTIPOLE MATRIX ELEMENTS FOR DH-SYSTEMS AND THEIR ASYMPTOTICS

1995 ◽  
Vol 09 (20) ◽  
pp. 2699-2718 ◽  
Author(s):  
V.F. TARASOV
Keyword(s):  
Hydrogen Atom ◽  
Singular Point ◽  
Diagonal Matrix ◽  
New Method ◽  
Matrix Elements ◽  
Exact Asymptotics ◽  
Radial Functions ◽  
Quantum Numbers ◽  
Analytical Expressions ◽  
Math Phys

A “DH-system” is defined as a multidimensional hydrogen atom (or its one-particle analogue), D≥1. Investigating many Coulomb problems in ℝD it is necessary to know exact analytical expressions of multipole matrix elements <q|rk|q'>D for DH-systems, where q=(N, µ) is a set of parameters, N —"principal” and µ — "orbital” quantum numbers. The paper deals with the new method for the evaluation of similar matrix elements using new properties of Appell’s function F2(x, y) to the vicinity of the singular point (1, 1). Such approach allows: 1) to get exact analytical expressions of these matrix elements (considering the selection rules) by means of Appell’s F2 (or Clausen’s 3F2) functions; 2) to reveal “latent” symmetry of diagonal matrix elements with respect to the point k0=−3/2, the above symmetry is connected with the property of Appell’s function F2 (1,1) mirror-like symmetry; 3) to find (exact) asymptotics of the off-diagonal matrix elements in terms of Horn’s function ψ1 (x, y); 4) to prove that the orthogonality of radial functions fNµ (D, r) over N and μ for DH-systems is connected with the properties of Appell’s F2 function to the vicinity of the singular point (1, 1), it generalizes the known result for 3H-atom by Pasternack and Sternheimer, J. Math. Phys.3, 1280 (1962).

Synchrotron radiation of a magnetic moment in classical electrodynamics

1982 ◽  
Vol 25 (2) ◽  
pp. 83-87 ◽  
Author(s):  
I. M. Ternov ◽  
V. A. Bordovitsyn ◽  
G. K. Razina
Keyword(s):  
Synchrotron Radiation ◽  
Magnetic Moment ◽  
Classical Electrodynamics

Layered and ion implantation specimens as possible reference materials for the electron-probe microanalysis

1992 ◽  
Vol 50 (2) ◽  
pp. 1652-1653
Author(s):  
G. Remond ◽  
R.H. Packwood ◽  
C. Gilles ◽  
S. Chryssoulis
Keyword(s):  
Ion Implantation ◽  
Reference Materials ◽  
Analytical Techniques ◽  
Thin Film Deposition ◽  
Film Deposition ◽  
X Ray ◽  
Spatially Resolved ◽  
Analytical Expressions ◽  
Original Approach ◽  
Depth Concentration

Merits and limitations of layered and ion implanted specimens as possible reference materials to calibrate spatially resolved analytical techniques are discussed and illustrated for the case of gold analysis in minerals by means of x-ray spectrometry with the EPMA. To overcome the random heterogeneities of minerals, thin film deposition and ion implantation may offer an original approach to the manufacture of controlled concentration/ distribution reference materials for quantification of trace elements with the same matrix as the unknown.In order to evaluate the accuracy of data obtained by EPMA we have compared measured and calculated x-ray intensities for homogeneous and heterogeneous specimens. Au Lα and Au Mα x-ray intensities were recorded at various electron beam energies, and hence at various sampling depths, for gold coated and gold implanted specimens. X-ray intensity calculations are based on the use of analytical expressions for both the depth ionization Φ (ρz) and the depth concentration C (ρz) distributions respectively.

A Simple Real-Space Channelling Theory for Electron Diffraction and HREM

1990 ◽  
Vol 48 (1) ◽  
pp. 64-65
Author(s):  
D. Van Dyck
Keyword(s):  
High Resolution ◽  
Electron Diffraction ◽  
Direct Method ◽  
Real Space ◽  
Zone Axis ◽  
Phase Object ◽  
High Resolution Images ◽  
The Many ◽  
Analytical Expressions ◽  
Electron Wavefunction

The computation of the many beam dynamical electron diffraction amplitudes or high resolution images can only be done numerically by using rather sophisticated computer programs so that the physical insight in the diffraction progress is often lost. Furthermore, it is not likely that in this way the inverse problem can be solved exactly, i.e. to reconstruct the structure of the object from the knowledge of the wavefunction at its exit face, as is needed for a direct method [1]. For this purpose, analytical expressions for the electron wavefunction in real or reciprocal space are much more useful. However, the analytical expressions available at present are relatively poor approximations of the dynamical scattering which are only valid either for thin objects ((weak) phase object approximation, thick phase object approximation, kinematical theory) or when the number of beams is very limited (2 or 3). Both requirements are usually invalid for HREM of crystals. There is a need for an analytical expression of the dynamical electron wavefunction which applies for many beam diffraction in thicker crystals. It is well known that, when a crystal is viewed along a zone axis, i.e. parallel to the atom columns, the high resolution images often show a one-to-one correspondence with the configuration of columns provided the distance between the columns is large enough and the resolution of the instrument is sufficient. This is for instance the case in ordered alloys with a column structure [2,3]. From this, it can be suggested that, for a crystal viewed along a zone axis with sufficient separation between the columns, the wave function at the exit face does mainly depend on the projected structure, i.e. on the type of atom columns. Hence, the classical picture of electrons traversing the crystal as plane-like waves in the directions of the Bragg beams which historically stems from the X-ray diffraction picture, is in fact misleading.

Direct Observation of Monolayer Zones in Al-wt 4% Cu

1990 ◽  
Vol 48 (1) ◽  
pp. 14-15
Author(s):  
B. Jouffrey ◽  
D. Dorignac ◽  
A. Bourret
Keyword(s):  
Solid Solution ◽  
Synchrotron Radiation ◽  
Direct Observation ◽  
Supersaturated Solid Solution ◽  
Original Model ◽  
X Ray ◽  
Image Position

Since the early works on GP zones and the model independently proposed by Preston and Guinier on the first steps of precipitation in supersaturated solid solution of aluminium containing a few percent of copper, many works have been performed to understand the structure of different stages in the sequence of precipitation.The scheme which is generally admitted can be drawn from a work by Phillips.In their original model Guinier and Preston analysed a GP zone as composed of a single (100) copperrich plane surrounded by aluminum atomic planes with a slightly shorter distance from the original plane than in the solid solution.From X-ray measurements it has also been shown that GP1 zones were not only copper monolayer zones. They could be up to a few atomic planes thick. Different models were proposed by Guinier, Gerold, Toman. Using synchrotron radiation, proposals have been recently made.

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