scholarly journals Применение формулы Донкина в теории отражающих и поворотных устройств

2019 ◽  
Vol 89 (12) ◽  
pp. 1947
Author(s):  
Ю.К. Голиков ◽  
А.С. Бердников ◽  
А.С. Антонов ◽  
Н.К. Краснова ◽  
К.В. Соловьёв
Keyword(s):  
Electric Fields ◽  
Symmetry Plane ◽  
Optical Elements ◽  
Small Deviations ◽  
Similarity Principle ◽  
Beam Stability ◽  
Analytic Expressions ◽  
Electric Potentials ◽  
Direction Of Movement ◽  
Trajectory Similarity

Abstract Electrostatic turning devices are electron- and ion-optical elements changing the direction of movement of a parallel monochromatic beam of charged particles by a given angle without affecting a beam’s parallelism. The trajectory similarity principle for electric fields homogeneous in Euler terms ensures the fulfillment of this property for the fields with a homogeneity of a zero power. The Donkin formula for 3D homogeneous harmonic functions produces extremely wide class of analytic expressions describing homogeneous electric potentials of a zero power. This paper considers the algorithm of synthesis of electrostatic turning devices that transform input parallel monochromatic beams into output parallel monochromatic beams. The algorithm is based on the Donkin formula and ensures beam stability for small deviations from the electric field’s symmetry plane.

scholarly journals Buckling analysis of nano-scale magneto-electro-elastic plates using the nonlocal elasticity theory

2018 ◽  
Vol 10 (8) ◽  
pp. 168781401879333 ◽  
Author(s):  
Weon-Tae Park ◽  
Sung-Cheon Han
Keyword(s):  
Electric Fields ◽  
Constitutive Relations ◽  
Shear Deformation Theory ◽  
Nonlocal Elasticity Theory ◽  
Nonlocal Theory ◽  
Buckling Analysis ◽  
Numerical Results ◽  
Elastic Plates ◽  
Electric Boundary Condition ◽  
Electric Potentials

Buckling analysis of nonlocal magneto-electro-elastic nano-plate is investigated based on the higher-order shear deformation theory. The in-plane magnetic and electric fields can be ignored for magneto-electro-elastic nano-plates. According to magneto-electric boundary condition and Maxwell equation, the variation of magnetic and electric potentials along the thickness direction of the magneto-electro-elastic plate is determined. To reformulate the elastic theory of magneto-electro-elastic nano-plate, the nonlocal differential constitutive relations of Eringen is applied. Using the variational principle, the governing equations of the nonlocal theory are derived. The relations between local and nonlocal theories are studied by numerical results. Also, the effects of nonlocal parameters, in-plane load directions, and aspect ratio on buckling response are investigated. Numerical results show the effects of the electric and magnetic potentials. These numerical results can be useful in the design and analysis of advanced structures constructed from magneto-electro-elastic materials.

scholarly journals Simple Solutions of Lattice Sums for Electric Fields Due to Infinitely Many Parallel Line Charges

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1040
Author(s):  
Erik Vigren ◽  
Andreas Dieckmann
Keyword(s):  
Electric Fields ◽  
Elliptic Functions ◽  
Parallel Line ◽  
Closed Form Solutions ◽  
Lattice Sums ◽  
Duality Symmetry ◽  
Long Line ◽  
Arbitrary Position ◽  
Electric Potentials ◽  
Lemniscate Functions

We present surprisingly simple closed-form solutions for electric fields and electric potentials at arbitrary position ( x ,   y ) within a plane crossed by infinitely long line charges at regularly repeating positions using angular or elliptic functions with complex arguments. The lattice sums for the electric-field components and the electric potentials could be exactly solved, and the duality symmetry of trigonometric and lemniscate functions occurred in some solutions. The results may have relevance in calculating field configurations with rectangular boundary conditions. Several series related to Gauss’s constant are presented, established either as corollary results or via parallel investigations conducted in the spirit of experimental mathematics.

THE MONTE CARLO METHOD APPLIED TO CARRIER TRANSPORT IN Si/SiGe QUANTUM WELLS

2005 ◽  
Vol 19 (21) ◽  
pp. 3353-3377 ◽  
Author(s):  
V. A. VETTCHINKINA ◽  
A. BLOM ◽  
M. A. ODNOBLYUDOV
Keyword(s):  
Monte Carlo ◽  
Quantum Wells ◽  
Electric Fields ◽  
Carrier Transport ◽  
Impurity Scattering ◽  
Resonant Scattering ◽  
Interface Roughness ◽  
The Monte Carlo Method ◽  
Analytic Expressions ◽  
Different Temperatures

We present a complete Monte Carlo simulation of the transport properties of a Si/SiGe quantum well. The scattering mechanisms, viz. intervalley phonons, acoustic phonons, interface roughness and impurity scattering (including resonant scattering), are considered in detail, and we derive analytic expressions for the scattering rates, in each case properly taking the quantized electron wave functions into account. The numerically obtained distribution function is used to discuss the influence of each scattering mechanism for different electric fields applied parallel to the interfaces and also different temperatures.

scholarly journals Влияние магнитных и электрических полей на динамику образования плазмоидов в гатчинском разряде

2022 ◽  
Vol 92 (3) ◽  
pp. 366
Author(s):  
Shixin Zhao ◽  
Chengxun Yuan ◽  
А.А. Кудрявцев ◽  
Jingfeng Yao ◽  
Г.Д. Шабанов
Keyword(s):  
Magnetic Fields ◽  
Electric Fields ◽  
Electric Charge ◽  
Active Phase ◽  
Ball Lightning ◽  
Electric And Magnetic Fields ◽  
Direction Of Movement

The behavior in magnetic and electric fields of the Gatchina discharge, which is used mainly to create an analog of ball lightning in the laboratory in a normal atmosphere, is analyzed. Shown that in these studies it is possible to determine the sign of an uncompensated electric charge as in the active phase of the discharge, and in the forming long-lived luminous formations. Also shown that electric and magnetic fields can change the direction of movement of the forming luminous formation and even completely block its formation. The type and mechanism of existence firework ball lightning are considered, photos of which are presented in widely known monographs on the ball lightning.

scholarly journals Current-voltage and kinetic energy flux relations for relativistic field-aligned acceleration of auroral electrons

2006 ◽  
Vol 24 (1) ◽  
pp. 325-338 ◽  
Author(s):  
S. W. H. Cowley
Keyword(s):  
Kinetic Energy ◽  
Electric Fields ◽  
Energy Flux ◽  
Current Density ◽  
Source Population ◽  
Auroral Electron ◽  
Current Voltage ◽  
Auroral Electrons ◽  
Relativistic Regime ◽  
Analytic Expressions

Abstract. Recent spectroscopic observations of Jupiter's "main oval" auroras indicate that the primary auroral electron beam is routinely accelerated to energies of ~100 keV, and sometimes to several hundred keV, thus approaching the relativistic regime. This suggests the need to re-examine the classic non-relativistic theory of auroral electron acceleration by field-aligned electric fields first derived by Knight (1973), and to extend it to cover relativistic situations. In this paper we examine this problem for the case in which the source population is an isotropic Maxwellian, as also assumed by Knight, and derive exact analytic expressions for the field-aligned current density (number flux) and kinetic energy flux of the accelerated population, for arbitrary initial electron temperature, acceleration potential, and field strength beneath the acceleration region. We examine the limiting behaviours of these expressions, their regimes of validity, and their implications for auroral acceleration in planetary magnetospheres (and like astrophysical systems). In particular, we show that for relativistic accelerating potentials, the current density increases as the square of the minimum potential, rather than linearly as in the non-relativistic regime, while the kinetic energy flux then increases as the cube of the potential, rather than as the square.

scholarly journals Penetration of the electric fields of the geomagnetic sudden commencement over the globe as observed with the HF Doppler sounders and magnetometers

2021 ◽  
Vol 73 (1) ◽  
Author(s):  
Takashi Kikuchi ◽  
Jaroslav Chum ◽  
Ichiro Tomizawa ◽  
Kumiko K. Hashimoto ◽  
Keisuke Hosokawa ◽  
...  
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Sudden Commencement ◽  
Ionospheric Currents ◽  
Republic Of China ◽  
F Region ◽  
Electric And Magnetic Fields ◽  
Magnetometer Data ◽  
Electric Potentials ◽  
Geomagnetic Sudden Commencement

AbstractUsing the HF Doppler sounders at middle and low latitudes (Prague, Czech Republic; Tucuman, Argentina; Zhongli, Republic of China, and Sugadaira, Japan), we observed the electric fields of the geomagnetic sudden commencement (SC) propagating near-instantaneously (within 10 s) over the globe. We found that the electric fields of the preliminary impulse (PI) and main impulse (MI) of the SC are in opposite direction to each other and that the PI and MI electric fields are directed from the dusk to dawn and dawn to dusk, respectively, manifesting the nature of the curl-free potential electric field. We further found that the onset and peak of the PI electric field are simultaneous on the day and nightsides (0545, 1250, 1345 MLT) within the resolution of 10 s. With the magnetometer data, we confirmed the near-instantaneous development of the ionospheric currents from high latitudes to the equator and estimated the location of the field-aligned currents that supply the ionospheric currents. The global simultaneity of the electric and magnetic fields does not require the contribution of the magnetohydrodynamic waves in the magnetosphere nor in the F-region ionosphere. The global simultaneity and day–night asymmetry of the electric fields are explained with the ionospheric electric potentials transmitted at the speed of light by the TM0 mode waves in the Earth-ionosphere waveguide.

Exact solutions for the electron distribution in plane magnetrons

1965 ◽  
Vol 287 (1409) ◽  
pp. 183-200 ◽  
Keyword(s):  
Space Charge ◽  
Electric Fields ◽  
Stream Flow ◽  
Electron Distribution ◽  
Practical Interest ◽  
Space Charge Density ◽  
Complete Analysis ◽  
Field Variation ◽  
Self Consistent ◽  
Electric Potentials

The old problem of electron distribution in crossed electric and magnetic fields, such as exist in magnetrons, has in the past proved full of pitfalls, owing to the decisive influence which even very small initial electron velocities can have on the character of the solution. A complete analysis of the plane magnetron is presented, with a thermal emitter, i.e. with Maxwellian distribution of the initial velocities. Instead of looking for self-consistent solutions, which vary strongly with the space charge, the solution is given for three simple types of prescribed electric potentials, zero, linear and parabolic. The first two are mainly for orientation, the third is of practical interest as it is approximately self-consistent. For zero or weak electric fields the distribution is ‘triangular’, i.e. the function decreases monotonically as we move away from the cathode. For strong electric fields, the distribution has a peak away from the cathode and strongly resembles that obtained in the so called ‘double-stream’ flow. Finally, for a parabolic potential distribution (linear field variation) the space charge density exhibits a pronounced plateau which is highly reminiscent of the conditions in a Brillouin or ‘single-stream’ flow, although the electron motion is anything but rectilinear.

The breakdown of superfluidity in liquid 4 He V. Measurement of the Landau critical velocity for roton creation

1985 ◽  
Vol 315 (1532) ◽  
pp. 259-300 ◽  
Keyword(s):  
Critical Velocity ◽  
Electric Fields ◽  
High Pressures ◽  
Negative Ions ◽  
Pure Liquid ◽  
Small Deviations ◽  
Theoretical Predictions ◽  
The Matrix ◽  
Excitation Model

We report a precise experimental determination of the Landau critical velocity v L for roton creation in Hen. The technique used was based on measurements of the drift velocity, v , of negative ions through isotopically pure liquid 4 He at ca . 80 m K , under the influence of weak electric fields, E , for pressures, P , within the range 13 < P < 25 bar. It relied on the use of the equation ( v — v L ) oc E 1/3 , which is believed to correspond to the creation of rotons occurring predominantly in pairs and which fitted the experimental data to very high precision for E > 500 V m -1 . At lower values of E , however, small deviations from this equation were observed. These are tentatively attributed, not to the predicted onset of single-roton emission, but to a novel form of ion-vortex scattering. The values of v L ( P ) deduced from the measurements of v ( E ) at various pressures for E > 500 V m -1 agree to within 1.5% with theoretical predictions based on Landau’s excitation model of HeII, incorporating accepted numerical values of the roton parameters. The observed pressure dependence of v L ( P ) is significantly stronger than that predicted ; however, a discrepancy that appears to point towards the decreasing accuracy with which the roton parameters are known at high pressures. The modulus of the matrix element | V k0,k0 | characterizing roton-pair emission has also been deduced and is found to decrease rapidly with falling pressure. A linear extrapolation of the data suggests that | V k0,k0 | falls to zero at P « 3 bar (1 bar = 10 5 Pa).

Chondrocyte Translocation Response to Direct Current Electric Fields

2000 ◽  
Vol 122 (3) ◽  
pp. 261-267 ◽  
Author(s):  
Pen-Hsiu Grace Chao ◽  
Rani Roy ◽  
Robert L. Mauck ◽  
Wendy Liu ◽  
Wilmot B. Valhmu ◽  
...  
Keyword(s):  
Cell Migration ◽  
Electric Fields ◽  
Direct Current ◽  
Time Lapse ◽  
Field Application ◽  
The Novel ◽  
Cartilage Healing ◽  
Direction Of Movement ◽  
Chondrocyte Migration ◽  
Cytoplasmic Processes

Using a custom galvanotaxis chamber and time-lapse digital video microscopy, we report the novel observation that cultured chondrocytes exhibit cathodal migration when subjected to applied direct current (DC) electric fields as low as 0.8 V/cm. The response was dose-dependent for field strengths greater than 4 V/cm. Cell migration appeared to be an active process with extension of cytoplasmic processes in the direction of movement. In some cells, field application for greater than an hour induced elongation of initially round cells accompanied by perpendicular alignment of the long axis with respect to the applied field. Antagonists of the inositol phospholipid pathway, U-73122 and neomycin, were able to inhibit cathodal migration. Cell migration toward the cathode did not require the presence of serum during field application. However, the directed velocity was nearly threefold greater in studies performed with serum. Studies performed at physiologic temperatures ∼37°C revealed a twofold enhancement in migration speed compared to similar studies at room temperature ∼25°C. Findings from the present study may help to elucidate basic mechanisms that mediate chondrocyte migration and substrate attachment. Since chondrocyte migration has been implicated in cartilage healing, the ability to direct chondrocyte movement has the potential to impact strategies for addressing cartilage healing/repair and for development of cartilage substitutes. [S0148-0731(00)00803-7]

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