scholarly journals NONLOCAL EQUATIONS FOR THE ELECTROMAGNETIC FIELD IN THE INHOMOGENEOUS ACCELERATING STRUCTURES

2019 ◽  
pp. 71-76
Author(s):  
M.I. Ayzatsky
Keyword(s):  
Magnetic Field ◽  
Difference Equation ◽  
Electric Field ◽  
Boundary Conditions ◽  
Good Accuracy ◽  
Nonlocal Model ◽  
Nonlocal Equations ◽  
The Difference ◽  
Set Of Points ◽  
Infinite Set

The procedure for obtaining a difference equation, the solution of which is the components of the electric (or magnetic) field at the chosen set of points in the volume of the resonator chain, was developed. We started with the wave equation with boundary conditions and obtained the difference equation without boundary conditions. Boundary conditions were included into the coefficients of the difference equation for the electric field. As the obtained equation connects the field values in different points (in general case, on an infinite set of points), the proposed procedure represents a nonlocal model for field description. Solutions of the difference equation for the electric field were analyzed. It was shown that they coincide with good accuracy with the ones that were obtained by direct summing of relevant series.

scholarly journals Storm-time ring current: model-dependent results

2012 ◽  
Vol 30 (1) ◽  
pp. 177-202 ◽  
Author(s):  
N. Yu. Ganushkina ◽  
M. W. Liemohn ◽  
T. I. Pulkkinen
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Boundary Conditions ◽  
Electric Fields ◽  
Ring Current ◽  
Current Model ◽  
Current Data ◽  
Storm Events ◽  
Boundary Location ◽  
Field Lines

Abstract. The main point of the paper is to investigate how much the modeled ring current depends on the representations of magnetic and electric fields and boundary conditions used in simulations. Two storm events, one moderate (SymH minimum of −120 nT) on 6–7 November 1997 and one intense (SymH minimum of −230 nT) on 21–22 October 1999, are modeled. A rather simple ring current model is employed, namely, the Inner Magnetosphere Particle Transport and Acceleration model (IMPTAM), in order to make the results most evident. Four different magnetic field and two electric field representations and four boundary conditions are used. We find that different combinations of the magnetic and electric field configurations and boundary conditions result in very different modeled ring current, and, therefore, the physical conclusions based on simulation results can differ significantly. A time-dependent boundary outside of 6.6 RE gives a possibility to take into account the particles in the transition region (between dipole and stretched field lines) forming partial ring current and near-Earth tail current in that region. Calculating the model SymH* by Biot-Savart's law instead of the widely used Dessler-Parker-Sckopke (DPS) relation gives larger and more realistic values, since the currents are calculated in the regions with nondipolar magnetic field. Therefore, the boundary location and the method of SymH* calculation are of key importance for ring current data-model comparisons to be correctly interpreted.

Boundary Conditions and Initial Value Lines for Unsteady Homentropic Flow Calculations

1970 ◽  
Vol 21 (2) ◽  
pp. 145-162 ◽  
Author(s):  
W. A. Woods ◽  
H. Daneshyar
Keyword(s):  
Boundary Condition ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Good Accuracy ◽  
Numerical Calculations ◽  
Time Dependent ◽  
Straight Pipe ◽  
Initial Value ◽  
Use Of Time ◽  
The Difference

SummaryA detailed discussion on the difference between an initial value line and a line characterised by a boundary condition has been presented. Two types of boundaries are described and illustrated. To examine each boundary, several different calculations have been performed for a straight pipe. The results of the numerical calculations are compared with an analytical solution. It is shown that known pressure and velocity at the pipe ends give the most accurate results. Comparisons are also made between several practical types of calculations which give similar findings. The use of time-dependent boundaries can lead to errors as large as 40 per cent in derived results. It is shown that good accuracy can be restored by converting the boundaries into initial value lines. It is concluded that in general no more than one time-dependent boundary should be used in any calculation. Finally it is demonstrated that errors are not revealed by means of pressure diagrams alone.

The effect of surface-charge convection on the settling velocity of spherical drops in a uniform electric field

2016 ◽  
Vol 797 ◽  
pp. 536-548 ◽  
Author(s):  
Ehud Yariv ◽  
Yaniv Almog
Keyword(s):  
Difference Equation ◽  
Electric Field ◽  
Surface Charge ◽  
Settling Velocity ◽  
Numerical Solutions ◽  
Weak Field ◽  
Uniform Electric Field ◽  
Electrostatic Problem ◽  
Settling Speed ◽  
The Difference

The mechanism of surface-charge convection, quantified by the electric Reynolds number $Re$, renders the Melcher–Taylor electrohydrodynamic model inherently nonlinear, with the electrostatic problem coupled to the flow. Because of this nonlinear coupling, the settling speed of a drop under a uniform electric field differs from that in its absence. This difference was calculated by Xu & Homsy (J. Fluid Mech., vol. 564, 2006, pp. 395–414) assuming small $Re$. We here address the same problem using a different route, considering the case where the applied electric field is weak in the sense that the magnitude of the associated electrohydrodynamic velocity is small compared with the settling velocity. As convection is determined at leading order by the well-known flow associated with pure settling, the electrostatic problem becomes linear for arbitrary value of $Re$. The electrohydrodynamic correction to the settling speed is then provided as a linear functional of the electric-stress distribution associated with that problem. Calculation of the settling speed eventually amounts to the solution of a difference equation governing the respective coefficients in a spherical harmonics expansion of the electric potential. It is shown that, despite the present weak-field assumption, our model reproduces the small-$Re$ approximation of Xu and Homsy as a particular case. For finite $Re$, inspection of the difference equation reveals a singularity at the critical $Re$-value $4S(1+R)(1+M)/(1+S)M$, wherein $R$, $S$ and $M$ respectively denote the ratios of resistivity, permittivity and viscosity values in the suspending and drop phases, as defined by Melcher & Taylor (Annu. Rev. Fluid Mech., vol. 1, 1969, pp. 111–146). Straightforward numerical solutions of this equation for electric Reynolds numbers smaller than the critical value reveal a non-monotonic dependence of the settling speed upon the electric field magnitude, including a transition from velocity enhancement to velocity decrement.

The theory of inoizing shock waves in a magnetic field. Part 1. Skew and oblique shock waves, boundary conditions and ionization stability

1981 ◽  
Vol 26 (1) ◽  
pp. 29-53 ◽  
Author(s):  
M. A. Liberman ◽  
A. L. Velikovich
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Shock Waves ◽  
Electric Field ◽  
Boundary Conditions ◽  
Wave Front ◽  
Shock Wave Front ◽  
Neutral Gas ◽  
Supersonic Shock ◽  
Photo Ionization

The general theory of ionizing shock waves in a magnetic field has been constructed. The theory takes into account precursor ionization of a neutral gas ahead of the shock wave front, caused by photo-ionization, as well as by the impact ionization with electrons accelerated by a transverse electric field induced by the shock front in the incident flow of a neutral gas. The concept of shock wave ionization stability, being basic in the theory of ionizing shock waves in a magnetic field, is introduced. An additional equation for the electric field in the shock wave is obtained. This equation, together with the investigation of the singular point in the downstream flow behind the shock wave front, provides all the information required for solving the problem. For example, this provides two additional boundary conditions for the shock waves of type 2, determining the value and direction of the electric field in the incident flow. One additional boundary condition determines a relation between the value and direction of the electric field for supersonic shock waves of type 3. There are no additional boundary conditions for supersonic shock waves of type 4. The electric field ahead of the shock front has two degrees of freedom. As well as for shocks of other types, its value is less than that of the transverse electric field at which an ionization wave could be emitted by the shock wave front (the ionization stability condition). The additional relationship for supersonic waves of type 4 determines the onset of an isomagnetic (viscous) jump in the structure of the shock wave front. The boundary conditions and ionizing shock wave structures, considered earlier by the authors of the present paper in the ‘limit of electrostatic breakdown’, as well as the structural determination of the electric field, considered earlier by Leonard, are limiting cases in the theory developed here. The ionizing shock wave structures are shown to transform from the GD regime at a low shock velocity to the MHD regime at an enhanced intensity of the shock wave. The abruptness of such a transition (e.g. the transition width on the Mach number scale) is determined by precursor photo-ionization.

Light Mixing and the Generation of the Second Harmonic in a Plasma in an External Magnetic Field

1965 ◽  
Vol 20 (6) ◽  
pp. 793-800 ◽  
Author(s):  
Wilhelm H. Kegel
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
External Electric Field ◽  
Second Harmonic ◽  
Scattered Light ◽  
Homogeneous Magnetic Field ◽  
Density Fluctuations ◽  
Wave Number ◽  
The Difference ◽  
Electron Gyrofrequency

The theory of light scattering in a plasma is extended by including an external electric field (e.g. the field of a laser beam) in calculating the density fluctuations. It is shown that in the presence of a time constant homogeneous magnetic field there arise density fluctuations with the frequency and the wave number of the external electric field. Expansions of the general expressions are obtained for the case that the frequency is large compared to the electron gyrofrequency. The special case that the external electric field is a transverse wave is discussed in detail.The light of a second beam may be scattered by these forced density fluctuations. The scattered light has the sum and the difference frequency of the two light beams, i.e. light mixing occurs. In the framework of this theory the effect occurs only if the two beams are parallel. - If one considers the scattering of the same beam that forces the density fluctuations, the scattered light is the second harmonic

On the Field-Induced Cholesteric-Nematic Transition in Cholesteric Liquid Crystals with Homeotropic Boundary Conditions

1983 ◽  
Vol 38 (1) ◽  
pp. 1-9 ◽  
Author(s):  
J. Brokx ◽  
G. Vertogen ◽  
E. W. C. van Groesen
Keyword(s):  
Magnetic Field ◽  
Liquid Crystals ◽  
Boundary Conditions ◽  
Difference Method ◽  
Lagrange Equation ◽  
Helix Axis ◽  
Cholesteric Liquid Crystals ◽  
Director Field ◽  
Fréedericksz Transition ◽  
The Difference

Abstract The influence of homeotropic boundary conditions on the cholesteric-nematic transition is discussed, starting from the assumption that the director field consists of only components perpendicular to the helix axis, which is directed parallel to the boundary planes. Attention is paid to the solution of Cladis and Kléman for the simpler case without magnetic field. Their solution, consisting of regularly spaced line signularities, is derived in another more transparent way. Besides it is shown that even director fields without singularities are possible. The presence of a magnetic field complicates the solution considerably. Now the relevant Euler-Lagrange equation is solved in an approximate way by partly resorting to the difference method. The usefulness of the method is demonstrated by applying this technique to the nematic-cholesteric transition and the Fréedericksz transition in nematics.

The Impact of Boundary Conditions on the Response of NiMnGa Samples in Actuation and Power Harvesting Applications

2013 ◽  
Author(s):  
Isaac Nelson ◽  
Constantin Ciocanel ◽  
Doug LaMaster ◽  
Heidi Feigenbaum
Keyword(s):  
Magnetic Field ◽  
Boundary Conditions ◽  
Cross Section ◽  
Effective Length ◽  
Power Harvesting ◽  
Simply Supported ◽  
Voltage Output ◽  
The Cross ◽  
The Difference ◽  
The Impact

Magnetic shape memory alloys (MSMAs) are materials that can display up to 10% recoverable strain in response to the application of a magnetic field or compressive mechanical stress. The magnetomechanical response of the material makes MSMAs suitable for applications such as actuation, sensing, and power harvesting. While the magnetomechanical response of the material has been extensively investigated to date, there is no report in the literature on the effect of the boundary conditions (BCs) on its response. The response of MSMAs is primarily driven by the reorientation of internal martensite variants, in conjunction with rotation of magnetization vectors, and domain wall motion. During the reorientation process a change in material’s magnetization occurs. For sensing and power harvesting applications, a pick-up coil may be used to convert this change in magnetization into an electric potential/voltage. To date, it has been confirmed experimentally that, according to Faraday’s law of induction, the magnitude of the output voltage depends on the number of turns of the pick-up coil, the amplitude of the reorientation strain, the magnitude and direction of the biased magnetic field, and the frequency at which the reorientation occurs. However, to our knowledge, no study has been carried out to investigate the effect of the BCs on the voltage output. This paper examines the effect of the BCs on the material’s magnetomechanical response, as well as on the corresponding voltage output. Three BCs are considered in the performed experiments: i) simply supported, ii) clamped, and iii) mixed (i.e. one end clamped and one end guided). The difference observed in the magnetomechanical response of the material, between the tested BCs, is attributed to the local effects caused by the grips (particularly the clamped and mixed conditions) and by the rotation of the specimen within the grips (in the simply supported condition). The latter is facilitated by the difference between the cross section of the specimen and the cross section of the cavity receiving the sample and by the larger effective length of the specimen in this case.

PEMANFAATAN RADIASI ENERGI TEGANGAN 150 KV UNTUK LAMPU LED PENERANGAN JALAN

Jurnal Teknik ◽  
2018 ◽  
Vol 7 (1) ◽  
Author(s):  
Mauludi Manfaluthy
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
High Voltage ◽  
Low Frequency ◽  
Energy Utilization ◽  
World Health ◽  
Electromagnetic Signals ◽  
Health Organization ◽  
The Magnetic Field ◽  
Low Frequency Waves

WHO (World Health Organization) concludes that not much effect is caused by electric field up to 20 kV / m in humans. WHO standard also mentions that humans will not be affected by the magnetic field under  100 micro tesla and that the electric field will affect the human body with a maximum standard of 5,000 volts per meter. In this study did not discuss about the effect of high voltage radiation SUTT (High Voltage Air Channel) with human health. The research will focus on energy utilization of SUTT radiation. The combination of electric field and magnetic field on SUTT (70-150KV) can generate electromagnetic (EM) and radiation waves, which are expected to be converted to turn on street lights around the location of high voltage areas or into other forms. The design of this prototype works like an antenna in general that captures electromagnetic signals and converts them into AC waves. With a capacitor that can store the potential energy of AC and Schottky diode waves created specifically for low frequency waves, make the current into one direction (DC). From the research results obtained the current generated from the radiation is very small even though the voltage is big enough.Keywords : Radiance Energy, Joule Thief, and  LED Module.

scholarly journals Mode Shape-Based Damage Detection Method (MSDI): Experimental Validation

2021 ◽  
Vol 11 (10) ◽  
pp. 4589
Author(s):  
Ivan Duvnjak ◽  
Domagoj Damjanović ◽  
Marko Bartolac ◽  
Ana Skender
Keyword(s):  
Boundary Conditions ◽  
Damage Detection ◽  
Mode Shape ◽  
Experimental Validation ◽  
Detection Method ◽  
Dynamic Properties ◽  
Damage Index ◽  
Main Principle ◽  
The Difference ◽  
Different Levels

The main principle of vibration-based damage detection in structures is to interpret the changes in dynamic properties of the structure as indicators of damage. In this study, the mode shape damage index (MSDI) method was used to identify discrete damages in plate-like structures. This damage index is based on the difference between modified modal displacements in the undamaged and damaged state of the structure. In order to assess the advantages and limitations of the proposed algorithm, we performed experimental modal analysis on a reinforced concrete (RC) plate under 10 different damage cases. The MSDI values were calculated through considering single and/or multiple damage locations, different levels of damage, and boundary conditions. The experimental results confirmed that the MSDI method can be used to detect the existence of damage, identify single and/or multiple damage locations, and estimate damage severity in the case of single discrete damage.

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