Classical harmonic oscillator approach of a helical-wiggler free-electron laserwith axial guide field

2000 ◽  
Vol 78 (12) ◽  
pp. 1069-1085 ◽  
Author(s):  
M N Rhimi ◽  
R El-Bahi ◽  
A W Cheikhrouhou
Keyword(s):  
Fixed Point ◽  
Free Electron ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Basic Feature ◽  
Operating Conditions ◽  
The Other ◽  
Guide Field ◽  
Constants Of Motion ◽  
Definition Of

Electron beam dynamics in a helical-wiggler free-electron laser (FEL) with a uniform axial guide magnetic field are studied using a three-dimensional Hamiltonian approach. The basic feature of the analysis is the definition of a rotational variable, [Formula: see text], that plays the primordial role in lowering to the half the dimension of the quadratic Hamiltonian as a system of two uncoupled oscillators with definite frequencies and amplitudes. It is through applying this variable in the vicinity of a fixed point that the Heisenberg picture of the dynamics of the particles comes to light, leading thus to the association of the steady-state ideal helical trajectories with arbitrary trajectories. The approach recognized the usual two constants of motion, one being the total energy while the other is the canonical axial angular momentum, Pz'. If the value of the latter is such that a fixed point exists, the Hamiltonian is expanded about the fixed point up to second order. The so-obtained oscillator characteristic frequencies allowed one to study the different modes of propagation and to identify, and then avoid the problematic operating conditions of the FEL concerned. On the other hand, the amplitudes of the oscillations, which do depend on the frequencies, are fortunately found to be constants of motion and then controlled by the boundary conditions (initial conditions). PACS Nos.: 52.40-w, 52.60+h, 42.55.Tb, 52.75Ms

Correction to a definition of negation

1984 ◽  
Vol 49 (1) ◽  
pp. 47-50 ◽  
Author(s):  
Frederic B. Fitch
Keyword(s):  
Fixed Point ◽  
Personal Communication ◽  
The Other ◽  
Transfinite Induction ◽  
Original Form ◽  
Basic Logic ◽  
Double Negation ◽  
Original Letter ◽  
The Law ◽  
Definition Of

In [3] a definition of negation was presented for the system K′ of extended basic logic [1], but it has since been shown by Peter Päppinghaus (personal communication) that this definition fails to give rise to the law of double negation as I claimed it did. The purpose of this note is to revise this defective definition in such a way that it clearly does give rise to the law of double negation, as well as to the other negation rules of K′.Although Päppinghaus's original letter to me was dated September 19, 1972, the matter has remained unresolved all this time. Only recently have I seen that there is a simple way to correct the definition. I am of course very grateful to Päppinghaus for pointing out my error in claiming to be able to derive the rule of double negation from the original form of the definition.The corrected definition will, as before, use fixed-point operators to give the effect of the required kind of transfinite induction, but this time a double transfinite induction will be used, somewhat like the double transfinite induction used in [5] to define simultaneously the theorems and antitheorems of system CΓ.

Darstellung und Kristallstruktur von K2Sb4S7 · H2O / Preparation and Crystal Structure of K2Sb4S7 · H2O

1979 ◽  
Vol 34 (3) ◽  
pp. 383-385 ◽  
Author(s):  
Brigitte Eisenmann ◽  
Herbert Schäfer
Keyword(s):  
Crystal Structure ◽  
Free Electron ◽  
Electron Pair ◽  
Three Dimensional ◽  
The Other ◽  
Water Molecules ◽  
Triclinic System ◽  
Dimensional Network ◽  
Free Electron Pair

Abstract K2Sb4S7 · H2O crystallizes in the triclinic system with a = 1171.4(5) pm, b = 952.0(5) pm, c = 715.6(5) pm and α = 99.36(5)°, β = 86.80(5)°, γ= 103.48(5)°. One half of the Sb atoms has three sulfur neighbours forming with the free electron pair a ψ-ShS3 tetrahedron, while the other half is coordinated by four S atoms to build a ψ-trigonal SbS4 bipyramid. These polyhedra are connected by common edges and corners to a three-dimensional network with two types of channels, in which either K+ ions only or K+ ions and water molecules are located.

Computational Studies on Charge Stratification and Fuel-Air Mixing in a New Two-Stroke Engine

2005 ◽  
Author(s):  
Shamit Bakshi ◽  
T. N. C. Anand ◽  
R. V. Ravikrishna
Keyword(s):  
Initial Conditions ◽  
Computational Study ◽  
Three Dimensional ◽  
The State ◽  
Operating Conditions ◽  
Injection System ◽  
Critical Parameters ◽  
Mixing Process ◽  
Air Mixing ◽  
Stroke Engine

In this paper, detailed computational study is presented which helps to understand and improve the fuel-air mixing in a new direct-mixture-injection two-stroke engine. This new air-assisted injection system-based two-stroke engine is being developed at the Indian Institute of Science, Bangalore over the past few years. It shows the potential to meet emission norms such as EURO-II and EURO-III and also deliver satisfactory performance. This work proposes a comprehensive strategy to study the air-fuel mixing process in this engine and shows that this strategy can be potentially used to improve the engine performance. A three-dimensional compressible flow code with standard k–ε turbulence model with wall functions is developed and used for this modeling. To account for the moving boundary or piston in the engine cylinder domain, a non-stationary and deforming grid is used in this region with stationary cells in the ports and connecting ducts. A flux conservation scheme is used in the domain interface to allow the in-cylinder moving mesh to slide past the fixed port meshes. The initial conditions for flow parameters are taken from the output of a three-dimensional scavenging simulation. The state of the inlet charge is obtained from a separate modeling of the air-assisted injection system of this engine. The simulation results show that a large, near-stoichiometric region is present at most operating conditions in the cylinder head plane. The state of the in-cylinder charge at the onset of ignition is studied leading to a good understanding of the mixing process. In addition, sensitivity of two critical parameters on the mixing and stratification is investigated. The suggested parameters substantially enhance the flammable proportion at the onset of combustion. The predicted P–θ from a combustion simulation supports this recommendation.

scholarly journals Distinctive features of the structure of current sheets formed in plasma in three-dimensional magnetic configurations with an X line (a review)

2021 ◽  
Vol 9 (6) ◽  
pp. 464-478
Author(s):  
Anna Frank
Keyword(s):  
Longitudinal Magnetic Field ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Limited Range ◽  
Transverse Plane ◽  
Plasma Current ◽  
Initial Value ◽  
Distinctive Features ◽  
Current Sheets ◽  
Guide Field

A review is presented on experimental results related to investigation of distinctive features of the structure and evolution of plasma current sheets formed in three dimensional (3D) magnetic configurations with an X line, in the presence of a longitudinal magnetic field component (guide field) directed along the X line. It is shown that formation of a plasma current sheet results in enhancement of the guide field within the sheet. The excessive guide field is maintained by plasma currents that flow in the transverse plane relative to the main current in the sheet. As a result, the structure of the currents becomes three-dimensional. Increasing the initial value of the guide field brings about a decrease of compression into the sheet of both the electric current and plasma. This effect is caused by changing the pres- sure balance in the sheet when an excessive guide field appears in it. Deformation of plasma current sheets in 3D magnetic configurations, namely, an appearance of asymmetric and tilted sheets, results from excitation of the Hall currents and their interaction with the guide field. It is shown that the formation of current sheets in 3D magnetic configurations with an X line is possible in a relatively wide, but limited range of initial conditions

Three-dimensional natural convection in a confined porous medium heated from below

1979 ◽  
Vol 92 (4) ◽  
pp. 751-766 ◽  
Author(s):  
Roland N. Horne
Keyword(s):  
Porous Medium ◽  
Energy Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Governing Equations ◽  
Flow Situation ◽  
Definition Of ◽  
The Relationship

Previous analyses of natural convection in a porous medium have drawn seemingly contradictory conclusions as to whether the motion is two- or three-dimensional. This investigation uses numerical results to show the relationship between previous contending observations, and demonstrates that there exists more than one mode of convection for any particular physical configuration and Rayleigh number. In some cases, a particular flow situation may be stable even though it does not maximize the energy transfer across the system.The methods used are based on the efficient numerical solution of the governing equations, formulated with the definition of a vector potential. This approach is shown to be superior to formulating the equations in terms of pressure.For a cubic region the flow pattern at a particular value of the Rayleigh number is not unique and is determined by the initial conditions. In some cases there exist four alternatives, two- and three-dimensional, steady and unsteady.

Characteristics of Discharge Coefficient in a Rotating Disk System

1999 ◽  
Vol 121 (4) ◽  
pp. 663-669 ◽  
Author(s):  
D. J. Maeng ◽  
J. S. Lee ◽  
R. Jakoby ◽  
S. Kim ◽  
S. Wittig
Keyword(s):  
Discharge Coefficient ◽  
Three Dimensional ◽  
Compressibility Factor ◽  
Rotating Disk ◽  
Operating Conditions ◽  
Disk System ◽  
Rotating System ◽  
Rotor Disk ◽  
Discharge Behavior ◽  
Definition Of

The discharge coefficient of a long orifice in a rotating system is measured to examine the rotational effect on discharge behavior. The rotating system is comprised of a rotating disk and two stators on both sides of the rotating disk. Test rig is constructed to simulate the real turbine operating conditions. Pressure ratios between upstream and downstream cavities of the orifice range from 1.05 to 1.8, and rotational speed of the rotor disk is varied up to 10,000 rpm. The orifice hole bored through the rotor disk has length-to-diameter ratio of 10. For a better interpretation of discharge behavior, three-dimensional velocity field in the downstream and upstream cavities of the rotor is measured using a Laser Doppler Velocimetry. A new definition of the rotational discharge coefficient is introduced to consider the momentum transfer from the rotor to the orifice flow. Additional loss in the discharge coefficient due to pressure loss in the orifice hole at the inlet and exit regions is quantitatively presented in terms of the Rotation number and the compressibility factor. The effect of corner radiusing at the orifice inlet is also investigated at various rotational conditions.

scholarly journals Characteristics of Discharge Coefficient in a Rotating Disk System

1998 ◽  
Author(s):  
D. J. Maeng ◽  
J. S. Lee ◽  
R. Jakoby ◽  
S. Kim ◽  
S. Wittig
Keyword(s):  
Discharge Coefficient ◽  
Three Dimensional ◽  
Compressibility Factor ◽  
Rotating Disk ◽  
Operating Conditions ◽  
Disk System ◽  
Rotating System ◽  
Rotor Disk ◽  
Discharge Behavior ◽  
Definition Of

The discharge coefficient of a long orifice in a rotating system is measured to examine the rotational effect on discharge behavior. The rotating system is comprised of a rotating disk and two stators on both sides of the rotating disk. Test rig is constructed to simulate the real turbine operating conditions. Pressure ratios between upstream and downstream cavities of the orifice range from 1.05 to 1.8, and rotational speed of the rotor disk is varied up to 10,000 rpm. The orifice hole bored through the rotor disk has length-to-diameter ratio of 10. For a better interpretation of discharge behavior, three-dimensional velocity field in the downstream and upstream cavities of the rotor is measured using a Laser Doppler Velocimetry. A new definition of the rotational discharge coefficient is introduced to consider the momentum transfer from the rotor to the orifice flow. Additional loss in the discharge coefficient due to pressure loss in the orifice hole at the inlet and exit regions is quantitatively presented in terms of the Rotation number and the compressibility factor. The effect of comer radiusing at the orifice inlet is also investigated at various rotational conditions.

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