A first-order analytical investigation on emittance evolution of relativistic space-charge dominated beams

2006 ◽  
Vol 560 (2) ◽  
pp. 197-203 ◽  
Author(s):  
He Xiaozhong ◽  
Tang Chuanxiang ◽  
Huang Wenhui ◽  
Lin Yuzheng
Keyword(s):  
Space Charge ◽  
Analytical Investigation ◽  
First Order ◽  
Emittance Evolution

scholarly journals A Three Species Ecological Model with a Prey, Predator and Competitor to the Predator and Optimal Harvesting of the Prey

2012 ◽  
Vol 1 ◽  
pp. 21-32
Author(s):  
A.V. Papa Rao ◽  
K. Lakshmi Narayan ◽  
Shahnaz Bathul
Keyword(s):  
Ecological Model ◽  
Equilibrium Points ◽  
Single Species ◽  
Analytical Investigation ◽  
Optimal Harvesting ◽  
Stability Criteria ◽  
Linear Ordinary Differential Equations ◽  
First Order ◽  
Analytical Stability ◽  
The Stability

The present paper is devoted to an analytical investigation of three species ecological model with a Prey (N1), a predator (N2) and a competitor (N3) to the Predator without effecting the prey (N1). in addition to that, the species are provided with alternative food. The model is characterized by a set of first order non-linear ordinary differential equations. All the eight equilibrium points of the model are identified and local and global stabilitycriteria for the equilibrium states except fully washed out and single species existence are discussed. Further exact solutions of perturbed equations have been derived. The analytical stability criteria are supported by numerical simulations using mat lab. Further we discussed the effect of optimal harvesting on the stability.

First-order covariant treatment of the influence of space charge and external fields on finite-emittance relativistic beams of charged particles in generalized curvilinear coordinates

1989 ◽  
Vol 67 (7) ◽  
pp. 678-685
Author(s):  
Giulio Bosi
Keyword(s):  
Distribution Function ◽  
Space Charge ◽  
Charged Particles ◽  
Curvilinear Coordinates ◽  
Coordinate Space ◽  
Transverse Motion ◽  
Metric Tensor ◽  
First Order ◽  
Dimensional Phase Space ◽  
Principal Axes

A first-order covariant treatment of space-charge effects on relativistic beams of charged particles under the influence of applied fields of arbitrary forms is presented. The beams and fields are assumed to fulfill no particular symmetry conditions, and curvilinear orthogonal coordinates are used. Relative to a given distribution function, a suitable choice of both metric tensor and optical axis allows for the selection of appropriate coordinates, reducing the overall transverse motion of a charged particle to a pair of independent motions along the principal axes of a tensor that is related to both geometry and field. Detailed formulas applying to a microcanonical distribution in an eight-dimensional phase space are worked out, and the envelope equations for a monokinetic beam are carried out explicitly. The distribution function is shown to separate into the product of a stationary distribution in transverse-coordinate space and momentum space by using factors carrying the relativistic corrections. As a result, the envelope equations are formally identical to the customary equations describing the envelope of a nonrelativistic beam under the influence of merely transverse forces. A few numerical applications are finally presented; the behavior of beams moving through a magnetic prism and through a cycloidal analyzer is displayed graphically.

Die Raumladungsbremsung von Elektronenlawinen

1959 ◽  
Vol 14 (11) ◽  
pp. 989-994
Author(s):  
K. J. Schmidt-Tiedemann
Keyword(s):  
Electric Field ◽  
Space Charge ◽  
Electron Avalanche ◽  
Homogeneous Electric Field ◽  
First Order ◽  
Charge Field ◽  
The Common ◽  
Negative Space ◽  
Theoretical Results ◽  
First Order Perturbation

The electric field generated by the positive and negative space charge of a single electron avalanche moving in a homogeneous electric field is calculated. Treating the interaction of the avalanche with its own space charge field as a first order perturbation, a growth formula is obtained which differs markedly from the common TOWNSEND formula. The theoretical results fit well with experimental data on avalanche statistics reported in the literature.

Analysis, design and experimentation of high-pass negative group delay lumped circuit

Circuit World ◽  
2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Hongyu Du ◽  
Rong Yang ◽  
Taochen Gu ◽  
Xiang Zhou ◽  
Samar Yazdani ◽  
...  
Keyword(s):  
Printed Circuit Boards ◽  
Analytical Investigation ◽  
Experimental Investigations ◽  
Circuit Boards ◽  
Content Type ◽  
First Order ◽  
Optimal Values ◽  
Analysis Design ◽  
High Pass ◽  
Good Agreement

Purpose The purpose of this paper is to introduce an innovative theoretical, numerical and experimental investigations on the HP NGD function. The identified HP NGD topology under study is constituted by first order passive RC-network. The simulations and measurements confirm in very good agreement the HP NGD behaviors of the tested circuits. NGD responses with optimal values of about -1 ns and cut-off frequencies of about 20 MHz are obtained. Design/methodology/approach The identified HP NGD topology understudy is constituted by a first-order passive Resistor-capacitor RC network. An innovative approach to HP NGD analysis is developed. The analytical investigation from the voltage transfer function showing the meaning of HP properties is established. Findings This paper introduces innovative theoretical, numerical and experimental investigations on the HP NGD function. Originality/value The NGD characterization as a function of the resistance and capacitance parameters is investigated. The feasibility of the HP NGD function is verified with proofs of concept constituted of lumped surface mounted components on printed circuit boards. The simulations and measurements confirm in very good agreement the HP NGD behaviors of the tested circuits. NGD responses with optimal values of about −1 ns and cut-off frequencies of about 20 MHz are obtained.

First‐Order Space‐Charge Correction

1963 ◽  
Vol 34 (5) ◽  
pp. 1568-1569 ◽  
Author(s):  
D. S. Colburn ◽  
G. S. Kino
Keyword(s):  
Space Charge ◽  
First Order
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