Streamlined Darwin simulation of nonneutral plasmas

Hewett, D.W.; Boyd, J.K.

doi:10.1016/0021-9991(87)90007-6

Cited by 29 publications

(9 citation statements)

References 4 publications

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“…All the numerical studies of Darwin model to problems (ii) and (iii) in fact were carried on to this point and gave their own ways to manage it. D.W.Hewett and J.K.Boyd analyzed the solutions of Darwin model by streamline method in [3], and they discussed methods for calculating the magnetic field without formal vector decomposition and offered a new procedure for finding the inductive electric field. As a consequence, the numerical efforts required for each of the field time-steps are reduced, and more importantly, the needs to specify several nonintuitive boundary conditions are eliminated.…”

Section: Darwin Model and Its Numerical Methodsmentioning

confidence: 99%

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Darwin Approximation to Maxwell’s Equations

Fang

Liao

Ying

2009

Lecture Notes in Computer Science

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Abstract. Maxwell's equations are the foundation of electromagnetics, its extensive applications make computational electromagnetics a new rapidly growing subject. However, since the electric and the magnetic fields are coupling in the Maxwell system, the numerical solution of the full system of Maxwell's equations is extremely expensive in terms of computer time. Darwin model, which decouple the coupled system, is such a good approximation to Maxwell's equations. In three dimensional space case, it neglects the transverse component of the displacement current; while in two dimensional space case, Darwin model is equivalent to TE, TM models. For these reasons, it is worthwhile to investigate Darwin model, and a lot of works have been done to it. In this paper, we review the advance in the Darwin model and introduce some of our new results about the exterior problems of Darwin model and its numerical solutions with infinite elements methods.

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Section: Darwin Model and Its Numerical Methodsmentioning

confidence: 99%

“…Some earlier investigations have been done by D.W.Hewett and C.W.Nielson etc, please refer to [2,3,4] for a derivation of the Darwin model from the plasma point and its numerical implementation by streamline methods in two dimensional bounded domains.…”

Section: Introductionmentioning

confidence: 99%

Darwin Approximation to Maxwell’s Equations

Fang

Liao

Ying

2009

Lecture Notes in Computer Science

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“…Numerical simulations of increasingly sophisticated models are used in the design of electron guns: see [3], [5], [6], [9]. The most complete mathematical model is the boundary value problem for the relativistic Vlasov-Maxwell evolution equations in a geometrically complicated spatially three-dimensional domain.…”

Section: Introductionmentioning

confidence: 99%

A boundary‐value problem for the stationary vlasov‐poisson equations: The plane diode

Greengard¹,

Raviart

1990

Comm Pure Appl Math

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The stationary Vlasov-Poisson boundary value problem in a spatially one-dimensional domain is studied. The equations describe the flow of electrons in a plane diode. Existence is proved when the boundary condition (the cathode emission distribution) is a bounded function which decays superlinearly or a Dirac mass. Uniqueness is proved for (physically realistic) boundary conditions which are decreasing functions of the velocity variable. It is shown that uniqueness does not always hold for the Dirac mass boundary conditions. IntroductionThe construction of particle accelerators and free electron lasers requires electron guns which produce relativistic electron beams of high quality (low emittance and high current). Numerical simulations of increasingly sophisticated models are used in the design of electron guns: see Among these are the study of boundary conditions (which give rise to problems well known to physicists: the existence of a boundary layer near the cathode due to space-charge-limited currents, existence of wakes, etc.) and the study of the stationary equations.In this paper, we shall consider the most basic model-the stationary Vlasov-Poisson equations for classical electronic conduction in a plane diode. Although physically elementary, even this model contains difficulties due to space-charge limitation of the current, and so our study may be of value as a background for a study of the full multi-dimensional, time-dependent problem. In addition, the current paper is one of the few to include boundaries in a study of the Vlasov-Poisson equations (another discussion can be found in [S]).

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“…It is known that there are more and more scientific problems which involve the solutions of Maxwell's équations, e g , plasma physics, microwave devices, diffraction of electromagnetic waves In many cases, the numencal resolution of the full System of Maxwell's équations may be very expensive in terms of the computational cost However, for some problems, e g the simulation of charged particle beams when no high frequency phenomenon or no rapid current change occurs, it is possible to use some simphfied model which approximates Maxwell System in some sense and can be solved more economically The Darwin model is such a simplified model which is obtamed from Maxwell's équations by neglectmg the transverse component of the displacement current, see Hewett-Nielson [12], Hewett-Boyd [11] and Nielson-Lewis [17] Degond-Raviart [8] considered how to choose the boundary conditions so that the Darwm model is mathematically well-posed and charactenzed the electnc field and the magnetic field as the solutions of elhptic boundary value problems…”

Section: Introductionmentioning

confidence: 99%