# Boundary conditions for the solution of the three-dimensional Poisson equation in open metallic enclosures

## Abstract

Numerical solution of the Poisson equation in metallic enclosures, open at one or more ends, is important in many practical situations, such as high power microwave or photo-cathode devices. It requires imposition of a suitable boundary condition at the open end. In this paper, methods for solving the Poisson equation are investigated for various charge densities and aspect ratios of the open ends. It is found that a mixture of second order and third order local asymptotic boundary conditions is best suited for large aspect ratios, while a proposed non-local matching method, based on the solution of the Laplace equation, scores well when the aspect ratio is near unity for all charge density variations, including ones where the centre of charge is close to an open end or the charge density is non-localized. The two methods complement each other and can be used in electrostatic calculations where the computational domain needs to be terminated at the open boundaries of the metallic enclosure.

- Authors:

- Bhabha Atomic Research Centre, Mumbai 400085 (India)

- Publication Date:

- OSTI Identifier:
- 22493769

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 22; Journal Issue: 9; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ASPECT RATIO; BOUNDARY CONDITIONS; CHARGE DENSITY; LAPLACE EQUATION; MICROWAVE RADIATION; NUMERICAL SOLUTION; PHOTOCATHODES; POISSON EQUATION; THREE-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Biswas, Debabrata, Singh, Gaurav, and Kumar, Raghwendra.
```*Boundary conditions for the solution of the three-dimensional Poisson equation in open metallic enclosures*. United States: N. p., 2015.
Web. doi:10.1063/1.4931738.

```
Biswas, Debabrata, Singh, Gaurav, & Kumar, Raghwendra.
```*Boundary conditions for the solution of the three-dimensional Poisson equation in open metallic enclosures*. United States. doi:10.1063/1.4931738.

```
Biswas, Debabrata, Singh, Gaurav, and Kumar, Raghwendra. Tue .
"Boundary conditions for the solution of the three-dimensional Poisson equation in open metallic enclosures". United States. doi:10.1063/1.4931738.
```

```
@article{osti_22493769,
```

title = {Boundary conditions for the solution of the three-dimensional Poisson equation in open metallic enclosures},

author = {Biswas, Debabrata and Singh, Gaurav and Kumar, Raghwendra},

abstractNote = {Numerical solution of the Poisson equation in metallic enclosures, open at one or more ends, is important in many practical situations, such as high power microwave or photo-cathode devices. It requires imposition of a suitable boundary condition at the open end. In this paper, methods for solving the Poisson equation are investigated for various charge densities and aspect ratios of the open ends. It is found that a mixture of second order and third order local asymptotic boundary conditions is best suited for large aspect ratios, while a proposed non-local matching method, based on the solution of the Laplace equation, scores well when the aspect ratio is near unity for all charge density variations, including ones where the centre of charge is close to an open end or the charge density is non-localized. The two methods complement each other and can be used in electrostatic calculations where the computational domain needs to be terminated at the open boundaries of the metallic enclosure.},

doi = {10.1063/1.4931738},

journal = {Physics of Plasmas},

number = 9,

volume = 22,

place = {United States},

year = {Tue Sep 15 00:00:00 EDT 2015},

month = {Tue Sep 15 00:00:00 EDT 2015}

}