Calculation of Coulomb energies for uniform charge distributions of arbitrary shape

Journal Article · Tue Jul 01 04:00:00 EDT 1975 · J. Comput. Phys., v. 18, no. 3, pp. 311-325

DOI:https://doi.org/10.1016/0021-9991(75)90005-4· OSTI ID:4156847

Davies, K T.R.; Sierk, A J

Three distinct surface-integral formulas are derived for calculating the Coulomb energies of uniform charge distributions of arbitrary shape. Of particular interest is an equation obtained by applying Gauss' divergence theorem twice. It is shown that this equation can be simply transformed to another expression which has been widely used for calculating Coulomb energies, with this derivation implying a third formula. The three formulas are also expressed in cylindrical coordinates for charge distributions possessing axial symmetry. For such shapes, numerical studies are presented showing the computational times and errors involved in calculating the Coulomb energies and generalized forces using Gaussian-Legendre quadrature formulas. It is shown that the double- divergence-derived formula is faster and more accurate than the other two surface- integral formulas and other formulas used in the literature. (auth)

• Research Organization: Los Alamos Scientific Lab., NM
• Sponsoring Organization: USDOE
• NSA Number: NSA-33-011049
• OSTI ID: 4156847
• Journal Information: J. Comput. Phys., v. 18, no. 3, pp. 311-325, Journal Name: J. Comput. Phys., v. 18, no. 3, pp. 311-325; ISSN JCTPA
• Country of Publication: United States
• Language: English

Related Subjects

*HEAVY ION REACTIONS-- COULOMB ENERGY
*NUCLEAR REACTIONS-- FISSION
643503*
CYLINDRICAL CONFIGURATION
DISTRIBUTION
ELECTRIC CHARGES
ERRORS
GAUSS FUNCTION
INTEGRALS
N69230* --Physics (Nuclear)--Nuclear Theory--Nuclear Reactions & Scattering
N69260 --Physics (Nuclear)--Nuclear Theory--Spontaneous & Induced Fission
SURFACES
SYMMETRY
TIME DEPENDENCE