Orbiting Scalar Charges

Gabrielle Allen

\( \)Date\( \)

Abstract

1 Introduction

This thorn provides a source term to the scalar field evolution for two rotating binary charges.

2 Physical System

The 3D scalar wave equation with a source term \(\rho (t,x,y,z)\) is written

∇ ϕ = 4πρ

Each scalar source with charge \(Q\) and radius \(R\) contributes

-3Q-- ρ = 4πR3

3 Numerical Implementation

The only involved part of this thorn arise in working out where the sources are located (if at all) on each local grid for a multiprocessor run. The source terms are not numerically evolved, but are calculated exactly, based on the physical time and their orbital velocity.

A routine is scheduled to run after the homogeneous equation for the scalar field has been evolved, and simply updates the value of the scalar field by adding on the source contribution.

4 Parameters


binary_charge	Scope: private	REAL

Description: Charge of source

Range		Default: 0.1
:	No restriction


binary_omega	Scope: private	REAL

Description: Frequency of the circular binary orbit

Range		Default: 2.0
0.0:	Some positive value


binary_radius	Scope: private	REAL

Description: Radius of the circular binary orbit

Range		Default: 2.0
0.0:	Some positive value


binary_size	Scope: private	REAL

Description: Radial extension of the binary source

Range		Default: 0.5
0.0:	Some positive value


binary_verbose	Scope: private	KEYWORD

Description: Rotating binary source verbose

Range		Default: no
yes	Info on charge location/extension on first iteration
debug	Info on charge location/extension on all iterations
no	no output

5 Interfaces

General

Implements:

binarysource

Inherits:

wavetoy

grid

6 Schedule

This section lists all the variables which are assigned storage by thorn CactusWave/WaveBinarySource. Storage can either last for the duration of the run (Always means that if this thorn is activated storage will be assigned, Conditional means that if this thorn is activated storage will be assigned for the duration of the run if some condition is met), or can be turned on for the duration of a schedule function.

Storage

NONE

Scheduled Functions

CCTK_EVOL

wavebinaryc

provide binary source during evolution (c)

	After:	wavetoy_evolution
	Language:	c
	Storage:	wavetoy::scalarevolve[1]
	Type:	function