xx Orbiting Scalar Charges

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 is written . ∇ϕ = 4πρ

Each scalar source with charge and radius contributes

. ρ = \frac{3Q}{4πR^{3}}

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

11binaryxcharge10Scope: privatex01  REAL

11Description: Charge of source

11 Range 10 x01 Default: 0.1
11:  10No restriction

11binaryxomega10Scope: privatex01  REAL

11Description: Frequency of the circular binary orbit

11 Range 10 x01 Default: 2.0
110.0:  10Some positive value

11

11binaryxradius10Scope: privatex01  REAL

11Description: Radius of the circular binary orbit

11 Range 10 x01 Default: 2.0
110.0:  10Some positive value

11

11binaryxsize 10Scope: privatex01  REAL

11Description: Radial extension of the binary source

11 Range 10 x01 Default: 0.5
110.0:  10Some positive value

11

11binaryxverbose 10Scope: privatex01  KEYWORD

11Description: Rotating binary source verbose

11 Range 10 x01 Default: no
11yes  10Info on charge location/extension on first iteration
11debug  10Info on charge location/extension on all iterations
11no  10no output

11

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

CCTKxEVOL x wavebinaryc x provide binary source during evolution (c) x

11x11After: 11wavetoyxevolution
11 x 11Language:11c
11 x 11Storage: 11wavetoy::scalarevolve[1]
11 x 11Type: 11function