axi_green Module Reference

Detailed Description

Object and supporting functions for axisymmetric coil sets.

Authors

Chris Hansen

Date

March 2014

Data Types
type	axi_coil_set
	Needs Docs. More...

Functions/Subroutines
real(r8) function	elle (phi, ak)
	Legendre elliptic integral of the 2nd kind E(; j), evaluated using Carlson's functions RD and RF. The argument ranges are 0 =2, 0 ksin 1.
real(r8) function	ellf (phi, ak)
	Legendre elliptic integral of the 1st kind F(; k), evaluated using Carlson's function RF. The argument ranges are 0 =2, 0 ksin 1.
subroutine, public	grad_green (r, z, rc, zc, fg, gg)
	Evaluate gradient of Green's function for axisymmetric current filament.
real(r8) function, public	green (r, z, rc, zc)
	Evaluate Green's function for axisymmetric current filament.
real(r8) function, public	green_brute (r, z, rc, zc)
	Evaluate Green's function using brute force integration with 360 points.
real(r8) function	rd (x, y, z)
	Computes Carlson's elliptic integral of the second kind, RD(x; y; z). x and y must be nonnegative, and at most one can be zero. z must be positive. TINY must be at least twice the negative 2/3 power of the machine overflow limit. BIG must be at most 0:1ERRTOL times the negative 2/3 power of the machine underflow limit.
real(r8) function	rf (x, y, z)
	Computes Carlson's elliptic integral of the first kind, RF(x; y; z). x, y, and z must be nonnegative, and at most one can be zero. TINY must be at least 5 times the machine undeflow limit, BIG at most one fifth the machine overflow limit.

Variables
real(r8), parameter	roff = 1.d-13

Function/Subroutine Documentation

elle()

real(r8) function elle ( real(r8), intent(in)  phi, real(r8), intent(in)  ak  )

private

Legendre elliptic integral of the 2nd kind E(; j), evaluated using Carlson's functions RD and RF. The argument ranges are 0 =2, 0 ksin 1.

ellf()

real(r8) function ellf ( real(r8), intent(in)  phi, real(r8), intent(in)  ak  )

private

Legendre elliptic integral of the 1st kind F(; k), evaluated using Carlson's function RF. The argument ranges are 0 =2, 0 ksin 1.

grad_green()

subroutine, public grad_green	(	real(r8), intent(in)	r,
		real(r8), intent(in)	z,
		real(r8), intent(in)	rc,
		real(r8), intent(in)	zc,
		real(r8), intent(out)	fg,
		real(r8), dimension(2), intent(out)	gg
	)

Evaluate gradient of Green's function for axisymmetric current filament.

See also

green

Parameters

[in]	r	Radial location of observation point
[in]	z	Vertical location of observation point
[in]	rc	Radial location of filament
[in]	zc	Radial location of filament
[out]	fg	Value of Green's function
[out]	gg	Gradient of Green's function

green()

real(r8) function, public green	(	real(r8), intent(in)	r,
		real(r8), intent(in)	z,
		real(r8), intent(in)	rc,
		real(r8), intent(in)	zc
	)

Evaluate Green's function for axisymmetric current filament.

Legendre elliptic integral of the 2nd kind E(; k), evaluated using Carlson's functions RD and RF. The argument ranges are 0 =2, 0 ksin 1.

Parameters

[in]	r	Radial location of observation point
[in]	z	Vertical location of observation point
[in]	rc	Radial location of filament
[in]	zc	Radial location of filament

Returns

Value of Green's function

green_brute()

real(r8) function, public green_brute	(	real(r8), intent(in)	r,
		real(r8), intent(in)	z,
		real(r8), intent(in)	rc,
		real(r8), intent(in)	zc
	)

Evaluate Green's function using brute force integration with 360 points.

Parameters

[in]	r	Radial location of observation point
[in]	z	Vertical location of observation point
[in]	rc	Radial location of filament
[in]	zc	Radial location of filament

Returns

Value of Green's function

rd()

real(r8) function rd ( real(r8), intent(in)  x, real(r8), intent(in)  y, real(r8), intent(in)  z  )

private

Computes Carlson's elliptic integral of the second kind, RD(x; y; z). x and y must be nonnegative, and at most one can be zero. z must be positive. TINY must be at least twice the negative 2/3 power of the machine overflow limit. BIG must be at most 0:1ERRTOL times the negative 2/3 power of the machine underflow limit.

rf()

real(r8) function rf ( real(r8), intent(in)  x, real(r8), intent(in)  y, real(r8), intent(in)  z  )

private

Computes Carlson's elliptic integral of the first kind, RF(x; y; z). x, y, and z must be nonnegative, and at most one can be zero. TINY must be at least 5 times the machine undeflow limit, BIG at most one fifth the machine overflow limit.

Variable Documentation

roff

real(r8), parameter roff = 1.d-13