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fennecs/magnet/librairie/greenem_jph.m
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greenem_jph.m
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function b = greenem_jph(mode,r1,z1,r2,z2)
%
% Call: b = greenem_jph(mode,r1,z1,r2,z2)
%
% Green's functions
%
% The Green's functions are estimated at the position of the system 1 for a unit current flowing in system 2,
% for example BR_1_2 is the radial magnetic field at position 1 produced by 1A at position 2.
% In the formulae given bellow, system 1 is at position (r1,z1) and system 2 at position (r2,z2).
%
%
% Version: 1.0 J.-P. Hogge Oct. 4, 2001 (based on an original routine written by J.-M. Moret)
% 1.1 J.-P. Hogge Jul. 10 2002 Added aphi as an option for the mode
% 1.2 J.-P. Hogge Nov. 5 2002 Corrected mistake in dbzdr calculation
%
% mode : 'bz','br','dbzbz','dbzdr','dbrdz','dbrdr', 'd2bzdz2' or 'aphi'
% r1 : 1D array of radial locations where field is computed
% z1 : 1D array of longitudinal locations where field is computed
% r2 : 1D array of radii of the subcoils producing the field
% z2 : 1D array of z-locations of the subcoils producing the field
%
%
%
% Definitions
% -----------
% h = z2 - z1
% d^2 = (r2 - r1)^2 + h^2
% u^2 = (r2 + r1)^2 + h^2
% k^2 = 4 * r1 * r2 / u^2
% v^2 = r2^2 + r1^2 + h^2
% w^2 = r2^2 - r1^2 - h^2
%
% E(k^2) and K(k^2) and the complete elliptic integrals of the first and second kind respectively
%
% Magnetic field
% --------------
% br = -(1/2/pi/r1) * (dmut/dh) = (mu0/2/pi) * (h/r1/u) * ((v^2 / d^2) * E(k^2) - K(k^2))
% bz = (1/2/pi/r1) * (dmut/dr1) = (mu0/2/pi) * (1/u) * ((w^2 / d^2) * E(k^2) + K(k^2))
% bt = br * cos(ang) + bz * sin(ang)
% bn = bz * cos(ang) - br * sin(ang)
%
% Magnetic field derivatives
% --------------------------
% d(bz)/dr1 = (mu0/2/pi) * (1/r1/d^2/u^3) * ((v^2*d^2*u^2 - h^2*(d^4+k^2*u^4))/d^2 * E(k^2) + (h^2*v^2-u^2*d^2) * K(k^2))
% d(bz)/dz1 = (mu0/2/pi) * ( h/d^2/u^3) * ( (-4*v^2*w^2-3*u^2*d^2)/d^2 * E(k^2) + w^2 * K(k^2))
% d(br)/dr1 = -d(bz)/dz1 - br/r1
% Here is a small change w respect to J-M Moret's original routine
% d(br)/dz1 = (mu0/2/pi) * ( h^2/d^2/u/r1) * ( (-u^2/d^2 - d^2/u^2 + v^2/h^2 +1) * E(k^2) + (-d^2/h^2 - v^2/u^2) * K(k^2))
mu0 = 4 * pi * 1.0e-7;
% Since we want to know the fields at locations (r1,z1) produced by sources
% at locations (r2,z2), we construct rectangular matrices of dimension
% (length(r1), length(r2)).
if size(r1,1) > 1 | size(r2,1) > 1 , error('Input must be row vectors'); end
R1 = repmat(r1', 1 , length(r2) ); % R1 is a matrix length(r1)xlength(r2)
Z1 = repmat(z1', 1 , length(r2) ); % Z1 is a matrix length(r1)xlength(r2)
R2 = repmat(r2 , length(r1), 1 ); % R2 is a matrix length(r1)xlength(r2)
Z2 = repmat(z2 , length(r1), 1 ); % Z2 is a matrix length(r1)xlength(r2)
h = Z1 -Z2;
d = sqrt( (R2 - R1).^2 + h.^2 );
u = sqrt( (R2 + R1).^2 + h.^2 );
k = sqrt( 4*R1.*R2 ./ u.^2 );
v = sqrt( R2.^2 + R1.^2 + h.^2);
w = sqrt( R2.^2 - R1.^2 - h.^2);
[K,E] = ellipke(k.^2);
if(~iscell(mode))
mode={mode};
end
b=zeros([size(k),length(mode)]);
for i=1:length(mode)
switch lower(mode{i})
case 'bz',
b(:,:,i) = (mu0/2/pi) * (1./u) .* ( (w.^2./d.^2).*E + K );
case 'br',
b(:,:,i) = (mu0/2/pi) * (h./R1./u) .* ( (v.^2./d.^2).*E - K );
case 'dbzdz',
b(:,:,i) = (mu0/2/pi) * (h./d.^2./u.^3) .* ( (-4*v.^2.*w.^2-3*u.^2.*d.^2)./d.^2.*E + w.^2 .* K );
case 'dbzdr',
%JPH 5_11_2002 b = (mu0/2/pi) * (1./R2./d.^2./u.^3) .* ( (v.^2.*d.^2.*u.^2 - h.^2.*(d.^4+k.^2.*u.^4))./d.^2.*E + (h.^2.*v.^2 - u.^2.*d.^2) .* K );
b(:,:,i) = (mu0/2/pi) * (1./R1./d.^2./u.^3) .* ( (v.^2.*d.^2.*u.^2 - h.^2.*(d.^4+k.^2.*u.^4))./d.^2.*E + (h.^2.*v.^2 - u.^2.*d.^2) .* K );
case 'dbrdr',
% d(br)/dr1 = -d(bz)/dz1 - br/r1
b(:,:,i) = - (mu0/2/pi) * (h./d.^2./u.^3) .* ( (-4*v.^2.*w.^2-3*u.^2.*d.^2)./d.^2.*E + w.^2 .* K ) ...
- (mu0/2/pi) * (h./R1./u) .* ( (v.^2./d.^2).*E - K ) ./R1;
case 'dbrdz',
b(:,:,i) = (mu0/2/pi) * (h.^2./d.^2./R1./u) .* ( ( -u.^2./d.^2 - d.^2./u.^2 + v.^2./h.^2 +1).*E + (-d.^2./h.^2 + v.^2./u.^2) .* K );
case 'd2bzdz2',
b(:,:,i) = (mu0/2/pi) * (1./d.^4./u.^3) .* ( ( ( -d.^2.*u.^2 + 4*h.^2.*( 2*R1.*R2 + d.^2)) + 8 * h.^2.*u.^2.*w.^2./d.^2 ...
+ 2 * ( -u.^2.*w.^2 + 4*h.^2.*( u.^2 + w.^2)) - 2 * d.^2.*( u.^2 + w.^2 ) ...
- h.^2 .* ( -8*d.^2 - (7 - 8*k.^2).*w.^2) ) .* E ...
- ( d.^2.*h.^2 + 4 * h.^2.*w.^2 + ...
d.^2./u.^2 .* ( -u.^2.*w.^2 + 4*h.^2.*( u.^2 + w.^2)) ) .* K );
case 'aphi'
b(:,:,i) = (mu0/pi) * sqrt(R2./(k.^2.*R1)) .* ( (1-k.^2/2).*K - E);
otherwise,
disp('Unknown mode')
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
end
end
return
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