# Plotting 3D thoroidal field streamline

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Massimo Carpita on 11 Sep 2019
Commented: Massimo Carpita on 12 Sep 2019
Hi everyone!
I'm having some trouble trying to plot streamlines of a field I'm using in a code. It is a 3D field whose components are represented by 3 functions (Bx,By,Bz) I defined.
I'm interested in plotting the streamlines of the field into a 3D thoroidal volume but I don't really have a clue about the right way to do this; I tried to use this code but it doesn't work.
Babs=5;
R0=0.1; %major R
r0=linspace(0,0.005,3); %inner R
th=linspace(0,2*pi,20); %poloidal angle
phi=linspace(0,2*pi,30); %thoroidal angle
[Phi,Th,rr0]=meshgrid(phi,th,r0);
xx=(R0+rr0.*cos(Th)).*cos(Phi);
yy=(R0+rr0.*cos(Th)).*sin(Phi);
zz=rr0.*sin(Th);
[starty,startz]=meshgrid(yy,zz);
streamline(xx,yy,zz,Bx(Babs,xx,yy,zz,R0),By(Babs,xx,yy,zz,R0),Bz(Babs,xx,yy,zz,R0),starty.*0,starty,startz);
%definisco le funzioni per il campo B
function a1 = Bx(Babs,x,y,z,R0)
RR=sqrt(x.^2+y.^2);
a1=R0.*Babs.*(-1.*sin(atan2(y,x)))./RR;
end
function b1 = By(Babs,x,y,z,R0)
RR=sqrt(x.^2+y.^2);
b1=R0.*Babs.*(cos(atan2(y,x)))./RR;
end
function c1 = Bz(Babs,x,y,z,R0)
c1=Babs.*x.*0;
end
the error I get is
Error using griddedInterpolant
The grid vectors must contain unique points.
I'm also not sure about what way would be the best to define startx, starty and startz in this case.
Thanks in advance for everyone who will try to help me!

darova on 11 Sep 2019
I used quiver3
Can't you just draw circles if it is that straight?

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darova on 12 Sep 2019
I wrote a simple script for streamlines
As you can see it's not that accurate as i wanted it to be
(it also depends on number of points for one streamline)
c1 (nz) vector modificated (looks like russian tokamak)
See the script i attached
darova on 12 Sep 2019
Algorithm of the script as on the picture:
Since you know the vector field a new position of a points can be calculated
Massimo Carpita on 12 Sep 2019
Dear Darova, for my purpose this will do!
Thank you very much again :)