Plotting 3D thoroidal field streamline

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!

Answer 1

[darova]

I used quiver3

Can't you just draw circles if it is that straight?

[Massimo Carpita]

Dear darova, thank you for your answer!

I tried to use quiver but I would like to plot streamlines because it would be more suitable for my purpose.

You're actually right, in the code I posted my streamlines would look like circles but that is not the only field I need to plot! Other fields have a more complicated geometry.

[darova]

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]

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]

Dear Darova, for my purpose this will do!

Thank you very much again :)