I got two responses quickly, and one of them furnishes partial answer, First I need to generate the data, which was furnished by Rohit Namjoshi Then I found how to convert the spherical coordinate data to Cartesian coordinates so that I can plot them from an earlier discussion, https://stackoverflow.com/questions/16758837/multiple-listpolarplots-in-3d-in-mathematica the content is copied below, When you want to make a 3D plot you will need to have 3D data first. Therefore, I assume you really meant a ListSphericalPlot3D. If you already have the list of your points in spherical coordinates, it's not really hard to plot them. What we do is, basically first changing the coordinates to "Cartesian", then plotting it:

ListSphericalPlotPoints3D[list_List] := ListPointPlot3D[Map[CoordinateTransformData["Spherical" -> "Cartesian","Mapping", #] &,Map[{#[[1]], Mod[#[[2]], [Pi]], Mod[#[[3]], 2 [Pi]]} &, list]]]; ListSphericalPlot3D[list_List] := ListPlot3D[Map[CoordinateTransformData["Spherical" -> "Cartesian", "Mapping", #] &, Map[{#[[1]], Mod[#[[2]], [Pi]], Mod[#[[3]], 2 [Pi]]} &,list]]]; These two functions will hopefully do, what you are asking for. Update: Since this transformation is rather simple, it is straightforward to write the whole transformation by hand: ListSphericalPlotPoints3D[list_List] := ListPointPlot3D[Map[{#[[1]] Sin[#[[2]]] Cos[#[[3]]], #[[1]] Sin[#[[2]]] Sin[#[[3]]], #[[1]] Cos[#[[2]]]} &,Map[{#[[1]], Mod[#[[2]], [Pi]], Mod[#[[3]], 2 [Pi]]} &, list]]]; ListSphericalPlot3D[list_List] := ListPlot3D[Map[{#[[1]] Sin[#[[2]]] Cos[#[[3]]], #[[1]] Sin[#[[2]]] Sin[#[[3]]], #[[1]] Cos[#[[2]]]} &, Map[{#[[1]], Mod[#[[2]], [Pi]], Mod[#[[3]], 2 [Pi]]} &,list]]];

so now I have the answers. Thanks

I am not sure exactly what you mean by "discrete 3d set of plots for magnetic field lines".

Is this the correct WL definition of the equation?

r[?_, ?_] := Module[{rn = 1, ?0 = 0, ? = -0.18}, rn Cos[? + ? Cos[? + ?0]]^2]

If so, you can use Table to generate a list of values of the function for a range of ? and ? that you can then plot. e.g.

Table[{?, ?, r[?, ?]}, {?, 0, 2 Pi, Pi/12}, {?, 0, 0.4, 0.1}];