plotting - StreamPlot segmented lines

I am plotting this vector field:

Q[k_, N_] := Show[ContourPlot[3 - 3 BesselJ[0, r[x, y] a^-1], {x, -N, N}, {y, -N, N}, 
ContourStyle -> Opacity[0.3]], 

StreamPlot[{Sin[θ[x, y]], -Cos[θ[x, y]]}, {x, -N, N}, {y, -N, N}, 
PlotRange -> {Full, Full}, RegionFunction -> 
Function[{x, y}, a^2 - a^2/100 < x^2 + y^2 <=  a^2 + a^2/100], 
StreamStyle -> Red, StreamPoints -> {pts, Automatic, Scaled[2]}, 
StreamScale -> None],

StreamPlot[{Abs[(1 - a/r[x, y])^(1/2)] + 

a^(1/2)/r[x, y]^(1/2) Cos[θ[x, y] k], 
a^(1/2)/r[x, y]^(1/2) Sin[θ[x, y] k]}, {x, -N, N}, {y, -N, 
N}, PlotRange -> {Full, Full}, 
RegionFunction -> Function[{x, y}, x^2 + y^2 > a^2], 
StreamStyle -> {Blue, Thick, "Line"}, PerformanceGoal -> "Quality", 
StreamScale -> Full], 

ImageSize -> Large]

with

r[x_, y_] := Sqrt[x^2 + y^2];
θ[x_, y_] := ArcTan[x, y];

a = 3;
pts = Flatten[
Table[{x, y}, {x, -a - a/10, a + a/10, 0.1}, {y, a - a/10, a + a/10, 0.1}], 1];

But I can't find a set of StreamPoints to avoid the segmentation of the lines near the x-axes.

Q[1/2,10]

enter image description here

Any ideas? Thanks!

Answer

r[x_, y_] := Sqrt[x^2 + y^2];
θ[x_, y_] := ArcTan[x, y];

a = 3;
pts = Flatten[Table[{x, y}, {x, -a - a/10, a + a/10, 0.1}, {y, a - a/10, a + a/10, 0.1}], 1];

Q[k_, n_] := Module[{pts1}, pts1 = Table[{0, x}, {x, -2 n, 2 n, 1/2}];

  Show[ContourPlot[ 3 - 3 BesselJ[0, r[x, y] a^-1], {x, -n, n}, {y, -n, n}, 
                   ContourStyle -> Opacity[0.3]], 
       StreamPlot[{Sin[θ[x, y]], -Cos[θ[x, y]]}, {x, -n, n}, {y, -n, n}, PlotRange -> {Full, Full}, 
                 RegionFunction -> Function[{x, y}, a^2 - a^2/100 < x^2 + y^2 <= a^2 + a^2/100], 
                 StreamStyle -> Red, StreamPoints -> {pts, Automatic, Scaled[2]},  
                 StreamScale -> None], 
       StreamPlot[{Abs[(1 - a/r[x, y])^(1/2)] +  a^(1/2)/r[x, y]^(1/2) Cos[θ[x, y] k], 
                      a^(1/2)/r[x, y]^(1/2) Sin[θ[x, y] k]}, {x, -2 n, 2 n}, {y, -2 n, 2 n}, 
                 RegionFunction -> Function[{x, y}, x^2 + y^2 > a^2 && Abs@x < n && Abs@y < n], 
                 StreamPoints -> {pts1, Automatic, Scaled[2]}, StreamStyle -> {Blue, Thick, "Line"}, 

                 PerformanceGoal -> "Quality", StreamScale -> Full], 
   ImageSize -> Large]]

Q[1/2, 10]

Mathematica graphics

Comments

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