Playing with many options, I find that to remove the jagged edges from the tube, the best solution is to Rasterize with high ImageResolution (which is probably not what you want). Using Antialiasing
alone did not do as well a job, but it was still better than the image shown. Here is what I get in windows 7, V 10.02
turns = r = 10;
Rasterize[Style[
Graphics3D[First@ParametricPlot3D[
Piecewise[{{{1, x, 0}, x <= 0}, {{Cos[2 Pi turns x/r], x,
Sin[2 Pi turns x/r]}, 0 < x <= r}, {{1, x, 0}, x > r}}],
{x, -.5, r + .5},
PlotStyle -> {Gray, Specularity[Gray, 10]},
Lighting -> "Neutral",
PlotRange -> {{-10, 10}, {-1, 15}, {-5, 5}},
Axes -> None, PlotPoints -> 1000, ImageSize -> 600,
Boxed -> False, ViewPoint -> {10000, 1, 5}
] /. Line[pts_, rest___] :> Tube[pts, .2, rest], Boxed -> False],
Antialiasing -> True], ImageResolution -> 240]

Using Antialiasing -> True
alone:
turns = r = 10;
Style[
Graphics3D[First@ParametricPlot3D[
Piecewise[{{{1, x, 0}, x <= 0}, {{Cos[2 Pi turns x/r], x,
Sin[2 Pi turns x/r]}, 0 < x <= r}, {{1, x, 0}, x > r}}],
{x, -.5, r + .5},
PlotStyle -> {Gray, Specularity[Gray, 10]},
Lighting -> "Neutral",
PlotRange -> {{-10, 10}, {-1, 15}, {-5, 5}},
Axes -> None, PlotPoints -> 1000, ImageSize -> 500,
Boxed -> False, ViewPoint -> {10000, 1, 5}
] /. Line[pts_, rest___] :> Tube[pts, .2, rest],
Boxed -> False], Antialiasing -> True]

Changing Mesh
, PlotPoints
and such options had no effect on the jagged problem.
Line -> Tube
and simply addTube[0.2]
to thePlotStyle
options instead, combined withExclusions -> None
. $\endgroup$ – Jens Mar 30 '15 at 17:18