Hello, I am trying to plot a contour; code is given below. Contour colors pattern looks absurd and its not smooth. Also can i get rid of the contour lines too ?

ClearAll["Global`*"];
F = 0;
\[Epsilon] = 0.2;
\[Lambda] = 1;
\[Beta] = ArcSin[\[Lambda]/Sqrt[1 + \[Lambda]^2] ];
ucap = 1 - 
   r \[Epsilon] Sin[\[Zeta]] + \[Epsilon]^2 (-(1/4) + 
      r^2 Sin[\[Zeta]]^2) + \[Epsilon]^3 (1/4 r Sin[\[Zeta]] - 
      r^3 Sin[\[Zeta]]^3 + 
      1/6 F r^2 \[Lambda] Cos[\[Beta]] Sin[2 \[Zeta]]);
plot =
 ContourPlot[
  ucap /. {r -> Norm[{x, y}], \[Zeta] -> ArcTan[y, x]}, {x, -1, 
   1}, {y, -1, 1},
  RegionFunction -> (Norm[{#, #2}] <= 1 &),
  ColorFunction -> "DarkRainbow",
  Frame -> False,
  Axes -> True,
  TicksStyle -> Directive[FontOpacity -> 0],
  ContourShading -> Automatic,
  Contours -> 30,
  ContourLabels -> {Style[Text[#3, {#1, #2}], 20] &, 
    Tooltip[#3, #2, TooltipStyle -> FontSize -> 20] &},
  ImageSize -> Large
  ]