1. A Simulator for the LWA Masaya Kuniyoshi (UNM)

2. Outline 1.Station Beam Model 2.Asymmetry Station Beam 3.Station Beam Error 4.Summary

3. (Aaron Cohen LWA Memo Series [55])

4. (Leonid Kogan LWA Memo Series [21]) 256 dipoles

5. E(θ,φ)=ΣGaussian(θ,φ)exp(iP )exp(Ψ － Φ ）＋ Noise Simulation model for a station beam Ψ = 2π λ ( D ・ u ) j j Φ = 2π λ ( D ・ S ) j j j j j =0 255 Gaussian(θ,φ) = individual primary beam θ[degree] φ[degree] θ[degree] φ[degree] = Zenith S (0,0 ） 。 。 S (10,0 ) 。 。 Station beam j

6. Normalized Power Pattern θ [°] (angle form zenith)

7. Normalized Power Pattern θ [°] (angle form zenith)

8. Normalized Power Pattern θ [°] (angle form zenith)

9. Normalized Power Pattern θ [°] (angle form zenith)

10. Normalized Power Pattern θ [°] (angle form zenith)

11. Normalized Power Pattern θ [°] (angle form zenith)

12. Normalized Power Pattern θ [°] (angle form zenith)

13. Normalized Power Pattern θ [°] (angle form zenith)

14. Normalized Power Pattern θ [°] (angle form zenith)

15. Normalized Power Pattern θ [°] (angle form zenith)

16. Normalized Power Pattern θ [°] (angle form zenith)

17. Normalized Power Pattern θ [°] (angle form zenith)

18. Normalized Power Pattern θ [°] (angle form zenith)

19. Normalized Power Pattern θ [°] (angle form zenith)

20. Normalized Power Pattern θ [°] (angle form zenith)

21. Normalized Power Pattern θ [°] (angle form zenith)

22. Normalized Power Pattern θ [°] (angle form zenith)

23. Normalized Power Pattern θ [°] (angle form zenith)

24. Normalized Power Pattern θ [°] (angle form zenith)

25. Normalized Power Pattern θ [°] (angle form zenith)

26. Normalized Power Pattern θ [°] (angle form zenith)

27. Normalized Power Pattern θ [°] (angle form zenith)

28. Symmetry Normalized Power Pattern θ [°] (angle form zenith)

29. Asymmetry θ [°] (angle form zenith) Normalized Power Pattern

30. θ [°] (angle form zenith) Asymmetry Normalized Power Pattern

31. ８°８° ９°９° ２８ ° １３ ° Normalized Power Pattern θ [°] (angle form zenith)

32. Asymmetry rate HPBW left side/ HPBW right side θ[°] angle from zenith 20MHz 50MHz 80MHz

33. As the angle θgoes from 0 to π/2, the value of cosθ(differentiation of sinθ) gets smaller. As a result, the beam becomes asymmetric. This effect increases as the frequency decreases. θ D Dsinθ Ｓ

34. θ ＝ -70° θ (degree) Zenith = 0 ° peak Beam pattern

35. θ ＝ -60 ° Zenith = 0 ° peak θ (degree) Beam pattern

36. θ ＝ -50 ° Zenith = 0 ° θ (degree) Beam pattern

37. θ ＝ -40 ° Zenith = 0 ° θ (degree) Beam pattern

38. θ ＝ -30 ° Zenith = 0 ° θ (degree) Beam pattern

39. θ ＝ -20 ° θ Zenith = 0 ° θ (degree) Beam pattern

40. θ ＝ -10 ° θ Zenith = 0 ° θ (degree) Beam pattern

41. θ ＝ 0 ° θ Zenith = 0 ° θ (degree) Beam pattern

42. θ ＝ 10 ° θ Zenith = 0 ° θ (degree) Beam pattern

43. θ ＝ 20 ° θ Zenith = 0 ° θ (degree) Beam pattern

44. θ ＝ 30 ° θ Zenith = 0 ° θ (degree) Beam pattern

45. θ ＝ 40 ° θ Zenith = 0 °

46. θ ＝ 50 ° θ Zenith = 0 ° θ (degree) Beam pattern

47. θ ＝ 60 ° θ Zenith = 0 ° peak θ (degree) Beam pattern

48. θ ＝ 70 ° θ Zenith = 0 ° peak θ (degree) Beam pattern

49. θ ＝ -70 ° Zenith = 0 ° λ d ・ 57.3 ≒ 43° θ (degree) Beam pattern Grating lobe

50. θ ＝ -60 ° Zenith = 0 ° θ (degree) Beam pattern Grating lobe

51. θ ＝ -50 ° Zenith = 0 ° θ (degree) Beam pattern Grating lobe

52. θ ＝ -40 ° Zenith = 0 ° θ (degree) Beam pattern Grating lobe

53. θ ＝ -30 ° Zenith = 0 ° θ (degree) Beam pattern Grating lobe

54. θ ＝ -20 ° Zenith = 0 ° θ (degree) Beam pattern Grating lobe

55. θ ＝ -10 ° Zenith = 0 ° θ (degree) Beam pattern Grating lobe

56. θ ＝ 0 ° Zenith = 0 ° θ (degree) Beam pattern Grating lobe

57. θ ＝ 10 ° Zenith = 0 ° θ (degree) Beam pattern Grating lobe

58. θ ＝ 20 ° Zenith = 0 ° θ (degree) Beam pattern Grating lobe

59. θ ＝ 30 ° Zenith = 0 ° θ (degree) Beam pattern Grating lobe

60. θ ＝ 40 ° Zenith = 0 ° θ (degree) Beam pattern Grating lobe

61. θ ＝ 50 ° Zenith = 0 ° θ (degree) Beam pattern Grating lobe

62. θ ＝ 60 ° Zenith = 0 ° Grating lobe

63. θ ＝ 70 ° Zenith = 0 ° θ (degree) Beam pattern Grating lobe

64. (-60,0) θ[°] Φ[°] 0 20 40 60 -60 Station Beam Station beam at 20MHz

65. (-50,0) θ[°] Φ[°] 0 20 40 60 -60 Station Beam Station beam at 20MHz

66. (-40,0) θ[°] Φ[°] 0 20 40 60 -60 Station Beam Station beam at 20MHz

67. (-30,0) θ[°] Φ[°] 0 20 40 60 -60 Station Beam Station beam at 20MHz

68. (-20,0) θ[°] Φ[°] 0 20 40 60 -60 Station Beam Station beam at 20MHz

69. (-10,0) θ[°] Φ[°] 0 20 40 60 -60 Station Beam Station beam at 20MHz

70. (0,0) θ[°] Φ[°] 0 20 40 60 -60 Station Beam Station beam at 20MHz

71. (10,0) θ[°] Φ[°] 0 20 40 60 -60 Station Beam Station beam at 20MHz

72. (20,0) θ[°] Φ[°] 0 20 40 60 -60 Station Beam Station beam at 20MHz

73. (30,0) θ[°] Φ[°] 0 20 40 60 -60 Station Beam Station beam at 20MHz

74. (40,0) θ[°] Φ[°] 0 20 40 60 -60 Station Beam Station beam at 20MHz

75. (50,0) θ[°] Φ[°] 0 20 40 60 -60 Station Beam Station beam at 20MHz

76. (60,0) θ[°] Φ[°] 0 20 40 60 -60 Station Beam Station beam at 20MHz

77. θ[°] Φ[°] 0 20 40 60 -60 Station Beam (-60,0) Grating lobe Station beam at 60MHz

78. θ[°] Φ[°] 0 20 40 60 -60 Station Beam (-40,0) Grating lobe Station beam at 60MHz

79. θ[°] Φ[°] 0 20 40 60 -60 Station Beam (-20,0) Grating lobe Station beam at 60MHz

80. θ[°] Φ[°] 0 20 40 60 -60 Station Beam Station beam at 60MHz

81. θ[°] Φ[°] 0 20 40 60 -60 Station Beam (20,0) Grating lobe Station beam at 60MHz

82. θ[°] Φ[°] 0 20 40 60 -60 Station Beam (40,0) Grating lobe Station beam at 60MHz

83. θ[°] Φ[°] 0 20 40 60 -60 Station Beam (60,0) Grating lobe Station beam at 60MHz

84. Summary 1. Asymmetry rate of a station beam → beam elevation & observing frequency 2.The direction error of a station beam → beam elevation & primary beam Future Plan @ Addition of a real dipole beam pattern to the simulator @ Addition of band widths to the simulator @ Dipole configuration to remove the grating lobes @ ・ ★ Completion of the simulator for the LWA

86. 同じ方向を見た場合 ２０～８０ＭＨｚ

101. 29MHz ->172 degrees 30MHz -> 115 degrees 40MHz -> 86 degrees 50MHz -> 69 degrees 60MHz -> 57 degrees 70MHz -> 49 degrees 80MHz -> 43 degrees The gap between beams.

102. 20MHz Station Beam

104. 3D one station beam figure 20MHz 0deg 20deg 40deg 60deg

105. HPBW θ ∝ P

106. 規格化バージョン ０、３０、６０ °

113. -40 degrees 軸を消してもいいかも！ zenith なぜ小さいか理由も入れる

129. We need a simulator because there is no LWA station. If you get the simulator, you could find some problems in LWA before the construction.

130. ここに kumar からもらったシミュレーションソフトを 改造してＬＷＡ１００ｍバージョンにした 最終的な（クリーン後）を入れる 最終的にこのようなソフトを作りたい しかし、これは１ステーションを１００ｍと 考えた時の、実際のステーションの位置 を入れたデータである。 実際に２５６ダイポールからなるステーションビーム でシミュレーションソフトを作成することが目的。

131. θ D Dsinθ Ｓ