1. Performance of station array configurations Sparse vs. Dense, Regular vs Random Jaap D. Bregman AAVP Workshop,Cambridge, 2010-12-09

2. Overview Setting the Scene for SKA-Low –Some Antenna Basic –Why Sparse Arrays for F < 300 MHz LOFAR 20 – 240 MHz (sparse, regular & random) –Station & Array Calibratability –Element & Sparse Array Beam –EM-coupling effects Vivaldi Element & Array (dense regular) Antenna Cost Extrapolation –Peak sensitivities for SKA Low –Balancing Lowest against Highest frequency octave Conclusions (combine)

3. Setting the Scene for SKA-Low Memo 125 defines SKA 1 with 2 Synthesis Arrays –100 M€ for AA-Low70 – 450 MHz2000 m 2 /K @ z = 10 –100 M€ for Dishes0.3 – 10 GHz1000 m 2 /K0.45 – 3 GHz Effective supporting surveys requires –30% of cost in Receivers, Beamforming, Correlation & Imaging –70% of cost in collecting area & Low Noise Amplifier What could we do with 70 M€ in view of –Limitations set by the Sky –Limitations set Antenna Theory –Limitations set by Ionosphere calibration –Limitations set by Station Beam calibration

4. Some Antenna Basic Array has set of N antenna element separated by a pitch P When /2 > P we are in the dense regime and A e = N P 2 = N p 2 /4 A dense array has a projected area ~ cos(  ) with zenith angle  A dipole above a ground plane has a beam pattern ~ cos(  ) in H-plane and ~ cos 2 (  ) in E-plane, A free dipole above ground has A e = 2 /  with beam solid angle  ~ 3 In the sparse regime are the pitch cells not fully filled so A e < P 2 and sparse < ( 3/4 ) 1/2 P A dipole with length L and height H above a ground plane has below resonance impedance Z ~ 377 L H / 2 (real part) The EM coupling between the elements in the dense regime increases the effective impedance in a dense array, which is important to get appropriate matching to low noise amplifiers

5. Why Sparse Arrays for F < 300 MHz Sparse Array stations have –Aeffective < Aphysical –Ae ~ N   –Tsky ~  –Sensitivity Ss ~ Ts / Ae ~  –Typical source flux So ~  –Source Count N(S > So) ~ So -1 –Beam solid angle   / Ap –So constant detection sensitivity –But sources/beam ~  Expo-Shell configuration –Exponential decreasing element separation towards centre of station –LBA 50% subsets of LOFAR –Select 50% of elements to limit sparseness at higher frequencies 60 MHz subset 30 MHz subset

6. LOFAR 20 – 240 MHz Two different sparse array configurations –Randomized expo-shell for 96 elements 20 - 80 MHz –24/48/96 Tiles with 16 elements on regular grid 120 - 240 MHz Two different dipole like elements –Free standing thin wired short inverted V-dipole –Boxed Vertical bowtie as fat dipole –Both above ground plane Descent receiver noise match –LBA sky noise limited 30 - 60 MHz –HBA sky noise limited 120 - 180 MHz

7. Station & Array Calibratability VLA 75 MHz could not be selfcalibrated –A single single source available in only a few fields –Ae/Ap = 0.15 is too small –Beam too wide, 25 m dish to small for ionosphere patch size –1.5 MHz bandwidt not enough with 10 sec to match ionosphere LOFAR will do full ionosphere multi direction selfcal –40 m remote stations allow multi direction at 120 MHz –30 m core stations could provide combined solution for core –56 m international stations still see partly resolved calibrators –10 MHz, 10 sec, allows for ~20 directions when Ae/Ap = 1.0 –33 m station at 60 MHz Ae/Ap = 0.47 reasonable ionosphere needed –83 m station at 30 MHz Ae/Ap = 0.29 good ionosphere needed

8. Element & Sparse Array Beam Include EM Coupling –Pitch < few wavelength –Element beam gets ~30 % bumps –Every element beam is “different” Effective Station Beam –Average element beam depends on direction in which array is pointed –Also for element impedance to which LNA needs to matched –Average element pattern has blind angles for specific freq & directions –Especially for regular array –Array factor has grating lobes –Randomization reduces both effects Ignore EM Coupling –True in very sparse arrays –True for arrays like WSRT –Not true for ATA Effective Station beam –Product of element beam and “array factor” –Element beam is smooth –Array factor has side lobes –Array factor has grating lobes –Array factor independent of direction where it is pointed to

9. Vivaldi Element & Array Free Vivaldi is wide band –At least 3 octaves –However narrow beam Array of connected elements –Good impedance P/2 <  < 4 P –Constant Ae = Ap for  > P 3 -1/2 –Cos (  ) “element” beam  > P –Narrower “element” beam  P –In sparse regime Ae/Ap ~  –Array factor has grating lobes –No grating for  < 47 o at  = P 3 -1/2

10. Antenna Cost Extrapolations LOFAR Actuals –Free LBA element (~2 m)€ 150 –Container + Combiner + Cables€ 500 –5*5 m 2 Tile + Combiner + Cables€ 1800 –Embedded HBA element + delay€ 75 –Production for ~5,000 LBA ~3000 HBA Extrapolated SKA Upper Bound Costs – 8 element cluster6*6 m 2 k€ 1.7(2 m separation) –16 element bowtie tile6*6 m 2 k€ 3.0 –32 element Vivaldi tile6*6 m 2 k€ 4.5 –64 element Vivaldi tile6*6 m 2 k€ 6.0

11. Peak Sensitivity for 70 M€ in antenna arrays “Tiles” of 6*6 m2 with 8 or 16 dipoles and 32 or 64 Vivaldi elements Frequency and element pitch increment 2 1/2 Purple is receiver noise dominated Yellow is relevant EoRrange Blue is actual LOFAR range Red is relevant Pulsar range * indicates max frequency with 3 sr element beam and  max = 47 o to avoid grating lobes A p 1.5 km 2 0.84 km 2 0.59 km 2 0.42 km 2 Freq T sys A e8 /T s A e16 /T s A e32 /T s A e64 /T s MHz Km 2 K -1 43 9400 160 90 65 45 60 4000 375 210 150 105 85* 1600 940* 525 370 265 120* 700 1070 1200* 840 600 170* 320 1170 1310 1840* 1315 240* 160 1310 1840 2625* 340 85 1735 2470 480 60 1750

12. Balancing Lowest against Highest octave Tiles of 6*6 m 2 with 64 elements have unprecedented sensitivity in 200- 480 MHz range or 2 < z < 6 Free element clusters provide best sensitivity for EoR application Combining Vivaldi tiles in centre of a station with dipole clusters in expense ratio 1:2 gives 720 m 2 /K at 85 & 400 MHz and 1220 m 2 /K at 170 MHz In “Dense” regime could tapering reduce the station side lobes In the sparse regime will grating lobes rise above the horizon when the array is pointed toward large zenith angles and pick up sky noise and disturbing sources.

13. Conclusions A full 1 km 2 array could be realized Combine Vivaldi tiles and Dipole clusters in station –Still 720 m 2 /K at 85 & 400 MHz –Peak sensitivity of 1220 m 2 /K at 170 MHz at octave “centre” of band Calibratability limits practical ranges of sparse regime –1 octave in Sky noise limited regime by  ~  –1/2 octave In receiver noise limited regime by additional Ae ~  Full instantaneous U,V-coverage for core possible Stay for EoR in “dense” regime –Avoid grating lobes and blind angles –Apply taper to reduce side lobes –Reduces sensitivity for low frequency