Solar Orbiter RPW - Low Frequency Receiver LFR team at LPP Thomas Chust Lead Co-I (CNRS) science, calibration, tests Paul Leroy Technical Manager (CNRS) flight software development + SGSE Alexis Jeandet Lead Engineer (CNRS) GSE + SGSE Martin Morlot Study Engineer (CDD) VHDL developement Jean-Christophe Pellion Gérald Saule flight software specification/validation Vincent Leray (20%) Engineer (CDD) product assurance software William Recart (20%) product assurance hardware Bruno Katra Study Engineer (CNRS) software development, calibration, tests Fouad Sahraoui Co-I (CNRS) Yannis Zouganelis Co-I (UPMC) Alessandro Retino ... LPP/CNRS – SO RPW Team Meeting #14 – January 29-30, 2014 – CNES Paris, France

Status of LFR resolution (design) Outline Status of LFR resolution (design) Need for a greater gain of the BIAS differential AC signals ? LPP/CNRS – SO RPW Team Meeting #14 – January 29-30, 2014 – CNES Paris, France

LFR downsampling and processing strategy 8 ADCs @ 98 304 Hz decimation down to  24 576 Hz ( f0 ) (14 bits ideally) :32 :3 (16 bits) => 18 bits ? (15 bits) (16 bits) (16 bits) 24 576 Hz 4 096 Hz 16 Hz 256 Hz shaping :3 :2 :64 :4 => 20 bits ? ( f1 ) ( f3 ) ( f2 ) :4 ( f0 ) 2  E 3  B 1  V 2  E 3  B 2  E 3  B 1  V 2  E 3  B 1  V 2  E (3  B) 2  E 3  B 1  V 2  E 3  B FFT FFT FFT (15 bits) Spectral matrices (ASM) Waveforms (WF) Spectral matrices (ASM) Waveforms (WF) Waveforms (WF) Spectral matrices (ASM) Waveforms (WF) Basic parameters (BP) Basic parameters (BP) Basic parameters (BP) LPP/CNRS – SO RPW Team Meeting #14 – January 29-30, 2014 – CNES Paris, France

BIAS 5 analogue inputs DC V (G=1/15) DC dV ~ E (G=1) AC dV ~ E (G=5, 50Hz) LPP/CNRS – SO RPW Team Meeting #14 – January 29-30, 2014 – CNES Paris, France

Current set of Basic Parameters 𝐒𝐌 ω 𝑗 𝑚 = 𝐵 1 𝐵 1 ∗ 𝐵 1 𝐵 2 ∗ 𝐵 1 𝐵 3 ∗ 𝐵 1 𝐸 1 ∗ 𝐵 1 𝐸 2 ∗ 𝑐𝑐 𝐵 2 𝐵 2 ∗ 𝐵 2 𝐵 3 ∗ 𝐵 2 𝐸 1 ∗ 𝐵 2 𝐸 2 ∗ 𝑐𝑐 𝑐𝑐 𝐵 3 𝐵 3 ∗ 𝐵 3 𝐸 1 ∗ 𝐵 3 𝐸 2 ∗ 𝑐𝑐 𝑐𝑐 𝑐𝑐 𝐸 1 𝐸 1 ∗ 𝐸 1 𝐸 2 ∗ 𝑐𝑐 𝑐𝑐 𝑐𝑐 𝑐𝑐 𝐸 2 𝐸 2 ∗ 𝐀𝐒𝐌 ω 𝑗 𝑚 = 1 𝑁 𝑆𝑀 𝑚 𝑘=1 𝑁 𝑆𝑀 𝑚 𝐒𝐌 𝑘 ω 𝑗 𝑚 = 𝐒𝐌 𝑡𝑖𝑚𝑒 𝐒 ω 𝑗 𝑚 = 𝐀𝐒𝐌 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 BP1 set 1: Power spectrum of the magnetic field BP1 set 2: Power spectrum of the electric field BP1 set 3: Wave normal vector (from B) BP1 set 4: Wave ellipticity estimator (from B) BP1 set 5: Wave planarity estimator (from B) BP1 set 6: XSO-component of the Poynting vector BP1 set 7: Phase velocity estimator BP2 set 1: Autocorrelations BP2 set 2: Normalized cross correlations [ RPW Team Meeting #6 – Prague ] [ RPW Team Meeting #7– Toulouse ] LPP/CNRS – SO RPW Team Meeting #14 – January 29-30, 2014 – CNES Paris, France

Cadences of the spectral matrix computation FSM_m sampling frequency 𝑁 𝐹𝐹𝑇 =256 f0 = 24576 Hz 96 SM / s ... ... f1 = 4096 Hz 16 SM / s ... ... ... ... f2 = 256 Hz 1 SM / s ... ... time 1 s LPP/CNRS – SO RPW Team Meeting #14 – January 29-30, 2014 – CNES Paris, France

LFR Normal Mode (1) Basic Parameters sampling frequency ... BP: 1080 bps WF: 2734 bps ASM: 32 bps TM: 3846 bps Basic Parameters sampling frequency BP1 & BP2 BP1 & BP2 BP1 BP1 BP1 ASM BP1 4 SMs 64 SMs 384 SMs 4 SMs 64 SMs 384 SMs 4 SMs 64 SMs 384 SMs 4 SMs 64 SMs 384 SMs 4 SMs 64 SMs 384 SMs 4 SMs 64 SMs 384 SMs 4 SMs 64 SMs 384 SMs f0 = 24576 Hz ... TBP1_0= 4 s ... f1 = 4096 Hz ... TBP1_1= 4 s ... f2 = 256 Hz ... TBP1_2= 4 s ... ... 4 s continuous WF ... f3 = 16 Hz 20 s time LPP/CNRS – SO RPW Team Meeting #14 – January 29-30, 2014 – CNES Paris, France

LFR spectral frequencies The spectral matrices are averaged over packets of 8 consecutive frequencies : 128 possible frequencies for NFFT = 256 (mean value is dropped) Δ 𝑓 𝑚 = 𝑓 𝑚 𝑁 𝐹𝐹𝑇 × 𝑁 𝑓𝑟𝑒𝑞 𝑚 𝑁 𝑓𝑟𝑒𝑞 𝑚 =8 f3 = 16 Hz => wave form [DC, 8Hz] f3 / 2.5 = 6.4 Hz f2 = 256 Hz => 12 frequencies [6.5Hz, 102.5Hz] Δ f (2) = 8 Hz f2 / 2.5 = 102.4 Hz f1 = 4096 Hz => 13 frequencies [88Hz, 1752Hz] Δ f (1) = 128 Hz f1 / 2.5 = 1638.4 Hz f0 = 24576 Hz => 11 frequencies [1584Hz, 10032Hz] Δ f (0) = 768 Hz f0 / 2.5 = 9830.4 Hz 10-1 100 101 102 103 104 Hz 6.4Hz 6.5Hz 102.5Hz 88Hz 1752Hz 1584Hz 10032Hz 𝐒= 𝐀𝐒𝐌 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 LPP/CNRS – SO RPW Team Meeting #14 – January 29-30, 2014 – CNES Paris, France

LFR Normal Mode (2) WaveForms & Averaged Spectral Matrices TASM= 3600 s sampling frequency TWF= 300 s WF BP1 ASM BP1 WF 384 SMs 384 SMs 384 SMs f0 = 24576 Hz 1/12 s ... ... ... 64 SMs 64 SMs 64 SMs f1 = 4096 Hz 1/2 s ... ... ... 4 SMs 4 SMs 4 SMs f2 = 256 Hz 8 s ... ... ... 2048 pts ... f3 = 16 Hz 4 s ... continuous WF ... time LPP/CNRS – SO RPW Team Meeting #14 – January 29-30, 2014 – CNES Paris, France

Binary representation of the waveform data 14-bit ADCs : (@ 98304 Hz) x 𝐴𝐷𝐶 𝑡 𝑗 = 𝑏 13 2 13 + 𝑏 12 2 12 + 𝑏 11 2 11 +...+ 𝑏 3 2 3 + 𝑏 2 2 2 + 𝑏 1 2 1 + 𝑏 0 2 0 ≡ 𝑏 13 𝑏 12 𝑏 11 𝑏 10 𝑏 9 𝑏 8 𝑏 7 𝑏 6 𝑏 5 𝑏 4 𝑏 3 𝑏 2 𝑏 1 𝑏 0 𝐿𝑆𝐵 14 = 2× 𝑉 𝑚𝑎𝑥 2 𝑛 with𝑛=14and 𝑉 𝑚𝑎𝑥 =3.0V ≃366μV (at LFR input) 16 bits in the FPGA after decimation down to f0 = 24576 Hz and f1 = 4096 Hz : x 𝐹𝑃𝐺𝐴 𝑡 𝑗 = 𝑏 13 2 13 + 𝑏 12 2 12 + 𝑏 11 2 11 +...+ 𝑏 3 2 3 + 𝑏 2 2 2 + 𝑏 1 2 1 + 𝑏 0 2 0 + 𝑏 −1 2 −1 + 𝑏 −2 2 −2 ≡ 𝑏 13 𝑏 12 𝑏 11 𝑏 10 𝑏 9 𝑏 8 𝑏 7 𝑏 6 𝑏 5 𝑏 4 𝑏 3 𝑏 2 𝑏 1 𝑏 0 𝑏 −1 𝑏 −2 𝐿𝑆𝐵 15 = 𝐿𝑆𝐵 14 2 1 ≃183μV 𝐿𝑆𝐵 16 = 𝐿𝑆𝐵 14 2 2 ≃92μV In case of small signals, possibility of 18 bits for f2 = 256 and 20 bits for f3 = 16 Hz : x 𝐹𝑃𝐺𝐴 𝑡 𝑗 = 𝑏 9 2 9 + 𝑏 8 2 8 +...+ 𝑏 2 2 2 + 𝑏 1 2 1 + 𝑏 0 2 0 +...+ 𝑏 −4 2 −4 + 𝑏 −5 2 −5 + 𝑏 −6 2 −6 ≡ 𝑏 13 𝑏 12 𝑏 11 𝑏 10 𝑏 9 𝑏 8 𝑏 7 𝑏 6 𝑏 5 𝑏 4 𝑏 3 𝑏 2 𝑏 1 𝑏 0 𝑏 −1 𝑏 −2 𝑏 −3 𝑏 −4 𝑏 −5 𝑏 −6 Should be ok for SCM data but for BIAS data? 𝐿𝑆𝐵 20 = 𝐿𝑆𝐵 14 2 6 ≃6μV LPP/CNRS – SO RPW Team Meeting #14 – January 29-30, 2014 – CNES Paris, France

Finite number of bits in computation of the FFT The FFT input are 16-bit integers : x 𝐹𝑃𝐺𝐴 𝑡 𝑗 = 𝑏 13−𝑑 2 13−𝑑 + 𝑏 12−𝑑 2 12−𝑑 +...+ 𝑏 0−𝑑 2 0−𝑑 + 𝑏 −1−𝑑 2 −1−𝑑 + 𝑏 −2−𝑑 2 −2−𝑑 ≡ 𝑏 13−𝑑 𝑏 12−𝑑 𝑏 11−𝑑 𝑏 10−𝑑 𝑏 9−𝑑 𝑏 8−𝑑 ... 𝑏 2−𝑑 𝑏 1−𝑑 𝑏 0−𝑑 𝑏 −1−𝑑 𝑏 −2−𝑑 The FFT output are also16-bit integers : FFT 𝑚𝑖𝑛 = 𝐿𝑆𝐵 16 - Currently X 𝐹𝑃𝐺𝐴 ω 𝑖 = 𝑏 13−𝑑 2 13−𝑑 +...+ 𝑏 −1−𝑑 2 −1−𝑑 + 𝑏 −2−𝑑 2 −2−𝑑 ≡ 𝑏 13−𝑑 𝑏 12−𝑑 𝑏 11−𝑑 𝑏 10−𝑑 𝑏 9−𝑑 𝑏 8−𝑑 ... 𝑏 2−𝑑 𝑏 1−𝑑 𝑏 0−𝑑 𝑏 −1−𝑑 𝑏 −2−𝑑 - with 1 extra bit X 𝐹𝑃𝐺𝐴 ω 𝑖 = 𝑏 12−𝑑 2 12−𝑑 +...+ 𝑏 −1−𝑑 2 −1−𝑑 + 𝑏 −2−𝑑 2 −2−𝑑 + 𝑏 −3−𝑑 2 −3−𝑑 ≡ 𝑏 13−𝑑 𝑏 12−𝑑 𝑏 11−𝑑 𝑏 10−𝑑 𝑏 9−𝑑 𝑏 8−𝑑 ... 𝑏 2−𝑑 𝑏 1−𝑑 𝑏 0−𝑑 𝑏 −1−𝑑 𝑏 −2−𝑑 𝑏 −3−𝑑 FFT 𝑚𝑖𝑛 = 𝐿𝑆𝐵 16 2 = 𝐿𝑆𝐵 17 LPP/CNRS – SO RPW Team Meeting #14 – January 29-30, 2014 – CNES Paris, France

SCM preamp noise & LFR resolution 1 extra bit for the FFT result : FFT 𝑚𝑖𝑛 = 𝐿𝑆𝐵 16 2 = 𝐿𝑆𝐵 17 𝑑𝑓= 𝑓 sampling 256 𝑁 𝐹𝐹𝑇 =256 f3 = 16 Hz Smallest onboard calculable FFT : 768 PSD_FFT≃ FFT 𝑚𝑖𝑛 2 × 2 𝑑𝑓 f2 = 256 Hz 768 192 Quantification noise for n-bit (ideal) digitization : PSD_WF≃ 𝐿𝑆𝐵 𝑛 2 2 3 × 2 𝑓 sampling f1 = 4096 Hz f0 = 24576 Hz LPP/CNRS – SO RPW Team Meeting #14 – January 29-30, 2014 – CNES Paris, France

SCM dynamic range MAXIMUM EXPECTED MAGNETIC PERTURBATION AT LFR INPUT sigma 1Hz-100kHz = 2.357 V sigma 1Hz-10kHz = 2.354 V sigma 1Hz-1750Hz = 2.252 V sigma 1Hz-100Hz = 1.925 V sigma 1Hz-6.5Hz = 0.031 V => 16 (+ 4 bits) for WF @ f3=16Hz ? LPP/CNRS – SO RPW Team Meeting #14 – January 29-30, 2014 – CNES Paris, France

LPP/CNRS – SO RPW Team Meeting #14 – January 29-30, 2014 – CNES Paris, France

BIAS required sensitivity level & LFR resolution f2 = 256 Hz f1 = 4096 Hz f3 = 16 Hz f0 = 24576 Hz LPP/CNRS – SO RPW Team Meeting #14 – January 29-30, 2014 – CNES Paris, France

BIAS required sensitivity level & max PSD AC cutoff at : MAXIMUM EXPECTED ELECTRIC PERTURBATION AT LFR INPUT 1) DC dV (Gain=1) & PSD_max = 1.0e-05 (V/m)^2/Hz sigma_f0 (0.0Hz-10kHz) = 1.897 V sigma_f1 (0.0Hz-1750Hz) = 0.794 V => 4 (+ 2 bits) for FFT @ f1=4096Hz ? sigma_f2 (0.0Hz-100Hz) = 0.190 V => 16 (+ 4 bits) for FFT @ f2=256Hz ? sigma_f3 (0.0Hz-6.5Hz) = 0.048 V 5 Hz ? 50 Hz 2) AC dV (Gain=5, cutoff=50Hz) & PSD_max = 1.0e-09 (V/m)^2/Hz sigma_f0 (50.0Hz-10kHz) = 0.1 V sigma_f1 (50.0Hz-1750Hz) = 0.039 V sigma_f2 (50.0Hz-100Hz) = 0.007 V => 4 (+ 2 bits) for FFT @ f1=4096Hz ? => 16 (+ 4 bits) for FFT @ f2=256Hz ? MOREOVER ! 20 times larger seems possible for AC signals => Gain = 100 ? push AC cutoff frequency down to 5 Hz ? LPP/CNRS – SO RPW Team Meeting #14 – January 29-30, 2014 – CNES Paris, France

An additional mode for the BIAS AC dV signals ? DC V (G=1/15) DC dV ~ E (G=1) AC dV ~ E (G=5, 50Hz) ? R2 LPP/CNRS – SO RPW Team Meeting #14 – January 29-30, 2014 – CNES Paris, France

Additional slides I LPP/CNRS – SO RPW Team Meeting #14 – January 29-30, 2014 – CNES Paris, France

Averaging random variables LPP/CNRS – SO RPW Team Meeting #14 – January 29-30, 2014 – CNES Paris, France

Increase of the precision by averaging (1) LPP/CNRS – SO RPW Team Meeting #14 – January 29-30, 2014 – CNES Paris, France

Increase of the precision by averaging (2) LPP/CNRS – SO RPW Team Meeting #14 – January 29-30, 2014 – CNES Paris, France

LFR block diagram

L.F.R Processing chain

LFR 11 analogue inputs LPP/CNRS – SO RPW Team Meeting #14 – January 29-30, 2014 – CNES Paris, France

BIAS configurations LPP/CNRS – SO RPW Team Meeting #14 – January 29-30, 2014 – CNES Paris, France

LFR operational modes data produced and sent to DPU: data subsequently transmitted to S/C:   NM all (SW In-Situ) BM LFR ~10 min all NM (Shock) SBM1 ~15 min NM all (Type III) SBM2 90 - 120 min LPP/CNRS – SO RPW Team Meeting #14 – January 29-30, 2014 – CNES Paris, France

LFR (Shock) Selected-Burst Mode 1 BP: 12672 bps WF: 393216 bps ASM: 0 bps TM: 405888 bps sampling frequency BP1 & BP2 BP1 & BP2 BP1 BP1 BP1 BP1 BP1 24 SMs 24 SMs 24 SMs 24 SMs 24 SMs 24 SMs 24 SMs f0 = 24576 Hz ... TBP1_0= 0,25 s ... 0,25 s f1 = 4096 Hz ... ... continuous WF 1 s time LPP/CNRS – SO RPW Team Meeting #14 – January 29-30, 2014 – CNES Paris, France

LFR (Solar Wind In-Situ) Burst Mode BP: 5760 bps WF: 24576 bps ASM: 0 bps TM: 30336 bps sampling frequency BP1 & BP2 BP1 & BP2 BP1 BP1 BP1 BP1 BP1 96 SMs 96 SMs 96 SMs 96 SMs 96 SMs 96 SMs 96 SMs f0 = 24576 Hz ... TBP1_0= 1 s ... 16 SMs 16 SMs 16 SMs 16 SMs 16 SMs 16 SMs 16 SMs f1 = 4096 Hz ... TBP1_1= 1 s ... ... 1 s f2 = 256 Hz continuous WF ... 5 s time LPP/CNRS – SO RPW Team Meeting #14 – January 29-30, 2014 – CNES Paris, France

LFR (Type III) Selected-Burst Mode 2 BP: 5760 bps WF: 24576 bps ASM: 0 bps TM: 30336 bps Same products as for the BM sampling frequency BP1 & BP2 BP1 & BP2 BP1 BP1 BP1 BP1 BP1 96 SMs 96 SMs 96 SMs 96 SMs 96 SMs 96 SMs 96 SMs f0 = 24576 Hz ... TBP1_0= 1 s ... 16 SMs 16 SMs 16 SMs 16 SMs 16 SMs 16 SMs 16 SMs f1 = 4096 Hz ... TBP1_1= 1 s ... f2 = 256 Hz ... 1 s continuous WF ... 5 s time LPP/CNRS – SO RPW Team Meeting #14 – January 29-30, 2014 – CNES Paris, France