1. In-situ LF electric and magnetic field
measurements of the solar wind expansion:
Solar Orbiter capabilities
Thomas Chust1, Fouad Sahraoui1, Alessandro Retinò1, Matthieu Berthomier1, Paul Leroy1, Alexis Jeandet1, Ondrej Santolik2,3, Andris Vaivads4, Volodya Krasnoselskikh5, Milan Maksimovic6 and Stuart D. Bale7
(1) LPP/CNRS-Ecole Polytechnique-UPMC-P11, Palaiseau–St Maur, France
(2) Institute of Atmospheric Physics, Czech Academy of Sciences, Prague, Czech Republic
(3) Charles University, Prague, Czech Republic
(4) Swedish Institute of Space Physics, Uppsala, Sweden
(5) LPC2E/CNRS, Orléans, France
(6) LESIA, Observatoire de Paris, Meudon, France
(7) Department of Physics and Space Sciences Laboratory, University of California Berkeley, USA

2. Outlines Electron kinetics Ions kinetics Turbulence
Solar Orbiter mission and Radio & Plasma Waves (RPW) instrument
RPW Low Frequency Receiver (LFR)
Science objectives
Electron kinetics
Ions kinetics
Turbulence
Science requirements
Overall description and working modes
Engineering model
Conclusion / Summary

3. Solar Orbiter Solar Orbiter Exploring the Sun-Heliosphere Connection
First medium-class mission of ESA’s Cosmic Vision programme, implemented jointly with NASA
Dedicated and combined payload of 10 remote-sensing and in-situ instruments measuring from the photosphere into the solar wind
Nominal launch 2017

4. Solar Orbiter Exploring the Sun-Heliosphere Connection Mission Summary
Launch Date: 2017
Cruise Phase: 3 years
Nominal Mission: 3.5 years
Extended Mission: 2.5 years
Orbit: 0.28–0.91 AU (P= days)
Out-of-Ecliptic View:
Multiple gravity assists with Venus to
increase inclination out of the ecliptic
to >24° (nominal mission),
>34° (extended mission)
Reduced relative rotation:
Observations of evolving structures
on solar surface & in heliosphere for
almost a complete solar rotation

6. RPW Instrument Overview
Will allow the characterization of the electric and magnetic fields associated
to the dynamics of the near-Sun heliosphere from near DC up to 20 MHz
Main Electronic Box (MEB)
Electric Antennas (ANT)
3xV V LF
Bias Unit Sp W 1 V
1HF
Floating volt
age dr
iver V
5xV
BIAS
2HF V
3HF
3xV HF
TNR-HFR V
Auto & cr
oss-spectr a Sp W
1LF
(4kHz-20MHz) V
1xB HF
2LF V V V 2
3LF 3
3xV
Nom. SpW HF
TDS
to/from S/C
1xB HF
Wavefor
500kS/s Sp W
3xV
BIAS
+ LFR Redundancy
RPW-DPU
Search Coil Magnetometer
3xB LF
(SCM)
Red. SpW
to/from S/C B
2LF
5xV
LFR
BIAS
Waveform up
to 25kS/s Sp W B
3LF +
Auto &
cross-
spectr a
3xB LF + k-
vector
(~DC-10kHz) B
1LF
3.3V 2. 5V 5V +/ -1 2V B
1HF
28 V
LVPS-PDU
from S/C
Low Frequency Receiver

7. LFR Science Objectives
Study the electromagnetic/electrostatic activity in the extended corona and the near-Sun solar wind, from near DC to 10 kHz.
Will cover the electron gyrofrequency and most of the Doppler- shifted frequencies of the low frequency/small scale plasma waves, structures & turbulence.
Kinetic or inertial Alfven waves
Ion cyclotron waves
Ion acoustic waves
Magnetosonic or whistler mode waves
...
Their characterization and the determination of their respective role in heating and accelerating the solar wind, during its expansion, is the main scientific issue addressed by LFR.
Role of the low frequency/small scale plasma waves & structures associated to solar wind disturbances, e.g. interplanetary shocks, current sheets...

8. Doppler-Shifted Spatial Scales
whistler mode waves
→ a fraction of fce
ion acoustic waves
→ possibly up to
10 kHz and more
electron Larmor radius → Hz
electron inertial length
→ Hz
proton Larmor radius
→ 1-50 Hz
Δ𝑓= 𝑉 𝑆𝑊 λ
(k ρ = 1)

9. Kinetics of the Solar Wind Electrons
Fundamental role of the field/particle interactions.
Role of electron-scale
(k┴ ρe ≥ ~1),
low-frequency
(~fp ≤ f ≤ ~fe)
plasma processes
(waves, structures, turbulence, …) ?
Core (95 %)
bi-Maxwellian
Halo
Isotropic
Strahl
Magnetically field-aligned
Stverak et al., JGR, 2009

10. Radial Evolution of the Electron Core Temperature
Continuous heating of the SW electrons ?
Helios + Ulysses
Stepan Stverak, Thesis
Double-adiabatic CGL laws :
𝑇= 𝑇 ∥ 𝑇 ⊥ ∝ 𝑅 −4 3
BUT :
𝑣 𝑡ℎ𝑒 ≥ 𝑉 𝑆𝑊
Thus, it is not possible to conclude ...
0.3 4

11. Evidence for Instabilities Shaping the Electron VDFs
Helios, Cluster, Ulysses
Data set : ~ 125,000 samples
from 0.3 to 4 AU
Stverak et al., JGR, 2008
β ∥𝑒 = 𝑛 𝑒 𝑘 𝑏 𝑇 ∥𝑒 𝐵 μ 0
Similar for protons
(Kasper et al., SW Ten, 2003; Hellinger et al., GRL, 2006;
Marsch et al., AG, 2006)
Strong departures from isotropy are constrained by e.m. instabilities?

12. Radial Evolution of the Electron VDF Components
Helios, Cluster, Ulysses
Data set : ~ 240,000 samples
from 0.3 to 4 AU
Stverak et al., JGR, 2009
During expansion, strahl is transformed into halo by wave-particle interactions ?
0.3 4
Similar to fast solar wind (Maksimovic et al., JGR, 2005)

13. Continuous Heating of the Solar Wind Protons
Fundamental role of field/particle interactions.
Proton magnetic moment with distance to Sun
𝑣 𝑡ℎ𝑝 ≪ 𝑉 𝑆𝑊
Role of proton-scale
(k┴ ρp ≥ ~1),
low-frequency
(~fp ≤ f ≤ ~fe)
plasma processes
(waves, structures, turbulence, …) ?
Thus,
for a stationary
SW expansion,
CGL laws should apply ...
(E. Marsch 1991)

14. Evidence for Instabilities Shaping the Proton VDFs
Wind
Slow solar wind (< 600 km/s) core protons
Data set: 1995–2001
Proton cyclotron
Mirror
Hellinger et al., GRL, 2006 Ωp Ωp
% ∥𝑝 = 𝑛 𝑝 𝑘 𝑏 𝑇 ∥𝑝 𝐵 μ 0
Similar for electrons
(Stverak et al., JGR, 2008)
Parallel fire hose
Oblique fire hose
Strong departures from isotropy are constrained by e.m. instabilities?

15. Radial Evolution of the SW Proton Temperature Anisotropy
Helios, Ulysses
Proton cyclotron
instability
Mirror instability
Fast solar wind (> 600 km/s)
protons (all)
Matteini et al., GRL, 2007
CGL adiabatic prediction
Strong departures from isotropy are constrained by e.m. instabilities?
Extended heating needed for the protons ?
Parallel fire hose
β ∥𝑝 = 𝑛 𝑝 𝑘 𝑏 𝑇 ∥𝑝 𝐵 μ 0
Oblique fire hose

16. Ion Kinetics and Micro-turbulence
Wind
Solar wind expansion and compression drive the proton distributions towards pressure anisotropy instability thresholds:
1. Alfven/Ion-cyclotron
2. Mirror mode
3. Firehose instabilities
Wind measurements (> 1M) show δB fluctuations associated with these instability thresholds, suggest mirror and oblique firehose.
These instabilities inject fluctuation power directly at kρi~1 (in contrast to the turbulent cascade).
mirror
oblique
fire hose
β ∥𝑝 = 𝑛 𝑝 𝑘 𝑏 𝑇 ∥𝑝 𝐵 μ 0
Bale et al., PRL, 2009

17. Enhanced proton temperatures near the instability thresholds
Parallel heating near firehose threshold
Perpendicular heating near
Ion Cyclotron/Mirror threshold
Wind
Kasper et al., ArXiv, 2009

18. Turbulent Heating by KAW / Whistler Waves?
Turbulence: “energy” flows from large to small scales
This is manifested by power-law spectra connecting these scales
LFR range of observation ? ? ?
𝑘 ⊥ ρ 𝑒 ∼1
In SW at AU :
(Δf ~ 1-50 Hz)
(Δf ~ Hz)

19. Evidence for a ┴ Cascade up to the Proton Scale
Cluster
wavelet
Phase speed is ~Alfven speed
Dispersion at short wavelength is like Kinetic Alfvén Wave
Strong evidence/consistency with KAW turbulence
FFT E B
(FGM data)
(22 samples / sec)
Evidence for a turbulent dissipation at the proton gyroscale?
What above kρp ~ 1 ?
Cascade up to the electron scale?
~ phase speed
(dispersion like KAW)
Bale et al., PRL, 2005
(also Sahraoui et al., PRL, 2009)

20. Evidences for a Cascade well above the Proton Scale
Cluster
A first case study
Another similar study (several cases)
SCM
spectral data
SCM
waveform data
FGM
SCM noise floor
Alexandrova et al., PRL, 2009
Sahraoui et al., PRL, 2009
Evidences of a cascade up to the electron gyroscale?
What after ? Exponential spectral feature or power law?
Observational limitations : noise floor both for δE and δB …

21. Observational Limitations : Signal to Noise Ratio
Cluster
(SCM waveforms)
Distribution of the spectral indices (magnetic data)
Solar Wind (moderate SNR)
(10<SNR<20)
SNR=10log 𝑆 𝑠𝑖𝑔𝑛𝑎𝑙 𝑆 𝑛𝑜𝑖𝑠𝑒
@ 30 Hz
Magnetosheath (high SNR)
(10<SNR<40)
[Sahraoui et al., ApJ, 2013;
Huang et al., arXiv, 2013]

22. LFR Science Requirements (1)
Characterizing the LF electromagnetic waves & fields in the solar wind involves the capability of LFR :
to cover turbulence and plasma instabilities
to distinguish solitary waves from broadband wave activity
to identify the wave modes at work (if any)
Performing a multi-component analysis of the data is thus mandatory, using either a classical Fourier analysis or another treatment more appropriate to turbulence analysis.
Transmission of waveforms (not only auto & cross spectra).
Good frequency and time resolutions are needed.
High SNR (instrument resolution) also needed !

23. LFR Science Requirements (2)
Magnetic field fluctuations
Electric field fluctuations
maxima of the magnetic level values observed with Helios
This is the required level for LFR strong electric field measurement
(Fix the dynamics of LFR magnetic field measurements)
SCM noise floor (LF band)
This is the required level for LFR weak electric field measurements
SCM noise floor
(HF band)
LFR have to be able
to measure it

24. LFR Decimation and Processing Strategy
8 ADCs @ Hz
decimation
down to ß Hz
( f0 )
(14 bits ideally)
:32 :3
(16 bits)
(15 bits)
(16 bits)
(16 bits) Hz
4 096 Hz
16 Hz
256 Hz
shaping :3 :2
:64 :4
[20 bits ?]
[18 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)

25. Current set of Basic Parameters
“Instantaneous” 5 x 5 spectral matrix
(256 FFT points)
Time Averaged Spectral Matrix (ASM)
𝐀𝐒𝐌 ω 𝑗 𝑚 = 1 𝑁 𝑆𝑀 𝑚 𝑘=1 𝑁 𝑆𝑀 𝑚 𝐒𝐌 𝑘 ω 𝑗 𝑚 = 𝐒𝐌 𝑡𝑖𝑚𝑒
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 ∗
Frequency average ...
𝐒 ω 𝑗 𝑚 = 𝐀𝐒𝐌 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦
... before computations of the BPs
(i.e. wave parameters)
BP1 set 1: Power spectrum of the magnetic field (B)
BP1 set 2: Power spectrum of the electric field (E)
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(radial)-component of the Poynting vector
BP1 set 7: Phase velocity estimator
BP2 set 1: Autocorrelations
BP2 set 2: Normalized cross correlations
Mono-k
assumption :
(Means, JGR, 1972)
(Samson & Olson, GJRA, 1980)
𝐧×𝐄 = ω 𝑘 𝐁
𝑆 𝑖𝑗 𝑆 𝑖𝑖 𝑆 𝑗𝑗

26. LFR Spectral Frequencies
Depending on the frequency channel, selection of 96, 104 or 88 consecutive frequency bins among 128 (NFFT = 256) of the time averaged spectral matrices.
Then, the ASMs are averaged over packets of Nfreq (8 or 4) consecutive bins :
Δ 𝑓 𝑚 = 𝑓 𝑚 𝑁 𝐹𝐹𝑇 × 𝑁 𝑓𝑟𝑒𝑞
𝑁 𝑓𝑟𝑒𝑞 =8
f3 = 16 Hz => waveform [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 = Hz
f1 = 4096 Hz => 13 frequencies [88Hz, 1752Hz] Δ f (1) = 128 Hz f1 / 2.5 = Hz
f0 = Hz => 11 frequencies [1584Hz, 10032Hz] Δ f (0) = 768 Hz f0 / 2.5 = Hz
10-1
100
101
102
103
104 Hz
6.4Hz
continuous waveform
6.5Hz
102.5Hz
96 bins
88Hz
1752Hz
104 bins
1584Hz
10032Hz
𝐒= 𝐀𝐒𝐌 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦
88 bins

27. LFR Normal Mode (1) Basic Parameters sampling frequency ...
BP: bps
WF: bps
ASM: bps
TM: 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 = 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

28. WaveForms & Averaged Spectral Matrices
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 = 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
...
4 s
...
continuous WF
...
f3 = 16 Hz
time

29. LFR Selected Burst Mode 1
BP: bps
WF: bps
ASM: bps
TM: 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 = Hz
...
TBP1_0= 0,25 s
...
0,25 s
f1 = 4096 Hz
...
continuous WF
...
1 s
time

30. LFR Selected Burst Mode 2
BP: bps
WF: bps
ASM: bps
TM: 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 = 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

31. LFR Engineering Model
FPGA
ADCs
(RTAX4000
emulator)
November 2013

32. Conclusion / Summary
LFR is one of the subsystems of the Solar Orbiter Radio and Plasma Waves (RPW) instrument.
Will perform the on-board digital processing of the low frequency electromagnetic field & wave data (1V, 2E, 3B), measured in the extended corona and the near-Sun solar wind.
Frequency range of investigation: ~0.1 Hz < f < 10 kHz.
[ microphysics of the SW (heating, turbulence, VDF, ...)]
Will combine different output data: from low-level (WF) to high-level (SM & BP) processed data.
[ assessment of k => dedopplerization ]
Will allow to increase the scientific return for a given telemetry by implementing different strategies for analyzing and transmitting the data.