ESS 265 Winter Quarter 2010MAGNETOMETERS: DC AND AC, AND TIME SERIES/WAVES ANALYSIS

Magnetometer Operation Principles/AccommodationCalibration and Noise SourcesCalibration and Noise Sources

Amplitude/Phase Frequency ResponseAccess and Use of Data from Various Regions

Solar Wind, Magnetosphere, Ground

References:Elphic et al., Magnetic field instruments for the FAST mission, Space Science Reviews, 2001

Auster et al., The THEMIS fluxgate magnetometer, Space Science Reviews, 2008.Snare, R.C. (1998) A History of Vector Magnetometry in Space Measurement Techniques in Space Plasmas -

Fields: Geophysical Monograph 103. Edited by Robert F. Pfaff, Joseph E. Borovsky and David T. Young.Published by the American Geophysical Union, Washington, DC USA, 1998, p.101

Roux et al., The Search Coil Magnetometer for THEMIS, Space Science Reviews, 2008LeContel et al., First results of the THEMIS search coil magnetometers , Space Science Reviews, 2008

Contributions from: Chris Russell, David Pierce, Uli Auster, Werner Magnes, Rumi Nakamura,

Alain Roux, Olivier le Contel, Christoffe Coillot, Peter Harvey

1 Lecture 2 Jan 14, 2010

Magnetometers: Where do we d ?need measurements?

• There are measurable magnetic fields almost everywhere one can explore They almost always provide very useful informationexplore. They almost always provide very useful information.

• They can provide information about the interiors of bodies that are otherwise inaccessible. They can provide information on physical y p p yprocesses that are occurring in remote locations.

• There are extensive magnetometer arrays on the surface of the EarthEarth.

• There are magnetometers being flown to every corner of the solar system.y

• While the techniques are similar on the ground and in space, each region has its own special requirements. Sometimes in fact, space is a more benign environment for instrumentation

2

a more benign environment for instrumentation.

Early MagnetometryEarly Magnetometry

• Early magnetometers were digital. Humans copied dawn readings on paper.• Magnetic measurements became quantitative about 1550, allowing us to

follow the long-term variation of the Earth’s internal field.

3

follow the long term variation of the Earth s internal field.• Eventually, the strip chart recorder was invented and it was possible to take

more rapid data using smoked chart paper, microfilm and eventually pens.

Types of Magnetometers

Type of magnetometer

Basic Principle Output quantity / limits Space application?

Classical Instruments manipulation with field direction (compass) NoClassical Instruments manipulation with magnets

field direction (compass)field variation (e.g. QHM) horizontal force (Theodolites) 100pT / (minutes ... DC)

No

Search Coil Faraday’s law of i d i

field vector (dB/dt) 0 01 10 T / (50kH 1H )

Yes induction 0.01..10pT / (50kHz ... 1Hz)

Fluxgate saturated transformer field vector 10pT / (100Hz ... DC)

Yes

Optical Pumped Zeeman splitting, Lamor frequency

scalar magnetometer with coil system vector

Rubidium in 60th He onboard Cassiniq y y

1pT (1kHz ... DC) Proton /Overhauser proton precession,

gyro magnetic ratio scalar magnetometer with coil system vector 10pT (1Hz ... DC absolute)

Yes

SQUID Josephson effect field vector (dB/dt) NoSQUID Josephson effect field vector (dB/dt) 0.1pT / (100kHz ... 0.001Hz)

No

Magneto resistive Anisotropic Magnetoresistive Effect

field vector 10nT / (100Hz ... DC)

(attitude control)

Hall Lorentz Force field vector No

4

1mT / (30kHz ... DC)

B-field measurement - overview

Fluxgate Magnetometer

BPickup Feedback

BExtern + BExcitationBExcitation

BBExtern Excitation

BExtern – BExcitation

U

ddt

d nA t H tdt

r 0 ( ) ( )

5B-field measurement - fluxgate (1)

Fluxgate Magnetometer

• Principle of Operation– Magnetic material saturated by symmetric AC (f0) drive current– Secondary signal becomes asymmetric if external field disturbs the

b hif i h i h h isymmetry by shifting the zero point on the hysteresis– Second harmonics of drive frequency is quantity for asymmetry =

magnitude of external field– Field feedback holds working point close to zeroField feedback holds working point close to zero

• Parameters– Measurement range: Solar Wind (10th of nT) - Earth field 60.000nT – Frequency range: 100Hz ... DCq y g– Stability: 1nT...10nT/year – Noise: 10pT/sqrt(Hz) at 1Hz – 1/f spectrum

• Application– Ground application: e.g. observatories, EMT-sounding, applied

physics– Space application: all magnetosphere, nearly all planetary

missions attitude control for low Earth missions

6

missions, attitude control for low Earth missions

Operation Principle

H

BB

2 t

U

2

t

t

A12

A1112 11

12 11

U

2221A21

U

t21 22A22

H

7

Search Coil Magnetometer

Pickup Feedback

dBExtern/dt

Pickup Feedback

Extern

dt

tHnAddtdU r )(0

dtdt

8B-field measurement - search coil (1)

• Principle of OperationSearch Coil Magnetometer

p p– Application of Faraday‘s law– Output signal depends on µr (long core to keep the

demagnetisation factor low), N (weight of copper) and A (weight of softmagnetic material)softmagnetic material)

– Sensitivity depends on frequency due to (dB/dt) behaviour and resonance of coil-electronics system.

• Parameter– Noise at 1Hz: 10pT/sqrt(Hz)– Noise at 10 kHz: 0.01pT/sqrt(Hz)

• Applicationpp– Ground application:

Audio EMT-sounding– Space application:

all magnetosphere missionspartly on planetary missions

9[D.A.Gurnett, 1998]B-field measurement - search coil (2)

Definition of the Noise Equivalent Magnetic Induction (NEMI) :

Equivalent output voltage noise (en): 2222 )(]Re[4 ZiZkTeGoe

ePA

output voltage :

)(]Re[4 PAPAn ZiZkTeGoe

Z(Sensor)

iPAGo (dB) ]Re[4222 ZkTeGoe PAn

PSD of output voltage :

):)((*)( FunctionTransferjTFBjTFVout

2)*)(( BTF 22B

NEMI is then defined as square root of the magnetic field spectral power density :

22

nout edf

V

22)*)((

nedf

BjTF

2

22

))(( jTFe

dfB n

NEMI is the ability of the magnetometer to measure weak magnetic fields

)/()()/(

)/(TVjTF

HzVeHzTNEMI n

dfBNEMI

2

See also: Pappas & Dolabdjian

10

NEMI is the ability of the magnetometer to measure weak magnetic fields.

Search-coil: N turns wounded around a high permeability magnetic core. Electrokinetics representation : Induced voltage eInductance L1, Resistance R1 (of the winding), capacitance C1(comes mainly from electrostatic energy stored between layers of the

R1

1k

L1

7 5H

1 2d/dt

N1*S*µapp--- Direct amplification

--- Feedback flux

Bout(comes mainly from electrostatic energy stored between layers of the winding)

Voute

0

1k7.5H

C155p

Bout

0

Go=

1001CLo

1 jC

11CL

Feedback flattens response

11

111

1

11

jCjLRjCeVout

Resonance degrades response

pintroduces 180o phase shift

Helium Magnetometry: Electron Larmor Resonance

Fundamental properties of an electron: Angular momentum: ] , [ 106.6 134 kgmsorNsmorsJ

)1(2 llme

Be

L µLµ

Magnetic moment along B:

Relation between both:

124102.9 TJmlBμμ

e

gyro magnetic ratio 1111 10 76.1 TsradeProperties of an electron in an external B-field

Torque:

Relation between L and T:

BμT

dtd LT

Precession:

This is: 176 rad/s/nT, or 28Hz/nT

dt0Be

12

• Principle of OperationHelium Magnetometer (Scalar)

p p– Get gas into metastable state that lasts a long time (10-4 s)– Use polarized light to pump one state (magnetize gas along field)– If no external damping force exists, then the electrons remain in polarized state– We then use RF signal to resonate with larmor frequency and de-pump electronse e use s g a o eso a e a o eque cy a d de pu p e ec o s

• De-pumping results in additional absorption of the polarized signal– This is detected by a cell on the other side

– The RF signal has an FM width ~356Hz to continuously search for the Larmon Freq.– Controlling FM frequency center with feedback ensures it “tracks” Larmor freq.

Output is in second harmonic (symmetric) unless FM signal is off centered– Output is in second harmonic (symmetric) unless FM signal is off-centered– Fundamental amplitude is isolated, integrated and is proportional to frequency shift

• Parameters– Measurement range: Solar Wind (10th of nT) - Earth field 60.000nT

F 10H DC– Frequency range: 10Hz ... DC– Stability: 0.05nT...0.2nT/year – Noise: 10pT/sqrt(Hz) at 1Hz – white noise

• ApplicationG d li ti b t i li d h i– Ground application: e.g. observatories, applied physics

– Space application: magnetospheres, ionospheres

13SAC-C

scalar magnetometers (2 ea)

Helium Magnetometer (Vector)• Principle of Operationp p

– Same components as Scalar sensor, except use Helmholz coils to null field– Optical axis, Z, along the circularly polarized excitation light has highest sensitivity– Coils use to also drive sine-signal on a plane (XZ or YZ) resulting in cos2 response– Output is in 2nd harmonic (symmetric/even) unless external field present Ou pu s a o c (sy e c/e e ) u ess e e a e d p ese

(fundamental/odd)– Fundamental amplitude is isolated, integrated and is proportional to B from zero.

• Parameters– Measurement range: Solar Wind (10th of nT) - Earth field 60.000nT g ( )– Frequency range: 10Hz ... DC– Stability: 0.05nT...0.2nT/year – Noise: 10pT/sqrt(Hz) at 1Hz – white noise

• Applicationpp– Ground application: e.g. observatories,

applied physics– Space application: magnetospheres,

ionospheres

14Ulysses

Vector helium magnetometer

Helium Vector MagnetometerHelium Vector Magnetometer

• Has null zone along optic axis• Sensor can be used for both scalar and vector mode• Is useful above 250 nT

15

Helium Magnetometer, ElectronicsElectronics

16

Proton Magnetometer (NMR)

Fundamental properties of a proton:Angular momentum: 123510275 smkgLAngular momentum:

Magnetic moment:

Relation between both:

2261041.1 mAμLµ P

1027.5 smkgL

Relation between both:

gyro magnetic ratio 11 267515528 TsradP

µ P

Properties of a proton in a B-fieldTorque: BμT

d LRelation between L and T:

Precession:dt

d LT

0BP

17This is: 0.27 rad/s/nT, or 0.043 Hz/nT

Proton Magnetometer

• Principle of Operation– Sensor is a bottle of water (alcohol) + coil for polarization and pick up( ) p p p– Polarization aligns all protons – Fast change from polarization to pick up provides in-phase precession– Frequency is measured, signal amplitude depends on time (relaxation)

• Parameter– Measurement range: 20.000nT ... 100.000nT – Frequency range: 1Hz ... DC

R l ti ti 1– Relaxation time: 1sec – Accuracy: 0.1nT absolute

• Application– Ground application: observatories applied physics– Ground application: observatories, applied physics– Space application: missions investigating the Earth field

18B-field measurement - NMR (2)

Vector measurement by scalar sensors• Measurement of field components using a scalar• Measurement of field components using a scalar

magnetometer– Sensor has to be equipped with a coil system for bias fields– Applying fields in + and - direction field components can be

ZHF 222

– Applying fields in + and - direction, field components can be derived by a set of three scalar measurements: F+, F and F-

HBBFZBHF

HBBFZBHF

2

222222

22222

22

2222

4

2

HBFF

BFFF

222

22

222 FFFFFH

19

Space Based Magnetometry Examples: Themis

• Fluxgate Magnetometer, FGM– PI: K.H. Glassmeier, TU-

Braunschweig– Single sensor (2m boom), digital

electronics

S h C il M t t SCM• Search Coil Magnetometer, SCM– PI: A.Roux, CEPT – The SCM 3-axis antennas are

located at the end of 1 meter SCMlocated at the end of 1 meter SCM boom

• Instrument Data Processing Unit– FGM processing ½ board– Digital Fields (full) Board (DFB)

20Examples - Themis

THEMIS Ground-based Fluxgate MMagnetometer

21• Three orthogonal sensors are put in a tube on a printed

circuit board.

THEMIS Ground-based Fluxgate MMagnetometers

Th i t i PVC t b d t d b l bl t

22

• The sensor is put in a PVC tube and connected by a long cable to the electronics.

• The sensor is buried in the ground.

THEMIS Ground-based Fluxgate MMagnetometers

• Millisecond timing is provided by a GPS s stem

23

GPS system.• The full set of equipment can be

packed in a small shipping container.

Spaceraft Accommodation of Sensor

• Boom Geometry– 1-3 segment boom

(Cluster Double Star, Themis )Themis ...)

– Boom made by spring elements (MMO)

– Wire Booms (Cluster, ( ,Themis ...)

• Release & launch lock mechanism

P– Pyro– Melting band,– Motor driven

• Deployment force• Deployment force– Centrifugal force– Spring driven– Motor driven

24

Motor drivenRequirements on S/C - Booms

Required Resources

101214

Cluster Experiment Mass

101214

Themis Experiment Mass

• Mass

02468kg

FGM Staff EDI EFW

Experiment Boom

02468kg

FGM SCM EFI IDPU

Experiment Boom

• Power

Experiment Boom Experiment Boom

910

Cluster Experiment Power

910

Themis Experiment Power

Power

12345678

W

12345678

W

01

FGM Staff EDI EFW01

FGM SCM EFI IDPU

25Requirements on S/C - Resources

Thermal Environment20

FGM - 30% AZ 2000 70% VDA (04/14/04)SAA 103 Hot - SAA 90 Cold - SAA 77 Cold - SAA 77 Cold Low Power

INNER BOOM OUTER BOOM DECK HINGE ELBOW HINGE SENSOR TOPDECK INNER BOOM OUTER BOOM

DECK HINGE ELBOW HINGE SENSOR TOPDECK INNER BOOM OUTER BOOM DECK HINGE ELBOW HINGE

SENSOR TOPDECK INNER BOOM OUTER BOOM DECK HINGE ELBOW HINGE SENSOR TOPDECK

-60

-40

-20

0

Tem

pera

ture

-100

-80

50K 100K 150K 200K 250K 300KTime

Sensitivity to Sensor Temperature

• Thermal requirements– Sensors have wide temperature range

Eclipse crossings must be buffered by high thermal capacity

Sensitivity to Electronics Temperature

26

– Eclipse crossings must be buffered by high thermal capacity– Averaged temperature depends on alpha/epsilon of MLI/OSR

CALIBRATION OF FLUXGATE MAGNETOMETERS

27

Parameter Error Source typ. value

CALIBRATION OF FLUXGATE MAGNETOMETERS

yp

Offsets (output at zero field) depends on time and temp.

asymmetry of sensor and excitation offsets of DC electronics, ADC ...

0-10nT 0.2nT/day; 0.05nT/°C

Scale value depends on temperature

scale value shall depends on feedback circuitry only – current source & feedback coil system

10-4 1-30ppm/°C

N li it t l fb f t 2f0 li it 10-4Non linearity at low fb factors: 2f0 non linearity at high fb factors: feedback circuitry non linearity

10 4

Orthogonality vector compensated: depends on fb coil system single sensors depends on ringcore /pick up coil

10-4

Bandwidth frequency behavior depends on analogue or digital filter. Has to be switched with telemetry rate

Noise should be ringcore property (no contribution of electronics), depends on frequency

10pT/Sqrt(Hz) at 1Hz

0.1

0.05

0.06

0.07

0.08

0.09

qrt(H

z)]

0.01nT/Sqrt(Hz) @ 1Hz1Hz: 28pT rms

0.01

0.02

0.03

0.04

[nT/

Sq

128Hz: 80pT rms 0.5nT

28

noise

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

[Hz]

Ground Calibration Methods

Using well controlled, synthesized test fields Sensor placed in coil systems

i i i d h fi ld i i ll quiet environment required, Earth field variations as well as technical disturbances under control

Precise measurement /setting of coil currents

Air conditioning necessaryy

Calibration of coil system by (absolute) scalar magnetometerscalar magnetometer possible

Example: Magnetsrode l B h i

29Calibration - on ground - methods (1)

close to Braunschweig

Ground Calibration Methods (2)

Using the Earth field measured by a independent magnetometer

S l d bl ( i ) ill Sensor placed on a stable (non magnetic) pillar Registration of Earth field in parallel to standard observatory

instruments (or between flight models)10.5 10.6 10.7 10.8 10.9 11 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 [h] 12

12007.5

12008

12008.5

12009

11626

11626.5

11627

11627.5 Noise can be checked by short term registration of pulsation

1nT

12005

12005.5

12006

12006.5

12007

11624

11624.5

11625

11625.5

pulsation Drift can be checked after

days-weeks registration

12003

12003.5

12004

12004.5

11622

11622.5

11623

11623.5 Most of the observatories offer this service

30

10.5 10.6 10.7 10.8 10.9 11 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 [h] 12

Calibration - on ground - methods (2)

Ground Calibration Methods (3)

Using „zero“fields Sensor placed in

ferromagnetic can which shields the Earth field

Noise and offset stability can ybe checked

If sensor can be rotated offsets in componentsoffsets in components perpendicular to rotation can be determinedE l bl Example: transportable mu-metal can, equipped with temperature chamber (Graz)

31Calibration - on ground - methods (3)

Ground Calibration Methods (4)

Using a controlled motion of the sensor in the Earth field Rotation about a well defined axis perpendicular to the Earth field Misalignment rotation and magnetic axis results in a sine function Misalignment rotation and magnetic axis results in a sine function Misalignment can be absolutely derived by amplitude and phase

Using an arbitrary motion of theUsing an arbitrary motion of the sensor in the Earth field Assuming a linear transfer

function 9 of 12 elements (offsetfunction, 9 of 12 elements (offset, scale values, orthogonality) can be derived by comparison with the Earth field magnitudeEarth field magnitude

32Calibration - on ground - methods (4)

Inflight Calibration

Aim of inflight calibration Determination of 12 elements of transformation BM to BSC

Assumption: transformation is linear MCal Calibration Matrix; ZCal: Calibration Offset

BZBM SCCalMCal BZBM

• Calibration Matrix MCal shall be split up in three quantitiesS: represents scale values with elements in the main axis– S: represents scale values with elements in the main axis

– O: represents the non orthogonality (triangular matrix)– R: represents the orientation of the orthogonal system

SCCalM BRZBSO

p g yversus S/C system (rotation matrix)

33Calibration - in flight - aim

Calibration Inputs

Calibration methods are based on the following l irelevant inputs No spin and double spin tone in field magnitude Field properties (Earth field model Alfven waves )Field properties (Earth field model, Alfven waves, …) Knowledge of preflight calibration and MC results Experiment specifics, mode and housekeeping

information Independent field measurements Inter-calibration: using spacecraft comparisons (B1=BnInter calibration: using spacecraft comparisons (B1 Bn,

RotB=0, DivB =0) to level all instruments errors

34Calibration - in flight - inputs overview

Methods (1)

Field magnitude has to be independent from sensor motion

ZBSO !

RZBSO CalM ! 0

C diti• Conditions:– Bexternal constant– R = R( , , ) variable– O, S, ZCal doesn't depend on time and external field

• Effects assuming S/C rotation as motion– spin and double spin tone in field magnitude (4 equations)spin and double spin tone in field magnitude (4 equations)– All three angle of orthogonality affected– Offsets and scale values perpendicular to rotation axis affected

35Calibration - in flight - methods (1)

Example

Cluster C4 before calibration

36Calibration - in flight - methods (3) - example

Example

Cluster C4 after calibration

37Calibration - in flight - methods (3) - example

Methods (2)

Field magnitude has to be equal to the magnitude measured by an independent (scalar) magnetometer

SCCalM BRZBSO B!

C di i Conditions: Bexternal shall be variable R can be arbitraryy O, S, ZCal doesn't depend on time and external field

Examplesp Proton magnetometer on board satellites investigating the Earth

magnetic field (low orbits, e.g. Magsat, Oersted, Champ) EDI onboard Equator-S Cluster and MMS

38

EDI onboard Equator S, Cluster and MMSCalibration - in flight - methods (2)

Example

39Calibration - in flight - methods (2) - example

Methods (3)

Measured field vector has to be in agreement with known physical features

CalMf ZBSO ! ExpectationC diti Conditions: Bexternal shall be variable R can be arbitraryy O, S, ZCal doesn't depend on time and external field

Examplesp In agreement with Earth field models Alfven waves in solar wind Divergence B=0 Cavity of Comets

40Calibration - in flight - methods (3)

Divergence B=0, Cavity of Comets ...

Example

41Calibration - in flight - methods (3) - example

Inflight Calibration Procedure

Non orthogonal sensor system

scale, offset, non orthogonalityrange, mode

Orthogonal sensor system

sensor alignmentboom alignment

update of sensorparameters

S/C system S/C momentsof inertia

removing of S/Cgenerated offsets

Spin aligned S/C system

sun sensor align.filter type

tuning of spin alignmentspin tone in spin axis

Spin and sun aligned system

tuning of phase alignment comparison with IGRF

42

g y

Calibration - in flight - procedure

Example of Cal FileThe following manipulations have to be done with the FGM raw data Bfs (in FS system - FGM Sensor system - a non orthogonal sensor system) to bring the data in the SSL system

Ranging by factor kr (range from fgm header)kr = 50000/2(16+range)

F5:

21.4

kr 50000/2(16+range)

00.352.0calO

61497.078449.000611.078855.062017.000680.0

calM

0.00.00.1

Calfile:time, -4.21 –0.52 3.00 –0.00680 0.62017 0.78855 –0.00611 0.78449 –0.61497 –1.00000 0.00000 0.00000 3.12345

43

44

Offset variation on single spacecraftOffset variation on single spacecraft

Offset variation on all spacecraft

45

Offset variation on all spacecraft

Offset Stability

Sensor temperature and offset behaviour after eclipse

-0,9

-0,7

-0,5

Temperature drop down

1 7

-1,5

-1,3

-1,1drop down during eclipse

March: -15°CA il 10°C

-2,1

-1,9

-1,7

04:00

05:00

06:00

07:00

08:00

09:00

10:00

11:00

12:00

13:00

14:00

15:00

16:00

17:00

18:00

19:00

April: -10°CMay: -6°CJune: -4°C

04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19

Offset X Offset Y

P b A M h 7 t t l i fl l th 1 T ft 4 h ithi 0 2 T

46

Probe A, March 7, total influence less than 1 nT; after 4 hours within 0.2 nT

Spacecraft DisturbancesPower system generated interferences:

Although solar cells have been backwired to cancel currents and strings arranged to reduce dipole, there is a remnant power system current loop (battery or p , p y p ( yIDPU) that is spin-locked.

Amplitude: 0.2 nT maximum (Probe D) Frequency: spin tone & harmonics Problem: elimination of spin tone and first harmonics in field

magnitude are inflight calibration criteriamagnitude are inflight calibration criteria Solution approach: spin tone and second harmonics can be

modelled and be removed (after a lot of work) from raw data. E pected res lt: interference ill be s ppressed belo 0 05 nT Expected result: interference will be suppressed below 0.05 nT Caution: data cosmetics by modifying calibration parameters to

remove spin tones leads to wrong data!

47

Power system generated interference: Solution

Spin-phase locked signal (top) Removal of spin tone after discerning

48

p ginterference signal and subtraction.

Conducted electromagnetic noise (and solution)

Conducted interference from particle sectoring Reason: sector clock interferes with FGM data processing.

A beat frequency effect (aliased from high frequency)A beat frequency effect (aliased from high frequency).Spin-frequency dependent, it is minimized at some frequencies

Solution: Changed spin frequency, minimized effect.

49

Shadow effects (and solution) As spacecraft cools spin changes but sun-pulse missing (loose lock)As spacecraft cools, spin changes but sun pulse missing (loose lock)

Solution: Model spin-period, minimize effect.

50

• Instrument Capabilities

Modes / Operation• Operationp

• Field resolution• Ranges (16 of 24bit)

Ti l ti

p• On during boom deployment• Ranging orbit dependent

• Time resolution• 128Hz in TMH• 4Hz – 128Hz selectable in

• Modes• Slow survey spin fit 0.33Hz

8 32TML• Spin fits• Filter modes

• Fast survey raw 8…32Hz• Particle burst raw 128Hz• Wave burst raw 128Hz

• Boxcar filter• Data decimation• Combination of bothCombination of both• Calibration modes• On and off of feedback

O d ff f f db k l51

• On and off of feedback relays• Step function

Data products

FGM: TML TMH s/e temp.

data preprocessing in IDPU

L0: ~ APID’s(.pkt) 460 461 410 405 404FGL FGH Fits FGE HK

8-128Hz 128Hz 1/spin eng.units 2 Temp.

L1:L1 + Cal_File + State_File + IDL_code = L2

L2:

52

CALIBRATION OF SEARCHCOIL MAGNETOMETERS

53

Need to measure for each axis: Transfer function (gain and phase) Sensitivity (NEMI) Sensitivity (NEMI) Exact orientations of the sensor Electronic cross-talk/coupling between axes Stability

Results form the reference for interpretation of space data Test environment

Helmholtz coil system to null Earth field (avoid saturation) Table with orientation accuracy of +/-0.5° Orientation/cross-talk by measuring response to 1kHz signal at 1 direction Orientation/cross-talk by measuring response to 1kHz signal at 1 direction

54

Initial tests take place in small, mu-metal can, toavoid saturation due to Earth field and 60Hz noise

Next test of entire instrument also take place in small, mu-metal can; test stability using internal CAL signal

Final test of entire instrument also take place in quiet facility, nulling external field and measuring noise

55

properties as well as G, Phase, NEMI injecting extrenal signal from coils.

Bottom: Example of NEMI test on the left, showing the data collection at variousleft, showing the data collection at various frequency bands (to avoid very high data volume needed for otherwise measuring at very high cadence for very long time)

Right: Results of calibration including orthogonality test from injecting test signal along Y. Top to bottom are: Gain, g g p ,Phase and NEMI (Sensitivity) test.

Environment noisenot important

56

Mechanical alignment: In addition to the electronic measurement of ortholonality,electronic measurement of ortholonality, mechanicam measurements are also made in order to guarrantee signals are orthogonal to within requirements.

57

End-to-end Result: Knowledge of noise level in ADC units and the calibration from nT to ADC values. This is included as a reference value in the preliminary calibration of the raw data as it is converted to nT. Further calibration included an ascii calibration table that may be changed with time but includes a time-dependent calibration of the instrument.

58

SCM on-board calibration: A free running onboard oscillatorrunning onboard oscillator generates a 9Hz internal signal (triangular shape) which is used to check the transfer function inflight. Activation by command on “CAL” mode This provides amode. This provides a response over a number of harmonics at the primary winding, used to h k f d tcheck frequency end-to-

end response to a known input. Also used during ground functional testing.g g

59

SCM calibration process (I)SCM calibration process (I)

Different possible ouputs (step parameter):

# 0: counts, NaN inserted into each gap for proper ‘tplotting’# 1: Volts, spinning sensor system, with DC field# 2: Volts, spinning sensor system, without DC field # 3: nTesla, spinning sensor system, without DC field# 4: nTesla, spinning SSL system, without DC field# 5: nTesla, fixed DSL system, without DC field, filtered <fmin# 6 T l fi d DSL t ith DC fi ld# 6: nTesla, fixed DSL system, with xy DC field

60

SCM calibration process (II)Description of calibration method steps 0-2p p

# 0 - TM data in counts, separated into gap-free batches of data at same sample rate.

For each gap free batch apply the steps 1 6 :For each gap-free batch, apply the steps 1-6 :# 1 - TM data in volts. ( tplot variable with '_volt' suffix)# 2a - remove spin tone using (interpolated) spin frequency from beginning of batch.

o Spin period assumed constant for batch, but not assumed constant for full day.p p yo Sliding spin fit to N_spinfit ( 2) complete spins, using sliding Hanning window.o Bdc and misalignment angle calculated from spin fit centered around each pointo DC field for data within one spin period of the edges is calculated using spin fit tofirst/last two spin periods of the batchfirst/last two spin periods of the batch.

o output Bdc and misalignment angle as tplot variables with '_dc' and '_misalign‘ suffix, respectively.

o subtract Bdc (in spin plane) from x, y, and z signals.b - detrend (optionally substract boxcar average by fixing the detrend frequency

parameter Fdet.)c - clean spin harmonics, power current signals, (to be detailed later)

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SCM calibration process (III) B(t) = in(t)[nT]

# 3 - Conversion volts -> nT

Description of calibration method step 3 out(t)

[Volts]

o Cluster: performed for a limited period in Fourier domain by FFTout(t) = in(t)*h(t) with h(t) the impulse response of the antennaout(f) = in(f).h(f) in(t) = FT-1[out(f)/h(f)]with h(f) the transfer function or frequency response of antennawith h(f) the transfer function or frequency response of antenna

o THEMIS: performed continously in time domain by convolutionin(t) = out(t) *c(t) with c(t)= FT-1[1/h(f)] being called Kernelnk is the size of the Kernel .

a large nk gives better calibration but time consuming a large nk gives better calibration but time consuming o Get kernel suitable for use by shifting by nk/2,

applying Hanning window.o Note: IDL convol function assumes that the center of the kernel is

t i d k/2 d l i i t d dat index nk/2, so no delay is introduced.Edge behavior determined by /edge_zero, /edge_wrap, or /edge_truncate. With no /edge keyword, set all data within nk/2 samples of the edge to zero.

62

SCM calibration process (III)

# 4 - rotate from spinning sensor system to SSL

Description of calibration method steps 4-6

# 5 - transform calibrated waveform to DSL using interpolated spin phase, which is calculated from the derived sun pulse datafrom state files (updated version will use cotrans as EFI)from state files (updated version will use cotrans as EFI).

# 6 - add Bx and By DC field from step 2a.

use thm cotrans to transform step 5 output to other coordinates _ p p(GSM, GSE)

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Removing spacecraft disturbances

In flight scm data are perturbed by two types of noise:1) spike at 2*f0 (f0 being the spin frequency) and

its harmonics due to power ripples 2) 8/32 Hz tones radiated from IDPU processing

Fortunately these noises are both constant in amplitude and phase-locked1) spike at 2*f0 is phase locked relative to the spin phase2) 8/32 Hz are phase locked to 1s clock

2 versions are available, give good results and can be selected byclnup_author keyword:

‘ccc’ written by C. Chastony C C‘ole’ written by O. Le Contel (by default)

Both routines perform successively 2 superposed epoch analysis (SEA):1) First SEA with an averaging window equal to a multiple of the spin period

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period2) Second SEA with an averaging window equal to a multiple of 1s

SCM: Removing spacecraft disturbancesCleanup process is included in thm_cal_scm at step 2c

with the following keywords:a) cleanup =‘spin’ for only cleanup of nxf0 tones, wind_dur_spin fixing the duration of the first averaging window (multiple of spinper)b) cleanup =‘full’ for full cleanup and with an additional keyword wind_dur_1s fixing the duration of the second averaging windowsc) commented cleanup keyword corresponds to: no cleanup (default)c) commented cleanup keyword corresponds to: no cleanup (default)

Example:thm_cal_scm, probe=satname, datatype=mode+'*', out_suffix = '_cal', $

trange=trange, $; nk = 512, $

k 4 $; mk = 4, $; Despin=1, $; N_spinfit = 2, $

clnup_author = ‘ccc’ or ‘ole’cleanup = ‘full‘ or ‘spin’ or ‘none’,$

i d d i 1 $wind_dur_spin=1.,$wind_dur_1s = 1.,$

; Fdet = 2., $; Fcut = 0.1, $; Fmin = 0.45, $

65

; Fmax = 0., $; step = 5, $; /edge_zero

A

B

SCM calibration andnoise removalB

C

D

noise removal process

tha on April 8th 2007 E

F

32 Hz2&4 f0A: raw waveform in voltsB: despinned waveform and

pbetween 0558-0600 UT

B

C

8 Hz B: despinned waveform andspectrum in dBV/sqrt(Hz)C: Spin phase locked noisebuilt by SEA an spectrum

D

built by SEA an spectrumD: cleaned (only power ripples)waveform and spectrum E: 1s phase locked noise (SEA)

E

F

E: 1s phase locked noise (SEA)F: Fully cleaned waveform and SpectrumNote that some spike still remain which

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Note that some spike still remain whichare not phase locked

SCM science data

• Physical quantities (L2 data):I SSL DSL GSE GSM d th di t• In SSL, DSL, GSE, GSM and other coordinates

– FS waveforms (scf) of Bx, By, Bz [8 S/s; Allocation~ 10.8h depending on which probe]

– PB waveforms (scp) [128 S/s; All.~ 1.2h]– WB waveforms (scw) [8192 S/s; All.~ 43s]

– Filterbank data (fbk) [1comp.; 6 freq.] throughout orbit– PB spectra (ffp) [2 comp.; 32 freq.]p ( p) [ p ; q ]– WB spectra (ffw) [2 comp.; 64 freq.]

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Operation modes IDPU Data type # Comp. # Frequencies APID Sample rate S/s (nominal)

Details about SCM modes

p yp p q p ( )

Slow survey (SS)Relative allocation: 50% (12h P3,P4,P5)

DFB filter banks 1 to 2 (1) 1 to 6 (6) 440 (FBK)

0.0625 to 8 (0.25)

Fast survey (FS) DFB filter banks 1 to 2 (1) 1 to 6 (6) 440 0 0625 to 8 (4)Fast survey (FS) DFB filter banks 1 to 2 (1) 1 to 6 (6) 440 0.0625 to 8 (4)

RA: 50 % (10,8h) DFB waveform 3 444 (SCF)

2 to 256 (8)

Particle burst (PB) DFB waveform 3 448 (SCP)

2 to 256 (128)(SCP)

RA: 10% of FS (1,2h) DFB spectra(Bpara & Bperp)

1 to 4 (2) 16 to 64 (32) 44D(FFP)

0.25 to 8 (1)

Wave burst (WB)RA 1% of PB (43 s)

DFB waveform 3 44C (SCW)

512 to 16384 (8192)RA: 1% of PB (43 s) (SCW)

DFB spectra 1 to 4 (2) 16 to 64 (64) 44F(FFW)

0.25 to 8 (8)

• Calibration mode• A Triangular signal generated by the PA, is applied to the feedback winding installed

around each antenna. • Once per orbit a calibration is run for 30 seconds (default)

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• Once per orbit a calibration is run for 30 seconds (default). • After 60 seconds, the calibration is automatically turned off.

Access and Use: Solar Wind

69

Access and Use: Solar Wind (P1/TH-B)cwd,'C:\...\class\Lecture04_Magnetic_Field'timespan '2008/08/13' 2 /daystimespan, 2008/08/13 ,2,/daysthm_load_fgm,level=2,probe='b'tplot,'thb_fgs_gsm'ylim,'thb_fgs_gsm',-30.,30.,0tplottdegap,'thb_fgs_gsm',dt=3.,margin=0.25,newname='thb_fgs_gsm_dg'

BxByBzBt

tclip,'thb_fgs_gsm_dg',-20.,20.,newname='thb_fgs_gsm_dg_cl'tdeflag,'thb_fgs_gsm_dg_cl','repeat',newname='B'tvectot,'B' ; creates and stores Btotal componenttplot,'B'; Obtain componentssplit vec 'B' Btsplit_vec, B; Limit data in specific intervalctime,tlimits ; Left-click twice to create time array of 2 values; Right-click to stop collecting times;tlimit,tlimits(0),tlimits(1)timespan,tlimits(0),tlimits(0)timespan,tlimits(0),tlimits(0)tplot,'B'tpwrspc,'B_0' ; default newname=B_0_pwrspcget_data,'B_0_pwrspc',data=Bxpwrplot,Bxpwr.x,Bxpwr.y,/xlog,/ylog,col=0tpwrspc,'B_1' ; default newname=B_1_pwrspcget_data,'B_1_pwrspc',data=Bypwroplot,Bypwr.x,Bypwr.y,col=1tpwrspc,'B_2' ; default newname=B_2_pwrspcget_data,'B_2_pwrspc',data=Bzpwroplot,Bzpwr.x,Bzpwr.y,col=2tpwrspc 'B 3' ; default newname=B 3 pwrspc

70

tpwrspc, B_3 ; default newname=B_3_pwrspcget_data,'B_3_pwrspc',data=Btpwroplot,Btpwr.x,Btpwr.y,col=3makepng,'psd'

Access and Use: Solar Wind (P1/TH-B)

Dynamic power spectrumDynamic power spectrum

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Access and Use: Ground/Ionosphere (gmags)timespan '2009/02/15' 1 /daytimespan, 2009/02/15 ,1,/daythm_load_gmag,site='hots',/subtract_medianoptions,1,'colors',[2,4,6]tplot,1;tdegap,'thg mag hots',dt=0.5,margin=0.1,newname='thg mag hots dg'g p, g_ g_ , , g , g_ g_ _ gtclip,'thg_mag_hots_dg',-100.,100.,newname='thg_mag_hots_dg_cl'tdeflag,'thg_mag_hots_dg_cl','repeat',newname='B‘;;; --------below is same as before-----------------Obt i t; Obtain components

split_vec,'B'; Limit data in specific intervalctime,tlimits ; Left-click twice to create time array of 2 values; Right-click to stop collecting times;tlimit,tlimits(0),tlimits(1)timespan,tlimits(0),tlimits(0)tplot 'B'tplot, Btpwrspc,'B_0' ; default newname=B_0_pwrspcget_data,'B_0_pwrspc',data=Bxpwrplot,Bxpwr.x,Bxpwr.y,/xlog,/ylog,col=0tpwrspc,'B_1' ; default newname=B_1_pwrspcget_data,'B_1_pwrspc',data=Bypwroplot,Bypwr.x,Bypwr.y,col=1tpwrspc 'B 2' ; default newname=B 2 pwrspctpwrspc, B_2 ; default newname=B_2_pwrspcget_data,'B_2_pwrspc',data=Bzpwroplot,Bzpwr.x,Bzpwr.y,col=2tpwrspc,'B_3' ; default newname=B_3_pwrspcget_data,'B_3_pwrspc',data=Btpwroplot,Btpwr.x,Btpwr.y,col=3makepng,'psd2‘

above is same as before

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--------above is same as before-----------------

Access and Use: Ground/Ionosphere (gmags)

From tplot data to GUI data

For better results (control of min/max frequencies of dpwrspc), use command line:; ;CALLING SEQUENCE:; tdpwrspc varname newname=newname extra= extra; tdpwrspc, varname, newname=newname,_extra=_extra;

;CALLING SEQUENCE:; dpwrspc, time, quantity, tdps, fdps, dps, nboxpoints = nboxpoints, $; nshiftpoints = nshiftpoints, bin = bin, tbegin = tbegin,$; tend = tend, noline = noline, nohanning = nohanning, $; notperhz = notperhz

73

Wave Polarization• We deal with plane-polarized waves, i.e., tip of wave vector perturbation lies on

a plane moving around in a periodic way, in general an ellipse.– When tip of vector moves around in a circle wave is circularly polarized.– When tip moves on straight line, wave is linearly polarized

In general a wave is elliptically polarized somewhere between circular and linear– In general a wave is elliptically polarized, somewhere between circular and linear.• Handidness. When viewed from direction towards which wave is propagating:

– Right handed if tip moves anti-clock wise– Left handed if tip moves clock-wiseLeft handed if tip moves clock wise

• A strictly monochromatic wave is always polarized, by definition.

)()(

)(

ti

tixx eatB x

– Represented by two normal directions in the plane of the wave• Ellipticity, : How elliptical is the wave, as opposed to how linear it is

in time.constant are,,, where,)( )(yxyx

tiyy aaeatB y major axis

minor axis

p y, p , pp– Defined as the ratio of the minor to major axis of the wave– Its sign is the direction of rotation (>0 for right hand)– When ellipticity is =0, wave is linearly polarized

ya ~0

~+1

74

– When ellipticity is =+1, it is right hand circularly polarized– When ellipticity is =-1, it is left hand circularly polarized– When ellipticity is in between, wave is elliptically polarized

xa

• Ellipticity, : Determined by the signed ratio jaij aa /

Ellipticity and Direction of polarization

– If is the angle between the minor and major axes– Positive when wave is right handed, negative when left handed– Then

The orientation of the polarization ellipse is defined by

ia

yellipticit)tan( and ,/|)tan(| ij aa– The orientation of the polarization ellipse is defined by – Then you can show that:

a 0

iaja

and ),sin(2

)2sin( 22 yyyxaa

ya >0

),cos(2

)2tan(

),()(

22

22

yyyx

yx

yyyx

aaaa

aa

– This determines both the ellipticity =tan(), andthe direction of polarization or, orientation of polarization ellipse

xayx

– Notice that orientation, ellipticity and sense of polarization are independent of time• Since amplitudes and phases are independent of time

– For quasi-monochromatic source, amplitudes and phases change with time

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– Coherence time: the time over which the amplitudes and phases are constant– Coherency can only be determined over coherence time scale

• The polarization properties of any wave field can be characterized in terms of H T*

Coherency Matrix

the coherency matrix (by construction Hermitian since J=JH=JT*), defined as:

**

*yx

*xx

yyyx

xyxx

BBBB

BB BB

JJ

JJJ

– Where Bx and By are orthogonal magnetic field components, the angle brackets denote time-average, and the asterisks denote complex conjugate.

• It can be shown that the averages of the coherency matrix can be also

yyxyyyyx BB BB

• It can be shown that the averages of the coherency matrix can be also obtained by averaging in the frequency domain, over the effective frequency width of the signal.

• The coherency matrix of a monochromatic wave is given by:y g y

2)(

)(2

yi

yx

iyxx

aeaa

eaaaJ

yx

yx

– Notice that: Det[J]=0 and: Trace[J]=ax2+ay

2 which is the total wave intensity.– Rotating by an angle results in a diagonal coherency matrix, where the ellipticity

can be readily evaluated. This is equivalent to diagonalizing the coherency matrix.

76

Degree of Polarization• A quasi-monochromatic wave can be viewed as the sum of a polarized signal

and an unpolarized signal. Because the superposition of waves is linear, the coherency matrix can be thought-of as composed of two independent wave fields: a polarized wave, with Hermitian coherency matrix P, and an unpolarized wave with coherency matrix U.unpolarized wave with coherency matrix U.

00

* D

DCBBA

UPJ

– The polarized part obeys AC-BB*=0 – The unpolarized part has zero non-diagonal elements because the mutual

coherency of the random x and y components Is zero.• Degree of polarization R is the power in the polarized signal over the total• Degree of polarization, R, is the power in the polarized signal over the total

power in the signal. R=Trace(P)/Trace(J). It is a quantity between 0 and 1.• Coherency of the signal is measure of cross-correlation in the x,y components

normalized to the auto-correlation of the individual signals. It is equivalent to g qthe coherence of two signals in cross-correlation analysis, but is specific to two components of a wave signal:

• Solving the equations you can obtain:yyxxxy JJJ /

77yxxyyyxx JBJBBBACJDCJDA ** 0

1/221/22 /41 and , 421-

21

yyxxyyxxyyxx JJJDetRJDetJJJJD

Minimum Variance• A magnetic signal is 3D, but the wave properties we discussed are 2D. A

planar propagating monochromatic wave’s magnetic field must be Divergence-less (DivB=0), so k*B=0, where is the wavenumber. Therefore, the magnetic field varies in the plane perpendicular to k, and this plane is defined in 3D space by its normal. The normal is direction along which the magnetic fieldspace by its normal. The normal is direction along which the magnetic field does not vary at all. With an unpolarized (noise) component superimposed we seek the direction of minimum variance of the field, that defines both the direction of propagation, and the plane of polarization.

• The minimum variance technique is used to identify the wave propagation but can also be used in other more general circumstances, such as identifying the normal to the magnetopause the shock normal or in any other situation thatnormal to the magnetopause, the shock normal, or in any other situation that the variance of the field is minimum at a fixed direction.

• Assume a wave field B that exhibits no systematic temporal change in theAssume a wave field B that exhibits no systematic temporal change in the direction n. The minimum variance technique finds the direction n by minimizing the variance of the component {Bm*n} in the set of measurements. This means that n is determined by minimizing, in the least squares sense, the

i

78

quantity:

1ˆ and field, average thei.e. 1 where, ˆ)(1 2

11

22

nBM

BnBBM

M

m

mM

m

m

Minimum Variance, continued (1)• To achieve the minimization of 2, using a constraint, we need to find solutions

by setting the derivatives of the above quantity with respect to the variables (nx,ny,nz) to zero, but subject to the condition that (|n|2-1)=0. We do this using a Lagrange multiplier, , that can take any value that satisfies both conditions:

– (|n|2-1)=0 and(|n| 1) 0, and– (2 -(|n|2-1))/ nj=0, j=0,1,2

Finding appropriate values of to satisfy the second equation ensures that both the constraint will be valid and the quantity will be 2 minimized.y

• The resultant equation can be written as:

0)1ˆ( 22

nnx

0)1ˆ(

0)1ˆ(

22

22

nn

nn

z

y

• The components can be expanded as:– Mxxnx+Mxyny+Mxznz= nx

– Myxnx+Myyny+Myznz= ny

z

79

– Mzxnx+Mzyny+Mzznz= nz, where Mij=<BiBj>-<Bi><Bj>

Minimum Variance, continued (2)• This is a matrix equation which has non trivial solutions (n non-zero) for

arbitrary Mij only when is the eigenvalue of the system, found by solving Det[M- I] =0, where I is the identity matrix.This results in a polynomial of 3rd order, with 3 solutions in general, the eigenvalues 1, 2, 3.

• For a symmetric matrix the eigenvalues are all real and the corresponding• For a symmetric matrix, the eigenvalues are all real and the corresponding eigenvectors orthogonal.

• The eigenvectors correspond to the solution of the equation [M- i I]ni=0, one for each eigenvalue. The eigenvectors represent directions in space g g p pcorresponding to the directions of maximum, intermediate and minimum variance.

A di t t th b t bli h d ith di ti d fi d• A new coordinate system can thus be established, with directions defined by the new orthogonal basis, in which the data have variances in the diagonal direction, Mii=<BiBi>-<Bi><Bi>= i, i.e., the diagonal elements are the variances in the principal axes of the variance ellipsoid.p p p

• The new system is consider diagonalized. In that system, the maximum and intermediate directions define the plane of polarization; whereas the minimum direction is the direction of wave propagation k

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minimum direction is the direction of wave propagation, k.