Progress on the Design of the Magnetic Field
Measurement System for eLISA
Ignacio Mateos
Instituto de Ciencias del Espacio (CSIC-IEEC)
Barcelona
10th International LISA Symposium
University of Florida, Gainesville
1
Outline
1
Introduction
2
Magnetic field interpolation based on AMR
3
Atomic magnetometer at eLISA frequencies
4
Conclusions
2
Introduction
Magnetic field interpolation based on AMR
Atomic magnetometer at eLISA frequencies
eLISA requirement
LPF heritage
Top level requirement for LISA
LISA free fall requirement to detect GW
("
1/2
Sδa,LISA (ω)
−15
≤ 3 × 10
1+
ω/2π
8 mHz
4 #
1+
0.1 mHz
ω/2π
)21
ms−2
√
Hz
0.1 mHz < ω/2π < 100 mHz
Internal forces contribution to the total acceleration noise
Magnetic effects
Brownian motion
Charge fluctuations
Spacecraft self-gravity
Thermal effects
Laser radiation pressure
3
Introduction
Magnetic field interpolation based on AMR
Atomic magnetometer at eLISA frequencies
eLISA requirement
LPF heritage
Top level requirement for LISA
LISA free fall requirement to detect GW
("
1/2
Sδa,LISA (ω)
−15
≤ 3 × 10
1+
ω/2π
8 mHz
4 #
1+
0.1 mHz
ω/2π
)21
ms−2
√
Hz
0.1 mHz < ω/2π < 100 mHz
Force due to the magnetic effect:
F=
M+
χ
B ·∇ B V
µ0
Magnetic subsystem will assess the magnetic contribution to Sδa (ω)
3
Introduction
Magnetic field interpolation based on AMR
Atomic magnetometer at eLISA frequencies
eLISA requirement
LPF heritage
In view of eLISA: Main drawbacks in LPF magnetic subsystem
4
Introduction
Magnetic field interpolation based on AMR
Atomic magnetometer at eLISA frequencies
eLISA requirement
LPF heritage
In view of eLISA: Main drawbacks in LPF magnetic subsystem
Sensors are distant from TMs due to their magnetic back action effect
Fluxgates are heavy and bulky (94 cm3 ) ⇒ less can be placed in the spacecraft
Classical interpolation methods do not achieve sufficient accuracy
Noise at lower eLISA frequencies needs to be improved
4
Introduction
Magnetic field interpolation based on AMR
Atomic magnetometer at eLISA frequencies
eLISA requirement
LPF heritage
In view of eLISA: Main drawbacks in LPF magnetic subsystem
Sensors are distant from TMs due to their magnetic back action effect
Fluxgates are heavy and bulky (94 cm3 ) ⇒ less can be placed in the spacecraft
Classical interpolation methods do not achieve sufficient accuracy
Noise at lower eLISA frequencies needs to be improved
4
Introduction
Magnetic field interpolation based on AMR
Atomic magnetometer at eLISA frequencies
eLISA requirement
LPF heritage
In view of eLISA: Main drawbacks in LPF magnetic subsystem
Sensors are distant from TMs due to their magnetic back action effect
Fluxgates are heavy and bulky (94 cm3 ) ⇒ less can be placed in the spacecraft
Classical interpolation methods do not achieve sufficient accuracy
Noise at lower eLISA frequencies needs to be improved
−7
10
LPF Fluxgate
Requirement
−8
ASD [T Hz
−1/2
]
10
−9
10
−10
10
−4
10
−3
10
−2
10
frequency [Hz]
−1
10
0
10
4
Introduction
Magnetic field interpolation based on AMR
Atomic magnetometer at eLISA frequencies
Experiment layout
Interpolation method: multipole expansion
Estimated magnetic field and errors
1
Introduction
eLISA requirement
LPF heritage
2
Magnetic field interpolation based on AMR
Experiment layout
Interpolation method: multipole expansion
Estimated magnetic field and errors
3
Atomic magnetometer at eLISA frequencies
Non-linear magneto optical rotation (NMOR)
Low-frequency noise
4
Conclusions
4
Introduction
Magnetic field interpolation based on AMR
Atomic magnetometer at eLISA frequencies
Experiment layout
Interpolation method: multipole expansion
Estimated magnetic field and errors
Magnetic sources and sensor location
For a first approach we consider:
8 magnetometers layout allocated around the vacuum enclosure.
The magnitude and location of the magnetic sources measured for LISA
Pathfinder.
A batch of simulated dipoles sources with random orientations to verify the
robustness of the interpolation.
VE
1
AMR
Z[m]
0.8
36.47
0.6
0.4
y
z
TM
x
0.2
0
−1
0
1
Y[m]
1
0
0.5
−0.5
46
y
46
97.58
97.58
138
−1
X[m]
5
Introduction
Magnetic field interpolation based on AMR
Atomic magnetometer at eLISA frequencies
Experiment layout
Interpolation method: multipole expansion
Estimated magnetic field and errors
Magnetic sources and sensor location
For a first approach we consider:
8 magnetometers layout allocated around the vacuum enclosure.
The magnitude and location of the magnetic sources measured for LISA
Pathfinder.
A batch of simulated dipoles sources with random orientations to verify the
robustness of the interpolation.
Sources
Test mass
Magnetometers
1
Z[m]
Z[m]
0.8
0.6
1
0
−1
−1
0.4
−0.5
0.2
−1
0
0
−1
0
1
Y[m]
1
0
0.5
−0.5
−1
0.5
Y[m]
0
1 1
X[m]
X[m]
5
Introduction
Magnetic field interpolation based on AMR
Atomic magnetometer at eLISA frequencies
Experiment layout
Interpolation method: multipole expansion
Estimated magnetic field and errors
Interpolation method: multipole expansion
The estimated magnetic field measured by an array of N sensors can be
expressed as:
Bestimated (x, t) =
L
l
µ0 X X
Mlm (t) ∇[r l Ylm (n)]
4π
l=1 m=−l
The number of magnetometers will be defined by the desired
multipole order:
Max. order
decomposition
L
Equivalent
multipole
Terms in
expansion
[L (L + 2)]
Num. of triaxial
magnetometers
[N]
1
2
3
4
dipole
quadrupole
octupole
hexadecapole
3
8
15
24
1
3
5
8
6
Introduction
Magnetic field interpolation based on AMR
Atomic magnetometer at eLISA frequencies
Experiment layout
Interpolation method: multipole expansion
Estimated magnetic field and errors
Magnetic field reconstruction: 8 triaxial sensors
Magnetic field created by the dipolar sources
Multipole expansion interpolation
7
Introduction
Magnetic field interpolation based on AMR
Atomic magnetometer at eLISA frequencies
Experiment layout
Interpolation method: multipole expansion
Estimated magnetic field and errors
Magnetic field reconstruction: Relative errors
Averaged relative errors for multipole expansion
Averaged relative errors at TM’s position for different layouts
40
Bx
By
Bz
modB
error (%)
30
20
10
0
4 Fluxgate LPF
4 AMR
Sensor configuration
8 AMR
8
Introduction
Magnetic field interpolation based on AMR
Atomic magnetometer at eLISA frequencies
Experiment layout
Interpolation method: multipole expansion
Estimated magnetic field and errors
Magnetic field reconstruction: Relative errors
Averaged relative errors for multipole expansion
Averaged relative errors at TM’s position for different layouts
40
Bx
By
Bz
modB
error (%)
30
20
Error < 1 %
10
0
4 Fluxgate LPF
4 AMR
Sensor configuration
8 AMR
8
Introduction
Magnetic field interpolation based on AMR
Atomic magnetometer at eLISA frequencies
Experiment layout
Interpolation method: multipole expansion
Estimated magnetic field and errors
Magnetic field reconstruction: Relative errors
Averaged relative errors for multipole expansion
Averaged relative errors at TM’s position for different layouts
40
Bx
By
Bz
modB
error (%)
30
20
Error
(%)
Bx
8 AMRs
By
Bz
|B|
10
εTM
σ
0.1
0.1
0.2
0.2
0.1
0.1
0
Error < 1 %
4 Fluxgate LPF
4 AMR
Sensor configuration
8 AMR
0.1
0.1
8
Introduction
Magnetic field interpolation based on AMR
Atomic magnetometer at eLISA frequencies
Experiment layout
Interpolation method: multipole expansion
Estimated magnetic field and errors
Magnetic field reconstruction: Robustness
Errors due to the offset and position of the sensors
7
1.2
Bx
By
Bz
1
5
error [%]
error [%]
6
4
3
2
0.8
0.6
0.4
0.2
1
0
0
Bx
By
Bz
10
20
30
offset [nT]
40
50
0
0
1
2
3
position [mm]
4
5
AMR’s offset can be measured in flight. Fluxgate magnetometers may suffer
from unpredictable offsets due to launch stresses (< 10 nT).
Spatial resolution will be determined for the size of the sensor head.
∆AMR < 1 mm and ∆Fluxgate < 4 mm.
9
Introduction
Magnetic field interpolation based on AMR
Atomic magnetometer at eLISA frequencies
Non-linear magneto optical rotation (NMOR)
Low-frequency noise
1
Introduction
eLISA requirement
LPF heritage
2
Magnetic field interpolation based on AMR
Experiment layout
Interpolation method: multipole expansion
Estimated magnetic field and errors
3
Atomic magnetometer at eLISA frequencies
Non-linear magneto optical rotation (NMOR)
Low-frequency noise
4
Conclusions
9
Introduction
Magnetic field interpolation based on AMR
Atomic magnetometer at eLISA frequencies
Non-linear magneto optical rotation (NMOR)
Low-frequency noise
Principle of operation
B
0000
1111
1111
0000
0000
1111
0000
1111
0000
1111
0000
1111
0000
1111
00000
11111
00000
11111
11111
00000
00000
11111
00000
11111
00000
11111
00000
11111
00000
11111
E
00000
11111
00000
11111
00000
11111
11111
00000
00000
11111
00000
11111
00000
11111
I
t
Pump pulse creates alignment in the
medium along ~
E
10
Introduction
Magnetic field interpolation based on AMR
Atomic magnetometer at eLISA frequencies
Non-linear magneto optical rotation (NMOR)
Low-frequency noise
Principle of operation
B
0000
1111
1111
0000
0000
1111
0000
1111
0000
1111
0000
1111
0000
1111
00000
11111
00000
11111
11111
00000
00000
11111
00000
11111
00000
11111
00000
11111
00000
11111
B
00000
11111
00000
11111
11111
00000
00000
11111
00000
11111
00000
11111
00000
11111
E
00000
11111
00000
11111
00000
11111
11111
00000
00000
11111
00000
11111
00000
11111
0000
1111
0000
1111
1111
0000
0000
1111
0000
1111
0000
1111
0000
1111
0000
1111
0000
1111
0000
1111
1111
0000
0000
1111
0000
1111
0000
1111
I
I
t
t
Pump pulse creates alignment in the
Atomic moments precess about ~
B at the
medium along ~
E
Larmor frequency
10
Introduction
Magnetic field interpolation based on AMR
Atomic magnetometer at eLISA frequencies
Non-linear magneto optical rotation (NMOR)
Low-frequency noise
Principle of operation
B
B
180
0000
1111
1111
0000
0000
1111
0000
1111
0000
1111
0000
1111
0000
1111
00000
11111
00000
11111
11111
00000
00000
11111
00000
11111
00000
11111
00000
11111
00000
11111
00000
11111
00000
11111
11111
00000
00000
11111
00000
11111
00000
11111
00000
11111
E
00000
11111
00000
11111
00000
11111
11111
00000
00000
11111
00000
11111
00000
11111
0000
1111
0000
1111
1111
0000
0000
1111
0000
1111
0000
1111
0000
1111
E
1111
0000
0000
1111
0000
1111
0000
1111
0000
1111
0000
1111
0000
1111
0000
1111
0000
1111
0000
1111
0000
1111
1111
0000
0000
1111
0000
1111
0000
1111
I
B
O
0000
1111
0000
1111
0000
1111
1111
0000
0000
1111
0000
1111
0000
1111
0000
1111
0000
1111
0000
1111
1111
0000
0000
1111
0000
1111
0000
1111
0000
1111
I
I
2ω L
t
t
t
Pump pulse creates alignment in the
Atomic moments precess about ~
B at the
Pump pulses are synchronized and
medium along ~
E
Larmor frequency
reinforce the macroscopic moments
10
Introduction
Magnetic field interpolation based on AMR
Atomic magnetometer at eLISA frequencies
Non-linear magneto optical rotation (NMOR)
Low-frequency noise
Principle of operation
B
B
180
0000
1111
1111
0000
0000
1111
0000
1111
0000
1111
0000
1111
0000
1111
00000
11111
00000
11111
11111
00000
00000
11111
00000
11111
00000
11111
00000
11111
00000
11111
00000
11111
00000
11111
11111
00000
00000
11111
00000
11111
00000
11111
00000
11111
E
00000
11111
00000
11111
00000
11111
11111
00000
00000
11111
00000
11111
00000
11111
0000
1111
0000
1111
1111
0000
0000
1111
0000
1111
0000
1111
0000
1111
E
1111
0000
0000
1111
0000
1111
0000
1111
0000
1111
0000
1111
0000
1111
0000
1111
0000
1111
0000
1111
0000
1111
1111
0000
0000
1111
0000
1111
0000
1111
I
B
O
0000
1111
0000
1111
0000
1111
1111
0000
0000
1111
0000
1111
0000
1111
0000
1111
0000
1111
0000
1111
1111
0000
0000
1111
0000
1111
0000
1111
0000
1111
I
I
2ω L
t
t
t
Pump pulse creates alignment in the
Atomic moments precess about ~
B at the
Pump pulses are synchronized and
medium along ~
E
Larmor frequency
reinforce the macroscopic moments
ψ
φ
E
After Cell
00000
11111
00000
11111
11111
00000
00000
11111
00000
11111
00000
11111
00000
11111
Before Cell
y
0000
1111
1111
0000
0000
1111
0000
1111
0000
1111
0000
1111
0000
1111
0000
1111
0000
1111
1111
0000
0000
1111
0000
1111
0000
1111
0000
1111
0000
1111
Bz
E
z
x
Aligned media rotates the polarization plane of the probe beam (Faraday effect)
10
Introduction
Magnetic field interpolation based on AMR
Atomic magnetometer at eLISA frequencies
Non-linear magneto optical rotation (NMOR)
Low-frequency noise
Amplitude modulated non-linear magneto optical rotation (AM NMOR)
Balanced polarimeter
Atomic Magnetometer
PD1
λ /2
Analizer
Signal
Probe
Lock−in
Ref
Polarizer
λ /2
Pump
PD2
Mod.
Laser is tuned to a magnetically sensitive transition (D1 or D2 line)
Light is linearly polarized before vapor cell
Optical rotation of the light is measured with a balanced polarimeter
Signal is demodulated with a reference frequency equal to the Larmor frequency
ITO heaters are not necessary at the cell
2-beams configuration optimize sensitivity
11
Introduction
Magnetic field interpolation based on AMR
Atomic magnetometer at eLISA frequencies
Non-linear magneto optical rotation (NMOR)
Low-frequency noise
AM NMOR: Block diagram
LD PD
Pulse
Gen.
DFB
PID
Lens
OI
BS
Iris
LD
Controller
AOM
0
th
Pump Laser
BD
λ /2
1
st
PBS
+BD
PD1
Iris
λ /4 DAVLL λ /2
Pump PD
Glass
TIA
R
LP
Glass
PBS
PD2
Balanced polarimeter
θ
ND
Thermal act.
TEC
5−layer shielding
PBS
+BD
λ /2
LP
Cs Cell
PD1
Ref
PBS
TIA
LD Frequency stabilization
Lock−in
Coils
Iris
Probe Laser
Current
Source
PD2
Balanced polarimeter
Monitored data
Output of the lock-in (X-in-phase and Y-out-phase and reference frequency)
Frequency and power at different points of the laser
LD current and temperature
Output of the polarimeters (single and differential)
Environmental and applied magnetic field (with environmental temperature)
12
Introduction
Magnetic field interpolation based on AMR
Atomic magnetometer at eLISA frequencies
Non-linear magneto optical rotation (NMOR)
Low-frequency noise
AM NMOR: Block diagram
LD PD
Pulse
Gen.
DFB
PID
Lens
OI
BS
Iris
LD
Controller
AOM
0
th
Pump Laser
BD
λ /2
1
st
PBS
+BD
PD1
Iris
λ /4 DAVLL λ /2
Pump PD
Glass
TIA
R
LP
Glass
PBS
PD2
Balanced polarimeter
θ
ND
Thermal act.
TEC
5−layer shielding
PBS
+BD
λ /2
LP
PD1
Ref
PBS
Cs Cell
TIA
LD Frequency stabilization
Iris
Probe Laser
PD2
Balanced polarimeter
Current
Source
8
Lorentzian distribution is obtained by sweeping around ΩL
X−Lockin
Y−Lockin
6
Zero-phase feedback loop to keep acquire Ωm locked to
resonance
Amplitude [mV]
Signal changes during long measurement
Zero phase is less sensitive to power fluctuations
Lock−in
Coils
4
2
0
−2
−4
1.93
1.935
1.94
1.945
1.95
frequency [Hz]
1.955
1.96
4
x 10
12
Introduction
Magnetic field interpolation based on AMR
Atomic magnetometer at eLISA frequencies
Non-linear magneto optical rotation (NMOR)
Low-frequency noise
AM NMOR: Block diagram
LD PD
Pulse
Gen.
DFB
Lens
OI
BS
Iris
LD
Controller
AOM
0
th
Pump Laser
BD
λ /2
1
st
PBS
+BD
PD1
Iris
λ /4 DAVLL λ /2
Pump PD
Glass
TIA
R
LP
Glass
PBS
PD2
Balanced polarimeter
θ
ND
Thermal act.
TEC
5−layer shielding
PBS
+BD
λ /2
LP
PD1
Ref
PBS
Cs Cell
TIA
LD Frequency stabilization
Iris
Probe Laser
PD2
Balanced polarimeter
Current
Source
8
Lorentzian distribution is obtained by sweeping around ΩL
Amplitude [mV]
Zero-phase feedback loop to keep acquire Ωm locked to
resonance
100
Amplitude
Phase
Signal changes during long measurement
Zero phase is less sensitive to power fluctuations
Lock−in
Coils
6
50
4
0
2
−50
0
1.93
1.935
1.94
1.945
1.95
frecuency [Hz]
1.955
Phase [degree]
PID
−100
1.96
4
x 10
12
Introduction
Magnetic field interpolation based on AMR
Atomic magnetometer at eLISA frequencies
Non-linear magneto optical rotation (NMOR)
Low-frequency noise
AM NMOR: Block diagram
LD PD
Pulse
Gen.
DFB
PID
Lens
OI
BS
Iris
LD
Controller
AOM
0
th
Pump Laser
BD
λ /2
1
st
PBS
+BD
PD1
Iris
λ /4 DAVLL λ /2
Pump PD
Glass
TIA
R
LP
Glass
PBS
PD2
Balanced polarimeter
θ
ND
Thermal act.
TEC
5−layer shielding
PBS
+BD
λ /2
LP
PD1
Ref
PBS
Cs Cell
TIA
LD Frequency stabilization
Lock−in
Coils
Iris
Probe Laser
PD2
Balanced polarimeter
Current
Source
Probe beam polarimeter
−12
Signal is modulated between 1 Hz and hundreds of kHz
2
2
2
Dominant noise contributions: en,op−TIA
, iSN
, eR
f
ASD [A Hz−1/2]
10
High gain TIA: 11 mV/nA
−13
10
Total noise
TIA + 2nd stage
−14
10
2nd stage
Shot noise
en,op−TIA
eR ,t
−15
10
High SNR measurements can be made
f
in,op−TIA
−16
10
−2
10
−1
10
0
10
1
10
2
10
frequency [Hz]
3
10
4
10
5
10
12
Introduction
Magnetic field interpolation based on AMR
Atomic magnetometer at eLISA frequencies
Non-linear magneto optical rotation (NMOR)
Low-frequency noise
AM NMOR: Block diagram
LD PD
Pulse
Gen.
DFB
PID
Lens
OI
BS
Iris
LD
Controller
AOM
0
th
Pump Laser
BD
λ /2
1
st
PBS
+BD
PD1
Iris
λ /4 DAVLL λ /2
Pump PD
Glass
TIA
R
LP
Glass
PBS
5−layer shielding
PBS
+BD
TEC
λ /2
LP
PD1
Ref
PBS
Cs Cell
Lock−in
TIA
LD Frequency stabilization
Coils
Iris
Probe Laser
PD2
Balanced polarimeter
Current
Source
Current source for the applied magnetic field
pT
pT
∼ 0.02 √ @100 Hz and ∼ 10 √ @0.1 mHz
Hz
Dominant noise contribution is due to the reference voltage
Thermal contribution appears outside the eLISA BW
−8
−12
10
Current noise [A Hz−1/2]
Main magnetic field to be applied is ' 2.5 µT
Hz
θ
ND
Thermal act.
10
−10
−13
10
10
−12
10
−14
−2
10
−1
10
0
10
frequency [Hz]
1
10
10
2
10
Eq. magnetic field noise [T Hz−1/2]
PD2
Balanced polarimeter
12
Introduction
Magnetic field interpolation based on AMR
Atomic magnetometer at eLISA frequencies
Non-linear magneto optical rotation (NMOR)
Low-frequency noise
Magnetometer setup: Optical board
13
Introduction
Magnetic field interpolation based on AMR
Atomic magnetometer at eLISA frequencies
Magnetometer setup:
133
Non-linear magneto optical rotation (NMOR)
Low-frequency noise
Cs Cell, probe and pump board
14
Introduction
Magnetic field interpolation based on AMR
Atomic magnetometer at eLISA frequencies
Non-linear magneto optical rotation (NMOR)
Low-frequency noise
Equivalent magnetic field noise: Bapp ' 2.5 µT
−9
10
Atomic Mag
Floating Load
High stable COTS
−10
ASD [T Hz
−1/2
]
10
−11
10
−12
10
−13
10
−14
10
−4
10
−3
10
−2
10
−1
10
frequency [Hz]
15
Introduction
Magnetic field interpolation based on AMR
Atomic magnetometer at eLISA frequencies
Non-linear magneto optical rotation (NMOR)
Low-frequency noise
Equivalent magnetic field noise: Bapp ' 2.5 µT
−9
10
Atomic Mag
Floating Load
High stable COTS
−10
ASD [T Hz
−1/2
]
10
−11
10
−12
10
50 pT Hz−1/2 @ 0.1 mHz!
−13
10
−14
10
−4
10
−3
10
−2
10
−1
10
frequency [Hz]
15
Introduction
Magnetic field interpolation based on AMR
Atomic magnetometer at eLISA frequencies
Non-linear magneto optical rotation (NMOR)
Low-frequency noise
Equivalent magnetic field noise: Fluxgate vs AMR vs atomic magnetometer
LPF Fluxgate
Requirement
−8
ASD [T Hz
−1/2
]
10
−9
10
−10
10
−11
10
−12
10
−13
10
−4
10
−3
10
−2
10
−1
10
0
10
frequency [Hz]
16
Introduction
Magnetic field interpolation based on AMR
Atomic magnetometer at eLISA frequencies
Non-linear magneto optical rotation (NMOR)
Low-frequency noise
Equivalent magnetic field noise: Fluxgate vs AMR vs atomic magnetometer
−1/2
]
10
ASD [T Hz
LPF Fluxgate
AMR Mag−Feedback + Flipping
Requirement
−8
−9
10
−10
10
−11
10
−12
10
−13
10
−4
10
−3
10
−2
10
−1
10
0
10
frequency [Hz]
16
Introduction
Magnetic field interpolation based on AMR
Atomic magnetometer at eLISA frequencies
Non-linear magneto optical rotation (NMOR)
Low-frequency noise
Equivalent magnetic field noise: Fluxgate vs AMR vs atomic magnetometer
−1/2
]
10
ASD [T Hz
LPF Fluxgate
AMR Mag−Feedback + Flipping
Atomic AM NMOR
Requirement
−8
−9
10
−10
10
−11
10
−12
10
−13
10
−4
10
−3
10
−2
10
−1
10
0
10
frequency [Hz]
16
Introduction
Magnetic field interpolation based on AMR
Atomic magnetometer at eLISA frequencies
Conclusions
Multipole expansion with the proposed sensor configuration has
produced reliable results to estimate the magnetic field at the positions
of the TM.
Improvement in the accuracy of the magnetic field reconstruction has
been achieved due to the small size and low magnetic back action of
the AMRs, which enables the possibility to place more sensors and
locate them closer to the TMs.
Based on the experience with LISA Pathfinder, the use of AMRs with a
dedicated noise reduction technique seems nowadays the most suitable
technology for eLISA.
Atomic magnetometer’s noise based on AM NMOR shows promising
results at eLISA frequencies ∼ 50 pT Hz−1/2 . Further work: what
happens at chip-scale?
17
Introduction
Magnetic field interpolation based on AMR
Atomic magnetometer at eLISA frequencies
Thank you!
17