G. Bao, L. Liu, D. Shaul, H. AraG. Bao, L. Liu, D. Shaul, H. Araúújo, jo, W.-T. Ni, T. SumnerW.-T. Ni, T. Sumner

Purple Mountain ObservatoryPurple Mountain ObservatoryImperial College LondonImperial College London

OutlineOutline

(1) Introduction

(2) Incident flux

(3) Physics model

(4) Geometry model

(5) Simulation results

(6) Charging rate

(7) Acceleration noise

(8) Conclusion

1.Introduction1.Introduction

The ASTROD I mission concept is based around The ASTROD I mission concept is based around a single, drag-free spacecraft and laser a single, drag-free spacecraft and laser interferometric ranging and pulse ranging with interferometric ranging and pulse ranging with ground stations. ground stations. It is the first step towards It is the first step towards realising the ASTROD mission (the realising the ASTROD mission (the Astrodynamical Space Test of Relativity using Astrodynamical Space Test of Relativity using Optical Devices) . Optical Devices) . The scientific goals of The scientific goals of ASTROD I include measuring relativistic ASTROD I include measuring relativistic parameters with better accuracy, improving the parameters with better accuracy, improving the sensitivity achieved in using the optical Doppler sensitivity achieved in using the optical Doppler tracking method for detecting gravitational tracking method for detecting gravitational waves, and measuring many solar system waves, and measuring many solar system parameters more precisely. parameters more precisely.

For a launch on August 4, 2010, after two encounters with Venus For a launch on August 4, 2010, after two encounters with Venus around 112 days and 336 days after launch, the orbital period can around 112 days and 336 days after launch, the orbital period can be shortened to 165 days. After about 370 days from launch, the be shortened to 165 days. After about 370 days from launch, the spacecraft will arrive at the other side of the Sun and relativistic spacecraft will arrive at the other side of the Sun and relativistic parameter parameter γγ can be determined accurately. A specific orbit trajectory can be determined accurately. A specific orbit trajectory in the X-Y plane of the heliocentric equatorial coordinate system is in the X-Y plane of the heliocentric equatorial coordinate system is shown in the Figure below.shown in the Figure below.

1E-4 1E-3 0.01 0.11E-15

1E-14

1E-13

1E-12

1E-11

1E-10

1E-9

Acc

eler

atio

n n

ois

e sp

ectr

al d

ensi

ty

(m

s-2H

z-1/2)

Frequency(Hz)

ASTROD I

LISA

LTP

A comparison of noise curve of ASTROD I with the LTP on LISA PF and LISA. The solid line is for ASTROD I, the dotted line is for the LTP and the dashed line is for LISA. At the lowest frequency in the ASTROD I bandwidth, 0.1mHz, the noise target is 10-13 ms-2 Hz -1/2 .

GEANT4 is a toolkit for the simulation of GEANT4 is a toolkit for the simulation of the passage of particles through matter. the passage of particles through matter. Charging simulation includes:Charging simulation includes:

1. Incident flux model;1. Incident flux model;2. Geometry model;2. Geometry model; spacecraft structure and materialspacecraft structure and material3. Physics model;3. Physics model;Programming language: C++Programming language: C++Operation system: Fedora Core 2Operation system: Fedora Core 2Toolkit: Geant4.6.1Toolkit: Geant4.6.1http://geant4.web.cern.ch/geant4/http://geant4.web.cern.ch/geant4/

2.Incident Flux2.Incident FluxThe particle fluxes we adopted in our simulation is the cosmic ray spectra near earth orbit as LISA.The three most abundant primary particle (p, 3He, 4He) fluxes at solar minimum and maximum were the main inputs in our simu-lation.The spectra are those shown in figure below.

0.01 0.1 1 10 100 10001E-5

1E-4

1E-3

0.01

0.1

1

10

100

1000

Flux,particles/s/m

2/Sr/(GeV/n)

GCR Energy GeV/n

Proton

4He

3He

3. Physics Model3. Physics ModelAs a result of their high energy and hadronic nature,

cosmic ray interactions bring forth complex nuclear

reactions which have large final-state multiplicities,

producing a plethora of secondaries. The physics

processes used in our simulation are electromagnetic,

hadronic and photonuclear interactions. A low energy

threshold of 250 eV was adopted for secondary particle

production in our simulation.

Inertial sensors

spacecraft

Figure 2. The schematic diagram for the

GEANT4 model with a simulated cosmic-ray event.

4. Geometry Model4. Geometry Model The spacecraft is 3 axis stabilized with a total mass The spacecraft is 3 axis stabilized with a total mass

300-350 kg and a total power 350 w. It contains a 300-350 kg and a total power 350 w. It contains a drag-free test mass and the spacecraft is to follow drag-free test mass and the spacecraft is to follow this test mass using FEEP (Field Emission Electric this test mass using FEEP (Field Emission Electric Propulsion ). Propulsion ).

(1)(1) A 50×50×35 mmA 50×50×35 mm33 rectangular parallelepiped Au-Pt rectangular parallelepiped Au-Pt alloy is initially planned.alloy is initially planned.

(2)(2) A 500 mm diameter f/1 Cassegrain telescope which A 500 mm diameter f/1 Cassegrain telescope which collects the incoming light.collects the incoming light.

(3)(3) The side surface of the spacecraft is covered by The side surface of the spacecraft is covered by solar panels.solar panels.

(4)(4) Interferometric ranging and pulse ranging.Interferometric ranging and pulse ranging.

Inertial SensorInertial Sensor

Overhead View Side View

Geometry ModelGeometry Model

The schematic diagram for the GEANT4 model with a simulated cosmic-ray event

Geometry ModelGeometry Model

Geometry ModelGeometry Model

5. Simulation Results5. Simulation ResultsQ = 26. 5 e+/ s

0

50

100

150

200

250

0 2 4 6 8

Q = 9. 0 e+/ s

0

50

100

150

200

250

300

0 5 10 15 20 25 30 35

The charging timeline for protons at solar minimum

The charging timeline for protons at solar maximum

Simulation ResultsSimulation ResultsQ = 0. 8 e+/ s

0

20

40

60

80

100

120

0 20 40 60 80 100 120 140 160

The charging timeline for 3He at solar minimum

Q = 0. 3 e+/ s

0

20

40

60

80

100

120

140

0 100 200 300 400

The charging timeline for 3He at solar maximum

Simulation ResultsSimulation ResultsQ = 6. 0 e+/ s

0

20

40

60

80

100

120

140

160

0 5 10 15 20 25

The charging timeline for 4He at solar minimum

Q = 2. 4 e+/ s

0

10

20

30

40

50

60

0 5 10 15 20 25

The charging timeline for 4He at solar maximum

6. Charging Rate6. Charging Rate

1. GEANT4 model predicted the charging rate from protons and alpha particles (3He and 4He):(1)Solar minimum: 33.3 e+/s(2)Solar maximum: 11.7 e+/s

2. Based on the study for LISA, the potential charging mechanism due to kinetic low energy secondary electron emission:(1)Solar minimum: 28.4 e+/s(2)Solar maximum: 17.2 e+/s

3. The contributions from other particle species (C, N, O, e-):(1)Solar minimum: 1.4 e+/s(2)Solar maximum: 0.9 e+/s

4. An additional uncertainty of ±30% in the simulation for the uncertainties of theCosmic-ray spectra, physics models and geometry implementation.

Charging RateCharging Rate

The worst case charging rate is estimated to be:

74.1 e+/s at solar minimum;

34.3 e+/s at solar maximum.

PP

Min MaxMin Max

33HeHe

Min MaxMin Max

44HeHe

Min MaxMin Max

SESE

Min MaxMin Max

OSOS

Min MaxMin Max

UncertaintyUncertainty

Min MaxMin Max

Charging rate(eCharging rate(e++/s)/s)

Charging noise(e/sHzCharging noise(e/sHz-1/2-1/2))

26.5 9.026.5 9.0

15.9 8.615.9 8.6

0.8 0.30.8 0.3

2.5 1.62.5 1.6

6.0 2.46.0 2.4

7.2 3.97.2 3.9

28.4 17.228.4 17.2

11.1 7.611.1 7.6

1.4 0.91.4 0.9

8.9 2.68.9 2.6

10.0 3.510.0 3.5

--- ------ ---

SE: Secondary Electron; OS: Other Species (C, N, O, e-)

7. Acceleration Noises7. Acceleration Noises

k

CV

mC

Q

k

C

mC

QV

k

C

mC

Qa Ni

N

ii

T

T

T

TT

TQk

,1

12

2

2

2

21

1

2

2

2

2

2 QQ

aV

V

ak

k

aa Qk

N

ii

i

QkQkQk

1 、 Coulomb

2 、 Lorentz

222222IISSIIIIL BQVBVQBVQBQVam

7. Acceleration Noises7. Acceleration Noises

1 、 Coulomb (0.1 mHz)

2 、 Lorentz (0.1 mHz)

At solar minimum: ~ 2.8×10-15 ms-2Hz-1/2

At solar maximum: ~ 1.4×10-15 ms-2Hz-1/2

At solar minimum: ~ 2.8×10-15 ms-2Hz-1/2

At solar maximum: ~ 1.3×10-15 ms-2Hz-1/2

ConclusionConclusion1) The charging of the ASTROD I test mass by cosmic ray

protons and alpha particles (3He and 4He) has been simulated using the GEANT4 toolkit at solar minimum and maximum. The model predicted a net charging rate of nearly 11.7 e+/s at solar maximum, rising to 33.3 e+/s at solar minimum. We have also considered an additional charging rate contribution from other particle species that were not included in our model, and a potential charging mechanism due to kinetic low energy secondary electron emission. There is an additional uncertainty of ±30% in the net charging rate due to uncertainties in the cosmic ray spectra, physics models and geometry implementation.

ConclusionConclusion

2) The ASTROD I acceleration noise limit target is 10-13ms-2Hz-1/2 at 0.1 mHz (the lowest frequency in the ASTROD I bandwidth), which is less stringent than the LISA requirement. We also estimated the magnitudes of the Coulomb and Lorentz acceleration noise. These increase with decreasing frequency and at 0.1 mHz, they are well below the acceleration noise target both at solar minimum and maximum. These results agree, to within 30%, with those from our earlier study, which was based on a simple geometry model. In the future, we will study the impact on the charging disturbances, of variations in the incident flux, due to, for example, changes in the heliocentric position of the spacecraft.

ReferencesReferences1. G. Bao, et al., "ASTROD I Charging Simulation and

Disturbances", Gen. Relat. Gravit,38 (2006) in press.2. C. Grimani, et al., Class. Quantum Grav. 21 (2004) S629.3. H. Ara¶ujo, et al., Astroparticle Physics 22 (2005) 451.4. H. Ara¶ujo, et al., Class. Quantum Grav.20 (2003) S201.5. W.-T. Ni, "ASTROD and ASTROD I" submitted to Nuclear

Physics B; W.-T. Ni, et al., J. Korean Phys. Soc. 45 (2004) S118.

6. C. Grimani, et al., Class. Quantum Grav. 22 (2005) S327.7. D. Shaul, et al., Class. Quantum Grav. 22 (2005) S297.8. S. Shiomi and W.-T. Ni, Class. Quantum Grav. 23 (2006)

4415.