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G. Bao, L. Liu, D. Shaul, H. Ara ú jo, W.-T. Ni, T. Sumner Purple Mountain Observatory

The Charging Simulation and Disturbances in ASTROD I. G. Bao, L. Liu, D. Shaul, H. Ara ú jo, W.-T. Ni, T. Sumner Purple Mountain Observatory Imperial College London. Outline. Introduction Incident flux Physics model Geometry model Simulation results Charging rate Acceleration noise

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G. Bao, L. Liu, D. Shaul, H. Ara ú jo, W.-T. Ni, T. Sumner Purple Mountain Observatory

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  1. The Charging Simulation and Disturbances in ASTROD I G. Bao, L. Liu, D. Shaul, H. Araújo, W.-T. Ni, T. Sumner Purple Mountain Observatory Imperial College London

  2. Outline • Introduction • Incident flux • Physics model • Geometry model • Simulation results • Charging rate • Acceleration noise • Conclusion

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

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

  5. 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.

  6. GEANT4 is a toolkit for the simulation of the passage of particles through matter. Charging simulation includes: 1. Incident flux model; 2. Geometry model; spacecraft structure and material 3. Physics model; Programming language: C++ Operation system: Fedora Core 2 Toolkit: Geant4.6.1 http://geant4.web.cern.ch/geant4/

  7. 2.Incident Flux The 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.

  8. 3. Physics Model As 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.

  9. Figure 2. The schematic diagram for the GEANT4 model with a simulated cosmic-ray event. spacecraft Inertial sensors

  10. 4. Geometry Model The spacecraft is 3 axis stabilized with a total mass 300-350 kg and a total power 350 w. It contains a drag-free test mass and the spacecraft is to follow this test mass using FEEP (Field Emission Electric Propulsion ). • A 50×50×35 mm3 rectangular parallelepiped Au-Pt alloy is initially planned. • A 500 mm diameter f/1 Cassegrain telescope which collects the incoming light. • The side surface of the spacecraft is covered by solar panels. • Interferometric ranging and pulse ranging.

  11. Inertial Sensor Overhead View Side View

  12. Geometry Model The schematic diagram for the GEANT4 model with a simulated cosmic-ray event

  13. Geometry Model

  14. Geometry Model

  15. 5. Simulation Results The charging timeline for protons at solar minimum The charging timeline for protons at solar maximum

  16. Simulation Results The charging timeline for 3He at solar minimum The charging timeline for 3He at solar maximum

  17. Simulation Results The charging timeline for 4He at solar minimum The charging timeline for 4He at solar maximum

  18. 6. 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 the Cosmic-ray spectra, physics models and geometry implementation.

  19. Charging Rate The worst case charging rate is estimated to be: 74.1 e+/s at solar minimum; 34.3 e+/sat solar maximum. SE: Secondary Electron; OS: Other Species (C, N, O, e-)

  20. 7. Acceleration Noises 1、Coulomb 2、Lorentz

  21. 7. Acceleration Noises 1、Coulomb (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 2、Lorentz (0.1 mHz) At solar minimum: ~ 2.8×10-15 ms-2Hz-1/2 At solar maximum: ~ 1.3×10-15 ms-2Hz-1/2

  22. Conclusion 1) 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.

  23. Conclusion 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.

  24. References 1. 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.

  25. Thanks

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