地面振动对测G实验的影响与扭秤“反常模式”研究
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摘要
万有引力常数G值的高精度绝对测量非常困难,在目前的各种基本物理常数测量值中,G值的精度是最低的,这除了与万有引力信号非常微弱、不可屏蔽以及在实验上极大程度地受到机械测量精度的限制外,还因为外界的干扰如温度波动,引力场的变化和地面振动也在很大程度上限制了G值测量精度的提高。
本文围绕扭秤周期法测G中地面振动对扭秤实验的影响这一主题,通过计算机仿真模拟的方法计算了扭秤悬点在不同的外界激励下扭秤的响应特性,以及对最终扭秤周期稳定性的影响。计算表明,在随机白噪声的激励下引起扭秤周期的波动与目前实验数据相吻合,证实了目前周期波动的原因之一是由于地面振动造成的。在数值计算的基础上,推导出扭秤反常模式的解析表达式,找到了扭秤单摆模式与扭转模式之间的耦合关系,相比数值解,解析解可以给出反常模式与单摆幅度,频率以及扭秤自身结构参数之间的依赖关系,这可以对扭秤的设计给出指导意见:在不影响待测实验信号的前提下,将扭秤设计为对称结构如圆盘,可以显著降低地面振动对扭秤实验的影响;可以同步监测扭秤单摆模式的运动,通过解析解计算其对实验数据的影响并从中扣除。采取隔振措施是降低地面噪声的一种有效途径,建立了实验中一级和二级磁阻尼隔振系统的数学模型,计算了涡流损耗的阻尼因子与阻尼盘安放位置和形状之间的关系,并提出了改进和优化的意见。减小地面振动对扭秤的影响不仅有利于测G实验中周期稳定性的提高,而且对其他的扭秤实验精度的提高也很有帮助。
The fact that the gravitational constant G is the least precisely determined constant among all the fundamental constants of nature shows that it still have many difficulties to improve the precision of determination of G. The difficulties in measuring G are mainly resulted from the extreme weakness of gravitational force and the measurement of the geometry of attracting and the attracted masses and the relative positions between them. Furthermore, the temperature drift, non-linear effect and seismic noise are also the reasons to limit the precision of G experiment.
This paper mainly deals with the points about the effect of seismic noise on the determination of G. The response of the torsion pendulum when the support point is motivated by different force is simulated. The fluctuation of the period from the simulated data agrees well with the experiment data. The equation describing the dynamics of torsion balance and analysis solution has been proposed. We find the coupling between swing modes and the torsional mode. The analytic solutions show that the amplitude of this coupling mode depends on the amplitude of the swing modes and the frequency of the coupling mode is the linear combinations of the frequency in the two orthogonal directions in horizon. Our improved magnetic damper system can suppress the seismic noise, which is not only benefit for the determining G, but also can improve the precision of other gravitational experiment.
本文围绕扭秤周期法测G中地面振动对扭秤实验的影响这一主题,通过计算机仿真模拟的方法计算了扭秤悬点在不同的外界激励下扭秤的响应特性,以及对最终扭秤周期稳定性的影响。计算表明,在随机白噪声的激励下引起扭秤周期的波动与目前实验数据相吻合,证实了目前周期波动的原因之一是由于地面振动造成的。在数值计算的基础上,推导出扭秤反常模式的解析表达式,找到了扭秤单摆模式与扭转模式之间的耦合关系,相比数值解,解析解可以给出反常模式与单摆幅度,频率以及扭秤自身结构参数之间的依赖关系,这可以对扭秤的设计给出指导意见:在不影响待测实验信号的前提下,将扭秤设计为对称结构如圆盘,可以显著降低地面振动对扭秤实验的影响;可以同步监测扭秤单摆模式的运动,通过解析解计算其对实验数据的影响并从中扣除。采取隔振措施是降低地面噪声的一种有效途径,建立了实验中一级和二级磁阻尼隔振系统的数学模型,计算了涡流损耗的阻尼因子与阻尼盘安放位置和形状之间的关系,并提出了改进和优化的意见。减小地面振动对扭秤的影响不仅有利于测G实验中周期稳定性的提高,而且对其他的扭秤实验精度的提高也很有帮助。
The fact that the gravitational constant G is the least precisely determined constant among all the fundamental constants of nature shows that it still have many difficulties to improve the precision of determination of G. The difficulties in measuring G are mainly resulted from the extreme weakness of gravitational force and the measurement of the geometry of attracting and the attracted masses and the relative positions between them. Furthermore, the temperature drift, non-linear effect and seismic noise are also the reasons to limit the precision of G experiment.
This paper mainly deals with the points about the effect of seismic noise on the determination of G. The response of the torsion pendulum when the support point is motivated by different force is simulated. The fluctuation of the period from the simulated data agrees well with the experiment data. The equation describing the dynamics of torsion balance and analysis solution has been proposed. We find the coupling between swing modes and the torsional mode. The analytic solutions show that the amplitude of this coupling mode depends on the amplitude of the swing modes and the frequency of the coupling mode is the linear combinations of the frequency in the two orthogonal directions in horizon. Our improved magnetic damper system can suppress the seismic noise, which is not only benefit for the determining G, but also can improve the precision of other gravitational experiment.
引文
[1] H. Cavendish, Experiments to determine the density of the Earth, Philos. Trans. Roy. Soc., 88 (1798) 469.
[2] G. T. Gillies and T. C. Ritter, Torsion balance, torsion pendulums, and related devices, Rev. Sci. Instrum. , 64(1993) 283.
[3] G. G. Luther, W. R. Towler, Redetermination of the Newtonian gravitational constant, Phys. Rev. Lett. , 48(1982) 121.
[4] G. T. Gillies, The Newtonian gravitational constant, Metrologia. , 24 (1987) 1.
[5] G. T. Gillies, The Newtonian gravitational constant: recent measurements and related studies, Rep. Prog. Phys., 60(1997)151.
[6] Luo J., Hu Z-K., Fu X-H., Fan S-H. and Tang M-X., Determination of Newtonian Gravitational Constant G with Considering the Non-linear effect, Phys. Rev. D., 59(1999)042001.
[7] R. Spero, J. K. Hosjins, R. Newman, J. Pellam and J. Schultz, Test of the Gravitational Inverse-Square Law at Laboratory Distances, Phys. Rev. Lett., 44(1980)1645.
[8] Y. T. Chen, A. H. Cook and A. J. F. Metherell, An experiment of test of the inverse Square law of gravitation at range of 0.1 m, Proc. Roy. Soc. A, 394(1984) 47.
[9] M. W. Moore, A. Boudreaux, M. DePue, J. Guthrie, R. Legere, A. Yan, P. E. Boynton, Testing the inverse-square law of gravity: a new class of torsion pendulum null experiments, Class. Quantum. Grav., 11(1994) A97.
[10] J. K. Hoskins, R. D. Newman, R. Spero, and J. Schultz, Experimental tests of the gravitational inverse-square law for mass separations from 2 to 105 cm, Phys. Rev. D., 32(1985)3084.
[11] C. D. Hoyle, U. Schmidt, B. R. Heckel, E. G. Adelberger, J.H. Gundlach, D. J. Kapner, and H. E. Swanson, Submillimeter Test of the Gravitational Inverse-Square Law: A Search for“Large”Extra Dimensions, Phys.Rev.Lett. , 86 (2001) 1418.
[12] E. Fishbach, G.. T. Gillies, D. E. Krause, J. G. Schwan and C. Talmadge,Non-Newtonian Gravity and New Weak Forces: an Index of Measurements and Theory, Metrologia., 29(1992)213.
[13] E. Fischbach, The search for non-Newtonian gravity, Springer 1999.
[14] C. W. Stubbs, E. G. Adelberger, Search for an Intermediate-Range Interaction, Phys. Rev. Lett. 58(1987)1070.
[15] Y. Su, B. R. Heckel, E. G. Adelberger, J. H. Gundlach, M. Har-ris, G. L. Smith, and H. E. Swanson, New tests of the universality of free fall, Phys. Rev. D., 50(1994) 3614.
[16] C. R. Rogers, E. G. Charles, Ni W. T., G. T. Gillies and C. C. Speake, Experimental test of equivalence principle with polarized masses, Phy. Rev. D., 42(1990) 4.
[17] J. H. Gundlach , G. L. Smith , C. D. Hoyle , E. G. Adelberger, B. R. Heckel and H. E. Swanson, Short-range Tests of the Equivalence Principle, Phys.Rev.Lett. , 78 (1997) 2523.
[18] V. M. Mostepanenko and I. Yu. Sokolov, The Casimir effect leads to new restrictions on long-range force constants,Phys. Lett. A, 125 (1987) 405.
[19] M. Bordag, G. L. Kilmchitskaya and V. M. Mostepanenko, Corrections to the Casimir force between plates with stochastic surfaces, Phys. Lett. A, 200 (1995) 95.
[20] V. M. Mostepanenko and I. Yu. Sokolov, Stronger restrictions on the constants of long-range forces decreasing as r-n Phys. Lett. A, 146 (1990) 373.
[21] V. M. Mostepanenko and I. Yu. Sokolov, Hypothetical long-range interactions and restrictions on their parameters from force measurements, Phys. Lett. A, 47 (1993) 2882.
[22] S. K. Lamoreaux, Demonstration of the Casimir Force in the 0.6 to 6um Range Phys.Rev.Lett., 78 (1997) 5.
[23] R. Lakes, Experimental Limits on the Photon Mass and Cosmic Magnetic Vector Potential, Phys.Rev.Lett., 80 (1998) 1826.
[24] J. Luo, C. G. Shao, Z. Z. Liu, Z. K. Hu, New Experimental Limit on the Photon Rest Mass with a Rotating Torsion Balance, Phys.Rev.Lett., 90 (2003) 1.
[25] P. R. Hely, A Redetermination of constant of gravitation, J. Res. Nat. Bur. Stand. (US), 5(1930) 1243.
[26] M. U. Sagitov, Current status of determination of the gravitational constant and the mass of the Earth. Soviet Astronm.-AJ., 13(1976) 712.
[27]罗俊,万有引力常数G的精确测量[博士论文],中国科学院测量与地球物理研究所,1999,p79.
[28] Hu Z. K. and Luo J., Determination of Fundamental Frequency of A Physical Oscillator with Period Fitting Method, Rev. Sci. Instrum., 70(1999) 4412.
[29] Y. T. Chen, A. Cook, Gravitational Experiments in the Laboratory(Cambridge University Press,Cambridge,1993).
[30] R. D. Newman and M. K. Bantel, On determination G using a cryogenic torsion pendulum, Meas. Sci. Technol., 10 (1999) 445.
[31] K. Kuroda, Does the time-of-swing method give a correct value of the Newtonian gravitational constant? Phys. Rev. Lett., 75(1995) 2796.
[32] T. L. Tian,Y. Tu and C. G.. Shao, Correlation method in period measurement of a torsion pendulum, Rev. Sci. Instrum., 75(2004) 1971.
[33] Z. K. Hu, J. Luo and Hsu Houtse, Nonlinearity of the Tungsten Fiber in the Time-of-swing Method, Phys. Lett. A, 264(1999) 112.
[34] Z. K. Hu, J. Luo, Amplitude dependence of quality factor of the torsion pendulum , Phys. Lett. A, 268(2000) 255.
[35] J. Luo, Z. K. Hu and Hsu H., Thermoelastic property of the torsion fiber in the gravitational experiments, Rev. Sci. Instrum., 71(2000) 1524.
[36] J. Luo, Z. K. Hu, X. J. Luo and Z. G. Wu, Determination of the unperturbed period of torsion pendulum in the time-of -swing method , Chin. Phys. Lett., 16(1999) 867.
[37] J. LUO, W. M. Wang and Z. K. Hu, Precise determination of separation between spherical attracting masses in measuring gravitational constant G, Chinese Phys. Lett. 2001 .
[38]赵亮,周期法测G中扭秤的精确定位与相关量的测量[硕士论文],华中科技大学,2003.
[39] Yue Su, Ph.D.thesis,University of Washington,1992.
[40]涂英,周期法测G中高精度周期拟和方法与“反常模式”研究[硕士论文],华中科技大学,2004.
[41] J. LUO, D. H. WANG, Q. LIU,C.G. SHAO, Precise Determination of Period of a Torsion Pendulum in Measurement of Gravitational Constant, Chinese Phys. Lett., 22(2005) 2169.
[42] Y. Tu, L. Zhao, Q. Liu,.H. L. Ye and J. Luo, An abnormal mode of torsion pendulum and its suppression., Phys.Lett.A, 331(2004) 354.
[43] L. Zhao, Y. Tu and B. M. GU, An abnormal vibrational mode of torsion pendulum. Chinese Phys. Lett., 20(2003) 1206.
[44] G. Q. FENG, S. Q. YANG, L. C. TU and J. LUO, Improvement of Test of Solar Neutrino Coherent Scattering with Torsion Pendulum. Chinese Phys. Lett. 23(2006) 2052.
[45]赵鹏飞,唐孟希,引力波探测中的被动隔振系统.力学进展. 33(2003) 187.
[46] P. R. Saulson et al., The inverted pendulum as a probe of anelasticity, Rev.Sci.Instrum., 65(1994) 182.
[47] G. Losurdo et al., An inverted pendulum preisolator stage for the VIRGO suspension system,Rev.Sci.Instrum., 70(1999) 2507.
[48] M. A. Barton and K. kuroda,Ultralow frequency oscillator using a pendulum with crossed suspension wires,Rev.Instrum., 65(1994 ) 3775.
[49] Sodano,H.A, Inman, D.J, New semi-active damping concept using eddy currents. Proc.of SPIE, 5760(2005) 293.
[50] Xue-Li Wang,Liang Zhao and Liang-Cheng TU, Eddy Current Loss Testing in the Torsion Pendulum.Phys.Lett.A, 290(2001)41.
[2] G. T. Gillies and T. C. Ritter, Torsion balance, torsion pendulums, and related devices, Rev. Sci. Instrum. , 64(1993) 283.
[3] G. G. Luther, W. R. Towler, Redetermination of the Newtonian gravitational constant, Phys. Rev. Lett. , 48(1982) 121.
[4] G. T. Gillies, The Newtonian gravitational constant, Metrologia. , 24 (1987) 1.
[5] G. T. Gillies, The Newtonian gravitational constant: recent measurements and related studies, Rep. Prog. Phys., 60(1997)151.
[6] Luo J., Hu Z-K., Fu X-H., Fan S-H. and Tang M-X., Determination of Newtonian Gravitational Constant G with Considering the Non-linear effect, Phys. Rev. D., 59(1999)042001.
[7] R. Spero, J. K. Hosjins, R. Newman, J. Pellam and J. Schultz, Test of the Gravitational Inverse-Square Law at Laboratory Distances, Phys. Rev. Lett., 44(1980)1645.
[8] Y. T. Chen, A. H. Cook and A. J. F. Metherell, An experiment of test of the inverse Square law of gravitation at range of 0.1 m, Proc. Roy. Soc. A, 394(1984) 47.
[9] M. W. Moore, A. Boudreaux, M. DePue, J. Guthrie, R. Legere, A. Yan, P. E. Boynton, Testing the inverse-square law of gravity: a new class of torsion pendulum null experiments, Class. Quantum. Grav., 11(1994) A97.
[10] J. K. Hoskins, R. D. Newman, R. Spero, and J. Schultz, Experimental tests of the gravitational inverse-square law for mass separations from 2 to 105 cm, Phys. Rev. D., 32(1985)3084.
[11] C. D. Hoyle, U. Schmidt, B. R. Heckel, E. G. Adelberger, J.H. Gundlach, D. J. Kapner, and H. E. Swanson, Submillimeter Test of the Gravitational Inverse-Square Law: A Search for“Large”Extra Dimensions, Phys.Rev.Lett. , 86 (2001) 1418.
[12] E. Fishbach, G.. T. Gillies, D. E. Krause, J. G. Schwan and C. Talmadge,Non-Newtonian Gravity and New Weak Forces: an Index of Measurements and Theory, Metrologia., 29(1992)213.
[13] E. Fischbach, The search for non-Newtonian gravity, Springer 1999.
[14] C. W. Stubbs, E. G. Adelberger, Search for an Intermediate-Range Interaction, Phys. Rev. Lett. 58(1987)1070.
[15] Y. Su, B. R. Heckel, E. G. Adelberger, J. H. Gundlach, M. Har-ris, G. L. Smith, and H. E. Swanson, New tests of the universality of free fall, Phys. Rev. D., 50(1994) 3614.
[16] C. R. Rogers, E. G. Charles, Ni W. T., G. T. Gillies and C. C. Speake, Experimental test of equivalence principle with polarized masses, Phy. Rev. D., 42(1990) 4.
[17] J. H. Gundlach , G. L. Smith , C. D. Hoyle , E. G. Adelberger, B. R. Heckel and H. E. Swanson, Short-range Tests of the Equivalence Principle, Phys.Rev.Lett. , 78 (1997) 2523.
[18] V. M. Mostepanenko and I. Yu. Sokolov, The Casimir effect leads to new restrictions on long-range force constants,Phys. Lett. A, 125 (1987) 405.
[19] M. Bordag, G. L. Kilmchitskaya and V. M. Mostepanenko, Corrections to the Casimir force between plates with stochastic surfaces, Phys. Lett. A, 200 (1995) 95.
[20] V. M. Mostepanenko and I. Yu. Sokolov, Stronger restrictions on the constants of long-range forces decreasing as r-n Phys. Lett. A, 146 (1990) 373.
[21] V. M. Mostepanenko and I. Yu. Sokolov, Hypothetical long-range interactions and restrictions on their parameters from force measurements, Phys. Lett. A, 47 (1993) 2882.
[22] S. K. Lamoreaux, Demonstration of the Casimir Force in the 0.6 to 6um Range Phys.Rev.Lett., 78 (1997) 5.
[23] R. Lakes, Experimental Limits on the Photon Mass and Cosmic Magnetic Vector Potential, Phys.Rev.Lett., 80 (1998) 1826.
[24] J. Luo, C. G. Shao, Z. Z. Liu, Z. K. Hu, New Experimental Limit on the Photon Rest Mass with a Rotating Torsion Balance, Phys.Rev.Lett., 90 (2003) 1.
[25] P. R. Hely, A Redetermination of constant of gravitation, J. Res. Nat. Bur. Stand. (US), 5(1930) 1243.
[26] M. U. Sagitov, Current status of determination of the gravitational constant and the mass of the Earth. Soviet Astronm.-AJ., 13(1976) 712.
[27]罗俊,万有引力常数G的精确测量[博士论文],中国科学院测量与地球物理研究所,1999,p79.
[28] Hu Z. K. and Luo J., Determination of Fundamental Frequency of A Physical Oscillator with Period Fitting Method, Rev. Sci. Instrum., 70(1999) 4412.
[29] Y. T. Chen, A. Cook, Gravitational Experiments in the Laboratory(Cambridge University Press,Cambridge,1993).
[30] R. D. Newman and M. K. Bantel, On determination G using a cryogenic torsion pendulum, Meas. Sci. Technol., 10 (1999) 445.
[31] K. Kuroda, Does the time-of-swing method give a correct value of the Newtonian gravitational constant? Phys. Rev. Lett., 75(1995) 2796.
[32] T. L. Tian,Y. Tu and C. G.. Shao, Correlation method in period measurement of a torsion pendulum, Rev. Sci. Instrum., 75(2004) 1971.
[33] Z. K. Hu, J. Luo and Hsu Houtse, Nonlinearity of the Tungsten Fiber in the Time-of-swing Method, Phys. Lett. A, 264(1999) 112.
[34] Z. K. Hu, J. Luo, Amplitude dependence of quality factor of the torsion pendulum , Phys. Lett. A, 268(2000) 255.
[35] J. Luo, Z. K. Hu and Hsu H., Thermoelastic property of the torsion fiber in the gravitational experiments, Rev. Sci. Instrum., 71(2000) 1524.
[36] J. Luo, Z. K. Hu, X. J. Luo and Z. G. Wu, Determination of the unperturbed period of torsion pendulum in the time-of -swing method , Chin. Phys. Lett., 16(1999) 867.
[37] J. LUO, W. M. Wang and Z. K. Hu, Precise determination of separation between spherical attracting masses in measuring gravitational constant G, Chinese Phys. Lett. 2001 .
[38]赵亮,周期法测G中扭秤的精确定位与相关量的测量[硕士论文],华中科技大学,2003.
[39] Yue Su, Ph.D.thesis,University of Washington,1992.
[40]涂英,周期法测G中高精度周期拟和方法与“反常模式”研究[硕士论文],华中科技大学,2004.
[41] J. LUO, D. H. WANG, Q. LIU,C.G. SHAO, Precise Determination of Period of a Torsion Pendulum in Measurement of Gravitational Constant, Chinese Phys. Lett., 22(2005) 2169.
[42] Y. Tu, L. Zhao, Q. Liu,.H. L. Ye and J. Luo, An abnormal mode of torsion pendulum and its suppression., Phys.Lett.A, 331(2004) 354.
[43] L. Zhao, Y. Tu and B. M. GU, An abnormal vibrational mode of torsion pendulum. Chinese Phys. Lett., 20(2003) 1206.
[44] G. Q. FENG, S. Q. YANG, L. C. TU and J. LUO, Improvement of Test of Solar Neutrino Coherent Scattering with Torsion Pendulum. Chinese Phys. Lett. 23(2006) 2052.
[45]赵鹏飞,唐孟希,引力波探测中的被动隔振系统.力学进展. 33(2003) 187.
[46] P. R. Saulson et al., The inverted pendulum as a probe of anelasticity, Rev.Sci.Instrum., 65(1994) 182.
[47] G. Losurdo et al., An inverted pendulum preisolator stage for the VIRGO suspension system,Rev.Sci.Instrum., 70(1999) 2507.
[48] M. A. Barton and K. kuroda,Ultralow frequency oscillator using a pendulum with crossed suspension wires,Rev.Instrum., 65(1994 ) 3775.
[49] Sodano,H.A, Inman, D.J, New semi-active damping concept using eddy currents. Proc.of SPIE, 5760(2005) 293.
[50] Xue-Li Wang,Liang Zhao and Liang-Cheng TU, Eddy Current Loss Testing in the Torsion Pendulum.Phys.Lett.A, 290(2001)41.