Nomination of Alex Chao Representative publications #1 A. W. Chao and J. Gareyte, “Scaling Law for Bunch Lengthening in SPEAR II”, SLAC Report SPEAR-197/PEP-224 (1976), journal reprinting Part. Accel. 25, 229 (1990). The Chao-Gareyte Scaling clarified the physical process of the anomalous bunch lengthening effect observed in electron storage rings. #2 Alexander W. Chao, “Evaluation of Beam Distribution Parameters in an Electron Storage Ring”, J. Appl. Phys., Vol.50, No.2, 595 (1979). This paper invented a concise and elegant way to calculate the beam distribution parameters in an electron storage ring. It is the only way to do such calculations for an accelerator with coupled lattice in 6-D phase space. It also paved the way to the realization of the possibility of the next paper #3. #3 Alexander W.Chao, “Evaluation of Radiative Spin Polarization in an Electron Storage Ring”, Nucl. Instru. and Meth. 180, 29 (1981). This paper invented an elegant technique for polarization calculation in electron storage rings. The technique clarified the physical process of radiative polarization, and provided a correct way to calculate polarization. It was later implemented in a program SLIM, which became a standard tool for polarization calculations. #4 Alexander W.Chao and Kaoru Yokoya, “An Alternative Longitudinal Polarization Scheme for TRISTAN”, KEK Report 81-7 (1981). The Chao-Yokoya Spin Transparency Conditions played a crucial role in the design and the understanding of longitudinal polarization in electron storage rings such as HERA in Germany or the Tau/Charm factories. #5 Alexander W.Chao, Burton Richter, and Chi-Yuan Yao, “Beam Emittance Growth Caused by Transverse Deflecting Fields in a Linear Accelerator”, Nucl. Instru. Meth. 178, 1 (1980). This paper pioneered the study of beam-break-up instability for high-intensity linear colliders. Beam-break-up instability is the basic effect that limits the performance of linear colliders. #6 Alexander W. Chao, “Coherent Instabilities of a Relativistic Bunched Beam”, US Summer School on High Energy Particle Accelerators, SLAC, AIP Conf. Proc. 105 (1982) p.353. This article was an acknowledged reference on the subject. It was later expanded into a book “Physics of Collective Beam Instabilities in High Energy Accelerators”, John Wiley & Sons, New York, 1993. It is the classic book reference on this topic. #7 A.W.Chao and R.D.Ruth, “Coherent Beam-Beam Instability in Colliding Beam Storage Rings”, Part. Accel. 16, 201 (1985). Chao wrote a series of papers which led the research avenue of coherent beam-beam effects. This view of the beam-beam effect (that limits the performance of storage ring colliders) was revolutionary at the time but has now become a standard vocabulary. #8 SSC Central Design Group, “Superconducting Super Collider Conceptual Design”, SSC-SR2020 (1986). Chao wrote Chapter 4. This was the design base of the project Superconducting Super Collider. Its completion represented a team work of many accelerator physicists. #9 A. Chao et al., “Experimental Investigation of Nonlinear Dynamics in the Fermilab Tevatron”, Phys. Rev. Lett. 61, 2752 (1988). This was the first study of nonlinear dynamics as formal experiment using accelerators. The results had impacted the way these experiments are carried out in later years. #10 “Handbook of Accelerator Physics and Engineering”, Editors Alexander Wu Chao and Maury Tigner, World Scientific, Singapore, 1999. This 650-page handbook is a concise summary of more than 200 world’s top experts on a wide range of accelerator topics. This was an ambitious project and is used widely by practitioners in the field. #11 Alexander W. Chao and Ernest D. Courant, "Spin Echo in Synchrotrons", Phys. Rev. Special Topics - Accelerators and Beams 10, 014001 (2007). This paper proposed an exciting spin dynamical effect called spin echo. The mechanism results from an intricate interplay of spin dynamical phase space. Experiments are being designed to test this theoretical prediction. This work. together with the understanding in spin dynamics that comes with it, have large implications for the polarization community in high energy physics. #12 Alexander W. Chao, "Gravitational Instability of a Nonrotating Galaxy", J. High Energy and Nuclear Physics, 2005. This insightful paper predicts a size of galaxy beyond which the galaxy becomes unstable. Results agree well with astrophysical observations. This paper is an application of sophisticated techniques, developed to analyze beam instability problems in accelerator physics, to the problem of galaxy instability in astrophysics. #13 Alexander W. Chao, "Matrix formalism for spin dynamics near a single depolarization resonance", Phys. Rev. Special Topics – Accelerators and Beams 8, 104001 (2005); "Experimental test of the new analytic matrix formalism for spin dynamics", V.S. Morozov et al, Phys. Rev. Special Topics - Accelerators and Beams 10, 041001 (2007); "Experimental verification of striking predicted oscillations near a spin resonance", V.S. Morozov, et al., submitted to Phys. Rev. Lett. (2007). These 3 publications address a striking interference phenomenon of spin dynamics. The first paper was theoretical, and the next two are experimental results beautifully confirming the theoretical predictions. Publications (Journals and Proceedings) Alexander Wu Chao and Chen Ning Yang, “Opaqueness of pp Collision from 30 to 1500 GeV/c”, Phys. Rev. D8, 2063 (1973). Alexander Wu Chao and C. Quigg, “Clustering in Multiple Production”, Phys. Rev. D9, 2016 (1974). A.W. Chao and M. Month, “Particle Trapping During Passage Through a High-Order Nonlinear Resonance”, Nucl. Instru. Meth. 121, 129 (1974). Alexander Wu Chao and Chen Ning Yang, “Possible Relationship Between the Ratio pi+/pi- and the Average Multiplicity”, Phys. Rev. D9, 2505 (1974). Alexander Wu Chao and Chen Ning Yang, “Charge Correlation Between Two Pions in a Statistical Charge Distribution Among Hadrons”, Phys. Rev. D10, 2119 (1974). Alexander Wu Chao and Alfred S. Goldhaber, “Effect of Nuclear Deformation on High-Energy Proton-Nucleus Scattering”, Phys. Rev. D11, 29 (1975). SPEAR Group, “SPEAR II Performance”, IEEE Trans. Nucl. Sci., NS-22, No.3, 1366 (1975). A.W. Chao, M.J. Lee, and P.L. Morton, “Higher Order Multipole Magnet Tolerances”, IEEE Trans. Nucl. Sci., NS-22, No.3,1878 (1975). A.W. Chao, “Some Effects of Random Errors in ISA Magnets”, Proc. ISABELLE Summer Study, BNL Report 20550 (1975) P.386. A.W. Chao, J.C. Herrera, and M. Month, “Betatron Tune Change Due to Direct Space Charge in ISA”, Proc. ISABELLE Summer Study, BNL Report 20550 (1975) p.418. A.W. Chao and M. Month, “Dynamic Beam Cleaning by a Nonlinear Resonance”, Nucl. Instru. Meth. 133, 405 (1976). Alexander W. Chao and Martin J. Lee, “Particle Distribution Parameters in an Electron Storage Ring”, J. Appl. Phys., Vol.47, No.10, 4453 (1976). A.W. Chao and M.J. Lee, “Vertical Beam Size due to Orbit and Alignment Errors”, IEEE Trans. Nucl. Sci., NS-24, No.3, 1203 (1977). P.B. Wilson, R. Servranckx, A.P. Sabersky, J. Gareyte, G.E. Fischer, M.H.R. Donald, and A.W. Chao, “Measurements of Bunch Lengthening at SPEAR II”, IEEE Trans. Nucl. Sci., NS-24, No.3, 1211 (1977). Alexander W.Chao, Tai Tsun Wu, and Chen Ning Yang, “Some Inequalities in the Eikonal Approximation”, CERN/TH-2224 (1976), The Ta-You Wu Festschrieft: Science of Matter, Gordon and Breach, editor S. Fujita, p.27 (1977). SPEAR Group, “Synchrobetatron Resonances”, Invited talk, IEEE Trans. Nucl. Sci., NS-24, No.3, 1863 (1977). A.W. Chao, “Quantum Lifetime in Electron Storage Rings”, IEEE Trans. Nucl. Sci., NS-24, No.3, 1885 (1977). A.W. Chao, “On the Control of Beam Polarization by Wigglers”, Proc. Wiggler Magnets Workshop, SLAC, SSRP-77/05 (1977). Alexander W. Chao, “Evaluation of Beam Distribution Parameters in an Electron Storage Ring”, J. Appl. Phys., Vol.50, No.2, 595 (1979). Mu-ming Poo, James W. Lam, Norman Orida, and Alexander W. Chao, “Electrophoresis and Diffusion in the Plane of the cell Membrance”, J. Biophysics, 26, 1 (1979). A.W. Chao, “Estimate of Spin Polarization for the Electron Storage Rings SPEAR and PEP”, IEEE Trans. Nucl. Sci., NS-26, No.3, 3482 (1979). A.W. Chao, P.L. Morton, and J.R. Rees, “Single Feedback Systems for Simultaneous Damping of Horizontal and Longitudinal Coherent Oscillations”, IEEE Trans. Nucl. Sci., NS-26, No.3, 3342 (1979). PEP I&C Group and PEP Theory Group, “PEP computer Control System”, IEEE Trans. Nucl. Sci., NS-26, No.3, 3268 (1979). A.W. Chao, “A Summary of Some Beam-Beam Models”, Invited talk, AIP Conf. Proc. on Nonlinear Dynamics and the Beam-Beam Interaction, BNL, No.57, p.42 (1979). A.W. Chao, B. Richter, and C.Y. Yao, “Transverse Wake Field Effects on Intense Bunches with Application to Linear Collider Operation”, Proc. XI-th Intern. Conf. on High Energy Accel., CERN, p.597 (1980). SLC Group, “The SLAC Linear Collider”, Proc. XI-th Intern. Conf. on High Energy Accel., CERN, p.168 (1980). A.W. Chao, “Problems in Obtaining Polarized e+ and e- Beams and Perspectives for PEP”, Invited talk, Proc. Internl. Symp. High Energy Physics with Polarized Beams and Polarized Targets, Lausanne, p.15 (1980). Alexander W. Chao, Burton Richter, and Chi-Yuan Yao, “Beam Emittance Growth Caused by Transverse Deflecting Fields in a Linear Accelerator”, Nucl. Instru. Meth. 178, 1 (1980). Alexander W. Chao and Kaoru Yokoya, “An Alternative Longitudinal Polarization Scheme for TRISTAN”, KEK Report 81-7 (1981). C.Y. Yao and A.W. Chao, “Estimate of Coherent Tune Shifts for PEP”, IEEE Trans. Nucl. Sci. NS28, 2571 (1981). M.J. Lee et al., “Mathematical models for the Control Program of SLAC Linear Collider”, IEEE Trans. Nucl. Sci. NS-28, 2155 (1981). M.H.R. Donald et al., “Some Schemes for 0n-line Correction of the Closed Orbit, Dispersion and Beta Function Errors in PEP”, IEEE Trans. Nucl. Sci. NS-28, 2207 (1981). K. Bane, A. Chao, and T. Weiland, “A Simple Model for the Energy Loss of a Bunched Beam Traversing a Cavity”, IEEE Trans. Nucl. Sci. NS-28, 2605 (1981). A.W. Chao, “Polarization of a Stored Electron Beam”, Lecture, Summer School on Hign Energy Particle Accelerators, AIP Conf. Proc. No.87, (1981) p.395. Alexander W. Chao, “Evaluation of Radiative Spin Polarization in an Electron Storage Ring”, Nucl. Instru. and Meth. 180, 29 (1981). R.D. Ruth and A.W. Chao, “Plasma Laser Accelerator: Longitudinal Dynamics, The plasms/Laser Interaction, and a Qualitative Design”, Workshop on Laser Accel. of Particles, Los Alamos, AIP Conf. Proc. No.91, (1982) p.94. Alexander W. Chao, “Coherent Instabilities of a Relativistic Bunched Beam”, Lecture, Summer School on High Energy Particle Accelerators, SLAC, AIP Conf. Proc. No.105 (1982) p.353. A.W. Chao, “Spin Matching for Polarized Protons”, Invited talk, 5-th Int. Symp. High Energy Spin Phys., BNL, 1982, AIP Conf. Proc. No.95, p.458. Alexander W. Chao and Richard K. Cooper, “Transverse Quadrupole Wake Field Effects in High Energy Linacs”, Part. Accel.,13, 1 (1983). A.W. Chao and S. Kheifets, “Beam Shape Distortion Caused by Transverse Wake Fields”, IEEE Trans. Nucl. Sci., NS-30, 2571 (1983). A.W. Chao, “Latest on Polarization in Electron Storage Rings”, Invited talk, IEEE Trans. Nucl. Sci., NS-30, 2383 (1983). R. Helm et al., “Recent Improvements in Luminosity at PEP”, IEEE Trans. Nucl. Sci., NS-30, 2001 (1983). Alexander W. Chao, “The Beam-Beam Instability”, Lecture, Summer School on High Energy Particle Accelerators, BNL, AIP Conf. Proc. No.127 (1983) p.201. PEP Group, “Comparison Between Experimental and Theoretical Results for the Fast Head-Tail Instability in PEP”, Proc. 12-th Intern. Conf. on High Energy Accel., Fermi Lab., 1983, p.209. Alexander W. Chao, “Calculation of Polarization Effects”, Invited talk, Euro. Conf. on Computing in Accel. Design and Operation, Berlin, 1983, Lectures Notes in Physics 215, Springer-Verlag, p.59. W.T. Weng and A.W. Chao, “Coupled Vibrational Modes of the SLC Arc Magnet and Support System”, IEEE Tran. Nucl. Sci., NS-32, 3663 (1985). A.W. Chao, P. Bambade, and W.T. Weng, “Nonlinear Beam-Beam Resonances”, Lecture, US/CERN School on Part. Accel., Sardinia, 1985, Lecture Notes in Physics 247, Springer-Verlag, p.77. A.W. Chao, “Accelerator Physics Studies for the SSC”, Invited talk, IEEE Tran. Nucl. Sci., NS-32, 3442 (1985). Miguel A. Furman and Alex W. Chao, “Effect of Long Range Beam-Beam Interaction on the Stability of Coherent Dipole Motion”, IEEE Tran. Nucl. Sci., NS-32, 2297 (1985). R.D. Ruth, A.W. Chao, P.L. Morton, and P.B. Wilson, “A Plasma Wake Field Accelerator”, Part. Accel. 17, 171 (1985). A.W. Chao and R.D. Ruth, “Coherent Beam-Beam Instability in Colliding Beam Storage Rings”, Part. Accel. 16, 201 (1985). Alexander W. Chao, “Accelerator Physics in SSC Design”, Invited talk, Proc. DPF annual meeting, Eugene 1985, edi. R. Hwa, World Scientific, p.170. Alexander W. Chao, “Elementary Design and Scaling Considerations of Storage Ring Coliders”, Lecture, Summer School on Hign Energy Particle Accelerators, SLAC, 1985, AIP Conf. Proc. No.153, p.103. A.W. Chao, “Magnet Field Quality Requirements for the SSC”, Invited talk, Proc. ICFA Workshop on Superconducting Magnets and Cryogenics, BNL, p.171 (1986). S. Kheifets et al., “Beam Optical Design and Studies of the SLC Arcs”, Proc. 13-th Inten. Conf. High Energy Accel., Novosibirsk, 1986, p.168. Alexander W. Chao, “Equations for Multiparticle Dynamics”, Lecture, US/CERN School on Frontiers of Particle Beams, S. Padre Island, Texas, 1986, Lecture Notes in Phys., No. 296, p. 51. A.W. Chao and J.M. Peterson, “Energy Acceptance of the SSC”, Proc. Summer Study of Phys. of the SSC, Snowmass, 1986, p.559. S. Chattopadhyay, A. Chao, S.Y. Lee, L. Rivkin, and R. Ruth, “On Damping Rings with Zero Momentum Compaction, and Other Issues”, Proc. ICFA Workshop on Low Emittance Beams, BNL Report 52090, 1987, p.76. W.T. Weng, J. Murray, and A. Chao, “Analysis of Orbit Perturbations of the SLC Arcs”, Proc. IEEE Part. Accel. Conf., Washinton D.C., 1987, p.1361. A. Chao, J. Hagel, F. Ruggiero, and B. Zotter, “A Flat-Beam Final-Focus System”, Proc. Workshop on New Developments in the Particle Acceleration Techniques, Orsay, ECFA-CAS/CERNIN2P3-IRF/CEA-EPS (1987), p.577. J. Peterson and A. Chao, “Tolerances of Beam-Tube Corrector Construction Errors”, Proc. Workshop on Distributed Multipole Correction Coils, BNL, 1987, SSC Report SSC-SR-1032, p.E-2. J.M. Peterson et al., “Dynamics Aperture Measurements at the Tevatron”, Proc. Euro. Part. Accel. Conf. Rome, 1988, p.266. N. Merminga et al., “An Experimental Study of the SSC Magnet Aperture Criterion”, Proc. Euro. Part. Accel. Conf., Rome, 1988, p.791. A.W. Chao, M.A. Furman, and K.Y. Ng, “A Possible Symplectic Coherent Beam-Beam Model”, Proc. Euro. Part. Accel. Conf., Rome, 1988, p.684. A.W. Chao, “Brief Comments on Nonlinear Dynamics Studies in Storage Rings”, Invited talk, Proc. Euro. Part. Accel. Conf., Rome, 1988, p.228. A.W. Chao, “The Criteria Working Group Summary”, Invited talk, Proc. ICFA Beam Dynamics Workshop on Aperture-Related Limitations, Lugano, 1988, CERN Report 88-04, p.152. A.W. Chao, “Comments on Nonlinear Dynamics Studies in Storage Rings”, Lecture, AIP Conf. Proc. No.184, Physics of Particle Accelerators, Fermilab 1987 and Cornell 1988, p.946. A.W. Chao et al., “Experimental Investigation of Nonlinear Dynamics in the Fermilab Tevatron”, Phys. Rev. Lett. 61, 2752 (1988). A.W. Chao and A. Piwinski, “Crab Crossing Near A Linear Synchro-betatron Resonance”, Proc. Advanced Beam Dynamics Workshop on Beam-Beam Effects in Circular Colliders, Novosibirsk, 1989, p.91. A.W. Chao and J. Gareyte, “Scaling Law for Bunch Lengthening in SPEAR II”, SLAC Report SPEAR-197/PEP-224 (1976); Part. Accel. 25, 229 (1990). A.W. Chao, “Recent Nonlinear Dynamics Studies for the SSC”, Invited talk, Proc. Workshop on Nonlinear Dynamics and Acceleration, U. Tsukuba, 1990, AIP Conf. Proc. No.230, p.203. Alex Chao, “Approaching Ultimate Luminosity at the SSC”, Invited talk, Proc. Meeting of the DPF, Rice Univ., Houston, 1990, World Scientific, p.958. A.W. Chao, “Coherent Beam-Beam Effects”, Lecture, US/CERN Joint School on Frontiers in Part. Accel., Hiltonhead, 1990. Alex W. Chao, Robert B. Palmer, Lyndon Evans, Jacques Gareyte, Robert H. Siemann, “Hadron Colliders (SSC/LHC)”, Invited talk, Proc. Symp. Research Directions for the Decade, Snowmass, 1990, World Scientific, p.667. A. Chao, “Summary Report of the Transverse Instability Group”, Invited talk, Proc. Advanced ICFA Beam Dynamics Workshop on Collective Effects in Short Bunches, KEK (1990). A. Chao, “Summary Report of the Mini-Workshop on Beam-Beam Simulations”, Invited talk, SSC Report SSC-N-702 (1990). A. Chao et al., “Workshop Summary”, AIP Conf. Proc. On Beam Dynamics Issues of HighLuminosity Asymmetric Collider Rings, No.214, 1990, p.2. S.Y. Lee et al., “Experimental Determination of a Nonlinear Hamiltonian in a Synchrotron”, Phys. Rev. Lett. 67, 3768 (1991). A.W. Chao, T. Sen, and Y.T. Yan, “Applications of ZMAP to the SSC”, Proc. IEEE Part. Accel. Conf., San Francisco, 1991, p.336. Tanaji Sen, A.W. Chao, and Y.T. Yan, “Effect of Tune Modulation on the Dynamic Aperture of the SSC Lattice”, Proc. IEEE Part. Accel. Conf., San Francisco, 1991, p.345. S.K. Dutt, A.W. Chao, D.E. Johnson, T. Sen, and Y.T. Yan, “Dynamic Aperture & Extraction Studies for the SSC High-Energy Booster” Proc. IEEE Part. Accel. Conf., San Francisco, 1991, p.360. Alexander W. Chao and Yaroslav S. Derbenev, “Cancellation of the Quadrupole Effect on Spin in High Energy Accelerators”, Part. Accel., 36, 25 (1991). S.Y. Lee et al., “Nonlinear Beam Dynamics Studies at the IUCF Cooler Ring”, AIP Conf. Proc. No.255, Advanced Beam Dynamics Workshop, Corpus Christi, 1991, p.370. D.D. Caussyn et al., “Longitudinal Phase-Space Measurements at IUCF”, AIP Conf. Proc. On Stability of Particle Motion in Storage Rings, No.292, 1992, p.163. M. Ellison et al., “Betatron Coupling Correction at the IUCF Cooler, Leading to Improved Determination of Fourth-Order Resonance Hamiltonian”, AIP Conf. Proc. On Stability of Particle Motion in Storage Rings, No.292, 1992, p.170. D.D. Caussyn et al., “Experimental Studies of Nonlinear Beam Dynamics”, Phys. Rev. A46, 7942 (1992). A.W. Chao, “Recent Efforts on Nonlinear Dynamics”, Invited talk, Proc. Intern. Conf. High Energy Accel., Hamburg, 1992, p.981. V.A. Anferov et al., “Effect of a Partial Siberian Snake on an rf Induced Depolarizing Resonance”, Phys. Rev. A46, 12, R7383 (1992). Alex Chao, “Nonlinear Dynamics in Accelerator Physics”, Chinese J. of Phys., 30, 1013 (1992); Invited talk, Proc. Chen Ning Yang, A Great Physicist of the Twentieth Century, International Press, p.35. M. Ellison et al., “Driven Response of the Synchrotron Motion of a Beam”, Phys. Rev. Lett. 70, 591 (1993). Bo Chen and A.W. Chao, “Longitudinal Head-Tail Instability in a Non-Harmonic Potential Well”, Proc. IEEE Accel. Conf., Washington D.C., 1993, p.3345. Bo Chen and A.W. Chao, “Bunch Lengthening Effect and Localized Impedance”, Proc. IEEE Accel. Conf., Washington D.C., 1993, p.3348. R. Schwitters, A. Chao, W. Chou, and J. Peterson, “The Parameters Spreadsheets and Their Applications”, Proc. IEEE Accel. Conf., Washington D.C., 1993, p.3781. Bo Chen and Alexander W. Chao, “Longitudinal Head-Tail Instability in a Non-Harmonic Hamiltonian System”, Part. Accel. 43, 77 (1993). Alex Chao, “Collective Instabilities in High Energy Accelerators”, Invited talk, AIP Conf. Proc. No.311, Physics of High Energy Particles in Toroidal Systems, Irvine, 1993, p.269. M. Syphers et al., “Experimental Study of Synchro-betatron Coupling Induced by Dipole Modulation”, Phys. Rev. Lett. 71, 719 (1993). D. Li et al., “Experimental Measurement of Resonance Islands Induced by RF Voltage Modulation”, Phys. Rev. E, Rapid Comm. 48, 1638 (1993). H. Huang et al., “Experimental Determination of the Hamiltonian for Synchrotron Motion with RF Phase Modulation”, Phys. Rev. E 48, 4678 (1993). D.D. Caussyn et al., “Longitudinal Tracking with Phase and Amplitude Modulated RF”, “, Proc. IEEE Part. Accel. Conf., Washington D.C., 1993, p.29. M. Ellison et al., “Experimental Results of the Betatron Difference Resonance”, Proc. IEEE Part. Accel. Conf., Washington D.C., 1993, p.224. Y. Wang et al., “Experimental Results of the Betatron Sum Resonance”, Proc. IEEE Part. Accel. Conf., Washington D.C., 1993, p.227. M.J. Syphers et al., “Experimental Simulation of Ground Motion Effects”, Proc. IEEE Part. Accel. Conf., Washington D.C., 1993, p.420. S.Y. Lee et al., “Comment on the Attainment of Space-Charge Dominated Beams in a Synchrotron” (1993). Alex Chao, Gerry Dugan, and Mike Harrison, “30x30 TeV – Summary Report”, Invited talk, Proc. Workshop on Future Hadron Facilities in the U.S., Indiana Univ., 1994, Fermilab Report TM1907, p.9. Y. Wang et. al., “Effects of the Synchro-Betatron Coupling Induced by Dipole-Field Modulation”, Phys. Rev. E 49, 1610 (1994). Y. Wang et. al., “Effects of Tune Modulation on Particles Trapped in One-Dimensional Resonance Islands”, Phys. Rev. E 49, 5697 (1994). A. Chao, “Report of the Working Group on Multi-bunch Instabilities”, Invited talk, Proc. Workshop on Beam Instabilities in Storage Rings, Hefei, China, 1994, p.315. Alex Chao, Bo Chen, and Katsunobu Oide, “Longitudinal Microwave Instability with Potential Well Distortion”, Proc. Workshop on Beam Instabilities in Storage Rings, Hefei, China, 1994, p.207. M. Ellison et. al., “Experimental Measurements of a Betatron Difference Resonance”, Proc. IEEE Part. Accel. Conf., Washington D.C., 1993, p.224; Phys. Rev. E 50, 4051 (1994). A.W. Chao, “Summary of the Working Group on Impedances”, Invited talk, Proc. Workshop on Collective Effects in Large Hadron Colliders, Montreux, 1994, Part. Accel. 50, 1 (1995). D. Liu et al., “Effects of rf Voltage Modulation on Particle Motion”, Nucl. Instr. Meth. A364, 205 (1995). A. Chao, “Particle Trapping with an RF Cavity”, Proc. Proc. Workshop on Crystalline Beams and Related Issues, Erice, Italy, 1995, SLAC-PUB-7072. A. Chao and H. Henke, “Wakefield and he Diffraction Model due to a Flat Beam Moving Past Conducting Wedge”, Proc. IEEE Part. Accel. Conf., Dallas, 1995, SLAC-PUB-95-6780. Chunxi Wang and Alex Chao, “Analytic Second- and Third-Order Achromat Designs”, SLACPUB-95-6794, Proc. IEEE Part. Accel. Conf., Dallas, 1995. A. Chao, B. Chen, and K. Oide, “A Weak Microwave Instability with Potential Well Distortion and Radial Mode Coupling”, “, Proc. IEEE Part. Accel. Conf., Dallas, 1995, SLAC-PUB-95-6859. M. Minty, A. Chao, and W. Spence, “Emittance Growth due to Decoherence and Wakefields”, Proc. IEEE Part. Accel. Conf., Dallas, 1995, SLAC-PUB-95-6815. G. Stupakov and A. Chao, “Study of Beam Decoherence in the Presence of Head-Tail Instability Using a Two-Particle Model”, Proc. IEEE Part. Accel. Conf., Dallas, 1995, SLAC-PUB-95-6804. K. Bane et al., “High-Intensity Single Bunch Instability Behavior In the New SLC Damping Ring Vacuum Chamber”, Proc. IEEE Part. Accel. Conf., Dallas, 1995, SLAC-PUB-95-6894. S. Heifets et al., “Impedance Study for the PEP-II B-Factory”, Proc. IEEE Part. Accel. Conf., Dallas, 1995, SLAC-PUB-95-6798. A.W. Chao, “Accelerators for High Energy Physics Research”, Invited talk, Proc. 1-st Intern. Conf. On Frontiers of Physics, Looking into the 21-th Century, World Scientific 1995, p.734. S. Heifets et. al., “Impedance Study for the PEP-II B-Factory”, Proc. Workshop on Collective Effects and Impedance for B-Factories, KEK, 1995, SLAC-PUB-6989. Alex Chao, “A Simulation Study of the Sawtooth Behavior”, Proc. Workshop on Collective Effects and Impedance for B-Factories, KEK, 1995. A.W. Chao and K.-J. Kim, “Collective Effects in Isochronous Storage Rings”, ICFA Workshop on Space Charge Dominated Beams, Bloomington, 1995, AIP Conf. Proc. No.377, p.451. Alex Chao, “Emittance of Linear Colliders”, ICFA Workshop on Space Charge Dominated Beams, Bloomington, 1995, AIP Conf. Proc. No.377, p.514. A.W. Chao, “Accelerators for High Energy Physics Research”, Nature (Chinese), 18, 1,1 (1996). S.Y. Lee, et.al., “Measurements of Nonlinear Electron Cooling Force at the IUCF Cooler Ring”, Proc. Crystal Beam Workshop, Erice, Italy, 1996, World Scientific. A.W. Chao et. al., “Summary Report of the Impedance and Instability Subgroup”, Invited talk, Proc. Tau-Charm Workshop, Beijing, 1996, SLAC-PUB-7116 (1996). A.W. Chao and F. Zimmermann, “Diffraction Model of a Step-Out Transition”, Proc. Euro. Part. Accel. Conf., Sitges, Spain, 1996, SLAC-PUB-7140 (1996). Y. Nosochkov, M. Minty, and A. Chao, “Expected Polarization in the Present PEP-II Design”, Proc. Intern. Symp. On High Energy Physics, Amsterdam, 1996, p.258 (1996). F. Zimmermann and A. Chao, “Diffraction Model of a Step-Out Transition for a Sheet Beam in Planar Geometry”, Proc. Summer Study on New Directions for High-Energy Physics, Snowmass, 1996, SLAC-PUB-7330 (1996). A.W. Chao and K.L. Bane, “On Wakefields with Two-Dimensional Planar Geometry”, Invited talk, Proc. Summer Study on New Directions for High Energy Physics, Snowmass, 1996, SLAC-PUB7322. A.W. Chao, “Report of the Working Group on Single-Particle Nonlinear Dynamics”, Invited talk, Proc. ICFA Workshop on Nonlinear and Collective Phenomena in Beam Physics, Arcidosso, 1996, AIP Proc. 395, p.3. J. Byrd et al., “Ion Instability Experiments on the ALS”, Proc. ICFA Workshop on Nonlinear and Collective Phenomena in Beam Physics, Arcidosso, 1996, AIP Proc. 395, p.175. S. Heifets and A. Chao, “Study of Microwave Instability”, Proc. ICFA Workshop on Nonlinear and Collective Phenomena in Beam Physics, Arcidosso, 1996, AIP Proc. 395, p.251. Ralph Assmann and Alex Chao, “Dispersion in the Presence of Strong Transverse Wakefields”, Proc. IEEE Part. Accel. Conf., Vancouver, 1997, SLAC-PUB-7581. K.L.F. Bane, M.G. Minty, and A.W. Chao, “Simulation of Bunch Precompression at High Currents in the SLC Damping Rings”, Proc. IEEE Part. Accel. Conf., Vancouver, 1997, SLAC-PUB-7470. G.V. Stupakov and A.W. Chao, “Effect of Diffusion on Bunched Beam Echo”, Proc. IEEE Part. Accel. Conf., Vancouver, 1997. K.L.F. Bane, C.K. Ng, and A.W. Chao, “Estimate of the Impedance Due to Wall Surface Roughness”, Proc. IEEE Part. Accel. Conf., Vancouver, 1997, SLAC-PUB-7514. J. Byrd et al., “First Observation of a ‘Fast Beam-Ion Instability’”, Phys. Rev. Lett. 79, 1 (1997). J. Byrd et al., “First Observation of a ‘Fast Beam-Ion Instability’ at the ALS”, Proc. IEEE Part. Accel. Conf., Vancouver, 1997, SLAC-PUB-7512. Alex Chao, “Summary of the Session on Other Effects”, Invited talk, Proc. Workshop on MultiBunch Instabilities in the Future Electron and Positron Accelerators, KEK, 1997, SLAC-PUB7608. A.W. Chao and G.V. Stupakov, “Effect of Feedback and Noise on Fast Ion Instability”, Proc. Workshop on Multi-Bunch Instabilities in the Future Electron and Positron Accelerators, KEK, 1997, SLAC-PUB-7607. F. Zimmermann et al., “Experiments on the Fast Beam-Ion Instability at the ALS”, Proc. Workshop on Multi-Bunch Instabilities in the Future Electron and Positron Accelerators, KEK, 1997, SLAC-PUB-7617. F. Zimmermann et al., “Recent Experiments on the Fast Beam-Ion Instability and a Study of Potential Cures at ALS and PEP-II”, Proc. Advanced ICFA Workshop on Beam Dynamics Issues for e+e- Factories, Frascati, 1997, SLAC-PUB-7736. Alex Chao, “Workshop Summary – Accelerator Issues”, Invited talk, Workshop on Polarized Protons at High Energies, DESY, 1999, SLAC-PUB-8180. Alex Chao, “Chaos in Accelerators”, Invited talk, Proc. OCPA Conf. on Recent Advances and Cross-Century Outlooks in Physics, Atlanta, 1999, SLAC-PUB-8144. Alex Chao, “Lecture on Beam Instability”, Asian Accel. School on Electron Storage Rings, Huairou, 1999, SLAC-PUB-8318. Sam Heifets and Alex Chao, “Characterizing an Improved Broad Band Impedance”, Proc. Broadband Impedance Measurements and Modeling Workshop, SLAC, 2000, SLAC-PUB-8398. Yunhai Cai, Alexander W. Chao, Stephan I. Tzenov, and Toshi Tajima, “Simulation of the BeamBeam Effects in e+e- Storage Rings with a Method of Reducing the Region of Mesh”, Phys. Rev. ST Accel. Beams 4, 011001 (2001). Alex Chao and Boaz Nash, “Possible Quantum Mechanical Effect on Beam Echo”, Proc. 18th Advanced ICFA Workshop on Quantum Aspects of Beam Physics, Capri, 2000, SLAC-PUB8726. Alex Chao, et al., “Report of VLHC Instability Workshop”, Proc. Very Large Hadron Collider Instability Workshop, SLAC, 2001, SLAC-PUB-8800. P.J. Chou and A.W. Chao, “Collective Beam Instability in the Taiwan Light Source”, Proc. Part. Accel. Conf., Chicago, 2001. M.H. Wang, P.J. Chu, and A.W. Chao, “Study of Uneven Fills to Cure the Coupled-Bunch Instability in SRRC”, Proc. Part. Accel. Conf., Chicago, 2001. Alexander Chao et al., “2001 Snowmass Accelerator R&D Report”, Proc. Snowmass Conference on the Future of High Energy Physics, SLAC-PUB-9483 (2001). Karl F. Bane and Alexander W. Chao, “Longitudinal space charge effect in slowly converging or diverging relativistic beams” Phys. Rev. Special Topics – Accel. And Beams, 5, 104401 (2002). Kazuhito Ohmi and Alexander W. Chao, “Combined phenomena of beam-beam and beam-electron cloud interactions in circular e+e- colliders”, Phys. Rev. Special Topics – Accel. And Beams, 5, 101001 (2002). Alexander Chao, Samuel Heifets, and Bruno Zotter, “Tune shifts of bunch trains due to resistive vacuum chambers without circular symmetry”, Phys. Rev. Special Topics – Accel. And Beams, 5, 111001 (2002). Alexandr W. Chao, Rainer Pitthan, Toshiki Tajima, and Dian Yeremian, “Space charge dynamics of bright electron beams”, Phys. Rev. Special topics – Accel. And Beams, 6, 024201 (2003). Erratum: 6, 049901 (2003). Frank T. Cole, Maury Tigner, and Alexander W. Chao, “Accelerator Physics and Engineering”, Encyclopedia of Physical Science and Technology, Third Edition, Vol.1, Academic Press (2002) Alex Chao, “Spontaneous Gravity Instability of Star Distribution in a Nonrotating Galaxy”, Proc. Workshop on Quantum Aspects of Beam Physics, Hiroshima, World Scientific (2003). Boaz Nash and Alex Chao, “A New Analysis of Intrabeam Scattering”, Proc. Part. Accel. Conf., Portland, 2003. Alex Chao, “Halo Generation and Beam Cleaning by Resonance Trapping”, Proc. 29th ICFA Advanced Beam Dynamics Workshop on Halo Beam Dynamics, Montauk, 2003. Alexander W. Chao, “Equilibrium beam distribution and quantum lifetime in the presence of a single nonlinear resonance”, Phys. Rev. Special topics – Accel. And Beams, 6, 094001 (2003). Georg H. Hoffstaetter and Alexander W. Chao, “Synchrobetatron stop bands due to a single crab cavity”, Phys. Rev. Special Topics – Accel. And Beams, 7, 071002 (2004). M.H. Wang and Alex Chao, “Investigation of Microwave Instability on Electron Storage Ring TLS”, Proc. Euro. Part. Accel. Conf., SLAC-PUB-11223 (2004). T.S. Ueng, A.W. Chao, C.C. Kuo, and H.J. Tsai, “Computer Simulation of Equlibrium Elecron Beam Distribution in the Proximity if 4-th Order Single Nonlinear Resonance”, Proc. Euro. Part. Accel. Conf., 2004. Juhao Wu, B.E. Nash, and A.W. Chao, “Equilibrium Beam Invariants of an Electron Storage Ring with Linear x-y Coupling”, Proc. Part. Accel. Conf., 2005. Juhao Wu, T.O. Raubenheimer, A.W. Chao, A. Seryi, and C.K. Sramek, “Luminosity Loss Due to Beam Distortion and the Beam-Beam Instability”, Proc. Part. Accel. Conf., 2005. R.H. Siemann and A.W. Chao, “Wakefields ina Dielectric Tube with Frequency Dependent Dielectric Constant”, Proc. Part. Accel. Conf., 2005. Alexander W. Chao, “Matrix formalism for spin dynamics near a single depolarization resonance”, Phys. Rev. Special topics – Accel. And Beams, 8, 104001 (2005). Alexander W. Chao, “Gravitational Instability of a Nonrotating Galaxy”, J. Hign Energy Phys. & Nuclear Phys., Vol. 30 Suppl. (2006). Boaz Nash, Juhao Wu, and Alexander W. Chao, “Equilibrium beam distribution in an electron storage ring near linear synchrobetatron coupling resonances”, Phys. Rev. Special Topics – Accel. And Beams, 9, 032801 (2006). Samuel A. Heifets and Alexander W. Chao, “Collective beam instability study using a correlationmoment analysis”, Phys. Rev. Special Topics – Accel. And Beams, 10, 034402 (2007). Alexander W. Chao, “Resource Letter PBA-1: Particle beams and accelerators”, Am. J. Phys. 74 (10), (2006). Alex Chao, “Spin Echo and Interference in Synchrotrons”, Proc. Spin Conf., Kyoto, 2006. R.S. Raymond, et al, “Chao Formalism & Kondratenko Crossing Tests”, Proc. Spin Conf., Kyoto, 2006. Alexander W. Chao and Ernest D. Courant, “Spin echo in synchrotrons”, Phys. Rev. Special Topics – Accel. and Beams, 10, 014001 (2007). V.S. Morozov, et al., “Experimental test of the new analytic matrix formalism for spin dynamics”, Phys. Rev. Special Topics – Accel. And Beams, 10, 041001 (2007). L. Wang, A. Chao, and J. Wei, “Geometric Effects on Electron Cloud”, Proc. Part. Accel. Conf., Albuquerque, 2007. Juhao Wu, Alexander W. Chao, and Jean R. Delayen, “Transverse Effect due to Short-range Resistive Wall Wakefield”, Proc. Part. Accel. Conf., Albuquerque, 2007. Daniel Ratner, Alex Chao, and Zhirong Huang, “Enhancing FEL Power with Phase Shifters”, Proc. FEL Conf., Novosibirsk, 2007. V.S. Morozov, et al., “Experimental verification of striking predictions near a spin resonance”, submitted to Phys. Rev. Lett. 2007 Z. Huang, K. Bane, Y. Cai, A. Chao, R. Hettel, and C. Pellegrini, “Steady State Analysis of Shortwavelength, High-gain FELs in a Large Storage Ring”, Proc. Intern. Workshop on Frontiers in FEL Physics and Realted Topics, Elba, SLAC-PUB-12858 (2007). M. Kando, et al., “On the Production of Flat Electron Bunches for Laser Wakefield Acceleraion” J. Experimental and Theoretical Phys., Vol. 105, No. 5, 1 (2007). Technical Reports A.W. Chao and M. Month, “Observables With linearly Coupled Oscillators”, BNL Report 19329, CRISP/74-16 (1974). A.W. Chao and M.J. Lee, “SPEAR II Toushek Lifetime”, SLAC Report SPEAR-181 (1974). A.W. Chao and P.L. Morton, “Physical Picture of the Electromagnetic Fields Between Two Infinite Conducting Plates Produced By a Point Charge Moving at the Speed of Light”, SLAC Report PEP-105/SPEAR-182 (1975). A.W. Chao, “Calculation of Single Resonance Effects”, SLAC Report SPEAR-183 (1975). A.W. Chao, “Parasitic Loss of a Gaussian Bunch in a Closed Cavity”, SLAC Report PEP-118 (1975). A.W. Chao and P.L. Morton, “Differential Energy Loss for a Particle in a Square Pulse of Charge Travelling Between Infinite Conducting Plates”, SLAC Report PEP-119 (1975). A.W. Chao, E. Keil, A.S. King, M.J. Lee, P.L. Morton, J.M. Paterson, “Betatron-Synchrotron Resonances in SPEAR II and a Possible Explanation”, SLAC Report SPEAR-187 (1975). A.W. Chao, “On the Horizontal Shape of an Electron Bunch”, SLAC Report PEP-129 (1975). A.W. Chao and M.J. Lee, “Stationary Solution of the Fokker-Planck Equation for Linearly Coupled Motion in an Electron Storage Ring”, SLAC Report PEP-130/SPEAR-188 (1975). A.W. Chao and M.J. Lee, “Transient Particle Distribution for Lineraly Coupled Motion in an Electron Storage Ring”, SLAC Report PEP-131/SPEAR-189 (1975). A.W. Chao, M.J. Lee and P.L. Morton, “Evaluation of the Field Quality of the Prototype PEP Cell Quadrupole Magnet”, SLAC Report PEP-132 (1975). A.W. Chao, “Particle Distribution and Beam Lifetime With Vacuum Chamber Walls”, SLAC Report PEP-136 (1975). A.W. Chao and M.J. Lee, “RF Distribution”, SLAC Report PTM-20 (1975). A.W. Chao and M.J. Lee, “Synchrobetatron Resonance Effects”, SLAC Report PTM-21(1975). A.W. Chao and M.J. Lee, “RF Distribution Effects”, SLAC Report PTM-22 (1975). A.W. Chao, M.J. Lee, and P.L. Morton, “Orbit Distortion Due to RF Distribution”, SLAC Report PTM-25 (1975). A.W. Chao and M.J. Lee, “Transverse Beam Shape in an Electron Storage Ring With Rotated Quadrupole and Solenoid Magnets”, SLAC Report PEP-207/SPEAR-191 (1976). A.W. Chao and M.J. Lee, “Betatron Frequency Deviations Due to Magnet Field Impurities”, SLAC Report PEP-212 (l976). A.W. Chao, “Electron Beam Lifetime Due To Horizontal Aperture Limitation”, SLAC Report PEP214 (1976). A.W. Chao and R.F. Schwitters, “Linear Theory of Beam Depolarization Due To Vertical Betatron Motion”, SLAC Report PEP-217/SPEAR-194 (1976). A. Chao, K. Huebner, M. Lee, P. Morton, and J. Paterson, “Work On Synchro-betatron Resonances in SPEAR II”, SLAC Report SPEAR-195 (1976). A.W. Chao, “Polarization Near Integer Resonances”, SLAC Report PTM-34 (1976). A. Chao, A. King, and M. Lee, “Magnetic Field Error Effects”, SLAC Report PTM-40 (1976). A.W. Chao, “Quantum Lifetime Due To Horizontal Scraping”, SLAC Report PTM-45 (1976). A. Chao, “Effects Due To Non-uniform RF Cavity Distribution”, SLAC Report PTM-53 (1976). A. Chao and M. Lee, “Rotated Quadrupole Coupling Effects”, SLAC Report PTM-60 (1976). A. Chao and M. Lee, “Beam Size Effects”, SLAC Report PTM-61 (1976). A.W. Chao and M.J. Lee, “Vertical Beam Size Due To Orbit and Misalignment Errors”, SLAC Report PTM-76 (1976). A.W. Chao and R.F. Schwitters, “More on Beam Depolarization at PEP”, SLAC Report PEP-237 (1977). A.W. Chao, “Some Linear-Lattice Calculations Using Generalized Matrices”, DESY Report PET77/07 (1977). A. Chao, “Effect of Wigglers on Spin Polarization”, SLAC Report PTM-100 (1977). A.W. Chao and A. Piwinski, “Linear Vertical Synchro-betatron Resonances Due to a Rotated Quadrupole and a Horizontal Dispersion at the Cavity”, DESY Report PET-77/09 (1977). A.W. Chao, “Depolarization Calculation Using Generalized Matrices”, SLAC Report SPEAR208/PEP-257 (1977). A. Chao and P. Morton, “Dependence of Closed-Orbit on Quadrupole Strength Errors”, SLAC Report PTM-129 (1977). A. Chao and R. Helm, “Energy Shift Due to Orbit Correction”, SLAC Report PTM-130 (1977). A. Chao and M. Lee, “Beam Coupling Control”, PEP Design Handbook (1977). A.W. Chao, “Estimate of Spin Polarization for PEP Using Generalized Transformation Matrices”, SLAC Report PEP-263 (1978). A.W. Chao and P.L. Morton, “Beam Tilt Due to e+e- Crossing at an Angle”, SLAC Report PEP267 (1978). A.W. Chao, “Effects of an RF Phase Feedback System on the Coherent Tunes and Damping Rates”, SLAC Report PEP-268 (1978). K. Bane, A.W. Chao, and M.J. Lee, “Some Bunch Shape Effects in SPEAR”, SLAC Report SPEAR-213 (1978). A. Chao and N. Spenser, “A Comparison Between RMS Orbit Correcting Routines”, SLAC Report PTM-135 (1978). A. Chao and A. Garren, “Synchrotron Phase Shift Due to Betatron Oscillations”, SLAC Report PTM-141 (1978). A. Chao, “Some Formulae for Local Orbit Corrections”, SLAC Report PTM-147 (1978). A. Chao, “On a Possible Monitor-Kicker Type of Feedback System”, SLAC Report PTM-166 (1978). A. Chao, “Effects of the Position-Monitor Reading Errors on the RF Phase Feedback Damping”, SLAC Report PTM-167 (1978). A. Chao, “Description of the Computer Code ---- Solution by LInear Matrices”, SLAC Report PTM-168 (1978); PTM-168-R1 (1980). A. Chao and M. Cornacchia, “Effect of Gradient Field Perturbations Caused by Beam-Beam Space Charge Forces”, SLAC Report PTM-170 (1978). A. Chao and M. Lee, “Skew Quadrupole Coupling Effects ---- New Locations”, SLAC Report PTM-180 (1978). A.W. Chao, P.L. Morton, and J.R. Rees, “Single Feedback Systems for Simultaneous Damping of Horizontal and Longitudinal Coherent Oscillations”, SLAC report PEP-281 (1979). A.W. Chao and E. Keil, “Coherent Beam-Beam Effect”, CERN-ISR-TH/79-31 and SLAC Report PEP-300 (1979). A.W. Chao, “Polarized Beams in High Energy Circular Accelerators”, Invited talk, APS Conf. Washington D.C., 1979, SLAC Report PEP-301 (1979). A.W. Chao, “Stability of the Higher Order Longitudinal Modes for PEP”, SLAC Report PEP-309 (1979). A.W. Chao, M.J. Lee, E. Linstadt, and N. Spencer, “On-Line Orbit and Dispersion Correction Schemes for PEP”, SLAC Report PEP-318 (1979). A.W. Chao and C.Y. Yao, “Transverse Instability Excited by RF Deflecting Modes for PEP”, SLAC Report PEP-321 (1979). S. Kheifets and A.W. Chao, “Steady State Distribution for Unbunched Beams Colliding in a Drift Space”, AATF/79/13 and SLAC Report PEP-325 (1979). A.Chao and T.Knight, “Compensation of Coupling”, SLAC Report PTM-190 (1979). A. Chao, “On Switching off the Electric Plate Voltages in Less Than One Revolution Time”, SLAC Report PTM-195 (1979). Alex Chao, “Lattice Stability with a Siberian-Snake-Solenoid”, SLAC Report PTM-197 (1979). A. Chao, “Orbit Effects Caused by Polarization”, SLAC Report PTM-198 (1979). A. Chao, “ETAy-Correction of a Perturbed Lattice”, SLAC Report PTM-201 (1979). A. Chao, “Rotated Quadrupoles --- back to the old locations”, SLAC Report PTM-180 and PTM180-R1 (1979). C.Y. Yao and A. Chao, “Accuracy of the ETAx/ETAy Correction Scheme”, SLAC Report PTM205 (1979). A.W. Chao, “On the Electromagnetic Field Produced by a Point Charge Passing Through a Hole in an Infinite Conducting Plate”, SLAC Report PEP-332 (1980). A.W. Chao, “Ploarization for the By-Pass SLAC/PEP Collider”, SLAC Report PEP-334 (1980). A. Chao, “A Possible Trajectory Correction Scheme”, SLAC Report CN-17 (1980). A.W. Chao, “Effect of Transverse Wake Field on Polarization”, SLAC Report CN-29 (1980). A.W. Chao and J.R. Rees, “Measuring Dispersion by Driving rf Voltage”, SLAC Report PEP-343 (1981). A.W. Chao and S. Kheifets, “Orbit Distortion and Beam Tilt Caused by Transverse Wake Fields”, SLAC Report PEP-365 (1981). A.W. Chao and P.L. Morton, “Beam Tilt Due to Lumped rf Distribution”, SLAC Report PEP-368 (1981). A.W. Chao, “Some Aspects of the PEP Control System”, KEK Report TN-81-005 (1981). A.W. Chao, “Can We Put the e-e- Beam Separation Kicker Magnet Inside the Linac Acceleration Section?”, SLAC Report CN-87 (1981). A.W. Chao, “Transport Matrix Through a Region with Superimposed Solenoidal and Skew Quadrupole Fields”, SLAC Report PTM-241 (1981). A.W. Chao, “Transport Matrix Through a Region with Superimposed Solenoidal and Accelerating Fields”, SLAC Report CN-109 (1981). A.W. Chao, “Effect of Ions in the Linac and the Arcs”, SLAC Report CN-121 (1981). A.W. Chao, “More on Ions in the Damping Ring”, SLAC Report CN-123 (1981). A.W. Chao, “Quadrupole Beam Break-up”, SLAC Report CN-127 (1981). A. Chao, J. Paterson and J. Rees, “Coupling Due to Earth's Curvature”, SLAC Report PTM-246 (1981). A.W. Chao and R.K. Cooper, “Beam Breakup Due to Quadrupole Wake Fields for Sector 1”, SLAC Report CN-142 (1982). A. Chao, “A Recipe for Skew-Quadrupole Polarities”, SLAC Report PTM-247 (1982). A. Chao and H. Wiedemann, “Some Effects in the Compressor”, SLAC Report CN-147 (1982). A. Chao and P. Morton, “Resistive Wall in the Damping Ring”, SLAC Report CN-176 (1982). A.W. Chao and P.L. Morton, “Energy Spread Caused by the Longitudinal Dipole Wake”, SLAC Report CN-180 (1982). Alex Chao and Helmut Wiedemann, “A Proposal to Increase the SLC Luminosity”, SLAC Report CN-190 (1982). A. Chao and R. Helm, “Radiation Damping in the SLC Arcs”, SLAC Report CN-201 (1982). A. Chao, “SLIM Program and its limitations”, Invited talk, Workshop Report on Polarized Electron Acceleration and Storage, Hamburg, 1982, DESY M-82/09, p.H1. A. Chao, “Spin Matching for Rotators and Snakes”, Invited talk, Workshop Report on Polarized Electron Acceleration and Storage, Hamburg, 1982, DESY Report M-82/09, p.K1. A. Chao and Y. Kamiya, “Bunch Shape at IP and the Pinch Effect”, SLAC Report CN-218 (1983). Y. Kamiya and A. Chao, “Stability of the Coherent Quadrupole Oscillations Excited by the BeamBeam Interaction”, SLAC Report AP-8 (1983). Y. Kamiya and A.W. Chao, “Coherent Synchro-Betatron Oscillations Excited by the Beam-Beam Interaction”, SLAC Report AP-10 (1983). S. Kheifets, A. Chao, J. Jaeger, and H. Shoaee, “Simulations of the Magnets Misalignments, Field Errors and Orbit Correction for the SLC North Arc”, SLAC Report CN-252 (1983). A. Chao and W. Weng, “An Attempt to Compare Two Arc Orbit Correction Schemes Analytically”, SLAC Report CN-254 (1983). A. Chao and S. Kheifets, “One Way to Save the Number of BPM Buttons in the Arcs That is Not Recommended”, SLAC Report CN-257 (1983). A. Chao and L. Rivkin, “Effect of Magnet. Alignment Jittering in the Damping Ring and RTL on Wake Fields in the Linac”, SLAC Report CN-263 (1984). W.L. Spence, A.W. Chao, and R.D. Ruth, “Coherent Linac Radiation”, SLAC Report AP-28 (1984). K. Wille and A.W. Chao, “Investigation of a Monochromator Scheme for SPEAR”, SLAC Report AP-32 (1984). W.T. Weng and A.W. Chao, “Vibrational Modes of the Pedestal Support System for the SLC Arc Magnets”, SLAC Report AP-35/CN-265 (1984). SSC Aperture Task Force, “SSC Aperture Workshop Summary”, SSC Report SSC-TR-2001 (1984). SSC Aperture Task Force, “Aperture Task Force Report”, SSC Report SSC-3 (1984). SSC Aperture Task Force, “Aperture Task Force Report”, SSC Report SSC-TR-2002 (1984). J. Peterson and A. Chao, “How Much Error in Circumference Between the Two Rings Can we Tolerate?”, SSC Report SSC-N-7 (1985). A. Chao and D. Douglas, “Preliminary Estimate of Emittance Growth Due to Position Jitter and Magnet Strength Noise in Quadrupole and Sextupole Magnets”, SSC Report SSC-N-34 (1985). A. Chao and J. Peterson, “A Quick Estimate of How Much More Inner Coil Diameter is Needed to Operate p-pbar”, SSC Report SSC-N-35 (1985). SSC Aperture Task Force, “Aperture Task Force Review”, SSC Report SSC-11 (1985). A. Chao and C. Leemann, “More on the Overlap Knock-out Resonances in the SSC”, SSC Report SSC-16 (1985). A. Chao and J. Peterson “Eddy Current in the SSC”, SSC Report SSC-17 (1985). S. Peggs, M. Furman, and A. Chao, “A Possible Screening Procedure for Random Multipole Field Errors Before Tracking Studies”, SSC Report SSC-20 (1985). A.W. Chao and S. Peggs, “Orbit Correction in the Long Arcs of the SSC”, SSC Report SSC-48 (1985). A. Chao, “Minutes of the Clustered IR Parameters Meeting”, SSC Report SSC-N-49 (1985). SSC Aperture Task Force, “SSC Aperture Estimate for Cost Comparisons”, SSC Report SSC-SR1013 (1985). SSC Aperture Task Force, “SSC Aperture Task Force Review”, SSC Report SSC-TR-2004 (1985). SSC Clustered Interaction Region Study Group, “The Clustered Interaction Region Option for the SSC”, SSC Report SSC-SR-1014 (1985). A. Chao and S. Peggs, “Orbit Distortion and Tune Shifts Due to the Long Range Beam-Beam Interactions”, SSC Report SSC-N-80 (1985). E. Forest and A. Chao, “A Comparison of Linear Aperture Between Lattices With 60° and 90° Per Cell”, SSC Report SSC-N-81 (1985). J.D. Lackson and A. Chao, “Estimate of the Bremsstrahlung Lifetime of Collider Beams”, SSC Report SSC-N-86 (1985). S. Peggs and A. Chao, “An Updated Look at Long Arc Orbit Correction”, SSC Report SSC-N-96 (1985). A. Chao, E. Forest, and J. Peterson, “Tune Dependence on Betatron Amplitudes Due to Persistent Current Sextupole Field Error”, SSC Report SSC-N-145 (1986). A. Chao, “Tune Shifts Due to Systematic Decapole Field Errors After Correction by Two Families of Lumped Decapoles”, SSC Report SSC-N-148 (1986). A. Chao and M. Tigner, “Requirements for Dipole Field Uniformity and Beam Tube Correction Windings”, SSC Report SSC-N-183 (1986). A.W. Chao and J.M. Peterson, “Tolerance of Recooler Temperature From Persistent Current Effects”, SSC Report SSC-N-62 and 62A (1986). A. Chao, “Random Error Multipoles Generated by the Trim Correction Coils”, SSC Report SSC-N239 (1986). SSC Central Design Group, “Preliminary Report on the Design of the Superconducting Super Collider”, SSC Report SSC-SR-1019 (1986). SSC Central Design Group, “Superconducting Super Collider Conceptual Design”, SSC Report SSC-SR-2020 (1986). SSC pbar-p Study Group, “An Assessment of the Antiproton-Proton Option for the SSC”, SSC Report SSC-SR-1022 (1986). SSC Cell Lattice Study Group, “Optimization of the Cell Lattice Parameters for the SSC”, SSC Report SSC-SR-1024 (1986). Karl Bane and Alex Chao, “Estimate of Impedance Due to Finite Grain Size of Copper Coating on the Beam Pipe”, SSC Report SSC-N-285 (1987). A. Chao and J. Peterson, “Strengths and Mechanical Tolerances of the Bore Tube Windings”, SSC Report SSC-N-313 (1987). R.E. Meller, A.W. Chao, J.M. Peterson, S.G. Peggs, and M.A. Furman, “Decoherence of Kicked Beams”, SSC Report SSC-N-360 (1987). B. Leemann and A. Chao, “More on Multipole Errors of the IR Triplets”, SSC Report SSC-N-369 (1987). E. Forest and A. Chao, “Resonances Due to Field Errors in the Dipole Magnet Ends”, SSC Report SSC-N-406 (1987). A. Chao, “More on Copper Coating Considerations”, SSC Report SSC-N-434 (1987). A. Chao, “On-Going Beam Dynamics Studies at SSC, LBL and SLAC”, ICFA Beam Dynamics Newsletter, DESY Report M-87-01 (1987) p.5. A. Chao, “Errors and Corrections”, SSC Report SSC-N-440 (1988). E778 Collaboration, “A Progress Report on Fermilab Experiment E778, An Experimental Study of the SSC Magnet Aperture Criterion”, SSC Report SSC-156, Fermilab Report FN-471 (1988). A. Chao, P. Limon, J. Rees, and J. Peoples, “Proposed Strength Specifications for Magnet Correctors Distributed in the Dipoles”, SSC Report SSC-N-493 (1988). M.A. Furman, K.Y. Ng, and A.W. Chao, “A Symplectic Model of Coherent Beam-Beam Quadrupole Modes”, SSC Report 174 (1988). A.W. Chao, “Workshop Report on SSC Linac Parameters”, SSC Report SSC-N-561 (1988). A. Chao, A.A. Garren, D.E. Johnson, S. Peggs, and J. Sanford, “Lattice and Siting Document”, SSC Report SSC-CN-584 (1988). A. Chao and J. Peterson, “Status Report (1988), SSC Aperture Determination”, SSC Report SSCN-682 (1988). K. Yokoya et al., “Report of the Workshop on Siberian Snakes for the SSC Collider Ring”, SSC Report SSC-SR-1036 (1988). D. Bintinger et al., “Compensation of SSC Lattice Optics in the Presence of Dipole Field Errors”, SSC Report SSC-SR-1038 (1989). A. Chao, “Possible Scenarios to Reach Higher Luminosity”, SSC Report SSC-N-684 (1989). Y. Yan, T. Sen, A. Chao, G. Bourianoff, A.J. Dragt, E. Forest, “Comment on Round-Off Errors and on One-Turn Taylor Maps”, SSC Report SSCL-301 (1989). E. Tsyganov, A. Chao et al., “Summary Report of Working Sessions on Bent Crystal Beam Extraction for the SSC”, SSC Report SSC-N-722 (1990). A. Chao, S. Dutt, D. Johnson, T. Sen, and Y. Tan, “Dynamic Aperture & Extraction Studies for the SSC High-Energy Booster”, SSC Report SSCL-296 (1990). A. Taratin et al., “Ultrathin Crystal Scatterer for the SSC Beam Extraction System”, SSC Report SSCL-545 (1991). V.A. Anferov et al., “RF Induced Depolarizing Resonances, Spin Flip, and Partial Siberian Snakes”, Univ. Michigan Report UM HE 92-11 (1992). G. Stupakov and A. Chao, “Collective Effects and Beam Decoherence”, SSC Report SSCL-621 (1993). V.A. Anferov et al., “Siberian Snake Overcoming ‘Overlapping’ Depolarizing Resonances” UM HEP (1993). Chunxi Wang and Alex Chao, “Notes on Lie Algebraic Analysis of Achromats”, SLAC Report AP100 (1995). S. Heifets et al., “Impedance Study for the PEP-II B-Factory”, SLAC Report AP-99 (1995). Chunxi Wang and A. Chao, “Transfer Matrices of Superimposed Magnets and RF Cavity”, SLAC Report AP-106 (1996). A. Chao, J. Dorfan, D. Hitlin, and J. Seeman, “PEP34: Upgrade Options for PEP-II for 2000-2005”, SLA PEP-II AP Report 96.10 (1996). A.W. Chao and M.G. Minty, “Polarization Algorithm SLIM: Solution by Linear Matrices”, SLAC Report AP-105 (1996). V. Bharadwaj, et al., “Ultrashort Optical Pulses in the Linac Coherent Light Source”, SLAC Report LCLS-TN-00-8 (2000). Boaz Nash and Alex Chao, “Searching for Transverse Sawtooth in Strong Head-Tail Instability by Adding Landau Damping”, SLAC Report AP-125 (2000). Yunhai Cai, Alexander W. Chao, Stephan I. Tzenov, and Toshi Tajima, “Nonlinear delta-f Method for Beam-Beam Simulation”, SLAC-PUB-8676 (2000). Wu-yen Chuang and Alexander W. Chao, “Stabilizing Head-Tail Instability by Head-Tail Split in Betatron Frequency and by Oscillating Chromaticity”, AP-Note (2001). Committee Report on the BEPC-II Project Design Review, SLAC, 2002, SLAC-R-0603 (2002). Bob Siemann and Alex Chao, “Wakefields in a Dielectric Tube with Frequency Dependent Dielectric Constant”, ARDB-368 (2004). Bob Siemann and Alex Chao, “Transverse Wakefield in a Dielectric Tube with Frequency Dependent Dielectric Constant”, ARDB-378 (2005).