Производство и накопление антипротонов для коллайдера Теватрон II тема диссертации и автореферата по ВАК РФ 01.04.20, доктор наук Лебедев Валерий Анатольевич

• Лебедев Валерий Анатольевич
• доктор наук
• 2022

Оглавление диссертации доктор наук Лебедев Валерий Анатольевич

Contents

Introduction

The Purpose of the Dissertation Work

Scientific Novelty and Practical Value

The following Items are Submitted for Defense

Structure and Volume of the Dissertation

Tevatron in Historical Context

Tevatron I - the Fermilab Collider

The path to high luminosity in the Tevatron

Overview of the Fermilab Accelerator Complex

Antiproton production

Chapter I Production of Antiprotons

1.1. Antiproton target

1.2. Circular machines of Antiproton Source

1.3. Optimization of the Antiproton production and collection

1.4. Lithium Lens

1.5. Optics Correction for Antiproton Source Rings and Transport Lines

1.5.1. Optics Correction for Antiproton Source Transport Lines

1.5.2. Optics Correction for Debuncher

1.5.3. Optics Correction for Accumulator

Chapter II Stochastic Cooling of Antiprotons

2.1. Stochastic Cooling: Theory

2.1.1. Beam Permeability for Longitudinal Cooling

2.1.2. Beam Permeability for Transverse Cooling

2.1.3. Fokker-Planck Equation for Longitudinal Cooling

2.1.4. Fokker-Planck Equation for Transverse Cooling

2.1.5. Cooling Rate Estimates

2.1.6. Stochastic Cooling with Strong Band Overlap

2.2. Stochastic Cooling: Technology and Systems

2.2.1. Pickups and Kickers

2.2.2. Preamplifiers

2.2.3. Recursive Notch Filters

2.2.4. Signal Transmission

2.2.5. Power Amplifiers

2.2.6. Equalizers

2.3. Operational Optimization of the Stacktail System

2.3.1. Stacktail Equalizer

2.3.2. Numerical Simulation of the Stacktail

2.3.3. Fast Computations of Beam Permeability

2.2.4. Transverse Core Heating

Chapter III Electron Cooling of Antiprotons

3.1. Introduction

3.2. Electron Cooling Formulae

3.3. Electron Beam Design Parameters and Choice of the Scheme

3.4. Electron cooler setup description

3.6. Design and Commissioning of Electron Beam Transport

3.7. The Energy Recovery Scheme and Beam Loss Limitations

3.8. Mode Emittances and Electron Angles in the Cooling Section

Thermal angles

Envelope mismatch

Non-linear perturbations

Effect from the ions generated by beam-background gas interactions

Coherent dipole motion

3.9. Cooling Force Measurements

Chapter IV Cooling and Accumulation in Recycler

4.1. Cooling and Beam Manipulations in the Recycler

4.1.1. Stashing cycle

4.1.2. Heating mechanisms

4.2. Intra-Beam Scattering

4.2.1. Multiple Scattering in Single Component Plasma

4.2.2. Multiple IBS in Accelerators

4.2.3. IBS in Recycler

4.3. Cooling Optimization in Recycler

4.3.1. Beam Cooling with Stochastic Cooling

4.3.1. Common Operation of Electron and Stochastic Cooling

4.3.3. Cooling Rates

4.3.4. Final performance

Conclusions

References

Appendix A: Symbols and Definitions

Appendix B: Frequent Abbreviations and Acronyms

Appendix C: Parameters of Fermilab Accelerators

Введение диссертации (часть автореферата) на тему «Производство и накопление антипротонов для коллайдера Теватрон II»

Introduction

This work provides a comprehensive overview of the development of the Fermilab Antiproton Source1 in the course of the Tevatron Run II carried out in 2001 - 2011. Up to now, only two antiproton sources were built: one in CERN and one in Fermilab. The CERN antiproton source was built to support the proton-antiproton collider SppS. This work culminated by the discovery of the W and Z bosons in 1983; and a year later, S. van der Meer and C. Rubbia received the Nobel Prize in Physics for their role in this discovery [1]. This source is still in use in CERN although with much smaller antiproton production rate rather determined by the physics program than inability to support the rate achieved earlier. The second antiproton source was built in Fermilab for the Tevatron collider. Its commissioning was started in the spring of 1985. 10 years later in the course of Tevatron Run I Fermilab reported the discovery of the top quark [2]. To the start of Tevatron Run II the antiproton source significantly upgraded. However, as the future showed, an achievement of projected antiproton production rate was extremely challenging. The Fermilab antiproton source was decommissioned after the end of Run II and presently is used for the g-2 [3] and Mu2e [4] experiments. The third antiproton source is planned to be built in the accelerator complex FAIR [5] which is under contraction in GSI, Germany.

The Fermilab Antiproton Source includes the target station, three rings (Accumulator, Debuncher and Recycler) and connecting transfer lines. To accumulate and cool antiprotons the stochastic and electron cooling are used. Below we discuss in detail all major technologies used in the Antiproton Source and the corresponding physics required to achieve the optimal usage of the hardware.

The Purpose of the Dissertation Work

The purpose of the dissertation work is to describe the challenges we encountered in increase of the antiproton accumulation rate in the accelerator complex of the Fermi National Accelerator Laboratory (USA). The work was carried out in 2001-2009 in the course of commissioning of the Tevatron Run II. This work was extremely important for the success of the project, since an increase in the integral luminosity of the collider was impossible without

1 Historically, in Fermilab, the Antiproton Source includes two rings the Debuncher and Accumulator. Additional ring - the Recycler - was added later and usually is considered separately. It plays the essential part of the antiproton production and therefore, in this work, we consider Recycler as part of the Antiproton Source.

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an increase of the antiproton production rate. The work included an optimization of the proton beam focusing on the target, optimization of the lithium lens operation, an increase of the acceptances of the antiproton source rings, an improvement and optimization of all stochastic cooling systems in the complex, and introduction and optimization of electron cooling in Recycler. The development and optimization of stochastic cooling, and, in particular, the stacktail system, was the most important part of the presented work. It required substantial efforts both in the development of the stochastic cooling theory and its application to solutions of practical problems. The achieved rate of antiproton accumulation of 2.5-1011 h-1 is the world record, many times exceeding all previous and present achievements, as well as antiproton stacking rate for the only machine under construction [5].

The practical results obtained on the record rate of antiproton accumulation, the development of the stochastic cooling theory and its practical applications, as well as the optimization of all systems of the Antiproton Source are the subject of the dissertation. They determine its content, relevance and practical value. The main results of the work are:

• Development of the theory of stochastic cooling required to describe cooling systems operating with Schottky bands close to be overlapped;

• Good agreement between calculated and measured cooling rates;

• Elaboration of optimal scenario of antiproton accumulation and cooling with three cooling rings which use stochastic and electron cooling;

• An achievement of the record antiproton accumulation rate many times higher than all previous, current and planned installations.

Author's personal contribution

The contribution of the author to the presented results is undoubtedly decisive. In 20062009 the author supervised the work on the Tevatron complex upgrades. He both determined the direction of the work of the involved departments, and did considerable part of purely scientific work aimed at an increase of the Tevatron luminosity. This work included carrying out numerical and analytical calculations, conducting experimental studies, analyzing the results and preparing publications. His participation in the Tevatron Run II made a decisive contribution into its success. In 2012 the author was elected to be a fellow of the American Physical Society (APS) with citation "For significant contributions to the accelerator physics underlying the outstanding performance of the Tevatron Collider complex, and the successful commissioning of the CEBAF at Jefferson Lab". The work carried out in the Tevatron Run-II

is presented in the form of scientific publications, as well as in the form of the book "Accelerator Physics at Tevatron Collider" (Springer, 2014, edited by V. Lebedev and V. Shiltsev). An important part of scientific achievements is the mentorship of many successful students and young researchers, peer review of scientific publications in a number of scientific journals. He lectured the course on the hadron colliders for US PAS (US Particle Accelerator school) in 2022. He was awarded to be an Outstanding Referee for Physical Review Journals in 2015, presently serves one-year term as a chair of the APS DPB Publication Committee.

An upgrade of the Antiproton Source, discussed in the dissertation, was essential part of the overall effort on Tevatron luminosity upgrade.

Scientific Novelty and Practical Value

The development of the theory of stochastic cooling created a way to understand in detail the operation of stochastic cooling systems when the Schottky bands are close to be overlapped or overlapped. An optimization of the operation of all Antiproton Source systems made it possible to achieve the theoretical maximum of the accumulation rate and the phase density of the antiproton beam needed for the collider. This work required a detailed analysis of the operation of all systems of the Antiproton Source; including: focusing the proton beam on the target, choosing the optimal design parameters for the lithium lens, correcting the optics of the storage rings of the Antiproton Source and increasing their acceptance, correction of the gain for all stochastic cooling systems, and construction and optimization of the high energy electron cooling.

Reliability of results

The reliability of the obtained results is confirmed by the record rate of antiproton accumulation, as well as good agreement between the calculated and measured parameters of the measured beam dynamics in the storage rings of the Antiproton Source.

The following Items are Submitted for Defense

1. Optimization of the Fermilab Antiproton Source operation. Including:

- Optimization of the proton beam focusing on the target.

- Choice of the direction for the upgrade of the lithium lens and an optimization of its

performance.

- Optics correction for all storage rings and transfer lines of the Antiproton Source. That

included an increase in their acceptance and, where applicable, optics optimization for the

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stochastic cooling, both for the transverse and the stacktail.

2. Improvement and optimization of all stochastic cooling systems of the accelerator complex. Including:

- Development of the stochastic cooling theory;

- Proving that the signal suppression makes relatively small effect on the cooling rate of well corrected and phased system;

- Measurement and correction of the gain of stochastic cooling systems;

- Development and optimization of equalizers that correct the amplitude and phase of the stochastic cooling system gain. These were the first equalizers in the world, the use of which resulted in faster stochastic cooling; in contrast to a removal unwanted signals/features at the band boundaries which was a typical application of equalizers before this work;

- The agreement between the calculated and measured cooling rates is within the measurement accuracy, ~ 15%. Prior to this work, typical calculations gave cooling rates twice as fast as those measured.

3. Measurement and correction of optics in an electron cooling system operating at the beam energy of 4.2 MeV

4. The joint work of stochastic and electron cooling systems made it possible to achieve:

- the phase density of the antiproton beam required for the collider;

- a good lifetime, ~600 hours, required for the accumulation of a large antiproton current;

- an optimal operation of the Antiproton Accumulator which maximized the stacking rate.

Most of the work was done at Fermilab in 2001-2009. Out of the work, which was carried out by the author for the Tevatron Run II, only the work directly related to the subject of the dissertation is listed below:

2001 - 2002 - calculations and optimization of the target and the lithium lens;

2002 - 2005 - selection of the optimal strategy for increasing the collider luminosity and, in particular, optimization of collider operation scenario;

2006 - 2009 - optimization of stochastic cooling systems, and optimization of common operation of stochastic and electron cooling in Recycler.

The results of the work were reported at seminars in the Fermilab and the following international conferences PAC, EPAC, IPAC, NAPAC and ECOOL. In particular, the author delivered plenary talks at EPAC 2006 titled "Tevatron Operational Status and Possible

Lessons for the LHC" and at PAC09 titled "Status of Tevatron Run II". The talks summarized main results of the Tevatron Run II commissioning and supporting developments of the beam physics and technology.

Structure and Volume of the Dissertation

The dissertation consists of an introduction, historical outline, four chapters and a conclusion. Historical outline shortly describes the history of Tevatron and an overview of the Fermilab Accelerator Complex of the Run II time. Chapter I presents the fundamentals of the antiproton production, focusing on the antiprotons coming out the target and beam optics correction for the rings and the transfer lines. Chapter II considers the stochastic cooling theory and its application to practical problems. Chapter III describes the electron cooling and optimization of its use for the Tevatron collider. Chapter IV considers optimal use of electron and stochastic cooling in Recycler.

The dissertation text contains 172 pages, 75 figures, 9 tables. The list of references consists of 123 works.

Standard character definitions are used throughout the text. Links are provided that are easily accessible to the reader. For example, all references to the proceedings of international, European and American accelerator conferences can be found on the JACOW website from https://www.jacow.org/ and all cited technical publications are available at http://inspirehep.net/.

Заключение диссертации по теме «Физика пучков заряженных частиц и ускорительная техника», Лебедев Валерий Анатольевич

Conclusions

As perhaps the most sophisticated research instruments ever built, hadron colliders are widely recognized for their many technological breakthroughs and numerous discoveries in physics. Their complexity and very high cost require the highest possible performance. That is not possible to achieve without outstanding engineering and very good understanding of underlying physics. To make a collider cost effective the highest integral luminosity is required in order to recoup the investment in building these machines. Obtaining the highest possible luminosity required the highest possible production rate of antiprotons in the Accelerator complex of Fermilab. The beam cooling has been absolutely essential for the Run II success. Note that it was used in the SppS and Tevatron colliders; it is presently used in the RHIC and LHC for cooling ions; and the next generation of hadron cooling is required for the presently planned electron ion collider to be built in the Brookhaven National Laboratory (USA). Although the dissertation is devoted to a wider project, production and storage of antiprotons, its major emphasis is on the electron and stochastic cooling of relativistic hadrons. The presented work carried out on the beam cooling research extends the horizons and built a road map for the next generation of colliders and accelerators. In the course of the last 10 years the optical stochastic cooling (OSC) has been a high priority in the author's research. He guided the project and has made major contributions to the experiment which recently experimentally demonstrated the OSC in Fermilab. The following Items are Submitted for Defense

1. Optimization of the Fermilab Antiproton Source operation. Including:

- Optimization of the proton beam focusing on the target.

- Choice of the direction for the upgrade of the lithium lens and an optimization of its performance.

- Optics correction for all storage rings and transfer lines of the Antiproton Source. That included an increase in their acceptance and, where applicable, optics optimization for the stochastic cooling, both for the transverse and the stacktail.

2. Improvement and optimization of all stochastic cooling systems of the accelerator

complex. Including:

- Development of the stochastic cooling theory;

- Proving that the signal suppression makes relatively small effect on the cooling rate of well corrected and phased system;

- Measurement and correction of the gain of stochastic cooling systems;

- Development and optimization of equalizers that correct the amplitude and phase of the stochastic cooling system gain. These were the first equalizers in the world, the use of which resulted in faster stochastic cooling; in contrast to a removal unwanted signals/features at the band boundaries which was a typical application of equalizers before this work;

- The agreement between the calculated and measured cooling rates is within the measurement accuracy, ~ 15%. Prior to this work, typical calculations gave cooling rates twice as fast as those measured.

3. Measurement and correction of optics in an electron cooling system operating at the beam energy of 4.2 MeV

4. The joint work of stochastic and electron cooling systems made it possible to achieve:

- the phase density of the antiproton beam required for the collider;

- a good lifetime, ~600 hours, required for the accumulation of a large antiproton current;

- an optimal operation of the Antiproton Accumulator which maximized the stacking rate.

About a hundred scientists and engineers have been involved in the commissioning of Tevatron Run II. The success of the collider is based on their work, knowledge and ingenuity. It needs to be noted that their work has been based on many discoveries of the previous generations. Here I would like to mention two institutions which discoveries made the Tevatron collider possible:

1) H- strip injection, lithium lenses and electron cooling were suggested and developed in BINP (Novosibirsk, Russia);

2) Stochastic cooling was suggested and developed in CERN (Geneva, Switzerland). We need also to mention the slip stacking suggested and developed in Fermilab. It doubled the proton flux, and, consequently, enabled doubling the antiproton production in the course of Run II.

The great team of scientists and engineers worked on the Tevatron Run II. It was unforgettable time for all of us. The author is grateful to all Fermilab colleagues, as well as to the colleagues from other labs (BNL, CERN, ORNL, JLAB) which he was lucky to meet and work on the project. In particular, I would like to express my special gratitude to Yu. Alexahin, G. Annala, C. Bhat, A. Burov, D. McGinnis, J. Morgan, S. Nagaitsev, V. Nagaslaev, R. Pasquinelli, A. Shemyakin, V. Shiltsev, D. Sun, D. Still, A. Valishev and S.

Werkema.

Under the guidance of the author or with his participation or consultations, a number of dissertations were defended:

1. Timofey Zolkin, "Beam Transverse Instability in the FNAL Booster", UNIVERSITY OF CHICAGO (2014).

2. Matt Andorf, "Light Transport and Amplification for a Proof-of-Principle Experiment of the Optical Stochastic Cooling", NORTHERN ILLINOIS UNIVERSITY (2018)

3. Ihar Lobach, "Statistical properties of undulator radiation: Classical and quantum effects", UNIVERSITY OF CHICAGO (2021)

Main results are published in a book:

Editors: Lebedev V., Shiltsev V. Accelerator Physics at the Tevatron collider. New York: Springer New York, 2014.

12 papers published in peer-reviewed scientific journals referenced by international databases recommended by the Higher Attestation Commission (ВАК):

1. V.A. Lebedev, J.S. Hangst, and J.S. Nielsen, "Schottky noise in a laser-cooled ion beam", Phys. Rev. E., 52, 4345 (1995)

2. J.S. Hangst, A. Labrador, V. Lebedev, N. Madsen, J.S. Nielsen, O. Poulsen, P. Shi and J.P. Schiffer, "Anomalous Schottky signals from a laser-cooled ion beam", Phys. Rev. Lett., 74, 86 (1995)

3. V. A. Lebedev, J. S. Hangst, N. Madsen, "Single and multiple intrabeam scattering in a laser cooled beam", Nucl. Instrum. Methods Phys. Res., Sect. A, 391, Issue 1, (1997) pp. 176-187.

4. V. Lebedev, et.al., "Measurement and correction of linear optics and coupling at Tevatron complex", Nucl. Instrum. Methods Phys. Res., Sect. A, 558 (2006) p. 299.

5. A. Burov and V. Lebedev, "Coherent motion with linear coupling", Physical Review Special Topics - Accelerators and Beams, 10, 044402 (2007)

6. V. A. Lebedev and S. Bogacz, "Betatron motion with coupling of horizontal and vertical degrees of freedom", 2010 JINST 5 P10010 doi:10.1088/1748-0221/5/10/P10010

7. A. V. Petrenko, A. A. Valishev and V. A. Lebedev, "Model-independent analysis of the Fermilab Tevatron turn-by-turn beam position monitor measurements", Physical Review Special Topics - Accelerators and Beams, 14, 092801 (2011)

8. M. B. Andorf, V. A. Lebedev, P. Piot, J. Ruan, "Wave-optics modeling of the optical-transport line for passive optical stochastic cooling", Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 883, 1 (2018), pp. 166-169.

9. V. Lebedev, J. Jarvis, H. Piekarz, A. Romanov, J. Ruan and M. Andorf, "The design of Optical Stochastic Cooling for IOTA", JINST 16 T05002 (2021)

10. V. Lebedev, S. Nagaitsev, A. Burov, V. Yakovlev, I. Gonin, I. Terechkine, A. Saini, N. Solyak, "Conceptual design report: A ring-based electron cooling system for the EIC", JINST 16 T01003 (2021)

11. V. Lebedev and A. Burov, "Betatron Motion with Coupling of Two Degrees of Freedom" in Handbook of Accelerator Physics and Engineering, 2nd edition, edited by A. Chao, K. Mess, M. Tigner and F. Zimmermann (2013).

12. V. Lebedev, "Intrabeam Scattering and Touschek Effect" in Handbook of Accelerator Physics and Engineering, 2nd edition, edited by A. Chao, K. Mess, M. Tigner and F. Zimmermann (2013). and the following conference reports:

Список литературы диссертационного исследования доктор наук Лебедев Валерий Анатольевич, 2022 год

1. V.A. Lebedev, "Single and Multiple Intrabeam Scattering in Hadron Colliders", Proceedings of 33rd ICFA Advanced Beam Dynamics Workshop on High Brightness Hadron Beams, October 2004, Bensheim, Germany.

2. V. Lebedev, V. Sajaev, V. Nagaslaev, A. Valishev, "Fully Coupled Analysis of Orbit Response Matrices at the FNAL Tevatron"; Proceedings of PAC 2005; Knoxville, May 2005.

3. V. A. Lebedev, "Stochastic Cooling with Schottky Band overlap", Workshop on Beam Cooling and Related Topics - C00L05. AIP Conference Proceedings, Volume 821, pp. 231-236 (2006).

4. V. A. Lebedev, V.P. Nagaslaev, K. Gollwitzer, A. Valishev, V. Sajaev, "Measurements and optimization of the lattice functions in the Debuncher ring in Fermilab", Proceedings of EPAC 2006; Edinburgh, Scotland, 2006.

5. A. V. Burov, V. A. Lebedev, "Instabilities of cooled antiproton beam in Recycler", PAC'07, p. 2009.

6. R.J. Pasquinelli, B.E. Drendel, K. Gollwitzer, SR. Johnson, V.A. Lebedev, A.F. Leveling, J.P. Morgan, V.P. Nagaslaev, D.W. Peterson, A.D. Sondgeroth, D. Vander Meulen, S.J. Werkema, "Progress in antiproton production at the Fermilab Tevatron collider", PAC-2009.

7. V. A. Lebedev, "Operation and upgrade of stacktail cooling system", C00L-2009.

References

1. Di Lella, L. & Rubbia, C., The discovery of the W and Z particles, Adv. Ser. Dir. High Energy Phys. 23 (2015) 137-163.

2. Campagnari, C. & Franklin, M., The discovery of the top quark, Rev. Mod. Phys., 69, No. 1, January 1997.

3. "Muon g-2 Experiment". Muon g-2 Experiment. Fermilab. April 26, 2017.

4. "Mu2e: muon-to-electron-conversion experiment". Fermilab. April 21, 2015.

5. Gutbrod, Hans H. (2006). FAIR - Baseline Technical Report. ISBN 3-9811298-0-6. Archived from the original on 2014-03-26. Retrieved 2013-02-12.

6. D.W. Kerst et al., Attainment of very high energy by means of intersecting beams of particles. Phys. Rev. 102(2), 590-591 (1956)

7. M. Tigner, A. Chao (eds.), Handbook of Accelerator Physics and Engineering (World Scientific, Singapore, 1999)

8. R.R. Wilson, The Tevatron. Phys. Today 30, 23-30 (1977)

9. CDF-II Collaboration (R. Blair et al.), The CDF-II detector: Technical design report, FERMILAB-Pub-96/390-E (1996)

10. D0 Collaboration (B. Pifer et al.), The D0 experiment at the Fermilab antiproton-proton collider: design report, FERMILAB-PUB-83-111-E, PRINT-84-0306 (FERMILAB), FERMILAB-DESIGN-1983-04 (1983)

11. C. Quigg, CERN Courier. 51(8), 20 (2011)

12. M. Church, J. Marriner, The antiproton sources: design and operation. Annu. Rev. Nucl. Part.Sci. 43, 253-295 (1993)

13. H. Edwards, The Tevatron energy doubler: a superconducting accelerator. Annu. Rev. Nucl.Part. Sci. 35, 605-660 (1985)

14. C.D. Curtis et al., Linac H- beam operations and uses at Fermilab. IEEE Trans. Nucl. Sci. 26(3), 3760-3762 (1979)

15. C.W. Schmidt, The Fermilab 400-MeV Linac Upgrade, in Proceedings of Particle Accelerator Conference, Washington, DC, 1993, pp. 1655-1659

16. E. Hubbard et al., Booster synchrotron. Fermilab Technical Memo TM-405 (1973)

17. S.D. Holmes, Design criteria and performance goals for the Fermilab Main Injector. Part. Accel. 58, 39 (1997)

18. G. Jackson (ed.), Fermilab Recycler Ring Technical Design Report, Fermilab Preprint TM-1991 (1997)

19. S. Nagaitsev et al., Experimental demonstration of relativistic electron cooling. Phys. Rev. Lett. 96, 044801 (2006)

20. B. Bayanov et al., Liquid lithium lens with high magnetic fields. in Proceedings of the 1999 I.E. PAC (New York, 1999), pp. 3086-3088

21. N.V. Mokhov, The MARS Code System User Guide, Version 13(95), Fermilab-FN-628 (1995); N.V. Mokhov et al., Fermilab-Conf-98/379 (1998); LANL Report LA-UR-98-5716 (1998); nucl-th/9812038 v2 16 Dec 1998;

http://wwwap.fnal. gov/MARS/

22. B.F. Bayanov et al., A lithium lens for axially symmetric focusing of high energy particles beams. NIM 190, 9-14 (1981)

23. T.A. Vsevolozskaya, The optimization and efficiency of antiproton production within a fixed acceptance. NIM 190, 479-486 (1981)

24. G. Dugan, P-bar Production and collection at the FNAL antiproton source. in Proceedings of the 13th International Conference of High Energy Accelerators, vol 2 (Novosibirsk, 1986), pp. 264-271

25. V. Lebedev, et.al., "Measurement and correction of linear optics and coupling at

Tevatron complex", Nucl. Instrum. Methods Phys. Res., Sect. A, 558 (2006) p. 299.

26. V. Nagaslaev, K. Gollwitzer, V. Lebedev, A. Valishev (Fermilab), V. Sajaev (Argonne). Measurement and optimization of the lattice functions in the Debuncher ring at Fermilab. In FERMILAB-CONF-06-200-AD (2006)

27. V. A. Lebedev and S. Bogacz, "Betatron motion with coupling of horizontal and vertical degrees of freedom", 2010 JINST 5 P10010 doi:10.1088/1748-0221/5/10/P10010

28. A. Burov and V. Lebedev, "Coherent motion with linear coupling", Physical Review Special Topics - Accelerators and Beams, 10, 044402 (2007)

29. V. Lebedev and A. Burov, "Betatron Motion with Coupling of Two Degrees of Freedom" in Handbook of Accelerator Physics and Engineering, 2nd edition, edited by A. Chao, K. Mess, M. Tigner and F. Zimmermann (2013).

30. W.J. Corbett, M. Lee, V. Ziemann, PAC''93, Washington, DC, 1993, p. 108.

31. J. Safranec, Nucl. Instr. and Meth. A 388 (1997) 27.

32. V. Sajaev, L. Emery, EPAC''02, Paris, France, 2002, p. 742

33. A. V. Petrenko, A. A. Valishev and V. A. Lebedev, "Model-independent analysis of the Fermilab Tevatron turn-by-turn beam position monitor measurements", Physical Review Special Topics - Accelerators and Beams, 14, 092801 (2011)

34. V.P. Nagaslaev, V.A. Lebedev, S.J. Werkema (Fermilab), Lattice optimization for the stochastic cooling in the Accumulator ring at Fermilab. in FERMILAB-CONF-07-712-AD (2007) 8. S. van der Meer, Rev. Mod. Phys. 57, 689 (1985)

35. S. van der Meer, Rev. Mod. Phys. 57, 689 (1985)

36. D. Möhl, "Stochastic Cooling" in CERN Accelerator School, Fifth Advanced Accelerator Physics Course, edited by S. Turner, CERN, Geneva, Switzerland, 1995, pp. 587-671.

37. J. Bisognano and C. Leemann, "Stochastic Cooling" in 1981 Summer School on High Energy Particle Accelerators, edited by R. A. Carrigan et al., AIP Conference Proceedings 87, American Institute of Physics, Melville, NY, 1982, pp. 584-655.

38. V. V. Parkhomchuk and D. V. Pestrikov, Sov. Phys. Tech. Phys, 25(7), 818 (1980).

39. V.A. Lebedev, J.S. Hangst, and J.S. Nielsen, "Schottky noise in a laser-cooled ion beam", Phys. Rev. E., 52, 4345 (1995)

40. J.S. Hangst, A. Labrador, V. Lebedev, N. Madsen, J.S. Nielsen, O. Poulsen, P. Shi and J.P. Schiffer, "Anomalous Schottky signals from a laser-cooled ion beam", Phys. Rev. Lett., 74, 86 (1995)

41. M. B. Andorf, V. A. Lebedev, P. Piot, J. Ruan, "Wave-optics modeling of the optical-transport line for passive optical stochastic cooling", Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 883, 1 (2018), pp. 166-169.

42. V. Lebedev, J. Jarvis, H. Piekarz, A. Romanov, J. Ruan and M. Andorf, "The design of Optical Stochastic Cooling for IOTA", JINST 16 T05002 (2021)

43. J. Jarvis, et.al., "First Experimental Demonstration of Optical Stochastic Cooling", https://arxiv. org/abs/2203.08899

44. S. van der Meer, Rev. Mod. Phys., 57 (1985), p.689

45. F.Voelker, et al, in Proc. 1983 PAC IEEE Conference (Santa Fe, NM), pp. 22622263

46. G. Lambertson, et al., in Proc. 1985 PAC IEEE Conference (Vancouver BC, Canada), pp. 2168-2170

47. D. McGinnis, "Theory and Design of Microwave Planar Electrodes for Stochastic Cooling of Particle Beams", Microwave and Optical Technology Letters, October 1991, Vol. 4/ No. 11, p. 439-443.

48. B. Autin et al., Proc. 1987PAC IEEE Conference, (Washington, DC), pp. 1549-1551.

49. D. McGinnis, "Slotted Waveguide Slow-Wave Stochastic Cooling Arrays", Proc. 1999 PAC IEEE Conference (New York), pp. 1713-1715.

50. A. Jansson, et al., Proc. 2004 European PAC, (Lucerne, Switzerland), pp.2777-2779.

51. D. Pozar, Microwave Engineering, third edition, John Wiley and Sons, 2005 pages 489-493.

52. B. Leskovar, Low-Noise Cryogenically Cooled Broad-Band Microwave Preamplifiers, 172nd meeting of the Low Temperature Electronics Symposium, October 1987, Honolulu, HI.

53. S. Weinreb et al, FET's and HEMT's at Cryogenic Temperature, Their Properties and Use in Low-Noise Amplifiers, IEEE Transactions on Microwave Theory and Techniques, Vol. 36, No.3, March 1988.

54. http://www.miteq.com/products/amplifiers/cryogenic-amplifiers.php

55. R. J. Pasquinelli, Noise Performance of the Debuncher Stochastic Cooling Systems, Antiproton Source Note 661, March 2001, internal document.

56. Y. Hoshiko, K1 Superconducting Communication Transmission, Proceedings Fifth International Cryogenics Engineering conference, ICEC5, p.282, Tokyo, 1975.

57. R. J. Pasquinelli, Superconducting Delay Line for Stochastic Cooling Filters, Proc. 1983 PAC IEEE Conference (Santa Fe, NM), pp. 3360-3362.

58. R. J. Pasquinelli, Superconducting Notch Filters for the Fermilab Antiproton Source, Proc. 12th International Conference on High Energy Accelerators (Fermilab, Batavia, IL, August 1983), pp.584-586.

59. R. J. Pasquinelli, Bulk Acoustic Wave (BAW) Devices for Stochastic Cooling Notch Filters, IEEE Nuclear Science, May 1991.

60. R. J. Pasquinelli, Fiber Optic Links for Instrumentation, Conference Proceedings of the Accelerator Instrumentation Workshop, October 1990.

61. R. J. Pasquinelli, Optical Notch Filters for Fermilab Debuncher Betatron Stochastic Cooling, Proc. 1989 PAC IEEE Conference (Chicago, IL), pp 694-696.

62. T. Kakuta, S. Tanaka, LCP Coated Optical Fiber with Zero Thermal Coefficient of Transmission Delay Time, Sumitomo Electric Industries, Ltd. 1, Proceedings 36th International Wire and Cable Symposium, pp234-240, 1987, Yokohama, Japan.

63. D. McGinnis, J. Marriner, Design of 4-8 GHz Stochastic Cooling Equalizers for Fermilab Accumulator, Proc. 1991 PAC IEEE Conference (San Francisco, CA), pp. 1392-1394.

64. S. Weinreb et al, NRAO, Waveguide System for a Very Large Antenna Array, Microwave Journal, March 1977.

65. R. J. Pasquinelli, Wide Band Free Space Transmission Link Utilizing a Modulated Infrared Laser, TUA12, Proc. 1999 PAC IEEE Conference (New York, NY), pp. 1094-1096.

66. A.S. Gilmour Jr., Microwave Tubes, Artech House, 1986.

67. V. Lebedev, Improvements to the Stacktail and Debuncher Momentum Cooling Systems, Proceedings of COOL 09 (Lanzhou, China, 2009), MOA1MCCO02.

68. R. J. Pasquinelli, Debuncher Momentum Cooling Systems Signal to Noise Measurements, Pbar note 667, Internal Antiproton Source Document, December 2001.

69. D. Sun et al., New Equalizers for Antiproton Stochastic Cooling at Fermilab, Proc. COOL-2007 (Bad Kreuznach, Germany, 2007),THAP16,

70. V. Lebedev, et al, Proc. COOL-2007 (Bad Kreuznach, Germany, 2007), p. 202.

71. V. Lebedev, Proc. COOL-2007 (Bad Kreuznach, Germany, 2007), p. 39.

72. R. Pasquinelli, et al, Proc. COOL-2007 (Bad Kreuznach, Germany, 2007), p.198.

73. Tevatron Design Report, FERMILAB-DESIGN-1984-01 (1984)

74. I. Nesmiyan and F. Nolden, Proceedings of EPAC-2004 (Lucern, Zwitzerland), p. 2170.

75. V. Lebedev, et al., Proceedings of COOL-2009, Lanzhou, China (2009), p. 27.

76. G.I. Budker, Sov. Atomic Energy, Vol. 22 (1967), p. 346.

77. G.I. Budker et al., IEEE Trans. Nucl. Sci., NS-22 (1975) p. 2093.

78. I. N. Meshkov, Phys. Part. Nucl., 25 (6), p. 631 (1994).

79. Fermilab Recycler Ring Technical Design Report, FERMILAB-TM-1991, 1996.

80. S. Nagaitsev et al., Phys. Rev. Lett. 96, 044801 (2006).

81. L. P. Pitaevskii and E.M. Lifshitz, "Physical kinetics, Landau Course of Theoretical Physics - vol.10," Butterworth-Heinemann Ltd, (1981).

82. A. Shemyakin and L.R. Prost, "Electron Cooling Rates in FNAL's Recycler Ring", Proc. of APAC'07, Indore, India, January 29-February 2, 2007, TUPMA094, 238240, https://accelconf.web.cern.ch/accelconf/a07/PAPERS/TUPMA094.pdf

83. A. Shemyakin, "Formulas for comparing the results of drag force and cooling rates measurements with a non-magnetized cooling model", FERMILAB-TM-2374-AD (2007), http://lss.fnal.gov/archive/test-tm/2000/fermilab-tm-2374-ad.pdf

84. V. Lebedev, S. Nagaitsev, A. Burov, V. Yakovlev, I. Gonin, I. Terechkine, A. Saini, N. Solyak, "Conceptual design report: A ring-based electron cooling system for the EIC", JINST 16 T01003 (2021)

85. Ya.S. Derbenev and A.N. Skrinsky, Particle Accelerators 8 (1977), 1.

86. J.A. MacLachlan, A. Burov, A.C. Crawford, T. Kroc, S. Nagaitsev, C. Schmidt, A. Sharapa, A. Shemyakin, A.Warner, Prospectus for an electron cooling system for the Recycler. FERMILAB-TM-2061 (1998).

87. M.E.Veis et al., Proc. EPAC'88 (Rome, 7-11 June. 1988), p.1361.

88. J.R Adney et al., in Proc. 1989 IEEE PAC (20-23 March 1989, Chicago, USA), p.348.

89. G.P.Jackson, Modified Betatron Approach to Electron Cooling, Proc. MEEC'97 (Novosibirsk, February 26-28, 1997).

90. I. Ben-Zvi, in Proc. of EPAC'06 (Edinburgh, UK, June 26-30, 2006), TUZBPA01.

91. J. Dietrich et al., Proc. Of COOL'11 (September 12-16, 2011, Alushta, Ukraine), MOIO05.

92. D.R.Anderson et al., Proc. of EPAC'92 (Berlin, 1992), p.836-838.

93. N. Dikansky et al., Electron beam focusing system, FERMILAB-TM-1998 (1996).

94. A.Burov, S.Nagaitsev, A.Shemyakin, and Ya.Derbenev, Optical principles of beam transport for relativistic electron cooling. Phys. Rev. Special Topics: Accelerators and Beams, v.3, 094002 (2000).

95. Pelletrons are manufactured by the National Electrostatics Corporation, www.pelletron.com.

96. A. Sharapa, A. Shemyakin, and S. Nagaitsev, Nucl. Instr. and Meth. A 417 (1998) 177 .

97. OptiM - V. Lebedev, A. Bogacz, "Betatron motion with coupling", JLAB-ACC-99-19 (1999).

98. Optics of the Fermilab electron cooler, by A. Burov, T. Kroc, V. Lebedev, S. Nagaitsev, A. Shemyakin, A.Warner, S. Seletskiy, Proc. of APAC'04 (Gyeongju, Korea, March 22-26, 2004), pp. 647-649.

99. B. Chase, private communication

100. The program for data recording was written by V. Lebedev and V. Nagaslaev.

101. A.V. Ivanov, M.A. Tiunov. ULTRASAM - 2D Code for Simulation of Electron Guns with Ultra High Precision. Proc. Eur. PAC'02 (Paris, 2002), p.1634.

102. M.A. Tiunov. BEAM - 2D-code package for simulation of high perveance beam

dynamics in long systems. Proceedings of International Symposium "SPACE CHARGE EFFECTS IN FORMATION OF INTENSE LOW ENERGY BEAMS". February 15-17, 1999, JINR, Dubna, Russia.

103. A. Warner, A. Burov, K. Carlson, G. Kazakevich, S. Nagaitsev, L.Prost, M. Sutherland, and M. Tiunov, AIP Conf.Proc. 821 (2006) 380-385.

104. T.K. Kroc, A.V. Burov , T.B. Bolshakov, A. Shemyakin, Proc. 2005 IEEE PAC(Knoxville, USA, May 16-20, 2005), p.3801.

105. A. Burov, G. Kazakevich, T. Kroc, V. Lebedev, S. Nagaitsev, L. Prost, S. Pruss, A. Shemyakin, M. Sutherland, M.Tiunov, A. Warner, Proc. of COOL'05 (Galena, USA, September 19-23, 2005), p. 139.

106. L.R. Prost, A. Burov, K. Carlson, A. Shemyakin, M. Sutherland, A. Warner, in Proc. of COOL'07 (Bad Kreuznach, Germany, September 10-14, 2007), MOA2I04.

107. A. Shemyakin, A. Burov, K. Carlson, L.R. Prost, M. Sutherland, A. Warner, Proc. 2009 IEEE PAC (Vancouver, Canada, May 4-8, 2009), TU6PFP076.

108. A. Shemyakin, L. Prost, and G.. Saewert, Proc. 2010 Int'l PAC (Kyoto, Japan, May 23-28, 2010), MOPD075.

109. A.C. Crawford, S. Nagaitsev, A. Shemyakin, S. Seletsky, V. Tupikov, Fermila preprint TM-2224 (2003)

110. V. Tupikov, G. Kazakevich, T.K. Kroc, S. Nagaitsev, L. Prost, A. Shemyakin, C.W. Shmidt, M. Sutherland, A. Warner, in Proceedings of COOL'05 (Galena, USA, September 19-23, 2005), p. 375

111. Fermilab Recycler Ring Technical Design Report, FERMILAB-TM-1991, 1996

112. S. Nagaitsev, C. Gattuso, S. Pruss, J. Volk, Experience with magnetic shielding of a large scale accelerator. in Proceedings of IEEE 2001 Particle Accelerator Conference (Chicago, IL, USA, June 18-22, 2001), RPPH062

113. E.M. Lifshitz, L.P. Pitaevskii, Physical Kinetics, vol. 10 (Pergamon Press, New York, 1981)

114. A. Piwinski, in Proceedings of the 9th International Conference on High Energy Accelerators, SLAC, Stanford, CA, USA, 1974, p. 405

115. J.D. Bjorken, S. Mtingwa, Intrabeam scattering. Particle Accelerators 13, 115-143 (1983)

116. L.D. Landau, Phys. Z. Sowjetunion 10, 154 (1936)

117. M.N. Rosenbluth, W.M. MacDonald, D.L. Judd, Phys. Rev. 107, 1 (1957)

118. S. Chandrasekhar, Rev. Mod. Phys. 15, 1 (1943)

119. S. Nagaitsev, Phys. Rev. ST Accel. Beams 8, 064403 (2005)

120. S. Ichimaru, M.N. Rosenbluth, Phys. Fluids 13, 2778 (1970)

121. V. Lebedev et al., NIM A 391, 176 (1997)

122. V. Parkhomchuk, Physics of fast electron cooling, in Proceedings of the Workshop on Electron Cooling and Related Applications, Karlsruhe, 1984

123. V. Lebedev, "Intrabeam Scattering and Touschek Effect" in Handbook of Accelerator Physics and Engineering, 2nd edition, edited by A. Chao, K. Mess, M. Tigner and F. Zimmermann (2013).