CASE - User contributions [en]

File:Homework 13 solution 2026.pdf

2026-05-11T16:40:12Z

GangWang:

PHY564 spring 2026

2026-04-24T15:11:47Z

2026-04-23T18:25:25Z

GangWang: /* Home Works */

<center>
<table width=40% border=1>
<tr>
<th width=50% align=center>Class meet time and dates</th>
<th align=center>Instructors</th>
</tr>

<tr><td align=left valign=center>

* '''When: TuTh 6:30PM - 7:50PM '''
* '''Where: Physics P 125 WESTCAMPUS'''
</td>

<td align=left valign=top>

* Prof. Vladimir Litvinenko
</td>

</tr></table>

</center>

[[Image:Accelerators.jpg|600px|Image: 600 pixels|center]]

==Course Overview==
This graduate level course focuses on the fundamental physics and explored in depth advanced concepts of modern particle accelerators and theoretical concept related to them.

==Course Content==
* Principle of least actions, relativistic mechanics and E&D, 4D notations
* N-dimensional phase space, Canonical transformations, symplecticity and invariants of motion
* Relativistic beams, Reference orbit and Accelerator Hamiltonian
* Parameterization of linear motion in accelerators, Transport matrices, matrix functions, Sylvester's formula, stability of the motion
* Invariants of motion, Canonical transforms to the action and phase variables, emittance of the beam, perturbation methods. Poincare diagrams
* Standard problems in accelerators: closed orbit, excitation of oscillations, radiation damping and quantum excitation, natural emittance
* Non-linear effects, Lie algebras and symplectic maps
* Vlasov and Fokker-Plank equations, collective instabilities & Landau Damping
* Spin motion in accelerators
* Types and Components of Accelerators

==Learning Goals==
Students who have completed this course should:
* Have a full understanding of transverse and longitudinal particles dynamics in accelerators
* Being capable of solving problems arising in modern accelerator theory
* Understand modern methods in accelerator physics
* Being capable to fully understand modern accelerator literature

==Main Texts and ''suggested materials''==
*Lecture notes presented after each class should be used as the main text. Presently there is no textbook, which covers the material of this course.
*''H. Wiedemann, "Particle Accelerator Physics" Springer, 2007''
*'' S. Y. Lee, "Accelerator Physics”, World Scientific, 2011''
*''L.D. Landau, Classical theory of fields''

==Course Description==

*Relativistic mechanics and E&D. Linear algebra.
*:This will be a brief but complete rehash of relativistic mechanics, E&M and linear algebra material required for this course.
*N-dimensional phase space, Canonical transformations, simplecticity, invariants
*:Canonical transformations and related to it simplecticity of the phase space are important part of beam dynamics in accelerators. We will consider connections between them as well as derive all Poincare invariants (including Liouville theorem). We will use a case of a coupled N-dimensional linear oscillator system for transforming to the action and phase variables. We finish with adiabatic invariants.
*Relativistic beams, Reference orbit and Accelerator Hamiltonian
*:We will use least action principle to derive the most general form of accelerator Hamiltonian using curvilinear coordinate system related to the beam trajectory (orbit).
*Linear beam dynamics
*:This part of the course will be dedicated to detailed description of linear dynamics of particles in accelerators. You will learn about particles motion in oscillator potential with time- dependent rigidity. You will learn how to calculate matrices of arbitrary element in accelerators. We will use eigen vectors and eigen number to parameterize the particles motion and describe its stability in circular accelerators. Here you find a number of analogies with planetary motion, including oscillation of Earth’s moon. You will learn some “standards” of the accelerator physics – betatron tunes and beta-function and their importance in circular accelerators.
*Longitudinal beam dynamics
*:Here you will learn about one important approximation widely used in accelerator physics – “slow” longitudinal oscillations, which are have a lot of similarity with pendulum motion. If you were ever wondering why Saturn rings do not collapse into one large ball of rock under gravitational attraction – this where you will learn of the effect so-called negative mass in longitudinal motion of particles when attraction of the particles cause their separation.
*Invariants of motion, Canonical transforms to the action and phase variables, emittance of the beam, perturbation methods, perturbative non-linear effects
*:In this part of the course we will remove “regular and boring” oscillatory part of the particle’s motion and focus on how to include weak linear and nonlinear perturbations to the particles motion. We will solve a number of standard accelerator problems: perturbed orbit, effects of focusing errors, “weak effects” such as synchrotron radiation, resonant Hamiltonian, etc. We will re-introduce Poincare diagrams for illustration of the resonances. You will learn how non- linear resonances may affect stability of the particles and about their location on the tune diagram. You will learn about chromatic (energy dependent) effects, use of non-linear elements to compensate them, and about problems created by introducing them.
*Non-linear effects, Lie algebras and symplectic maps
*:This part of the course will open you the door into and complex nonlinear beam dynamics. We will introduce you to non-perturbative nonlinear dynamics and fascinating world of non-linear maps, Lie algebras and Lie operators. These are the main tools in the modern non-linear beam dynamics. You will learn about dynamic aperture of accelerators as well as how our modern tools are similar to those used in celestial mechanics.
*Vlasov and Fokker-Plank equations
*:This part of the course is dedicated to the developing of tools necessary for studies of collective effects in accelerators. We will introduce distribution function of the particles and its evolution equations: one following conservation of Poincare invariants and the other including stochastic processes.
*Radiation effects
*:You will learn how to use the tools we had developed in previous lectures (both the perturbation methods and Fokker-Plank equation) to evaluate effect of synchrotron radiation on the particle’s motion in accelerator. You will see how the effect of radiation damping and quantum excitation lead to formation of equilibrium Gaussian distribution of the particles.
*Collective phenomena
*:Intense beam of charged particles excite E&M fields when propagate through accelerator structures. These fields, in return, act on the particles and can cause variety of instabilities. Some of these instabilities – such as a free-electron lasers (FEL) – can be very useful as powerful coherent X-rays sources. Others (and they are majority) do impose limits on the beam intensities or limit available range of the beam parameters. You will learn techniques involved in studies of collective effects and will use them for some of instabilities, including FEL. The second part of the collective effect will focus on how we can cool hadron beams, which do not have natural cooling.
*Spin dynamics
*:Many particles used in accelerators have spin. Beams of such particles with preferred orientation of their spins called polarized. Large number of high energy physics experiments using colliders strongly benefit from colliding polarized beams. You will learn the main aspects of the spin dynamics in the accelerators and about various ways to keep beam polarized. One more “tunes” to worry about - spin tune.
*Accelerator application
*:We will finish the course with a brief discussion of accelerator application, among which are accelerators for nuclear and particle physics, X-ray light sources, accelerators for medical uses, etc. You will also learn about future accelerators at the energy and intensity frontiers as well as about new methods of particle acceleration.

==Grades==
There will be a substantial number of problems. Most of them are aiming for better understanding of material covered during classes. The final grade will be based on:
*Homework assignments - 40% of the grade
*Presentation of a research topic - 40% of the grade
*Class Participation - 20% of the grade

==The Rules==
* You may collaborate with your classmates on the homework's if you are contributing to the solution. You must '''personally write up the solution of all problems'''. It would be appropriate and honorable to acknowledge your collaborators by mentioning their names. These acknowledgments will not affect your grades.
* We will greatly appreciate your homeworks being readable. Few explanatory words between equations will save us a lot of time while checking and grading your home-works. Nevertheless, your writing style will not affect your grades.
* Do not forget that simply copying somebody's solutions does not help you and in a long run we will identify it. If we find two or more identical homeworks, they all will get reduced grades. You may ask more advanced students, other faculty, friends, etc. for help or clues, as long as you personally contribute to the solution.
* You may (and are encouraged to) use the library and all available resources to help solve the problems. Use of Mathematica, other software tools and spreadsheets are encouraged. Cite your source, if you found the solution somewhere.
* You should return homework '''before the deadline'''. Homework returned after the deadline could be accepted with reduced grading - 15% per day. Otherwise, it will be unfair for your classmates who are doing their job on time. Therefore, you should be on time to keep your grade high. Exceptions are exceptions and do not count on them (if your dog eats your homework on a regular basis - feed it with something healthy, eating homework is bad for your pet and for you grade).

==Presentation on a Research Project==
* '''This presentation will be in place of the final exam'''. You will pick an accelerator project of your interest from a list provided by the instructors. We allow presentations on papers directly related to your research if they are linked to accelerator physics, but you will have to get it approved by the instructors. The presentations will be in a PowerPoint or equivalent a form.
*We will grade your presentations on: adequate understanding (good physics), adequate preparation (clear way of presentation, Visual Aids - pictures and figures), adequate references (where you find materials).
* The research project should be fun and we encourage you to choose an original topic and an original way of presentation. Nevertheless, any topic prepared and presented properly will have high grade.
*''' [[media:Projects_for_PHY_564.pdf ‎|Suggested topics for Projects]], by Prof. Litvinenko'''

== Lecture Notes==

*'''[[media:PHY564_Lecture_1-2_2026.pdf|Lectures 1 and 2: Least Action Principle, Geometry of Special Relativity, Particles in E&M fields]], by Prof. Litvinenko'''
*'''[[media:PHY564_Lecture_3_update.pdf|Lecture 3: Accelerator Coordinates and Hamiltonian]], by Prof. Litvinenko'''
*'''[[media:PHY564_2026_Lecture_4_update.pdf|Lecture 4: Accelerator 4-potential and expansion of Hamiltonian]], by Prof. Litvinenko'''
*'''[[media:PHY564_2026_Lecture_5_update.pdf|Lecture 5: Hamiltonian Method for Accelerators]], by Prof. Litvinenko'''
*'''[[media:PHY564_2026_Lecture_6.pdf‎|Lecture 6: Matrices and Matrix functions]], by Prof. Litvinenko'''
*'''[[media:PHY564_Lecture_7.pdf‎|Lecture 7: How to build a magnet]], by Prof. Litvinenko'''
*'''[[media:PHY564_Lecture_8_2026.pdf|Lecture 8: Matrices of accelerator elements]], by Prof. Litvinenko'''
*'''[[media:PHY564_Lectures_9_10.pdf|Lectures 9 and 10: 1D, 2D and 3D cases for exp[Ds]]], by Prof. Litvinenko'''
*'''[[media:PHY564_Lectures_11&12_2026.pdf|Lectures 11 and 12: Linear accelerators and RF cavities]], by Prof. Litvinenko'''
*'''[[media:PHY564_Lecture_13_2026.pdf|Lecture 13: " Periodic systems and parameterization of linearized particle’s motion"]], by Prof. Litvinenko'''
*'''[[media:PHY564_Lecture_11_compressed.pdf|Additional reading materials: 2022 Lecture 11]], by Prof. Litvinenko'''
*'''[[media:PHY564_Lecture_14_2026.pdf|Lecture 14: " Synchrotron oscillations"]], by Prof. Litvinenko'''
*'''[[media:PHY564_Lecture_15_2026.pdf|Lecture 15: " Parameterization and Action-angle variables"]], by Prof. Litvinenko'''
*'''[[media:PHY564_Lecture_16_2026.pdf|Lecture 16: " Applications of parameterization and the phase-action variables to standard accelerator problems"]], by Prof. Litvinenko'''
*'''[[media:PHY564_Lecture_17_2026.pdf|Lecture 17: Effects of synchrotron radiation]], by Prof. Litvinenko'''
*'''[[media:PHY564_Lecture_18_2026.pdf|Lecture 18: Fokker-Plank and Vlasov equations]], by Prof. Litvinenko'''
*'''[[media:PHY564_Lectures_19_20_2026.pdf|Lectures 19 and 20:Beam emittances and kinematic invariants]], by Prof. Litvinenko'''
*'''[[media:PHY564_Lectures_21_2026.pdf|Lectures 21:Collective Effects I: Wakefield and Impedances]], by Prof. Wang'''

== Home Works==

*'''[[media:Homework 1 2026.pdf|HW1]] Due February 17, [[media:Homework_1_2026_solutions.pdf|Solutions]]
*'''[[media:Homework_2_2026_.pdf|HW2]] Due February 19 [[media:Homework_2_2026_solutions.pdf|Solutions]]
*'''[[media:Home_work_2026_3.pdf|HW3]] Due February 24 [[media:Homework_3_2025_solutions.pdf|Solutions]]
*'''[[media:Homework_4_2026.pdf|HW4]] Due February 26. [[media:Homework_4_2026_solutions.pdf|Solutions]]
*'''[[media:Homework_5_2026.pdf|HW5]] Due March 3 [[media:Homework_5_2026_solutions_fixed.pdf|Solutions]]
*'''[[media:Homework_6_2022.pdf|HW6]] Due March 5 [[media:Homework_6_2022_solution_new.pdf|Solutions]]
*'''[[media:HW7 2026.pdf |HW7]] Due March 12 [[media:HW7_2026_solution.pdf|Solutions]]

*'''[[media:PHY_564_Midterm_exam.pdf|Mid-term exam]] Due March 25 [[media:PHY_564_Midterm_exam_solutions.pdf|Solutions]]

*'''[[media:Homework_8_2026.pdf|HW8]] Due April 7 [[media:Homework 8 solution 2026.pdf|Solutions]]
*'''[[media:Homework_9_2026.pdf|HW9]] Due April 9 [[media:Homework 9 solution 2026.pdf ‎|Solutions]]
*'''[[media:Homework_10_2026.pdf|HW10]] Due April 14
*'''[[media:Homework_11_2026.pdf|HW11]] Due April 16
*'''[[media:Homework_12_2026.pdf|HW12]] Due April 23

== Lecture Notes from 2022: New lectures will be posted after the class:

*'''[[media:PHY564_Lecture9_09212022.pdf|Lecture 9: Linear accelerators and RF systems]], by Prof. Petrushina'''

*'''[[media:PHY564_Lecture_18_19_compressed.pdf|Lectures 18 & 19: Eigen beam emittances and parameterization]], by Prof. Litvinenko'''
*'''[[media:PHY564_Lecture_21_2022.pdf|Lecture 21: Collective Effects II: Examples of Collective Instabilities]], by Prof. Wang'''
*'''[[media:PHY564_Lecture_22_2022.pdf|Lecture 22: Free Electron Lasers: Introduction and Small Gain Regime]], by Prof. Wang'''
*'''[[media:PHY564_Lecture_23_2022.pdf|Lecture 23: Free Electron Lasers: Free Electron Lasers: High Gain Regime]], by Prof. Wang'''
*'''[[media:PHY564_Lecture_24_2020.pdf|Lecture 24: Hadron Beam Cooling]], by Prof. Wang'''
*'''[[media:PHY564_Lecture_25_26_2022.pdf|Lecture 25 & 26: Nonlinear dynamics]], by Prof. Jing''' , '''Extra''' '''[[media:Resonance_crossing.pptx|3rd order resonance crossing movies]]'''
*'''[[media:PHY564_Lecture27_AdvancedAcceleratorConcepts.pdf|Lecture 27: Advanced Accelerator Concepts]], by Prof. Petrushina'''

This is a sample from 2022 HWs ==

*'''[[media:Homeworks_2&3_2022.pdf|HW2&3]]
*'''[[media:Homework_4_2022.pdf|HW4]]
*'''[[media:Homework_7_2022.pdf|HW7]]
*'''[[media:Homework_8_2022.pdf|HW8]]
*'''[[media:PHY564-HW9.pdf|HW9]]
*'''[[media:Homework_12_2022.pdf|HW12]]
*'''[[media:Homework_15_2022.pdf|HW15]]
*'''[[media:Homework_16_2022.pdf|HW16]]
*'''[[media:Homework_17_2022.pdf|HW17]]
*'''[[media:Homework_18_2022.pdf|HW18]]

*'''Additional Material'''
*'''[[media:PHY564_Lecture_3_2020.pdf|Linear Algebra]], by Prof. Wang'''
*'''[[media:Lorentz_Group.pdf|Lorentz Group]], by Prof. Litvinenko'''
*''' [[media:Special_relativity_intro.pdf|Special Relativity intro]], by Prof. Litvinenko'''
*''' [[media:Proof_detM_is_1.pdf|Proof: determinant of a symplectic matrix is 1]], by Prof. Wang'''
*'''[[media:Differential_operators.pdf |Differential operators in curve-linear coordinate systems ]], by Prof. Litvinenko'''
*'''[[media:Hamiltonian_expansion.pdf |Accelerator Hamiltonian expansion]], by Prof. Litvinenko'''
*'''[[media:Generalized_Sylvester_formula.pdf |Nonstandard derivation of Generalized Sylvester formula]], by Prof. Litvinenko'''
*''' [[media:Appendix_F.pdf|Solution of inhomogeneous equation ]], by Prof. Litvinenko'''
*'''[[media:Extra_RF_and_SRF_accelerators.pdf|Extra material - RF and SRF accelerators]], by Prof. Litvinenko'''
*'''[[media:Derive_Saldin_chap_2_1.pdf|Derivation of FEL Hamiltonian]], by Prof. Wang'''
*'''[[media:SC_test.pdf|Matlab script to test concept of Stochastic Cooling]], by Prof. Wang'''
*'''[[media:PHY564_Lecture_27_F2017.pdf|Lecture: Colliders]], by Prof. Litvinenko'''

2025-11-13T04:01:07Z

GangWang: /* Lecture Notes */

<center>
<table width=60% border=1>
<tr>
<th width=50% align=center>Class meet time and dates</th>
<th align=center>Instructors</th>
</tr>

<tr><td align=left valign=center>

* '''When: Mon/Wed, 6:30 pm - 7:50pm '''
* '''Where: Zoom ( Physics D103 , see the map https://www.stonybrook.edu/sb/map/map.pdf)'''
</td>

<td align=left valign=top>

* Prof. Yichao Jing
* Prof. Dmitry Kayran
* Prof. Vladimir N Litvinenko
* Dr. Jun Ma
* Prof. Gang Wang
* '''TA:''' Nikhil Bachhawat

</td>

</tr></table>
[[Image:Accelerators.jpg|350px|Image: 400 pixels|right]]

</center>

== Course Overview ==
The graduate/senior undergraduate level course focuses on the fundamental physics and key concepts of modern particle accelerators. The course is intended for graduate students and advanced undergraduate students who want to familiarize themselves with principles of accelerating charged particles and gain knowledge about contemporary particle accelerators and their applications.

It will cover the following contents:

* History of accelerators and basic principles (eg. centre of mass energy, luminosity, accelerating gradient, etc)

* Radio Frequency cavities, linacs, SRF accelerators;

* Magnets, Transverse motion, Strong focusing, simple lattices; Non-linearities and resonances;

* Circulating beams, Longitutdinal dynamics, Synchrotron radiation; principles of beam cooling,

* Applications of accelerators: light sources, medical uses

Students will be evaluated based on the following performances: '''homework assignments (40%), class participation (20%), mid-term exam (20%) and final presentation on specific research paper (20%), .'''

==Learning Goals==

Students who have completed this course should

* Understand how various types of accelerators work and understand differences between them.
* Have a general understanding of transverse and longitudinal beam dynamics in accelerators.
* Have a general understanding of accelerating structures.
* Understand major applications of accelerators and the recent new concepts.
== Textbook and ''suggested materials''==

Textbook is to be decided from the following:
*Accelerator Physics, by S. Y. Lee
*An Introduction to the Physics of High Energy Accelerators, by D. A. Edwards and M. J. Syphers
*''Introduction To The Physics Of Particle Accelerators'', by Mario Conte and William W Mackay
*''Particle Accelerator Physics'', by Helmut Wiedemann
*''The Physics of Particle Accelerators: An Introduction'', by Klaus Wille and Jason McFall

10+ S.Y. Lee's and Edwards-Syphers' books are available in BNL library and electronic copies are available upon requests.

== Course Description ==

*Introduction to accelerator physics <br />You will have a glance into the history of accelerators and will learn about a variety of accelerators from electrostatic TV-tubes to gigantic atom and nuclear smashers. Basic figures of merit will be introduced (center of mass energy, luminosity, accelerating gradient, etc.) You will learn general principles behing linear accelerators and circular accelerators, their relative advantages and disadvantages.

*Radio frequency cavities, linacs, superconducting RF accelerators <br />This part of the course will be dedicated to physics and technology of accelerating structures. You will learn basic principles of using radio frequency electromagnetic fields to accelerate particles to very high energies. Different types of accelerating structures will be introduced. You will also learn about brand new direction in linear accelerators – so-called energy recovery linacs. As many modern accelerators are based on superconducting RF (SRF) technlogy, you will learn fundamentals of the SRF accelerators and their advantages over conventional (normal conductoing) RF accelerators.

*Linear transverse beam dynamics <br />This part of the course will be dedicated to detailed description of linear dynamics of particles in accelerators. You will learn about similarity of particles motion to an oscillator with time-dependent rigidity, matrix optics of various elements in accelerators, equation for beam envelopes and stability of periodic (circular) motion of the particles. Here you find a number of analogies with planetary motion, including oscillation of Earth’s moon. You will learn some “standards” of the accelerator physics – betatron tunes and beta-function and their importance in circular accelerators.

*Nonlinear transverse beam dynamics <br />This lecture will open door in fascinating and never-ending elegance and complexity on nonlinear beam dynamics. You will learn about non-linear resonances, which may affect stability of the particles and about their location on the tune diagram. You will learn about chromatic (energy dependent) effects, use of non-linear elements to compensate them, and about problems created by introducing them. Some of traditional perturbation theory methods will be introduced during this lecture.

*Longitudinal beam dynamics <br />If you were ever wondering why Saturn rings do not collapse into one large ball of rock under gravitational attraction – this where you will learn of the effect so-called negative mass in longitudinal motion of particles. You will also learn about so-called synchrotron oscillations, which are have a lot of similarity with pendulum motion. One more “tunes” to remember about - synchrotron tune.

*Radiation effects <br />Charged particles going around an accelerator do radiate when their trajectory is bent – hence, there is entire range of topics arising from this fact. It goes from such effect as radiation damping of the particle oscillations, quantum excitation of such oscillation to the use of this extraordinary radiation as cutting-edge research tool. We will look both into positive (usefulness of synchrotron and FEL radiation) and negative (limiting the energy of electron storage rings) aspects of this natural phenomenon.

*Accelerator applications <br />We will devote this part of the course to the discussion of variety of accelerator application, among which are accelerators for nuclear and particle physics, X-ray light sources, accelerators for medical uses, etc. You will also learn about future accelerators at the energy and intensity forntiers as well as about new methods of particle acceleration.

== Lecture Notes ==

* [[media:PHY554_Lecture1_F2025.pdf|PHY554 Lecture 1, Modern Accelerators]], by Prof. V. N. Litvinenko
* [[media:PHY554_Lectures_2&3_2025.pdf ‎|PHY554 Lectures 2 and 3, History of Accelerators]], by Prof. V. N. Litvinenko
* [[media:PHY554_Lecture4_F2024.pdf|PHY554 Lecture 4, Transverse motion]], by Dr. J. Ma
* [[media:PHY554_Lecture5_F2024.pdf|PHY554 Lecture 5, Floquet Theorem]], by Dr. J. Ma
* [[media:PHY554_Lecture6_F2024.pdf|PHY554 Lecture 6, Beam Emittance, Dipole Field Error]], by Dr. J. Ma
* [[media:PHY554_Lecture7_F2025.pdf|PHY554 Lecture 7, Off-momentum particles, dispersion function]], by Prof. Y. Jing
* [[media:PHY554_Lecture8_F2025.pdf|PHY554 Lecture 8, Quadrupole field error and its application]], by Prof. Y. Jing
* [[media:PHY554_2023_Lecture10.pdf|PHY554 Lecture 9, Introduction to RF accelerators]], by Dr. J. Ma
* [[media:PHY554_2023_Lecture11.pdf|PHY554 Lecture 10, Fundamentals of RF accelerators]], by Dr. J. Ma
* [[media:PHY554_Lecture11_F2025.pdf|PHY554 Lecture 11, Synchrotron Radiation]], by Prof. G. Wang
* [[media:PHY554_Lecture12_F2025.pdf|PHY554 Lecture 12, Synchrotron Radiation Sources]], by Prof. G. Wang
* [[media:PHY554_Lecture13_F2024.pdf|PHY554 Lecture 13, Longitudinal Dynamics]], by Prof. Y. Jing
* [[media:PHY554_Lecture14_15_F2024.pdf|PHY554 Lecture 14-15, Electron storage rings]], by Prof. Y. Jing
* [[media:PHY554_Lecture16_F2024.pdf|PHY554 Lecture 16, Chromaticities and its correction]], by Prof. Y. Jing
* [[media:PHY554_Lecture17_F2024.pdf|PHY554 Lecture 17, Nonlinear Dynamics]], by Prof. Y. Jing
* [[media:PHY554_Lecture18_F2025.pdf|PHY554 Lecture 18, Collective Effects I: Wakefield and Impedances]], by Prof. G. Wang
* [[media:PHY554_Lecture19_F2025.pdf|PHY554 Lecture 19, Collective Effects II: Examples of Collective Instabilities]], by Prof. G. Wang

From 2024

* [[media:PHY554_Lecture_20-21_2024.pdf|PHY554 Lecture 20-21, Free Electron Lasers]], by Dr. J. Ma
* [[media:PHY554_Lecture_22_2024.pdf|PHY554 Lecture 22, Hadron Beam Cooling]], by Dr. J. Ma

Home-Reading:
* [[media:Reading_matertials.pdf| Least Action Principle, Geometry of Special Relativity, Particles in E&M fields]], by Prof. Litvinenko'''
* [[media:Matrix_calculus_refresher.pdf|Matrix calculus]]
* [[media:Complex_Analysis_Refresher.pdf| Complex analysis]]
* [[media:Vector_Calculus_Refresher.pdf| Vector calculus]]
* [[media:Derivation_of_radiation_power.pdf|Derivations for Synchrotron Radiation]], by Prof. G. Wang

== Homework ==
* [[media:HW1_2025.pdf|Homework 1]], August 27: due September 10, [[media:HW1_2025_Solutions.pdf|Solutions]]
* [[media:PHY554_2025_HW2.pdf|Homework 2]], September 8: due September 17, [[media:PHY554_2025_HW2_Solutions.pdf|Solutions]]
* [[media:PHY554_2025_HW3.pdf|Homework 3]], September 15: due September 24, [[media:PHY554_2025_HW3_Solutions.pdf|Solutions]]
* [[media:PHY554_2025_HW4.pdf|Homework 4]], September 29: due October 8, [[media:PHY554_2025_HW4_Solutions.pdf|Solutions]]
* [[media:PHY554_2025_HW5.pdf|Homework 5]], October 8: due October 15, [[media:PHY554_2025_HW5_Solutions.pdf|Solutions]]

== '''<span style="color: red">Exam ==
* [[media:Midterm_2025.pdf|Midterm]], due November 3 midnight

== List of suggested projects ==

Read and present

* [[media:Projects_PHY554.pdf| Suggested Projects‎]]

Design and present (can collaborate)

* [[media:Design topics.pdf| Suggested Projects‎]]

PHY554 Fall 2025

2025-11-12T06:05:34Z

GangWang: /* Lecture Notes */

<center>
<table width=60% border=1>
<tr>
<th width=50% align=center>Class meet time and dates</th>
<th align=center>Instructors</th>
</tr>

<tr><td align=left valign=center>

* '''When: Mon/Wed, 6:30 pm - 7:50pm '''
* '''Where: Zoom ( Physics D103 , see the map https://www.stonybrook.edu/sb/map/map.pdf)'''
</td>

<td align=left valign=top>

* Prof. Yichao Jing
* Prof. Dmitry Kayran
* Prof. Vladimir N Litvinenko
* Dr. Jun Ma
* Prof. Gang Wang
* '''TA:''' Nikhil Bachhawat

</td>

</tr></table>
[[Image:Accelerators.jpg|350px|Image: 400 pixels|right]]

</center>

== Course Overview ==
The graduate/senior undergraduate level course focuses on the fundamental physics and key concepts of modern particle accelerators. The course is intended for graduate students and advanced undergraduate students who want to familiarize themselves with principles of accelerating charged particles and gain knowledge about contemporary particle accelerators and their applications.

It will cover the following contents:

* History of accelerators and basic principles (eg. centre of mass energy, luminosity, accelerating gradient, etc)

* Radio Frequency cavities, linacs, SRF accelerators;

* Magnets, Transverse motion, Strong focusing, simple lattices; Non-linearities and resonances;

* Circulating beams, Longitutdinal dynamics, Synchrotron radiation; principles of beam cooling,

* Applications of accelerators: light sources, medical uses

Students will be evaluated based on the following performances: '''homework assignments (40%), class participation (20%), mid-term exam (20%) and final presentation on specific research paper (20%), .'''

==Learning Goals==

Students who have completed this course should

* Understand how various types of accelerators work and understand differences between them.
* Have a general understanding of transverse and longitudinal beam dynamics in accelerators.
* Have a general understanding of accelerating structures.
* Understand major applications of accelerators and the recent new concepts.
== Textbook and ''suggested materials''==

Textbook is to be decided from the following:
*Accelerator Physics, by S. Y. Lee
*An Introduction to the Physics of High Energy Accelerators, by D. A. Edwards and M. J. Syphers
*''Introduction To The Physics Of Particle Accelerators'', by Mario Conte and William W Mackay
*''Particle Accelerator Physics'', by Helmut Wiedemann
*''The Physics of Particle Accelerators: An Introduction'', by Klaus Wille and Jason McFall

10+ S.Y. Lee's and Edwards-Syphers' books are available in BNL library and electronic copies are available upon requests.

== Course Description ==

*Introduction to accelerator physics <br />You will have a glance into the history of accelerators and will learn about a variety of accelerators from electrostatic TV-tubes to gigantic atom and nuclear smashers. Basic figures of merit will be introduced (center of mass energy, luminosity, accelerating gradient, etc.) You will learn general principles behing linear accelerators and circular accelerators, their relative advantages and disadvantages.

*Radio frequency cavities, linacs, superconducting RF accelerators <br />This part of the course will be dedicated to physics and technology of accelerating structures. You will learn basic principles of using radio frequency electromagnetic fields to accelerate particles to very high energies. Different types of accelerating structures will be introduced. You will also learn about brand new direction in linear accelerators – so-called energy recovery linacs. As many modern accelerators are based on superconducting RF (SRF) technlogy, you will learn fundamentals of the SRF accelerators and their advantages over conventional (normal conductoing) RF accelerators.

*Linear transverse beam dynamics <br />This part of the course will be dedicated to detailed description of linear dynamics of particles in accelerators. You will learn about similarity of particles motion to an oscillator with time-dependent rigidity, matrix optics of various elements in accelerators, equation for beam envelopes and stability of periodic (circular) motion of the particles. Here you find a number of analogies with planetary motion, including oscillation of Earth’s moon. You will learn some “standards” of the accelerator physics – betatron tunes and beta-function and their importance in circular accelerators.

*Nonlinear transverse beam dynamics <br />This lecture will open door in fascinating and never-ending elegance and complexity on nonlinear beam dynamics. You will learn about non-linear resonances, which may affect stability of the particles and about their location on the tune diagram. You will learn about chromatic (energy dependent) effects, use of non-linear elements to compensate them, and about problems created by introducing them. Some of traditional perturbation theory methods will be introduced during this lecture.

*Longitudinal beam dynamics <br />If you were ever wondering why Saturn rings do not collapse into one large ball of rock under gravitational attraction – this where you will learn of the effect so-called negative mass in longitudinal motion of particles. You will also learn about so-called synchrotron oscillations, which are have a lot of similarity with pendulum motion. One more “tunes” to remember about - synchrotron tune.

*Radiation effects <br />Charged particles going around an accelerator do radiate when their trajectory is bent – hence, there is entire range of topics arising from this fact. It goes from such effect as radiation damping of the particle oscillations, quantum excitation of such oscillation to the use of this extraordinary radiation as cutting-edge research tool. We will look both into positive (usefulness of synchrotron and FEL radiation) and negative (limiting the energy of electron storage rings) aspects of this natural phenomenon.

*Accelerator applications <br />We will devote this part of the course to the discussion of variety of accelerator application, among which are accelerators for nuclear and particle physics, X-ray light sources, accelerators for medical uses, etc. You will also learn about future accelerators at the energy and intensity forntiers as well as about new methods of particle acceleration.

== Lecture Notes ==

* [[media:PHY554_Lecture1_F2025.pdf|PHY554 Lecture 1, Modern Accelerators]], by Prof. V. N. Litvinenko
* [[media:PHY554_Lectures_2&3_2025.pdf ‎|PHY554 Lectures 2 and 3, History of Accelerators]], by Prof. V. N. Litvinenko
* [[media:PHY554_Lecture4_F2024.pdf|PHY554 Lecture 4, Transverse motion]], by Dr. J. Ma
* [[media:PHY554_Lecture5_F2024.pdf|PHY554 Lecture 5, Floquet Theorem]], by Dr. J. Ma
* [[media:PHY554_Lecture6_F2024.pdf|PHY554 Lecture 6, Beam Emittance, Dipole Field Error]], by Dr. J. Ma
* [[media:PHY554_Lecture7_F2025.pdf|PHY554 Lecture 7, Off-momentum particles, dispersion function]], by Prof. Y. Jing
* [[media:PHY554_Lecture8_F2025.pdf|PHY554 Lecture 8, Quadrupole field error and its application]], by Prof. Y. Jing
* [[media:PHY554_2023_Lecture10.pdf|PHY554 Lecture 9, Introduction to RF accelerators]], by Dr. J. Ma
* [[media:PHY554_2023_Lecture11.pdf|PHY554 Lecture 10, Fundamentals of RF accelerators]], by Dr. J. Ma
* [[media:PHY554_Lecture11_F2025.pdf|PHY554 Lecture 11, Synchrotron Radiation]], by Prof. G. Wang
* [[media:PHY554_Lecture12_F2025.pdf|PHY554 Lecture 12, Synchrotron Radiation Sources]], by Prof. G. Wang
* [[media:PHY554_Lecture13_F2024.pdf|PHY554 Lecture 13, Longitudinal Dynamics]], by Prof. Y. Jing
* [[media:PHY554_Lecture14_15_F2024.pdf|PHY554 Lecture 14-15, Electron storage rings]], by Prof. Y. Jing
* [[media:PHY554_Lecture16_F2024.pdf|PHY554 Lecture 16, Chromaticities and its correction]], by Prof. Y. Jing
* [[media:PHY554_Lecture17_F2024.pdf|PHY554 Lecture 17, Nonlinear Dynamics]], by Prof. Y. Jing
* [[media:PHY554_Lecture18_F2025.pdf|PHY554 Lecture 18, Collective Effects I: Wakefield and Impedances]], by Prof. G. Wang

From 2024

* [[media:PHY554_Lecture19_F2024.pdf|PHY554 Lecture 19, Collective Effects II: Examples of Collective Instabilities]], by Prof. G. Wang
* [[media:PHY554_Lecture_20-21_2024.pdf|PHY554 Lecture 20-21, Free Electron Lasers]], by Dr. J. Ma
* [[media:PHY554_Lecture_22_2024.pdf|PHY554 Lecture 22, Hadron Beam Cooling]], by Dr. J. Ma

Home-Reading:
* [[media:Reading_matertials.pdf| Least Action Principle, Geometry of Special Relativity, Particles in E&M fields]], by Prof. Litvinenko'''
* [[media:Matrix_calculus_refresher.pdf|Matrix calculus]]
* [[media:Complex_Analysis_Refresher.pdf| Complex analysis]]
* [[media:Vector_Calculus_Refresher.pdf| Vector calculus]]
* [[media:Derivation_of_radiation_power.pdf|Derivations for Synchrotron Radiation]], by Prof. G. Wang

== Homework ==
* [[media:HW1_2025.pdf|Homework 1]], August 27: due September 10, [[media:HW1_2025_Solutions.pdf|Solutions]]
* [[media:PHY554_2025_HW2.pdf|Homework 2]], September 8: due September 17, [[media:PHY554_2025_HW2_Solutions.pdf|Solutions]]
* [[media:PHY554_2025_HW3.pdf|Homework 3]], September 15: due September 24, [[media:PHY554_2025_HW3_Solutions.pdf|Solutions]]
* [[media:PHY554_2025_HW4.pdf|Homework 4]], September 29: due October 8, [[media:PHY554_2025_HW4_Solutions.pdf|Solutions]]
* [[media:PHY554_2025_HW5.pdf|Homework 5]], October 8: due October 15, [[media:PHY554_2025_HW5_Solutions.pdf|Solutions]]

== '''<span style="color: red">Exam ==
* [[media:Midterm_2025.pdf|Midterm]], due November 3 midnight

== List of suggested projects ==

Read and present

* [[media:Projects_PHY554.pdf| Suggested Projects‎]]

Design and present (can collaborate)

* [[media:Design topics.pdf| Suggested Projects‎]]

<center>
<table width=60% border=1>
<tr>
<th width=50% align=center>Class meet time and dates</th>
<th align=center>Instructors</th>
</tr>

<tr><td align=left valign=center>

* '''When: Mon/Wed, 6:30 pm - 7:50pm '''
* '''Where: Zoom ( Physics D103 , see the map https://www.stonybrook.edu/sb/map/map.pdf)'''
</td>

<td align=left valign=top>

* Prof. Yichao Jing
* Prof. Dmitry Kayran
* Prof. Vladimir N Litvinenko
* Dr. Jun Ma
* Prof. Gang Wang
* '''TA:''' Nikhil Bachhawat

</td>

</tr></table>
[[Image:Accelerators.jpg|350px|Image: 400 pixels|right]]

</center>

== Course Overview ==
The graduate/senior undergraduate level course focuses on the fundamental physics and key concepts of modern particle accelerators. The course is intended for graduate students and advanced undergraduate students who want to familiarize themselves with principles of accelerating charged particles and gain knowledge about contemporary particle accelerators and their applications.

It will cover the following contents:

* History of accelerators and basic principles (eg. centre of mass energy, luminosity, accelerating gradient, etc)

* Radio Frequency cavities, linacs, SRF accelerators;

* Magnets, Transverse motion, Strong focusing, simple lattices; Non-linearities and resonances;

* Circulating beams, Longitutdinal dynamics, Synchrotron radiation; principles of beam cooling,

* Applications of accelerators: light sources, medical uses

Students will be evaluated based on the following performances: '''homework assignments (40%), class participation (20%), mid-term exam (20%) and final presentation on specific research paper (20%), .'''

==Learning Goals==

Students who have completed this course should

* Understand how various types of accelerators work and understand differences between them.
* Have a general understanding of transverse and longitudinal beam dynamics in accelerators.
* Have a general understanding of accelerating structures.
* Understand major applications of accelerators and the recent new concepts.
== Textbook and ''suggested materials''==

Textbook is to be decided from the following:
*Accelerator Physics, by S. Y. Lee
*An Introduction to the Physics of High Energy Accelerators, by D. A. Edwards and M. J. Syphers
*''Introduction To The Physics Of Particle Accelerators'', by Mario Conte and William W Mackay
*''Particle Accelerator Physics'', by Helmut Wiedemann
*''The Physics of Particle Accelerators: An Introduction'', by Klaus Wille and Jason McFall

10+ S.Y. Lee's and Edwards-Syphers' books are available in BNL library and electronic copies are available upon requests.

== Course Description ==

*Introduction to accelerator physics <br />You will have a glance into the history of accelerators and will learn about a variety of accelerators from electrostatic TV-tubes to gigantic atom and nuclear smashers. Basic figures of merit will be introduced (center of mass energy, luminosity, accelerating gradient, etc.) You will learn general principles behing linear accelerators and circular accelerators, their relative advantages and disadvantages.

*Radio frequency cavities, linacs, superconducting RF accelerators <br />This part of the course will be dedicated to physics and technology of accelerating structures. You will learn basic principles of using radio frequency electromagnetic fields to accelerate particles to very high energies. Different types of accelerating structures will be introduced. You will also learn about brand new direction in linear accelerators – so-called energy recovery linacs. As many modern accelerators are based on superconducting RF (SRF) technlogy, you will learn fundamentals of the SRF accelerators and their advantages over conventional (normal conductoing) RF accelerators.

*Linear transverse beam dynamics <br />This part of the course will be dedicated to detailed description of linear dynamics of particles in accelerators. You will learn about similarity of particles motion to an oscillator with time-dependent rigidity, matrix optics of various elements in accelerators, equation for beam envelopes and stability of periodic (circular) motion of the particles. Here you find a number of analogies with planetary motion, including oscillation of Earth’s moon. You will learn some “standards” of the accelerator physics – betatron tunes and beta-function and their importance in circular accelerators.

*Nonlinear transverse beam dynamics <br />This lecture will open door in fascinating and never-ending elegance and complexity on nonlinear beam dynamics. You will learn about non-linear resonances, which may affect stability of the particles and about their location on the tune diagram. You will learn about chromatic (energy dependent) effects, use of non-linear elements to compensate them, and about problems created by introducing them. Some of traditional perturbation theory methods will be introduced during this lecture.

*Longitudinal beam dynamics <br />If you were ever wondering why Saturn rings do not collapse into one large ball of rock under gravitational attraction – this where you will learn of the effect so-called negative mass in longitudinal motion of particles. You will also learn about so-called synchrotron oscillations, which are have a lot of similarity with pendulum motion. One more “tunes” to remember about - synchrotron tune.

*Radiation effects <br />Charged particles going around an accelerator do radiate when their trajectory is bent – hence, there is entire range of topics arising from this fact. It goes from such effect as radiation damping of the particle oscillations, quantum excitation of such oscillation to the use of this extraordinary radiation as cutting-edge research tool. We will look both into positive (usefulness of synchrotron and FEL radiation) and negative (limiting the energy of electron storage rings) aspects of this natural phenomenon.

*Accelerator applications <br />We will devote this part of the course to the discussion of variety of accelerator application, among which are accelerators for nuclear and particle physics, X-ray light sources, accelerators for medical uses, etc. You will also learn about future accelerators at the energy and intensity forntiers as well as about new methods of particle acceleration.

== Lecture Notes ==

* [[media:PHY554_Lecture1_F2024.pdf|PHY554 Lecture 1, Modern Accelerators]], by Prof. Y. Jing
* [[media:PHY554_Lectures_2&3.pdf|PHY554 Lecturs 2 and 3, History of Accelerators]], by Prof. V. N. Litvinenko
* [[media:PHY554_Lecture4_F2024.pdf|PHY554 Lecture 4, Transverse motion]], by Prof. Y. Jing
* [[media:PHY554_Lecture5_F2024.pdf|PHY554 Lecture 5, Floquet Theorem]], by Prof. Y. Jing
* [[media:PHY554_Lecture6_F2024.pdf|PHY554 Lecture 6, Beam Emittance, Dipole Field Error]], by Prof. Y. Jing
* [[media:PHY554_Lecture7_F2024.pdf|PHY554 Lecture 7, Off-momentum particles, dispersion function]], by Prof. Y. Jing
* [[media:PHY554_Lecture8_F2024.pdf|PHY554 Lecture 8, Quadrupole Field Error]], by Prof. Y. Jing
* [[media:PHY554_Lecture9_F2024.pdf|PHY554 Lecture 9, Synchrotron Radiation]], by Prof. G. Wang
* [[media:PHY554_Lecture10_F2024.pdf|PHY554 Lecture 10, Synchrotron Radiation Sources]], by Prof. G. Wang
* [[media:PHY554_2023_Lecture10.pdf|PHY554 Lecture 11, Introduction to RF accelerators]], by Dr. Jun Ma
* [[media:PHY554_2023_Lecture11.pdf|PHY554 Lecture 12, Fundamentals of RF accelerators]], by Dr. Jun Ma
* [[media:PHY554_Lecture13_F2024.pdf|PHY554 Lecture 13, Longitudinal Dynamics]], by Prof. Y. Jing
* [[media:PHY554_Lecture14_15_F2024.pdf|PHY554 Lecture 14-15, Electron storage rings]], by Prof. Y. Jing
* [[media:PHY554_Lecture16_F2024.pdf|PHY554 Lecture 16, Chromaticities and its correction]], by Prof. Y. Jing
* [[media:PHY554_Lecture17_F2024.pdf|PHY554 Lecture 17, Nonlinear Dynamics]], by Prof. Y. Jing
* [[media:PHY554_Lecture18_F2024.pdf|PHY554 Lecture 18, Collective Effects I: Wakefield and Impedances]], by Prof. G. Wang
* [[media:PHY554_Lecture19_F2024.pdf|PHY554 Lecture 18, Collective Effects II: Examples of Collective Instabilities]], by Prof. G. Wang

Home-Reading:
* [[media:Reading_matertials.pdf| Least Action Principle, Geometry of Special Relativity, Particles in E&M fields]], by Prof. Litvinenko'''
* [[media:Matrix_calculus_refresher.pdf|Matrix calculus]]
* [[media:Complex_Analysis_Refresher.pdf| Complex analysis]]
* [[media:Vector_Calculus_Refresher.pdf| Vector calculus]]

== Homework ==

* [[media:HW1_2024.pdf|Homework 1]], August 28: due September 11 [[media:HW 1 2024 solution.pdf|Solutions]]
* [[media:HW2_2024.pdf|Homework 2]], September 11: due September 18 [[media:HW2_2024_solutions.pdf|Solutions]]
* [[media:HW3_2024.pdf|Homework 3]], September 23: due September 30 [[media:HW3_2024_solutions.pdf|Solutions]]
* [[media:HW4_2024.pdf|Homework 4]], October 2: due October 9 [[media:HW4_2024_solutions_1.pdf|Solutions]]
* [[media:PHY554_2024_HW_5.pdf|Homework 5]], October 7: due October 16 [[media:PHY554_2024_HW_5_Soultions.pdf|Solutions]]
* [[media:HW6_2024.pdf|Homework 6]], October 28: due November 4

== '''<span style="color: red">Exam ==

* [[media:2024 PHY 554 Mid-term.pdf|Mid-term]], Oct 23 8:30 pm: due Oct 24 24:00 pm [[media:2024 PHY 554 Mid-term-solutions.pdf|'''<span style="color: red">Solutions]]

Mid-term course review:
* [[media:PHY554_review_transverse_longitudinal.pdf|Transverse and Longitudinal Dynamics]]
* [[media:PHY554_2024_RF_Review.pdf|RF cavities]]

== List of suggested projects ==

Read and present

* [[media:Projects_PHY554.pdf| Suggested Projects‎]]

Design and present (can collaborate)

* [[media:Design topics.pdf| Suggested Projects‎]]

File:PHY554 Lecture18 F2024.pdf

2024-11-13T06:08:58Z

GangWang:

PHY554 Fall 2024

2024-11-13T06:07:57Z

GangWang: /* Lecture Notes */

<center>
<table width=60% border=1>
<tr>
<th width=50% align=center>Class meet time and dates</th>
<th align=center>Instructors</th>
</tr>

<tr><td align=left valign=center>

* '''When: Mon/Wed, 6:30 pm - 7:50pm '''
* '''Where: Zoom ( Physics D103 , see the map https://www.stonybrook.edu/sb/map/map.pdf)'''
</td>

<td align=left valign=top>

* Prof. Yichao Jing
* Prof. Dmitry Kayran
* Prof. Vladimir N Litvinenko
* Dr. Jun Ma
* Prof. Gang Wang
* '''TA:''' Nikhil Bachhawat

</td>

</tr></table>
[[Image:Accelerators.jpg|350px|Image: 400 pixels|right]]

</center>

== Course Overview ==
The graduate/senior undergraduate level course focuses on the fundamental physics and key concepts of modern particle accelerators. The course is intended for graduate students and advanced undergraduate students who want to familiarize themselves with principles of accelerating charged particles and gain knowledge about contemporary particle accelerators and their applications.

It will cover the following contents:

* History of accelerators and basic principles (eg. centre of mass energy, luminosity, accelerating gradient, etc)

* Radio Frequency cavities, linacs, SRF accelerators;

* Magnets, Transverse motion, Strong focusing, simple lattices; Non-linearities and resonances;

* Circulating beams, Longitutdinal dynamics, Synchrotron radiation; principles of beam cooling,

* Applications of accelerators: light sources, medical uses

Students will be evaluated based on the following performances: '''homework assignments (40%), class participation (20%), mid-term exam (20%) and final presentation on specific research paper (20%), .'''

==Learning Goals==

Students who have completed this course should

* Understand how various types of accelerators work and understand differences between them.
* Have a general understanding of transverse and longitudinal beam dynamics in accelerators.
* Have a general understanding of accelerating structures.
* Understand major applications of accelerators and the recent new concepts.
== Textbook and ''suggested materials''==

Textbook is to be decided from the following:
*Accelerator Physics, by S. Y. Lee
*An Introduction to the Physics of High Energy Accelerators, by D. A. Edwards and M. J. Syphers
*''Introduction To The Physics Of Particle Accelerators'', by Mario Conte and William W Mackay
*''Particle Accelerator Physics'', by Helmut Wiedemann
*''The Physics of Particle Accelerators: An Introduction'', by Klaus Wille and Jason McFall

10+ S.Y. Lee's and Edwards-Syphers' books are available in BNL library and electronic copies are available upon requests.

== Course Description ==

*Introduction to accelerator physics <br />You will have a glance into the history of accelerators and will learn about a variety of accelerators from electrostatic TV-tubes to gigantic atom and nuclear smashers. Basic figures of merit will be introduced (center of mass energy, luminosity, accelerating gradient, etc.) You will learn general principles behing linear accelerators and circular accelerators, their relative advantages and disadvantages.

*Radio frequency cavities, linacs, superconducting RF accelerators <br />This part of the course will be dedicated to physics and technology of accelerating structures. You will learn basic principles of using radio frequency electromagnetic fields to accelerate particles to very high energies. Different types of accelerating structures will be introduced. You will also learn about brand new direction in linear accelerators – so-called energy recovery linacs. As many modern accelerators are based on superconducting RF (SRF) technlogy, you will learn fundamentals of the SRF accelerators and their advantages over conventional (normal conductoing) RF accelerators.

*Linear transverse beam dynamics <br />This part of the course will be dedicated to detailed description of linear dynamics of particles in accelerators. You will learn about similarity of particles motion to an oscillator with time-dependent rigidity, matrix optics of various elements in accelerators, equation for beam envelopes and stability of periodic (circular) motion of the particles. Here you find a number of analogies with planetary motion, including oscillation of Earth’s moon. You will learn some “standards” of the accelerator physics – betatron tunes and beta-function and their importance in circular accelerators.

*Nonlinear transverse beam dynamics <br />This lecture will open door in fascinating and never-ending elegance and complexity on nonlinear beam dynamics. You will learn about non-linear resonances, which may affect stability of the particles and about their location on the tune diagram. You will learn about chromatic (energy dependent) effects, use of non-linear elements to compensate them, and about problems created by introducing them. Some of traditional perturbation theory methods will be introduced during this lecture.

*Longitudinal beam dynamics <br />If you were ever wondering why Saturn rings do not collapse into one large ball of rock under gravitational attraction – this where you will learn of the effect so-called negative mass in longitudinal motion of particles. You will also learn about so-called synchrotron oscillations, which are have a lot of similarity with pendulum motion. One more “tunes” to remember about - synchrotron tune.

*Radiation effects <br />Charged particles going around an accelerator do radiate when their trajectory is bent – hence, there is entire range of topics arising from this fact. It goes from such effect as radiation damping of the particle oscillations, quantum excitation of such oscillation to the use of this extraordinary radiation as cutting-edge research tool. We will look both into positive (usefulness of synchrotron and FEL radiation) and negative (limiting the energy of electron storage rings) aspects of this natural phenomenon.

*Accelerator applications <br />We will devote this part of the course to the discussion of variety of accelerator application, among which are accelerators for nuclear and particle physics, X-ray light sources, accelerators for medical uses, etc. You will also learn about future accelerators at the energy and intensity forntiers as well as about new methods of particle acceleration.

== Lecture Notes ==

* [[media:PHY554_Lecture1_F2024.pdf|PHY554 Lecture 1, Modern Accelerators]], by Prof. Y. Jing
* [[media:PHY554_Lectures_2&3.pdf|PHY554 Lecturs 2 and 3, History of Accelerators]], by Prof. V. N. Litvinenko
* [[media:PHY554_Lecture4_F2024.pdf|PHY554 Lecture 4, Transverse motion]], by Prof. Y. Jing
* [[media:PHY554_Lecture5_F2024.pdf|PHY554 Lecture 5, Floquet Theorem]], by Prof. Y. Jing
* [[media:PHY554_Lecture6_F2024.pdf|PHY554 Lecture 6, Beam Emittance, Dipole Field Error]], by Prof. Y. Jing
* [[media:PHY554_Lecture7_F2024.pdf|PHY554 Lecture 7, Off-momentum particles, dispersion function]], by Prof. Y. Jing
* [[media:PHY554_Lecture8_F2024.pdf|PHY554 Lecture 8, Quadrupole Field Error]], by Prof. Y. Jing
* [[media:PHY554_Lecture9_F2024.pdf|PHY554 Lecture 9, Synchrotron Radiation]], by Prof. G. Wang
* [[media:PHY554_Lecture10_F2024.pdf|PHY554 Lecture 10, Synchrotron Radiation Sources]], by Prof. G. Wang
* [[media:PHY554_2023_Lecture10.pdf|PHY554 Lecture 11, Introduction to RF accelerators]], by Dr. Jun Ma
* [[media:PHY554_2023_Lecture11.pdf|PHY554 Lecture 12, Fundamentals of RF accelerators]], by Dr. Jun Ma
* [[media:PHY554_Lecture13_F2024.pdf|PHY554 Lecture 13, Longitudinal Dynamics]], by Prof. Y. Jing
* [[media:PHY554_Lecture14_15_F2024.pdf|PHY554 Lecture 14-15, Electron storage rings]], by Prof. Y. Jing
* [[media:PHY554_Lecture16_F2024.pdf|PHY554 Lecture 16, Chromaticities and its correction]], by Prof. Y. Jing
* [[media:PHY554_Lecture17_F2024.pdf|PHY554 Lecture 17, Nonlinear Dynamics]], by Prof. Y. Jing
* [[media:PHY554_Lecture18_F2024.pdf|PHY554 Lecture 18, Collective Effects I: Wakefield and Impedances]], by Prof. G. Wang

Home-Reading:
* [[media:Reading_matertials.pdf| Least Action Principle, Geometry of Special Relativity, Particles in E&M fields]], by Prof. Litvinenko'''
* [[media:Matrix_calculus_refresher.pdf|Matrix calculus]]
* [[media:Complex_Analysis_Refresher.pdf| Complex analysis]]
* [[media:Vector_Calculus_Refresher.pdf| Vector calculus]]

== Homework ==

* [[media:HW1_2024.pdf|Homework 1]], August 28: due September 11 [[media:HW 1 2024 solution.pdf|Solutions]]
* [[media:HW2_2024.pdf|Homework 2]], September 11: due September 18 [[media:HW2_2024_solutions.pdf|Solutions]]
* [[media:HW3_2024.pdf|Homework 3]], September 23: due September 30 [[media:HW3_2024_solutions.pdf|Solutions]]
* [[media:HW4_2024.pdf|Homework 4]], October 2: due October 9 [[media:HW4_2024_solutions_1.pdf|Solutions]]
* [[media:PHY554_2024_HW_5.pdf|Homework 5]], October 7: due October 16 [[media:PHY554_2024_HW_5_Soultions.pdf|Solutions]]
* [[media:HW6_2024.pdf|Homework 6]], October 28: due November 4

== '''<span style="color: red">Exam ==

* [[media:2024 PHY 554 Mid-term.pdf|Mid-term]], Oct 23 8:30 pm: due Oct 24 24:00 pm [[media:2024 PHY 554 Mid-term-solutions.pdf|'''<span style="color: red">Solutions]]

Mid-term course review:
* [[media:PHY554_review_transverse_longitudinal.pdf|Transverse and Longitudinal Dynamics]]
* [[media:PHY554_2024_RF_Review.pdf|RF cavities]]

== List of suggested projects ==

Read and present

* [[media:Projects_PHY554.pdf| Suggested Projects‎]]

Design and present (can collaborate)

* [[media:Design topics.pdf| Suggested Projects‎]]

File:HW4 2024 solutions 1.pdf

2024-10-22T00:28:55Z

GangWang:

PHY554 Fall 2024

2024-10-22T00:28:29Z

File:HW4 2024.pdf

2024-10-03T03:25:27Z

GangWang:

PHY554 Fall 2024

2024-10-03T03:25:16Z

GangWang: /* Homework */

<center>
<table width=60% border=1>
<tr>
<th width=50% align=center>Class meet time and dates</th>
<th align=center>Instructors</th>
</tr>

<tr><td align=left valign=center>

* '''When: Mon/Wed, 6:30 pm - 7:50pm '''
* '''Where: Zoom ( Physics D103 , see the map https://www.stonybrook.edu/sb/map/map.pdf)'''
</td>

<td align=left valign=top>

* Prof. Yichao Jing
* Prof. Vladimir N Litvinenko
* Dr. Jun Ma
* Prof. Gang Wang
* '''TA:''' Nikhil Bachhawat

</td>

</tr></table>
[[Image:Accelerators.jpg|350px|Image: 400 pixels|right]]

</center>

== Course Overview ==
The graduate/senior undergraduate level course focuses on the fundamental physics and key concepts of modern particle accelerators. The course is intended for graduate students and advanced undergraduate students who want to familiarize themselves with principles of accelerating charged particles and gain knowledge about contemporary particle accelerators and their applications.

It will cover the following contents:

* History of accelerators and basic principles (eg. centre of mass energy, luminosity, accelerating gradient, etc)

* Radio Frequency cavities, linacs, SRF accelerators;

* Magnets, Transverse motion, Strong focusing, simple lattices; Non-linearities and resonances;

* Circulating beams, Longitutdinal dynamics, Synchrotron radiation; principles of beam cooling,

* Applications of accelerators: light sources, medical uses

Students will be evaluated based on the following performances: '''homework assignments (40%), class participation (20%), mid-term exam (20%) and final presentation on specific research paper (20%), .'''

==Learning Goals==

Students who have completed this course should

* Understand how various types of accelerators work and understand differences between them.
* Have a general understanding of transverse and longitudinal beam dynamics in accelerators.
* Have a general understanding of accelerating structures.
* Understand major applications of accelerators and the recent new concepts.
== Textbook and ''suggested materials''==

Textbook is to be decided from the following:
*Accelerator Physics, by S. Y. Lee
*An Introduction to the Physics of High Energy Accelerators, by D. A. Edwards and M. J. Syphers
*''Introduction To The Physics Of Particle Accelerators'', by Mario Conte and William W Mackay
*''Particle Accelerator Physics'', by Helmut Wiedemann
*''The Physics of Particle Accelerators: An Introduction'', by Klaus Wille and Jason McFall

10+ S.Y. Lee's and Edwards-Syphers' books are available in BNL library and electronic copies are available upon requests.

== Course Description ==

*Introduction to accelerator physics <br />You will have a glance into the history of accelerators and will learn about a variety of accelerators from electrostatic TV-tubes to gigantic atom and nuclear smashers. Basic figures of merit will be introduced (center of mass energy, luminosity, accelerating gradient, etc.) You will learn general principles behing linear accelerators and circular accelerators, their relative advantages and disadvantages.

*Radio frequency cavities, linacs, superconducting RF accelerators <br />This part of the course will be dedicated to physics and technology of accelerating structures. You will learn basic principles of using radio frequency electromagnetic fields to accelerate particles to very high energies. Different types of accelerating structures will be introduced. You will also learn about brand new direction in linear accelerators – so-called energy recovery linacs. As many modern accelerators are based on superconducting RF (SRF) technlogy, you will learn fundamentals of the SRF accelerators and their advantages over conventional (normal conductoing) RF accelerators.

*Linear transverse beam dynamics <br />This part of the course will be dedicated to detailed description of linear dynamics of particles in accelerators. You will learn about similarity of particles motion to an oscillator with time-dependent rigidity, matrix optics of various elements in accelerators, equation for beam envelopes and stability of periodic (circular) motion of the particles. Here you find a number of analogies with planetary motion, including oscillation of Earth’s moon. You will learn some “standards” of the accelerator physics – betatron tunes and beta-function and their importance in circular accelerators.

*Nonlinear transverse beam dynamics <br />This lecture will open door in fascinating and never-ending elegance and complexity on nonlinear beam dynamics. You will learn about non-linear resonances, which may affect stability of the particles and about their location on the tune diagram. You will learn about chromatic (energy dependent) effects, use of non-linear elements to compensate them, and about problems created by introducing them. Some of traditional perturbation theory methods will be introduced during this lecture.

*Longitudinal beam dynamics <br />If you were ever wondering why Saturn rings do not collapse into one large ball of rock under gravitational attraction – this where you will learn of the effect so-called negative mass in longitudinal motion of particles. You will also learn about so-called synchrotron oscillations, which are have a lot of similarity with pendulum motion. One more “tunes” to remember about - synchrotron tune.

*Radiation effects <br />Charged particles going around an accelerator do radiate when their trajectory is bent – hence, there is entire range of topics arising from this fact. It goes from such effect as radiation damping of the particle oscillations, quantum excitation of such oscillation to the use of this extraordinary radiation as cutting-edge research tool. We will look both into positive (usefulness of synchrotron and FEL radiation) and negative (limiting the energy of electron storage rings) aspects of this natural phenomenon.

*Accelerator applications <br />We will devote this part of the course to the discussion of variety of accelerator application, among which are accelerators for nuclear and particle physics, X-ray light sources, accelerators for medical uses, etc. You will also learn about future accelerators at the energy and intensity forntiers as well as about new methods of particle acceleration.

== Lecture Notes ==

* [[media:PHY554_Lecture1_F2024.pdf|PHY554 Lecture 1, Modern Accelerators]], by Prof. Y. Jing
* [[media:PHY554_Lectures_2&3.pdf|PHY554 Lecturs 2 and 3, History of Accelerators]], by Prof. V. N. Litvinenko
* [[media:PHY554_Lecture4_F2024.pdf|PHY554 Lecture 4, Transverse motion]], by Prof. Y. Jing
* [[media:PHY554_Lecture5_F2024.pdf|PHY554 Lecture 5, Floquet Theorem]], by Prof. Y. Jing
* [[media:PHY554_Lecture6_F2024.pdf|PHY554 Lecture 6, Beam Emittance, Dipole Field Error]], by Prof. Y. Jing
* [[media:PHY554_Lecture7_F2024.pdf|PHY554 Lecture 7, Off-momentum particles, dispersion function]], by Prof. Y. Jing
* [[media:PHY554_Lecture8_F2024.pdf|PHY554 Lecture 8, Quadrupole Field Error]], by Prof. Y. Jing
* [[media:PHY554_Lecture9_F2024.pdf|PHY554 Lecture 9, Synchrotron Radiation]], by Prof. G. Wang
* [[media:PHY554_Lecture10_F2024.pdf|PHY554 Lecture 10, Synchrotron Radiation Sources]], by Prof. G. Wang

== Homework ==

* [[media:HW1_2024.pdf|Homework 1]], August 28: due September 11 [[media:HW 1 2024 solution.pdf|Solutions]]
* [[media:HW2_2024.pdf|Homework 2]], September 11: due September 18 [[media:HW2_2024_solutions.pdf|Solutions]]
* [[media:HW3_2024.pdf|Homework 3]], September 23: due September 30
* [[media:HW4_2024.pdf|Homework 4]], October 2: due October 9

== List of suggested projects ==

PHY554 Fall 2024

2024-10-03T03:25:03Z

GangWang: /* Homework */

<center>
<table width=60% border=1>
<tr>
<th width=50% align=center>Class meet time and dates</th>
<th align=center>Instructors</th>
</tr>

<tr><td align=left valign=center>

* '''When: Mon/Wed, 6:30 pm - 7:50pm '''
* '''Where: Zoom ( Physics D103 , see the map https://www.stonybrook.edu/sb/map/map.pdf)'''
</td>

<td align=left valign=top>

* Prof. Yichao Jing
* Prof. Vladimir N Litvinenko
* Dr. Jun Ma
* Prof. Gang Wang
* '''TA:''' Nikhil Bachhawat

</td>

</tr></table>
[[Image:Accelerators.jpg|350px|Image: 400 pixels|right]]

</center>

== Course Overview ==
The graduate/senior undergraduate level course focuses on the fundamental physics and key concepts of modern particle accelerators. The course is intended for graduate students and advanced undergraduate students who want to familiarize themselves with principles of accelerating charged particles and gain knowledge about contemporary particle accelerators and their applications.

It will cover the following contents:

* History of accelerators and basic principles (eg. centre of mass energy, luminosity, accelerating gradient, etc)

* Radio Frequency cavities, linacs, SRF accelerators;

* Magnets, Transverse motion, Strong focusing, simple lattices; Non-linearities and resonances;

* Circulating beams, Longitutdinal dynamics, Synchrotron radiation; principles of beam cooling,

* Applications of accelerators: light sources, medical uses

Students will be evaluated based on the following performances: '''homework assignments (40%), class participation (20%), mid-term exam (20%) and final presentation on specific research paper (20%), .'''

==Learning Goals==

Students who have completed this course should

* Understand how various types of accelerators work and understand differences between them.
* Have a general understanding of transverse and longitudinal beam dynamics in accelerators.
* Have a general understanding of accelerating structures.
* Understand major applications of accelerators and the recent new concepts.
== Textbook and ''suggested materials''==

Textbook is to be decided from the following:
*Accelerator Physics, by S. Y. Lee
*An Introduction to the Physics of High Energy Accelerators, by D. A. Edwards and M. J. Syphers
*''Introduction To The Physics Of Particle Accelerators'', by Mario Conte and William W Mackay
*''Particle Accelerator Physics'', by Helmut Wiedemann
*''The Physics of Particle Accelerators: An Introduction'', by Klaus Wille and Jason McFall

10+ S.Y. Lee's and Edwards-Syphers' books are available in BNL library and electronic copies are available upon requests.

== Course Description ==

*Introduction to accelerator physics <br />You will have a glance into the history of accelerators and will learn about a variety of accelerators from electrostatic TV-tubes to gigantic atom and nuclear smashers. Basic figures of merit will be introduced (center of mass energy, luminosity, accelerating gradient, etc.) You will learn general principles behing linear accelerators and circular accelerators, their relative advantages and disadvantages.

*Radio frequency cavities, linacs, superconducting RF accelerators <br />This part of the course will be dedicated to physics and technology of accelerating structures. You will learn basic principles of using radio frequency electromagnetic fields to accelerate particles to very high energies. Different types of accelerating structures will be introduced. You will also learn about brand new direction in linear accelerators – so-called energy recovery linacs. As many modern accelerators are based on superconducting RF (SRF) technlogy, you will learn fundamentals of the SRF accelerators and their advantages over conventional (normal conductoing) RF accelerators.

*Linear transverse beam dynamics <br />This part of the course will be dedicated to detailed description of linear dynamics of particles in accelerators. You will learn about similarity of particles motion to an oscillator with time-dependent rigidity, matrix optics of various elements in accelerators, equation for beam envelopes and stability of periodic (circular) motion of the particles. Here you find a number of analogies with planetary motion, including oscillation of Earth’s moon. You will learn some “standards” of the accelerator physics – betatron tunes and beta-function and their importance in circular accelerators.

*Nonlinear transverse beam dynamics <br />This lecture will open door in fascinating and never-ending elegance and complexity on nonlinear beam dynamics. You will learn about non-linear resonances, which may affect stability of the particles and about their location on the tune diagram. You will learn about chromatic (energy dependent) effects, use of non-linear elements to compensate them, and about problems created by introducing them. Some of traditional perturbation theory methods will be introduced during this lecture.

*Longitudinal beam dynamics <br />If you were ever wondering why Saturn rings do not collapse into one large ball of rock under gravitational attraction – this where you will learn of the effect so-called negative mass in longitudinal motion of particles. You will also learn about so-called synchrotron oscillations, which are have a lot of similarity with pendulum motion. One more “tunes” to remember about - synchrotron tune.

*Radiation effects <br />Charged particles going around an accelerator do radiate when their trajectory is bent – hence, there is entire range of topics arising from this fact. It goes from such effect as radiation damping of the particle oscillations, quantum excitation of such oscillation to the use of this extraordinary radiation as cutting-edge research tool. We will look both into positive (usefulness of synchrotron and FEL radiation) and negative (limiting the energy of electron storage rings) aspects of this natural phenomenon.

*Accelerator applications <br />We will devote this part of the course to the discussion of variety of accelerator application, among which are accelerators for nuclear and particle physics, X-ray light sources, accelerators for medical uses, etc. You will also learn about future accelerators at the energy and intensity forntiers as well as about new methods of particle acceleration.

== Lecture Notes ==

* [[media:PHY554_Lecture1_F2024.pdf|PHY554 Lecture 1, Modern Accelerators]], by Prof. Y. Jing
* [[media:PHY554_Lectures_2&3.pdf|PHY554 Lecturs 2 and 3, History of Accelerators]], by Prof. V. N. Litvinenko
* [[media:PHY554_Lecture4_F2024.pdf|PHY554 Lecture 4, Transverse motion]], by Prof. Y. Jing
* [[media:PHY554_Lecture5_F2024.pdf|PHY554 Lecture 5, Floquet Theorem]], by Prof. Y. Jing
* [[media:PHY554_Lecture6_F2024.pdf|PHY554 Lecture 6, Beam Emittance, Dipole Field Error]], by Prof. Y. Jing
* [[media:PHY554_Lecture7_F2024.pdf|PHY554 Lecture 7, Off-momentum particles, dispersion function]], by Prof. Y. Jing
* [[media:PHY554_Lecture8_F2024.pdf|PHY554 Lecture 8, Quadrupole Field Error]], by Prof. Y. Jing
* [[media:PHY554_Lecture9_F2024.pdf|PHY554 Lecture 9, Synchrotron Radiation]], by Prof. G. Wang
* [[media:PHY554_Lecture10_F2024.pdf|PHY554 Lecture 10, Synchrotron Radiation Sources]], by Prof. G. Wang

== Homework ==

* [[media:HW1_2024.pdf|Homework 1]], August 28: due September 11 [[media:HW 1 2024 solution.pdf|Solutions]]
* [[media:HW2_2024.pdf|Homework 2]], September 11: due September 18 [[media:HW2_2024_solutions.pdf|Solutions]]
* [[media:HW3_2024.pdf|Homework 3]], September 23: due September 30
* [[media:HW4_2024.pdf|Homework 3]], October 2: due October 9

== List of suggested projects ==