Syllabus

Special problems in physics under supervision of staff. Problems may be technical in nature or concerned with teaching procedure. May be repeated to a maximum of 15 semester hours, but no more than 10 semester hours may apply toward a master’s degree.

Class Room: FW202f

Instructor: Prof. M.J. Syphers

        La Tourette 204
        msyphers@niu.edu

Office Hours: Tuesdays 11:00-12:00 or by appointment

Prerequisites: Consent of Department

Credits: 2-3 (by prior arrangement)

Homework problems, both analytical and computational, will be assigned or suggested in order to assist in the learning experience.

Principle text to be used in this course: D.A. Edwards and M.J. Syphers, “An Introduction to the Physics of High Energy Accelerators”, Wiley (1993) (Edwards and Syphers 1993). Visit Wiley and Edwards and Syphers for more information.

Principle software packages to be used in this course:

Overview: The student in this course will be guided in studies of particle beam transport, beam optical systems and particle acceleration, with emphasis on sensitivity analyses and elements of system design. The student will be expected to learn, both through independent reading and through discussions with the instructor, the basic principles of particle beam dynamics relevant to the subject above, and will become proficient in the use of practical computer programs and programming environments used in the study of particle beam dynamics.

By the end of the course the student should have acquired sufficient knowledge and skills to be able to perform basic analyses of first-order beam optical systems in terms of stable beam transport and control of beam quality (emittance and polarization, in particular).

Topics to be covered in this course include [in “weeks”]:

Longitudinal Dynamics [4]

- Time of Flight and Path Length
- Time evolution due to dp/p, dW/W, dE/E
- Momentum Dispersion   
- Beam bunching basics
- RF cavity basics
- Repetitive Acceleration

Slides can be found here

Some animations can be found here: - v1 - - v2 - - v3 - - v4 - - v5 - - v6 -

This file contains code written in R to track particles in longitudinal phase space.

Some Accelerator Parameters: (some values are approximate)

Parameter FCC Delivery Ring Unit
Max. Kinetic Energy 49,999 8 GeV
Min. Kinetic Energy 3,300 2 GeV
Circumference, \(C\) 100,000 500 m
Transition \(\gamma_t\) 110 10.5
RF frequency, \(f_{rf}\) 400.8 2.4 MHz
RF voltage, \(V\) 16-48 0.02 MV
Ramp Time 900 5 sec
Bunch Length (rms, at max KE) 8 900 cm

HW

  • For each of the two cases in the table above, compute the area of a stationary bucket for the RF system. For the bunch lengths given above, estimate the rms and maximum energy spread of a bunch. What is the rms longitudinal emittance of each beam, in units of eV-seconds? Estimate the 95% longitudinal emittance. Does it fit within the bucket? What is the largest number of possible bunches that can be maintained in each synchrotron?
  • For the table above, are the ramp times consistent with the maximum RF voltages available to each system? Choose a reasonable \(\phi_s\) for your estimation and assume, for this exercise, an “average” rate for \(dE/dt\). For this \(\phi_s\), by how much will the bucket area be reduced?

Nonlinear Dynamics [3]

- RF and the Standard Map
- Consequences of nonlinear systems
- Sextupoles and the Henon Map
- Resonances and Carpet Plots
- Slow Resonant Extraction

Slides can be found here

Some animations can be found here: - v3 - - v4 -

This file contains code written in R to track particles in transverse phase space in presence of a sextupole field.

HW

  • Using the design parameters of the Fermilab Delivery Ring (DR), estimate the strength required for the chromaticity sextupoles to bring the horizontal and vertical chromaticities to zero. Assume the natrual chromaticity in each plane is \(\xi\) = -8.3.

  • In the DR above, assume four identical sextupoles are used “in phase” with each other in a resonant extraction process at a beam energy of 8 GeV (kinetic). For a tune distance to resonance of \(\delta\nu\) = 0.03, what integrated sextupole strength is required of these sextupoles to create a stable phase space area equivalent to the 95% (normalized) beam emittance of 20 \(\pi\) mm-mr? Assume the sextupoles are at locations of \(\hat{\beta}\) in the normal FODO cells of the DR.

Synchrotron Radiation [2]

- Radiation from accelerated charges
- Damping of oscillations
- Quantum excitations
- Equilibrium conditions

Spin Dynamics [2]

- Thomas BMT Equation (spin precession)
- magic momentum
- spinor notation and rotations
- storage ring designs for EDM "searches"

Special Topics [3]

- space charge considerations
- energy deposition calculations
- phase space manipulations
- others, TBD

Grading (tentative):

This is an independent study/research course. The evaluation will be performed through a set of homework assignments and in-class discussions.

Grading scale:

A (90 ≤ x), A- (85 ≤ x <90), B+ (80 ≤ x <85), B (75 ≤ x <80), B- (70 ≤ x <75), C+ (65 ≤ x <70), C (60 ≤ x <65), C- (55 ≤ x <60), D (50 ≤ x <55), F (x <50).

Grade points (assigned by University): A (4.00), A- (3.67), B+ (3.33), B (3.00), B- (2.67), C+ (2.33), C (2.00), C- (1.67), D (1.00), F (0.00).

Time line: August 28, 2017 – December 8, 2017


Accessibility Statement: Northern Illinois University is committed to providing an accessible educational environment in collaboration with the Disability Resource Center (DRC). Any student requiring an academic accommodation due to a disability should let his or her faculty member know as soon as possible. Students who need academic accommodations based on the impact of a disability will be encouraged to contact the DRC if they have not done so already. The DRC is located on the 4th floor of the Health Services Building, and can be reached at 815-753-1303 (V) or drc@niu.edu.


References

Edwards, D.A., and M.J. Syphers. 1993. An Introduction to the Physics of High Energy Accelerators. 2nd ed. New York, New York: Wiley. http://onlinelibrary.wiley.com/book/10.1002/9783527617272.

R Core Team. 2016. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. https://www.R-project.org/.

Laurent Deniau, et al. 2017. The Mad-X Program (Methodical Accelerator Design). https://madx.web.cern.ch.