1. Jefferson Lab Student Seminar Series
Electromagnetism and
the Accelerators at
Jefferson Lab
G. A. Krafft, Jefferson Laboratory
Old Dominion University
Jefferson Lab Student Seminar Series
June 6, 2017

2. Outline Electromagnetism Maxwell Equations Intensity, Power
Particle Motion
Accelerators
Elements
Big Ideas
Jefferson Lab Accelerators
CEBAF
Free Electron Laser (FEL)

3. Key Discoveries in Electromagnetism
Two kinds of electricity; they tend to neutralize each other (Franklin)
Force between charges goes as 1/r2 (Coulomb)
Electric currents generate magnetic fields (Ohm)
Electromagnetic induction (Henry, Faraday)
Field concepts in electromagnetism (Gauss, Maxwell)
Electromagnetic displacement current; Electromagnetic theory of light (Maxwell)
Radio waves generated and detected (Hertz)
Radio communication (Marconi)
High power microwaves (WW II)

4. Fundamental Concepts
Electric Field
Magnetic (Induction) Field

5. Maxwell’s Equations (free space)
Maxwell first to realize μ0ε0=1/c2, implying strongly that light itself
is electromagnetic. Note μ0 and ε0 appear in static measurements!

6. Power Considerations

7. Plane Wave Solutions

9. Numerical Examples

10. Energy Units
When a particle is accelerated, i.e., its energy is changed by an electromagnetic field, it must have fallen through an Electric Field. For electrostatic accelerating fields the energy change is
q charge, Φ, the electrostatic potentials before and after the motion through the electric field. Therefore, particle energy can be conveniently expressed in units of the “equivalent” electrostatic potential change needed to accelerate the particle to the given energy. Definition: 1 eV, or 1 electron volt, is the energy acquired by 1 electron falling through a one volt potential difference.

11. Energy Units To convert rest mass to eV use Einstein relation
where m is the rest mass. For electrons
Recent “best fit” value MeV

12. Lorentz Force
Following Einstein define the relativistic factors

13. van de Graaf Accelerator
Brookhaven
Tandem
van de Graaf
~ 15 MV
Tandem trick multiplies the output energy
Generator

14. Wideröe Thesis Experiment
Über ein neues Prinzip zur Herstellung hoher Spannungen, Archiv für Elektrotechnik 21, 387 (1928) (On a new principle for the production of higher voltages)

15. Sloan-Lawrence Heavy Ion Linac
The Production of Heavy High Speed Ions without the Use of High Voltages
David H. Sloan and Ernest O. Lawrence, Phys. Rev. 38, 2021 (1931)

16. Lawrence’s Question
Can you re-use “the same” accelerating gap many times?
is a constant of the motion
gap

17. Cyclotron Frequency
The radius of the oscillation r = v0/Ωc is proportional to the velocity after the gap. Therefore, the particle takes the same amount of time to come around to the gap, independent of the actual particle energy!!!! (only in the non-relativistic approximation). Establish a resonance (equality!) between RF frequency and particle transverse oscillation frequency, also known as the Cyclotron Frequency

18. U. S. Patent Diagram

19. What Correspond to Drift Tubes?
Dee’s!

20. Magnet for 27 Inch Cyclotron (LHS)

21. Alvarez Drift Tube Linac
The first large proton drift tube linac built by Luis Alvarez and Panofsky after WW II

22. Jefferson Lab Accelerating Cavities

23. Jefferson Lab Benders

24. Bend (Dipole) Magnet GeometryS
Top View Rectangular Magnet of Length L
Sector Magnet ρ
θ/2 ρ θ

25. Bend Magnet Trajectory
For a uniform magnetic field
For the solution satisfying boundary conditions:

26. Magnetic Rigidity The magnetic rigidity is:
It depends only on the particle momentum and charge, and is a convenient way to characterize the magnetic field. Given magnetic rigidity and the required bend radius, the required bend field is a simple ratio. Note particles of momentum 100 MeV/c have a rigidity of T m.
Normal Incidence (or exit)
Dipole Magnet
Long Dipole Magnet

27. Quadrupole Focusing N S N S

28. Strong Focusing
In quadrupole magnet field that focuses in one transverse direction, defocuses in the other
Question: is it possible to develop a system that focuses in both directions simultaneously?
Strong focusing: alternate the signs of focusing and defocusing: get net focusing!!
Order doesn’t matter!

29. Linear Magnetic Lenses: Quadrupoles
LHC Superconducting Quadrupoles
Source:

30. Weak vs. Strong Benders

31. Cosmotron (First GeV Accelerator)

32. Alternating Gradient Synchrotron (AGS)

33. Jefferson Lab

34. CEBAF Accelerator Schematic

35. CEBAF Beam Parameters Beam energy 6 GeV Beam current
A 100 μA, B nA, C 100 μA
Normalized rms emittance
1 mm mrad
Repetition rate
500 MHz/Hall
Charge per bunch
< 0.2 pC
Extracted energy spread
< 10-4
Beam sizes (transverse)
< 100 microns
Beam size (longitudinal)
<100 microns (330 fsec)
Beam angle spread
< 0.1/γ

36. CEBAF Superconducting LINAC

37. 12 GeV Upgrade

38. New 12 GeV Linac

39. IR FEL Upgrade

40. IR FEL 10 kW Upgrade Parameters
Kinetic Energy
Average Current
Bunch Charge
Bunch Length
Transverse Emittance
Longitudinal Emittance
Repetition Rate
Design Value
160 MeV
10 mA
135 pC
<300 fsec
10 mm mrad
30 keV deg
75 MHz

41. Summary
Have introduced some properties of the dynamic electromagnetic field
Have introduced some of the most important ideas in accelerator design.
Have shown the large accelerators at Jefferson Lab: CEBAF and the FEL