1. Lecture 15
ACCELERATOR PHYSICS
MT 2004
E. J. N. Wilson

2. Recap of previous lecture - Electrons II
Synchrotron light sources (ESRF)
The cone of synchrotron radiation
The spectrum
The scale of things
Diffraction
Diffraction experiment (synch.rad)
A very complex molecule
Lithography in practice
Brightness (importance of small emittance)
Rate of emission of quanta
Energy damping
Behaviour of particle with energy defect
Quantum emission
Equilibrium

3. Lecture 15 - Electrons I I-contents
Synchrotron light sources (ESRF)
The cone of synchrotron radiation
The spectrum
The scale of things
Diffraction
Diffraction experiment (synch.rad)
A very complex molecule
Lithography in practice
Brightness (importance of small emittance)
Rate of emission of quanta
Energy damping
Behaviour of particle with energy defect
Quantum emission
Equilibrium

4. Synchrotron light sources (ESRF)
AC9.8.95_16(ESRF).pct

5. The cone of synchrotron radiation
When an electron is bent in a circle it radiates synchrotron “light” along a tangent in a narrow cone (opening angle = 1/g)

6. The spectrum Spectrum is broad and looks the same when normalized to
Every quantity is normalized to the frequency of a characteristic quantum which is proportional to

7. The scale of things UV Hard X Energy [GeV] Photon [keV] l [A] BESSY-I
0.8
0.64
19.4 UV
HELIOS
0.7
1.5
8.5
SRS
2.0
3.2
3.9
Hard X
ESRF
6.0
20.7
0.60
LEP
50.0
88.5
0.14

8. Diffraction

9. Diffraction experiment (synch.rad)
Diff-phot.pct
Diff-diag.pct

10. A very complex molecule
RNA Polymerase – the structure that enables the code for each protein to be used to make each protein

11. Lithography in practice
AC9.8.95_11(mask).pct

12. Brightness (importance of small emittance)
Brightness is measured in :
Wigglers and undulators enhance this!

13. Rate of emission of quanta
If every quanta had the characteristic value
And the power emitted is
Then the rate of emission would be:
When the average over the spectrum is properly integrated:

14. Energy damping
The first figure shows a normal undamped synchrotron motion
The particles on the upper half of their trajectory lose more energy than they gain again on the lower - a consequence of the fact that energy loss is proportional to the square of the energy -they spiral in.

15. Behaviour of particle with energy defect
We use our expression for the power emitted being careful to go back to equation 14 since after that we made the assumption the energy was that which followed the axis of the machine
For a particle with a defect
The rate of energy loss is
The growth rate will be the logarithmic derivative
Equation of spiral is
The emittance shrinks at twice this rate

16. Quantum emission Emission rate Average loss
Choose the axes to make phase space a circle
This is a random walk such that the change in radius will be
The area grows as the square of the amplitude
Being more careful with the averaging the exponential growth rate is:

17. Equilibrium Equate this to the emittance shrink rate:
Solve for an equilibrium amplitude using earlier results
The fluctuations are statistical and result in a Gaussian projected energy spread of :

18. Electrons II – Summary Synchrotron light sources (ESRF)
The cone of synchrotron radiation
The spectrum
The scale of things
Diffraction
Diffraction experiment (synch.rad)
A very complex molecule
Lithography in practice
Brightness (importance of small emittance)
Rate of emission of quanta
Energy damping
Behaviour of particle with energy defect
Quantum emission
Equilibrium