1. The Strong RF Focusing:
a possible approach to get short bunches at the IP
A. Gallo, with P. Raimondi and M.Zobov

2. SUMMARY: Introduction: the need for short bunches at the IP;
A. Gallo, The Strong RF Focusing: a possible approach to get short bunches at the IP
SUMMARY:
Introduction: the need for short bunches at the IP;
The strong RF focusing concept;
Equilibrium energy spread in a strong RF focused ring;
Energy acceptance in a strong RF focused ring;
Bunch lengthening and m-wave regime: preliminary considerations and simulations;
Choice of the optimal working point for a super F-factory design based on the strong RF focusing concept

3. A. Gallo, The Strong RF Focusing: a possible approach to get short bunches at the IP

4. A. Gallo, The Strong RF Focusing: a possible approach to get short bunches at the IP
Hour-glass effect
by*
Squeezing the vertical dimensions by reducing the vertical b-function is effective only if the bunch length is also reduced to about the b* value.
Bunch length

5. A. Gallo, The Strong RF Focusing: a possible approach to get short bunches at the IP

6. A. Gallo, The Strong RF Focusing: a possible approach to get short bunches at the IP

7. A. Gallo, The Strong RF Focusing: a possible approach to get short bunches at the IP

8. Longitudinal Lattice Model
A. Gallo, The Strong RF Focusing: a possible approach to get short bunches at the IP
Longitudinal Lattice Model
Drift Space
RF Cavity = long. thin lens

9. A. Gallo, The Strong RF Focusing: a possible approach to get short bunches at the IP

10. A. Gallo, The Strong RF Focusing: a possible approach to get short bunches at the IP

11. A. Gallo, The Strong RF Focusing: a possible approach to get short bunches at the IP

12. A. Gallo, The Strong RF Focusing: a possible approach to get short bunches at the IP

13. A. Gallo, The Strong RF Focusing: a possible approach to get short bunches at the IP

14. A. Gallo, The Strong RF Focusing: a possible approach to get short bunches at the IP

15. A. Gallo, The Strong RF Focusing: a possible approach to get short bunches at the IP

16. A. Gallo, The Strong RF Focusing: a possible approach to get short bunches at the IP
DAFNE rms
longitudinal
phase space
DE/E
DE/E
DAFNE
separatrix

17. A. Gallo, The Strong RF Focusing: a possible approach to get short bunches at the IP
DE/E

18. A. Gallo, The Strong RF Focusing: a possible approach to get short bunches at the IP

19. A. Gallo, The Strong RF Focusing: a possible approach to get short bunches at the IP

20. A. Gallo, The Strong RF Focusing: a possible approach to get short bunches at the IP
DE/E
DE/E
z[m]
z[m]
z[m]
z[m]

21. A. Gallo, The Strong RF Focusing: a possible approach to get short bunches at the IP
DE/E
z[m]
z[m]

22. Bunch length Centroid position
A. Gallo, The Strong RF Focusing: a possible approach to get short bunches at the IP
Bunch length
Centroid position

23. A. Gallo, The Strong RF Focusing: a possible approach to get short bunches at the IP

24. A. Gallo, The Strong RF Focusing: a possible approach to get short bunches at the IP
WORKING POINT OPTIMIZATION FOR A SUPER F-FACTORY DESIGN BASED ON THE STRONG RF FOCUSING
The Working Point of a strongly RF focused ring consists in a set of values for the following fundamental parameters to obtain the required bunch length sz at the IP :

25. 1. One turn synchrotron phase advance
A. Gallo, The Strong RF Focusing: a possible approach to get short bunches at the IP
1. One turn synchrotron phase advance
Once the values of the bunch lengths at the IP and RF have been chosen, the one-turn synchrotron phase advance is automatically defined.
To get sz(RF)  12 mm, the following values of synchrotron phase advance are required:

26. 2. Bunch energy spread in the strong RF focusing regime
A. Gallo, The Strong RF Focusing: a possible approach to get short bunches at the IP
2. Bunch energy spread in the strong RF focusing regime
The bunch energy spread rapidly grows with the phase advance and its maximum acceptable value is limited by:
The F-resonance width;
The machine energy acceptance (quantum lifetime)
To avoid F production degradation:
sE/E  1.4 ‰

27. 3. One turn normalized path elongation R56(L)=acL
A. Gallo, The Strong RF Focusing: a possible approach to get short bunches at the IP
3. One turn normalized path elongation R56(L)=acL
The expression giving the bunch length at the IP can be conveniently written as:
that immediately leads to:
Since the values of both sz(RF) and sE/E do not depend much on the IP bunch length goal, the optimal one-turn path elongation is almost independent on the goal itself.

28. 4. Bunch “natural”energy spread ( “weak” focusing regime, m<<1)
A. Gallo, The Strong RF Focusing: a possible approach to get short bunches at the IP
4. Bunch “natural”energy spread ( “weak” focusing regime, m<<1)
The bunch energy spread in the strong RF focusing regime is related to the natural value according to:
smooth case, |r|=kost. and R56 linearly increasing in the arcs
with
The ring natural energy spread is not much a flexible parameter, varying in the 0.40.5 ‰ range for different lattice design at the F energy. We assume:

29. 4. Bunch “natural”energy spread ( cnt’d)
A. Gallo, The Strong RF Focusing: a possible approach to get short bunches at the IP
4. Bunch “natural”energy spread ( cnt’d)
To keep the energy spread growth at the desired values a proper lattice design is needed. To reduce the value of the A function with respect to the smooth case, it is convenient to concentrate more the synchrotron emission in the low bl regions of the ring (near the IP), and vice-versa to increase it (more emission near the RF).
For example the curvature radius of the bendings in half of the ring on the RF side can be changed by a factor k. The A value varies as shown.

30. 5-6. RF Voltage and Wavelength
A. Gallo, The Strong RF Focusing: a possible approach to get short bunches at the IP
5-6. RF Voltage and Wavelength
Once the synchrotron phase advance m and the normalized path elongation acL have been defined, the ratio between the RF voltage and wavelength is fixed by the relation:
Short wavelengths (high frequencies) require lower voltages, but reduce the energy acceptance. Therefore there is a minimum acceptable wavelength value corresponding to the minimum acceptable energy acceptance.
If an additional harmonic RF system is used, the total gradient is given by two contributions, so that:

31. 5-6. RF Voltage and Wavelength (cnt’d)
A. Gallo, The Strong RF Focusing: a possible approach to get short bunches at the IP
5-6. RF Voltage and Wavelength (cnt’d)
Since acL is almost equal in the three cases, the required voltages and the resulting acceptances are similar too. To have at least 1% of acceptance at the IP position, RF frequencies higher than 500 MHz can not be used unless an extra gradient is provided by an harmonic RF voltage to restore the proper synchrotron phase advance.

32. A. Gallo, The Strong RF Focusing: a possible approach to get short bunches at the IP
Summary Table

33. A possible candidate cavity
A. Gallo, The Strong RF Focusing: a possible approach to get short bunches at the IP
A possible candidate cavity
Tested beyond 2.5 MV/module
Operated in high beam loading
Length ≈ 2.2 m /module

34. A. Gallo, The Strong RF Focusing: a possible approach to get short bunches at the IP
CONCLUSIONS:
The strong RF focusing concept has been illustrated and analyzed by means of the linear transfer matrix formalism;
Longitudinal optical functions have been derived, showing that the bunch length varies along the ring and may be minimized at the IP;
The longitudinal emittance and energy spread of the bunch equilibrium distribution, whose analytical expressions have been validated by comparison with results of multiparticle tracking simulations, diverge as the phase advance approaches 180°;
The energy acceptance is no longer an invariant. It is a function of the azimuth and assumes its maximum value in the longitudinal waist (IP)
To avoid bunch lengthening and µ-wave instability, the location of the impedance is the crucial point. Good results can be obtained if the ring wake is almost completely concentred near the RF cavity, where the bunch is longest.

35. A. Gallo, The Strong RF Focusing: a possible approach to get short bunches at the IP
CONCLUSIONS (cnt’d):
There are no many degrees of freedom in the choice of the WP parameters;
The “wiggling machine” (a zero-order reference design presented in this workshop) with small modifications can already provide IP bunch length down to 2 mm;
RF frequencies higher than 500 MHz are not suitable since a too small RF acceptance would result (unless harmonic cavities in the lengthening regime are used);
23 mm seems a reasonable goal, but 1 mm requires exotic lattices. Many beam physics aspects remain to be seriously studied (especially for 1 mm goal)

36. A. Gallo, The Strong RF Focusing: a possible approach to get short bunches at the IP
CONCLUSIONS (final):
IS SOME ACCELERATOR GROUP WILLING OF MAKING A STRONG RF FOCUSING EXPERIMENT ON ITS MACHINE ?