1. Benchmarking MAD, SAD and PLACET Characterization and performance of the CLIC Beam Delivery System with MAD, SAD and PLACET
T. Asaka† and J. Resta López‡
†CERN, Geneve / SPring-8, Japan
‡CERN, Geneve / University of Valencia
I give the presentation of the characterization and performance of the CLIC Beam Delivery System with SAD, MAD and Placet.
ILC-European Regional Meeting at Royal Holloway, University of London from June, 2005

2. Introduction and Motivation
We study the performance of the CLIC Beam Delivery System (BDS) comparing the results of three tracking codes: MAD, SAD and PLACET.
The comparison of different codes is useful to assess the confidence in the simulation results.
The luminosity performance and energy bandwidth have been studied with three codes.
The higher order dispersion and the synchrotron radiation limit of the luminosity, further have been discussed.
For introduction and motivation in this study,
In order to study the characterization of CLIC Beam Delivery System, we use three codes, SAD, MAD and Placet.
The comparison of different codes is useful to assess the confidence in the simulation results.
In especially, the luminosity performance and energy bandwidth have been studied with three codes.
Moreover, the higher order dispersion and the synchrotron radiation limit of the luminosity have been discussed.

3. Outline » Overview of the main features of the considered codes
» SR implementation in each tracking codes
» CLIC BDS and simulation setup
» Comparison of the tracking results and luminosity performance
» Chromatic effects
» Energy bandwidth
» Luminosity reduction because of SR at the final quadrupole
» Summary and conclusions
The outline of this presentation is shown as follows.
Overview of the main features of the considered codes
Synchrotron radiation implementation in each tracking codes
CLIC Beam Delivery System and simulation setup
Comparison of the tracking results and luminosity performance
Chromatic effects
Energy bandwidth
Luminosity reduction because of synchrotron radiation at the final quadrupole
Summary and conclusions

4. Tracking codes • MAD: using transport formalism (up order two).
• PLACET: originally conceived for linac simulations. It has been upgraded for Linac + BDS.
• SAD: 6D full-symplectic tracking Also envelope formalism.
I explain the tracking codes first.
Mad is using transport formalism up order two.
Placet is originally conceived for linac simulations.
It has been upgraded for linac and Beam Delivery System.
Sad is 6 dimensional full symplectic tracking.
And it also is using envelope formalism.
You can see the detail explain in each codes on the Website.

5. Tracking codes: SR implementation
• MAD:
To correct for energy losses due to photon emission, the beam is artificially re-accelerated after each element: MATRIX,KICK(6)=#.
• PLACET:
PLACET can simulate beam re-acceleration and magnet rescaling.
• SAD:
In our lattice of the CLIC BDS with SAD the re-acceleration after every bending magnet is not included!
Synchrotron radiation implementation in each codes is different.
To correct for energy losses due to photon emission, the beam artificially re-accelerated after each element.
Placet implements the Monte Carlo generator for synchrotron radiation.
Placet can simulate beam re-acceleration and magnet re-scaling.

6. CLIC BDS and simulation setup
entrance bx m ax by m ay IP
b*x
7 mm
a*x
b*y
90 mm
a*y
The optics lattice for the CLIC Beam Delivery System is shown in here.
This optics is based on a compact final focus system.
This is a Raimondi-like compact design.
CLIC Beam Delivery System has 85 qudrupoles, 24 sextupoles and two octuples.
This lattice has been matched to the twiss parameters at the entrance and at the interaction point of the CLIC Beam Delivery System.
This optics is based on a compact final focus system, Raimondi-like compact design.
CLIC BDS has 60 quadrupoles, 11 sextupoles and two octupoles.
This lattice has been matched to the twiss parameters at the entrance and at the IP.

7. Beam profile at IP An example of the beam profile at the IP
A distribution of particles and 1% full width energy spread for a flat square energy distribution has been tracked.
The beam sizes have been calculated taking the size of the beam core by means of gaussian fit.
A distribution of particles and 1 % full width energy spread for a flat square energy distribution has been tracked.
This plots shows an example of the beam transversal profile at the interaction point.
The beam sizes have been calculated taking the size of of the beam core by means of gaussian fit.

8. Comparison of the tracking results
[nm]
MAD
PLACET
SAD
Std dev x
69.6
84.0
84.8 sx
47.3
48.0
Std dev y
1.11
1.27
1.28 sy
0.65
When the synchrotron radiation is switch off, the result from the three codes for the core beam size is very similar or same.
With the synchrotron radiation, we find a discrepancy for the vertical beam size with SAD up 14% from the others two codes, and discrepancies of about 15% for the horizontal standard deviation.
These discrepancies are considered the compensation for energy losses due to photon emission is implemented in the CLIC BDS lattice with MAD and PLACET and missing in SAD.
w/o SR
Std dev x
70.1
77.6
82.8 sx
57.5
57.1
Std dev y
1.96
2.19
2.63 sy
0.73
0.85
This table summarizes the results for the beam size at the interaction point as given by MAD, Placet and SAD.
When the synchrotron radiation is switch off, the result from the three codes for the core beam size is very similar or same.
With synchrotron radiation, we find a discrepancy for the vertical beam size with SAD up 14% from the others two codes, and discrepancies of about 15% for the horizontal standard deviation.
These discrepancies are considered the compensation for energy losses due to photon emission is implemented in the Beam Delivery System lattice with MAD and Placet and missing in SAD.
with SR

9. IP phase space and luminosity
The values of the luminosity from the beam distribution have been computed with GuineaPig.
w/o SR
with SR
[ x 1034
cm-2s-1 ]
MAD
PLACET
SAD
L w/o SR
10.714
11.655
11.305
L w SR
7.441
8.214
7.171
These plots are sample of the phase space at the IP as given by PLACET for horizontal and vertical transverse plane.
Since the geometric aberrations generate to the long tail of the horizontal phase space, it is necessary to optimize the optics.
These plots are sample of the phase space at the interaction point as given by Placet for horizontal and vertical plane.
This side is beam distribution without synchrotron radiation in phase space.
And this side is with synchrotron radiation in phase space.
Since the geometric aberrations generate to the long tail of the horizontal phase space, it is necessary to optimize the optics.
The values of the luminosity from the beam distribution have been computed with Guniea Pig.
This table shows the values obtained for the luminosity without and with synchrotron radiation.

10. Particle per particle comparison w/o SR
XMAD - XSAD
XPLACET - XMAD
XPLACET - XSAD
rms: nm
rms: nm
rms: nm
YMAD - YSAD
YPLACET - YMAD
YPLACET - YSAD
rms: 8.412e-2 nm
rms: 8.701e-2 nm
rms: 9.639e-3 nm
We have calculated the difference of the horizontal and vertical particle position at the IP from the tracking results with the different codes as a function of the energy.
A strong correlation with the energy offset is found for cases between the MAD and other codes.
A strong correlation with the energy offset is found for cases between the MAD and other codes (SAD and PLACET).
For PLACET and SAD, a light or no correlation with energy offset is observed.

11. Chromatic effect
Chromatic aberrations study by means of tracking from matched initial ellipses at 1s for the transversal plane X (Figure below is a sample with PLACET)
Red line: center ellipse movement in phase space
We consider monochromatic particles distributions arranged to form ellipses in phase space.
The ellipses are tracked for different energies from the nominal energy.
Here we give the example for off-set energies 0.3% and 0.4%.
The center of ellipse at interaction point is determined by the Taylor map, this equation, where we consider terms only up to third order.
Taylor map up to third order dispersion gives a good description of the center ellipse transport in phase space for different energy smaller than -0.3%.
Taylor map up to third order dispersion gives a good description of the center ellipse transport in phase space for off-set energies d < -0.3%.

12. CLIC BDS energy bandwidth
Tracking with different energy spread for flat beams on energy
w/o SR
with SR
In order to obtain the energy bandwidth, the tracking was made with particles for different energy spreads.
Both case without and with synchrotron radiation have been considered.
This plots show the beam sizes as a function of the beam energy spread for the horizontal plane.
The results have been normalized to the value of the given by Placet 0% energy spread without synchrotron radiation.
Without synchrotron radiation there is good agreement between the three codes for energy spread on.
Because of the lattice for the CLIC Beam delivery System in MAD includes the aperture of the collimators, particle losses are observed with MAD from 0.9% energy spread on.
Without synchrotron radiation there is good agreement between the three codes for energy spread on.
Because of the lattice for the CLIC BDS in MAD includes the aperture of the collimators, particle losses are observed with MAD from 0.9% energy spread on.

13. CLIC BDS energy bandwidth
Tracking with different energy spread for flat beams on energy
w/o SR
with SR
Next, this plots show the beam size as function of the beam energy spread for the vertical plane.
Without synchrotron radiation, there is good agreement between the three codes for energy spread on.
But, if the synchrotron radiation is included, the value of the vertical sizes obtain from SAD are up to 14% higher than those from simulations with MAD and PLACET.
Without synchrotron radiation, there is good agreement between the three codes for energy spread on.
But, if the synchrotron radiation is included, the value of the vertical sizes obtain from SAD are up to 14% higher than those from simulations with MAD and PLACET.

14. Luminosity for energy bandwidth
The curves of the luminosity as function of energy spread show a tolerable bandwidth up to 1% energy spread.
At this energy spread we have a luminosity loss 30%.
Comparing the curves of the luminosity bandwidth with and without synchrotron radiation, it is possible to observe that the synchrotron radiation is a limitation factor for the luminosity more important than the energy spread.
The curves of the luminosity as function of energy spread show a tolerable bandwidth up to 1% energy spread. At this energy spread we have a luminosity loss 30%.
Comparing the curves of the luminosity bandwidth with and without synchrotron radiation, it is possible to observe that the SR is a limitation factor for the luminosity more important than the energy spread.

15. SR limit of the luminosity in final doublet
In order to find out the beam size increase due to the synchrotron radiation in the final quadrupole, that is Oide effect, we calculated the beam sizes for different value b*y at IP with three codes.
The luminosity has been calculated through the these simulation results.
For the fixed value of b*x, the calculation of the luminosity as a function of b*y shows the strong decrease at b*y less than 50 micron.
In order to find out the beam size increase due to the synchrotron radiation in the final quadrupole, that is Oide effect, we calculated the beam sizes for different value beta_y at the interaction point.
The luminosity has been calculated through these simulation results.
This plot shows luminosity as function of the beta_y at the interaction point.
The lines are the analytical calculation, and the plots are obtained by using the tracking results with three codes.
For the fixed value of beta_x, the calculation of the luminosity as a function of beta_y shows the strong decrease at beta_y less than 50 micron.
Line: Analytical calculation
Oide: Taking into account the horizontal motion inside final quadrupole
Irwin: Taking into account the horizontal and vertical motion inside final quadrupole

16. Summary and conclusions
» SAD, MAD and PLACET have been compared for particle tracking in the CLIC BDS.
» Good agreement for the luminosity results with the three codes MAD, PLACET and SAD without SR.
» Particle per particle comparison of the transverse position shows differences between MAD and other codes, depending on energy offset.
» We use for SAD SR routine that does not account for the beam energy losses.
This explain the discrepancies between SAD and the other codes when the SR is active.

17. Summary and conclusions
» The collimation system introduces higher order geometric and chromatic aberrations.
The geometric aberrations are very strong for off-set energies d < -0.3%.
The chromatic aberrations are important up to 3rd order.
» The beam sizes at IP and the luminosity have been calculated as function of the energy spread with three codes.
Comparing the curves of the luminosity bandwidth with and without SR, it is possible to observe that the SR is a more important limitation for the luminosity than the energy spread.
» The Oide effect or beam size increase due to SR in the final quarupole.
In the luminosity as function of b*y, we found a strong decrease at b*y < 50 mm.