# Presentation: 004096

## The Beam-Based Adaptive Alignment of the Focusing Elements of Linear Collider.

**The Beam-Based Adaptive Alignment ****of the Focusing Elements ****of Linear Collider.**

- Presented by
- V.Alexandrov
*Branch of the Institute of Nuclear Physics,*
*Protvino, Russia.*

## General view of the FFTB facility

**(SLAC, Stanford, USA)**

| Nominal beam energy | 46.6 | GeV |
| --- | --- | --- |
| Invariant emittance |  2 · 10-6 | m · rad |
| Beam population | 6.5 · 109 | e+ per pulse |
| Vertical beam size at focal point | 50  70 | nm |

**The designed parameters**

## Location of the FFTB at the end of the SLAC 50-GeV linac

- The FFTB contains five optical sections.
- One section that controls the launch of the beam into the FFTB.
-  Two sections that contain sextupole magnets allow the chromaticity of the lattice to be tuned separately in the horizontal and vertical planes.
- Geometric aberrations are controlled with pairs of sextupoles placed at points of equal dispersion.
- The lattice includes a “P-exchanger” to match the optics from one chromatic correction section to the other. This section contains an intermediate focal point at which the vertical beam height is reduced to 1 micron.

**Location of the FFTB at the end of the SLAC 50-GeV linac**

## The FFTB beam line contains:

**The “standard” quadrupole magnet**

-  7 discrete dipole,
-  28 “standard” quadrupole,
-  3 “final” quadrupole,
-  4 sextupole
- magnetic elements.

## ~250 mm   ( 10”  )

## The BPM resolution: ~ 1 mkm

**Each of the FFTB quads has a BPM and mover, what makes this facility very suitable for the Adaptive Alignment testing.**

- The mover’s step:      ~ 0.3 mkm

## The main principle of the method

**The main principle of the method**

**The Adaptive Alignment is a “local” method**.
- The data from the BPMs of only 3 neighboring quads are using to determine the necessary shifting of the quad.

- Where:    Xi – quad displacement relative to reference line;
*                    **a**i* – beam position relative to quad’s center (BPM reading);

- The position of the quad number* i *relative to it neighbors can be determined by simple formulas:

## Adaptive Alignment is an iterative process. 

- The suggested shifts for each quad should be calculated by above formula in each iteration.

- Where:
- dE/E - beam energy spread,
*a**i* - data from BPM of the quad number i;
- L1 - distance to the previous quad;
- L2 - distance to the next quad;
*l**i**    *- length of the quad number i;
- Ki  - reverse focusing distance of the quad with number i;
- Bi  - coefficient, which takes into account the differences
-        of the real optics from the thin lens approximation.

- Solving the previous equations one can get the base formula of the Adaptive Alignment:

## The simple example.(Computer simulation)

- The single quad is displaced on 50 mkm

- The necessary  shifting, calculated by the Adaptive Alignment method

- New quads positions after the 1-st iteration

- Quads positions after 25 iterations
- (in enlarged scale)

- Suggested shifts  after 25 iterations
- (in very enlarged scale)

## The more complex case.

- All quads  are displaced randomly with rms 50 mkm

- The necessary  shifting, calculated by the Adaptive Alignment method

- New quads positions after the 10 iterations

## Quads positions after 20 and 50 iterations

## The decreasing of the beam oscillation during the Adaptive Alignment (Computer simulation)

- The initial conditions:
- 24 quads are displaced randomly with  = 50 mkm.

## The testing of the method on the Stanford Linear Collider, (SLAC , USA)

- Usual beam oscillations

- The necessary  shiftings, calculated by the Adaptive Alignment method

- The beam is deflected forcedly at the entrance of FFTB line

- The necessary  shiftings are the same as for the undeflected beam

**The Adaptive Alignment method is depends on the real quads displacements only, not  on the beam oscillations!**

## The Adaptive Alignment in action.

- Vertical component of the beam oscillations (upper part of the picture)
- and suggested shifts for quads (lower part of the picture)
- _before the Adaptive Alignment procedure_.

**The Adaptive Alignment in action.**

## Vertical component of the beam oscillations (upper part of the picture)

- and suggested shifts for quads (lower part of the picture)
- _after 7 iterations of  the Adaptive Alignment procedure._

## Conclusion

**It was experimentally confirmed that the method of Adaptive Alignment works enough fast and properly and can be applied to compensate any sharp or smooth technical displacements of quads as well as the seismic vibrations of the ground **_**right during the operation of the Linac.**_