# Presentation: 486680

## ALS specific assumptions and their justification for top-off radiation safety tracking studies

**Christoph Steier**
**Advanced Light Source Accelerator Physics Group**
**Accelerator and Fusion Research Division**
**April 26, 2007**

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## Contents

**Field modeling**
**Fault scenarios / error probabilities**
**Field ranges**
**Tuning/missetting/feedback**
**Power supply faults**
**Vertically off-center**
**Shorts**
**Apertures and tolerances**

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## Field Profile Model Used in Tracking

**Use full vertical magnetic fields from FEA**
**Nominal case**
**Single pole short**
**Both vertically on and off-axis**
**Used different approaches for main tracking code (Hiroshi Nishimura) and for validation code (Weishi Wan) – see next slide**
**Validation code used to track full inverse beamline (including off-energy), but not to do full field+aperture parameter scans**

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## Tracking Codes

**Reference code (see Hiroshi’s talk):**
**1-d fields B****y****(x) in bends, quadrupoles, sextupoles, correctors**
**Spline interpolation in all FEA fields**
**Symplectic integrator**
**Bends and Quads modeled as thick elements with 50-100 slices (longitudinally hard edge)**
**Sextupoles and correctors are modeled as thin elements**
**Superbends are modeled using 2-d fields B****y**** (x, s)**
**Validation code:**
**2-d fields B****y**** (x, s) in all bending magnets**
**Spline interpolation in all FEA fields**
**Quadrupoles and sextupoles are modeled as thick elements with 1-d field B****y**** (x) – longitudinally hard edge**
**7****th**** order Runge-Kutta integrator**
**Tracking in both codes is vertically on-axis**
**Include effect of vertical offsets and skew quadrupoles by increasing horizontal kick scan ranges**
**Differences between both codes were very small – few % of corrector scan range**

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## Error Probability

**High (Daily events)**
**Orbit Feedback / Feedforward**
**Quadrupole Feedforward**
**Insertion Device Gap Motion**
**Medium (Several times per year)**
**Human Missetting**
**System Failure**
**Power Supply**
**Water System**
**Controls Crate**
**Feedforward System**
**Low (About once in the lifetime of the facility)**
**Shorts in magnets**

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## Combining Events

**Simulate all possible combinations of High and Medium probability events**
**Simulate all possible combinations of High, all Medium (except shunt failure) and any one Low probability event**
**This allows lattice independence of the argument (within the range of current interlocks – range for bend short is determined by studying large family of possible lattices)**

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## Arc Sector

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## High and Medium Probability Events

| Parameter | PS / tuning | Shunt | Girder Water and Cont. Crate | Skew Quadupoles | FF and FB Systems  | Vertical Offset | Total |
| --- | --- | --- | --- | --- | --- | --- | --- |
| 1 QFA | +/-1% 
(current interlocked) | -5% | +/-1% (current interlocked) | NA | NA | +6.2% | 94% to 107.2%  of
 knom=2.954353 m-2  ** |
| QDA | 0 to 174% 
(fixed polarity) | NA | 0 to 174% (fixed polarity | NA | NA | +6.2% | 0 to 180.2%  of
 knom= -1.779475 m-2 |
| QF
 | 0 to 138% 
(fixed polarity) | NA | 0 to 138% (fixed polarity) | NA | 0 to 138% (fixed polarity) | +6.2% | 0 to 144.2%  of
 knom= 2.237111 m-2  ** |
| QD | 0 to 123% 
(fixed polarity) | NA | 0 to 123% (fixed polarity | NA | 0 to 123% (fixed polarity) | +6.2% | 0 to 129.2%   of
knom= -2.511045 m-2  ** |
| SF | 50 to 106% 
(current interlocked) | NA | 50 to 106% (current interlocked) | NA | NA | +6% | 50 to 112%  of
 Lknom=16.0 m-2 |
| SD | 50 to 139% 
(current interlocked) | NA | 50 to 139% (current interlocked) | NA | NA | +6% | 50 to 145%  of
 Lknom=12.0 m-2 |
| Bend | +/-0.5% 
(current interlocked) | NA | +/-0.5% (current interlocked) | NA | NA | 0% | +/- 0.5% |
| S-Bend | +/-0.5% 
(current interlocked) | NA | +/-0.5% (current interlocked) | NA | NA | 0% | +/- 0.5% |
| SF Correctors | +/-2.5 mrad | NA | +/-2.5 mrad
 | +/-0.4 mrad
 | NA | +3.8 mrad
(Sext Offset) | -2.9 mrad to +6.7 mrad |
| SD
Correctors | +/-2.5 mrad | NA | +/-2.5 mrad
 | +/-0.4 mrad | NA
 | -3.8 mrad (Sext Offset) | -6.7 mrad to +2.9 mrad |
| Standard
Correctors | +/-2.5 mrad | NA | +/-2.5 mrad | NA | +/- 0.25 mrad | 0% | -2.5 mrad to +2.5 mrad |

**High and Medium Probability Events**

- ** Nominal values are slightly different for “superbend” cells.

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## General Guidelines

**Power supplies/Tuning:**
**Assume full power supply range unless interlocked both for faults and tuning/mis-setting; fixed polarity**
**Shunt (QFA only):**
**Fuses and cables prevent higher currents than 5%**
**Controls Crate Failures and flowmeter trips:**
**Also assumed full PS range (unless interlocked)**
**Skew Quadrupoles:**
**Consider maximum horizontal kick for maximum vertical offset – incorporate into collocated corrector range**
**Feed-forward and feedback systems:**
**Only act on limited number of magnets (48 quadrupoles) and can use limited corrector range (10%)**
**Vertical offset and shorts – see following slides**
**We added nearly all ranges (except where interlocked)**
**Conservative assumption not making use of low probability of some faults – Reason is that we want to be lattice independent, i.e. we consider mis-settings not as low probability fault but routine occurrence**

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## Accounting for a vertical offset in a quadrupole

**Accounting for a vertical offset in a quadrupole**

**For such an offset, the upper limit for the quad scanning range must be increased by ~ + 6.2 % **

**The effect can be accounted by increasing the scanning range of the quadrupole strength**

**At the ALS, the maximum vertical offset can be 0.5 cm because of the anti-chamber slot in the vacuum chamber **

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## Accounting for a vertical offset in a sextupole

**Accounting for a vertical offset in a sextupole**

**For a 0.5 cm offset, the upper limit for the sextupole scanning range must be increased by ~ + 6.0 % **

**The increasing effect at the poles can be accounted by increasing the scanning range of the sextupole strength**

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## Accounting for a vertical offset in a sextupole

**The increasing By field at x=0 can be accounted by increasing the scanning range of the horizontal corrector included in the sextupole magnet (hybrid element).**

**At x = 0 and y = +/- 0.5 cm the maximum By ~ 133 Gauss (6000 A Turns), which integrated for 0.2 m magnet length at 1.9 GeV gives a kick of ~ 0.42 mrad.**

**However, vacuum chamber height at x = 0 is +/- 2 cm. Conservatively, the maximum vertical offset that a particle that can have and still propagate without hitting the chamber is |y| ~ 1.5 cm. In this situation the maximum extra kick is ~ 3.8 mrad.  The scanning range for the correctors is increased for the same amount (unipolar!)**

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## High and Medium Probability Events

| Parameter | PS / tuning | Shunt | Girder Water and Cont. Crate | Skew Quadupoles | FF and FB Systems  | Vertical Offset | Total |
| --- | --- | --- | --- | --- | --- | --- | --- |
| 1 QFA | +/-1% 
(current interlocked) | -5% | +/-1% (current interlocked) | NA | NA | +6.2% | 94% to 107.2%  of
 knom=2.954353 m-2  ** |
| QDA | 0 to 174% 
(fixed polarity) | NA | 0 to 174% (fixed polarity | NA | NA | +6.2% | 0 to 180.2%  of
 knom= -1.779475 m-2 |
| QF
 | 0 to 138% 
(fixed polarity) | NA | 0 to 138% (fixed polarity) | NA | 0 to 138% (fixed polarity) | +6.2% | 0 to 144.2%  of
 knom= 2.237111 m-2  ** |
| QD | 0 to 123% 
(fixed polarity) | NA | 0 to 123% (fixed polarity | NA | 0 to 123% (fixed polarity) | +6.2% | 0 to 129.2%   of
knom= -2.511045 m-2  ** |
| SF | 50 to 106% 
(current interlocked) | NA | 50 to 106% (current interlocked) | NA | NA | +6% | 50 to 112%  of
 Lknom=16.0 m-2 |
| SD | 50 to 139% 
(current interlocked) | NA | 50 to 139% (current interlocked) | NA | NA | +6% | 50 to 145%  of
 Lknom=12.0 m-2 |
| Bend | +/-0.5% 
(current interlocked) | NA | +/-0.5% (current interlocked) | NA | NA | 0% | +/- 0.5% |
| S-Bend | +/-0.5% 
(current interlocked) | NA | +/-0.5% (current interlocked) | NA | NA | 0% | +/- 0.5% |
| SF Correctors | +/-2.5 mrad | NA | +/-2.5 mrad
 | +/-0.4 mrad
 | NA | +3.8 mrad
(Sext Offset) | -2.9 mrad to +6.7 mrad |
| SD
Correctors | +/-2.5 mrad | NA | +/-2.5 mrad
 | +/-0.4 mrad | NA
 | -3.8 mrad (Sext Offset) | -6.7 mrad to +2.9 mrad |
| Standard
Correctors | +/-2.5 mrad | NA | +/-2.5 mrad | NA | +/- 0.25 mrad | 0% | -2.5 mrad to +2.5 mrad |

**High and Medium Probability Events**

- ** Nominal values are slightly different for “superbend” cells.

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## Combining with Shorts, Quenches

**Replace field profile in shorted/quenched element**
**In dipole a single pole short is identical to strength error**
**Use previous range table for other faults except:**
**exclude simultaneous shunt faults and shorts**
**Consider single pole shorts only**
**Each QFA, QDA, QF, QD **
**Right 50% and 100% short**
**Left 50% and 100% short**
**Each Bend, Superbend **
**0 to -5%****	****-> stored beam condition**
**Each SF, SD **
**Right 50% and 100% short**
**Left 50% and 100% short**
**Top 50% and 100% short**

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## Single pole shorts

**Protective lexan covers over all cable connections at magnet**
**Also true for small power supplies**
**Connections are inside big power supplies**
**All high power cables between magnets are enclosed in cable trays**
**Wires on magnets are spatially well separated for different poles**
**Only close contact is for wires on one pole**

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## Range for Bend Magnet Short/Quench

**Dipole short or quench of Superbends is simulated as scaling error of dipole (iron yoke closes field lines)**
**Vacuum chamber cut off frequency is about 2 Hz, i.e. much slower than ms response time of stored beam interlock**
**Range of magnet strength determined by tracking simulations, taking credit for stored beam interlock**
**Tracking simulations were carried out for lattices that have been used or are envisioned to be used (about 10); low emittance lattices had limits < 4% - use 5 % in tracking.**
**Will complete study with larger subset of lattices – horiz. tune from 12 – 24 (result can then be claimed to be lattice independent)**
**Bend magnet strength is reduced in small steps, orbit feedback is simulated until it stops when a single feedback corrector magnet reaches its 0.25 mrad strength limit**
**Bend magnet strength limit  =  no stable orbit found**

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## Accounting for a quadrupole short

**Accounting for a quadrupole short**

- Shorts in poles 2 or 3 have the same By profile along x for y = 0 (see figure).
- Shorts in poles 1 or 4 have the same By profile along x for y = 0 but horizontally flipped respect to the poles 2 and 3 cases.
- Back-tracking with the QFA field profile with 50% and 100 % shorts in one pole are performed for both the horizontally flipped cases (4 cases total)

**‘****Total’ short of  a quadrupole is not allowed by the mechanical lay-out of the ALS magnets. Only single pole shorts will be considered.**

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## Accounting for a sextupole short

**‘****Total’ short of  a sextupole is not allowed by the mechanical lay-out of the ALS magnets. Only single pole shorts will be considered.**

- Shorts in poles 2 or 3 have the same By profile along x for y = 0 (see figure).
- Shorts in poles 5 or 6 have the same By profile along x for y = 0 but horizontally flipped with respect to the poles 2 and 3 cases.
- Back-tracking with the SD and SF field profiles with 50% and 100 % short in one pole are performed for the cases of poles 2 or 3 shorted and for the horizontal flipped cases of poles 5 or 6 shorted (4 cases total per sextupole).

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## Accounting for a sextupole short

**Accounting for a sextupole short**

- Shorts in poles 1 or 4 have the same By profile along x for y = 0 (see figure).
- The main effect for such a case is a horizontal dipole kick around x = 0.
- Model the same way as shorts on side poles: Back-tracking with the SD and SF field profiles with 50% and 100 % short in one pole are performed for the cases of poles 1 or 4 shorted (2 cases total per sextupole).

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## BTS Energy Filter: Lattice

**BTS Energy Filter: Lattice**

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## Spectrometer/Energy Filter

**“****Ben” magnet**

**Spectrometer/Energy Filter**

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## Energy Resolution for different aperture sizes

- Output data at SLIT3

**Energy Resolution for different aperture sizes**

| Momentum Acceptance | SLIT1 Total Aperture [mm] | SLIT2 Total Aperture [mm] | SLIT3 Total Aperture [mm] |
| --- | --- | --- | --- |
| +- 2 % | 6.0 | 6.0 | 6.0 |
| +- 3 % | 9.0 | 9.0 | 10.0 |
| +- 4 % | 12.0 | 12.0 | 15.0 |

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## Controls+Interlocks

-  3 SLITS (one already installed) + 5 Interlocks (2 quads, 1 hor. corrector, 2 dipoles)
-  Field Tolerance on dipole interlock is about 0.5%; less stringent on quads and corrector – will conduct full tolerance study before completing interlock design
-  Plan to include (existing) Hall probe in bend magnet into interlock
-  Field tolerances and required 3% energy limit are achievable

- Interlocked magnets

- Collimators

**Controls+Interlocks**

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## Controls - Fields

**Interlocks (all interlocks will be implemented redundantly and with fast response time – order ms):**
**Stored beam interlock (beam current)**
**Energy + energy matching interlock (SR Bend magnet + 3 Superbends + BTS B1 + small BTS magnets)**
**QFA current interlock (4 power supplies)**
**Sextupole current interlock (2 power supplies)**
**Currently do not see necessity for any field or voltage interlocks.**

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## Introduction – Aperture Tolerances

**One crucial assumption in top-off safety tracking are the tolerance for apertures**
**Only practical way to implement aperture errors in simulations is widening every aperture on both sides**
**This is a very conservative assumption! In reality aperture misalignments typically lead to smaller overall apertures for beam to pass through.**
**We used 2 mm tolerance on most apertures in storage ring and photon beamlines**
**Only exception are photon stops/absorbers for which we are using 5 mm**

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## ALS Storage Ring Apertures

**All elements in one arc are on one common girder**
**All storage ring apertures are in (or mounted to) one continuous vacuum chamber**
**Every magnet can be (and has been aligned) individually**
**All elements have high precision fiducial marks and laser tracker allows fast survey of many elements**

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## Beamline Apertures

**Plan to take credit for 2 apertures in each beamline:**
**Aperture plate in frontend (very close to storage ring exit flange)**
**Generally already fiducialized and aligned with sufficient accuracy and under configuration control (for equipment safety so far)**
**Photon beam pipe at safepoint 1m before shield wall**
**Needs to be surveyed, aligned if necessary, and put under configuration control**
**All aperture surveys can be easily tied into storage ring coordinate system using laser tracker (are in same tunnel)**

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## Storage Ring Aperture Tolerance Summary

| Tolerance Category | Method in determining differences from ideal  | Tolerance budgeted  |
| --- | --- | --- |
| Apertures relative to Vacuum Chamber  | Construction tolerance  | ±0.25 mm |
| Vacuum chamber relative to magnet centers  | Beam-based alignment; double check with initial direct chamber survey | ±1.0 mm |
| Magnet center to magnet fiducial  | Mechanical and magnetic fiducialization  | ±0.05 mm  |
| Magnet fiducials relative to each other  | Survey measurement and alignment | ±0.2 mm (one arc)  |
| Expected magnet fiducials motion until next survey 
 | Statistical analysis of past survey measurements  | ±0.1 mm (one arc); ±0.5 mm (arc to arc) |
| Additional: Transverse precision of vertical photon stop drive system | Construction + guidance tolerance | 2.4 mm |

**Sum of all tolerances within one arc (no quadrature, use worst case):**
**+/- 1.6 mm for internal storage ring vacuum chamber apertures**
**Used +/- 2 mm in simulations**
**+/- 4.0 mm for photon stops (synchrotron radiation absorbers)**
**Used +/- 5 mm in simulations**

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## VC Manufacturing Tolerances

**Mechanical Precision of manufacturing is 10 mils, 0.25 mm for vacuum chamber**

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## Beam Based Alignment

**Measures BPM center relative to quadrupole center**
**Combines effects of chamber misalignment, BPM button errors, cable differences, electronic offsets**
**Therefore statistical info only, not maximum ...**
**Chamber misalignment relative to magnets will generally be (small) fraction of total**
**Propose to verify once with chamber (3 flanges per chamber) survey, later track differences with beam based alignment.**

**Values have been very stable over the years, except if**
**Cables are exchanged**
**BPM electronics are exchanged**
**Magnets or vacuum chambers are aligned differentially**
**Only value larger than 1 mm is caused by electronics!**

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## Magnetic Center to Fiducials (Quads)

**Every quadrupole was measured individually **
**On CMM**
**pole tip relative to fiducials**
**With rotating coil**
**Magnetic center relative to pole tips**
**Rotating coil is aligned with special fixture (which also was CMM measured) relative to poles**
**Fiducials get corrected for geometry changes that shims applied during magnetic measurements cause**
**All information for every individual magnet is used in survey and alignment**
**Overall tolerance for this procedure was <0.05 mm**

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## Magnet Survey and Alignment

**Goal is 0.075 mm**
**Largest errors are longitudinally**
**Transverse errors are always < 0.2 mm**
**Drift much smaller than 0.1 mm per year (one arc)**
**Arc to arc drifts have been smaller than 0.5 mm / year**

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## Photon Stops/Absorbers

**Most manchining tolerances again 0.25 mm**
**Complication: Photon stops are moveable vertically for sublimation of TSPs (up+down)**
**Precision of transverse alignment (2.4 mm)**
**How to ensure they are in place (other than EPS)**
**Make EPS RSS grade**
**Or disable vertical motion**

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## Beamline Apertures

**Aperture plates are fiducialized and surveyed**
**Beamline aperture/beam pipe can be verified with circle center (laser tracker) with high precision relative to storage ring**
**Need to do:**
**Verify all drawings against hardware (mostly completed)**
**Resurvey all aperture plates **
**Survey all downstream apertures taken credit for (1 m point) with circle center**
- If necessary align – might require additional bellows, apertures
**Establish tight configuration control program**
- No aperture that has been taken credit for is allowed to be moved without review and permission

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

##  Beamline Aperture Tolerance Summary

| Relative measurement  | Method in determining differences from ideal  | Tolerance budgeted  |
| --- | --- | --- |
| Internal aperture relative to external fiducial markers or outer beam pipe circle | Manufacturing Tolerance + Fiducialization | ±0.5 mm |
| Outer fiducial markers to SR magnets  | Survey measurement / alignment | ±1.0 mm |
| Expected beamline fiducial motion until next survey | Worst case ground settlement between SR girder and beamline based on past surveys | ±0.5 mm |

**Sum of all tolerances (no quadrature, use worst case):**
**+/- 2.0 mm for beamline apertures – valid both for aperture plate and photon beampipe**
**Use +/- 2 mm in simulations**

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## Beamline Aperture Tolerance Justification

**Manufacturing tolerance of beam pipe at 1m point not as high as other components – 2 mils, 0.5 mm**
**Survey allows determination of component position to much better than 1 mm; 1 mm tolerance was chosen to minimize how many photon beam pipes at the 1m point we have to realign**
**0.5 mm relative alignment drift between annual surveys is based on worst case experience of surveys for elements not on the same girder**

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## 3% B1 Energy Filter

**3% B1 Energy Filter**

** ****Will need configuration control of apertures in BTS energy filter as well**
** ****Verification includes**
**initial survey**
**Beam based calibration of apertures**
**BTS energy aperture measurement with beam**
** ****Apertures will get locked in place in work on apertures is contingent on configuration control**

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## Required Aperture Tolerances

- Output data at SLIT3

**Required Aperture Tolerances**

| Momentum Acceptance | SLIT1 Total Aperture [mm] | SLIT2 Total Aperture [mm] | SLIT3 Total Aperture [mm] |
| --- | --- | --- | --- |
| +- 2 % | 6.0 | 6.0 | 6.0 |
| +- 3 % | 9.0 | 9.0 | 10.0 |
| +- 4 % | 12.0 | 12.0 | 15.0 |

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## Controls (Apertures)

**Now (6 months):**
**File documentation about every aperture taken credit for (already done for large number of beamlines)**
**Initial survey (storage ring magnets + vacuum chamber; beamline aperture plates + beam pipes)**
**Circle centers on storage ring flanges and photon beam pipes**
**Initial Beam Based Alignment**
**Realign any magnet or chamber that is outside tolerances (do not expect any, except for pipes at 1 m safe point)**
**Block photon stop vertical motion or make limit switches RSS grade**
**Annually:**
**Yearly resurvey of all components (except SR vacuum chamber)**
**Yearly beam based alignment**
**Yearly verification of energy passband of BTS filter**
**Ongoing:**
**Configuration control of any aperture inside shield wall**
**As part of design/construction/commissioning of every new beamline do all necessary steps listed above and perform full set of simulations -> verify at beamline readiness review**

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## Summary

**Used FEA field models – verified integrator and 1d field assumption**
**Use probability argument for combining different types of faults in tracking analysis**
**Developed a complete table of field tolerances under all error conditions**
**Included effects of vertical off-center trajectories and skew quadrupoles as well as single shorts**
**Established detailed aperture tolerance budget**
**Used 2 mm tolerance on most apertures, 5 mm on photon stops in tracking**
**Have a plan to verify all aperture locations and sizes and to keep them under configuration control**

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## Backup slides	

**Following Slides are backup only ...**

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007

## Sign of the sextupole kick for a vertical offset

**In a focusing sextupole for y = 0 and for every x, the field has the same direction of the field in the dipole magnet**

**This means that in a focusing sextupole the extra kick will be always positive, while for a defocusing sextupole it will be always negative.**

**In the presence of an offset |y|, the resulting dipole ‘kick’ field has always opposite sign respect to the main field in the sextupole.**

**In the reference frame:**

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- April 26, 2007

## Input Data

- p/p = +- 5%
- x’= +- 3 mrad	          106 Particles
- x = +- 3 cm	     Tracked by ELEGANT
- “Ben” Magnet OFF
- Q2.1 is at the nominal set
- Q2.2 is at the nominal set
- HCM3 is OFF
- B1 is at the nominal set

**Input Data**

- C. Steier, ALS specific assumptions+justifications

- April 26, 2007