# Presentation: 193983

## ILC  MAIN  LINAC   SIMULATION

**KIRTI  RANJAN**
**Delhi University & Fermilab**
**&**
**NIKOLAY SOLYAK,   FRANCOIS OSTIGUY  **
**Fermilab**
**&  **** **
**SHEKHAR MISHRA**
** ****Fermilab**

## OVERVIEW

** ****Study ****single-bunch emittance dilution**** in Main Linac **
** ****Compare the emittance dilution performance of two different “****beam-based  steering****” algorithms :  ****“1:1” ****&**** “Dispersion Free Steering”**** under nominal conditions of static misalignments of the various beamline elements**
** ****Compare the ****sensitivity of the steering algorithms**** for conditions different from the nominal**
** ****Compare the ****different lattice configurations**** (with different Quad spacing)**

**Performed similar work for NLC**

** ****ILC Main Linac Simulation **
** ****Before Baseline Configuration Document (BCD)**
** ****Status till Snowmass,’05**** **
** ****After ILC BCD **
** ****Preliminary results for the ILC BCD curved Linac**
** ****Benchmarking among various codes**
** ****Summary / Plans**

## ILC MAIN LINAC

**   ****ILC Main linac will accelerate e****-****/e****+**** beam from ****~ 15 GeV ****→**** 250 GeV**** **
** ****Upgradeable to 500 GeV**
**  ****Two major design issues: **
** ****Energy : Efficient acceleration of the beams**
** ****Luminosity : Emittance preservation**
** ****Vertical plane would be more challenging:**
** ****Large aspect ratio (x:y) in both spot size and emittance **
** ****Primary sources of emittance dilution (single bunch):**
*** *****Transverse Wakefields: **
** ****Short Range : misaligned cavities or cryomodules**
** ****Dispersion from Misaligned Quads or Pitched cavities**
** ****XY-coupling from rotated Quads**
** ****Transverse Jitter **

- For High Luminosity
- high RF-beam conversion efficiency ***RF*
- high RF power *P**RF*
**small normalised vertical emittance ***********n,y***
- strong focusing at IP (small ***y* and hence _small_ ***z*)

## Before Baseline Configuration Document (BCD)

**Status till Snowmass,’05**

- (Acknowledgement to Peter Tenenbaum (SLAC))

##   SIMULATION: MATLAB + LIAR (MATLIAR)

-   LIAR (LInear Accelerator Research Code)
-  General tool to study beam dynamics
-  Simulate regions with accelerator structures
-  Includes wakefield, dispersive and chromatic emittance dilution
-  Includes diagnostic and correction devices, including BPMs, RF pickups, dipole correctors, magnet movers, beam-based feedbacks etc
-   MATLAB drives the whole package allowing fast  development of correction and feedback algorithms
-   CPU Intensive: Dedicated Processors for the purpose

## USColdLC MAIN LINAC

-   Linac Cryogenic system is divided into Cryomodules(CM), with **12 RF cavities / CM**
-  **1 Quad / 2CM** : Superconducting Quads in alternate CM, **330 Quads** (165F,165D)
-   Magnet Optics : FODO “constant beta” lattice, with **** phase advance of **60****0** in each plane
-   Each quad has a *Cavity style **BPM* and a *Vertical Corrector* magnet; horizontally focusing
-      quads also have a nearby *Horizontal Corrector* magnet.

**USColdLC MAIN LINAC**

-  Main Linac Parameters
-   ~**11.0 km** length
-    **9 Cell** cavities at **1.3 GHz**; Total cavities : **7920**
-   Loaded Gradient : **30 MV/m**
-   Injection energy = **5.0 GeV** &  Initial Energy spread = **2.5 %**
-   Extracted beam energy = **250 GeV** (500 GeV CM)

-  Beam Conditions
-   Bunch Charge: **2.0 x 10****10**** particles/bunch**
-   Bunch length = **300 ********m**
-   Normalized injection emittance:
- ******Y**** ****= ****20 nm-rad**

**12 “9-Cell Cavity” CryoModule**

**TESLA SC 9-Cell Cavity**

## USColdLC MAIN LINAC

| Tolerance | Vertical (y) plane |
| --- | --- |
| BPM Offset  w.r.t. Cryostat | 300 μm |
| Quad offset w.r.t. Cryostat | 300 μm |
| Quad Rotation w.r.t. Cryostat |   300 μrad |
| Cavity Offset w.r.t. Cryostat | 300 μm |
| Cryostat Offset w.r.t. Survey Line | 200 μm |
| Cavity Pitch w.r.t. Cryostat |   300 μrad |
| Cryostat Pitch w.r.t. Survey Line | 20 μrad |
| BPM Resolution | 1.0 μm |

**  ****BPM transverse position is fixed, and the BPM offset is w.r.t. Cryostat**
**  ****Only Single bunch used**
**  ****No Ground Motion and Feedback**
**  ****Steering is performed using Dipole Correctors**

**USColdLC MAIN LINAC**

***ab initio***** (Nominal) installation conditions**

**Normalized Emittance Dilution Budget **
- 		       **DR Exit    =>**  **ML Injection=> ML Exit  => IP **
**USColdLC:   **   Hor.**/**Vert (nm-rad):  **8000 / ****20** **=>    8800 / ****24**    **=> 9200 / ****34**** =>  9600 / ****40**

**10 nm**** (50%) Vertical emittance growth in main linac **

## ALIGNMENT & STEERING ALGORITHMS

-    Beam line elements are needed to be aligned with beam-based measurements
-   “Beam Based Alignments (BBA)” refer to the techniques which provide information on beamline elements using measurements with the beam
-   Quad strength variation
-   **“****One-to-One” Correction**
-   **Dispersion Free Steering**
-   Ballistic Alignment
-   Kick minimization method *and possibly others*....

- Considered here

- Estimate beam-to-quad offset

-  ***Quad Shunting:*** Measure beam kick vs. quad strength to determine BPM-to-Quad offset (routinely done)

-  In USColdLC, it was not assumed that all quads would be shunted
** ****Quads are Superconducting and shunting might take a very long time**
** ****No experimental basis for estimating the stability of the Magnetic center as a function of excitation current in SC magnets**
** ****In Launch region (1****st**** 7 Quads), we assume that offsets would be measured and **
**    ****corrected with greater accuracy (~30 ********m)**

## Beam based alignment - 1:1 Steering

-  Quad alignment – How to do?
** ****Find a set of corrector readings for which beam should pass through the exact center of every quad (zero the BPMs)**
** ****Use the correctors to steer the beam**

**  ****One-to-One alignment ****generates *****dispersion***** which contributes to emittance dilution and is sensitive to the BPM-to-Quad offsets**

**Beam based alignment - ****1:1 Steering**

- Solving the matrix equation:

- x is the vector containing the BPM measurements

- Θ is the vector containing the unknown kick angles

**m is the total number**
**of BPM measurements**

**n is the total number**
**correctors**

**Beam position at downstream BPM**

**corrector kick**

**MATRIX form**

**For equal no. of YCOR and BPM**

## Beam based alignment – Dispersion Free Steering

-      beamline **(proposed by ****Raubenheimer / Ruth, NIMA302, 191-208, 1991****)**
-   General principle:
** ****Measure dispersion (via mismatching the beam energy to the lattice)**
** ****Calculate correction needed to zero dispersion **
** ****Apply the correction **
-  **Successful in rings (LEP, PEP ) but less successful at SLC (Two-beam DFS achieved better results)*****  (Note: SLC varied magnet strengths (center motion?), others varied beam energy)***

**Beam based alignment – ****Dispersion Free Steering**

- Absolute orbit:

- Difference orbit:

- Constraint:

- (**2M********1**)

- (**2M********N**)

- (**N********1**)

- minimize the absolute orbit and the difference orbit simultaneously:

## STEERING ALGORITHM : ONE-to-ONE vs. DFS

**Read all Q-BPMs in a single pulse**
**Compute set of corrector readings and apply the correction**
**Constraint – minimize RMS of the BPM readings **
**Iterate few times before going to the next segment.**
**Performed for 100 Seeds**

**STEERING ALGORITHM : ONE-to-ONE vs. DFS**

**Divide linac into segments of ~40quads**
**Two orbits are measured**
**Vary energy by switching off cavities in front of a segment (no variation within segment)**
**Measure change in orbit (fit out incoming orbit change from RF switch-off)**
**Apply correction**
**Constraint – simultaneously minimize dispersion and RMS of the BPM readings (****weight ratio:****              )**
**Iterate twice before going to the next segment**
**Performed for 100 Seeds**

**DFS**

**1:1**

## BEAM BASED ALIGNMENT

-  **Launch Region (1****st**** seven BPMs) Steering (can not be aligned using DFS)**** **
** ****Emittance growth is very sensitive to the element alignment in this region, due to ****low beam energy**** and ****large energy spread**
** ****First, all RF cavities in the launch region are switched OFF to eliminate RF kicks from pitched cavities / cryostats**
** ****Beam is then transported through the Launch and BPM readings are extracted => estimation of Quad offsets w.r.t. survey Line**
**  ****Corrector settings are then computed which ideally would result in a straight trajectory of the beam through the launch region**
** ****The orbit after steering the corrector magnets constitutes a reference or “gold” orbit for the launch**
** ****The RF units are then restored and the orbit is re-steered to the Gold Orbit. (This cancels the effect of RF kicks in the launch region)**

## STEERING ALGORITHM : ONE-to-ONE vs. DFS

** ****Number of steering regions:             7**
**Overlap in steering regions:            0.1**
**Number iterations steering per region:  3**
**Number "front-end" BPMs:                7**
**   ****(used for launch region)****   **

**      ****DFS **
**      ****Number of DFS regions:                                18**
**      ****Overlap in DFS regions:                                0.5**
**      ****Number iterations DFS per region:                 2**
**      ****DFS Max relative energy change:                 0.2**
**      ****DFS Max absolute energy change [GeV]:      18**
**      ****DFS Endpoint for Region 1 Energy Change (Q#): 4**

**STEERING ALGORITHM : ONE-to-ONE vs. DFS**

## 

**Beta Function (m)**

** ****Lower mean emittance growth for DFS than One-to-One**
** ****Mean Growth under the Emittance dilution budget**

**No Jitter and No BNS energy spread!**

**FOR USColdLC NOMINAL CONDITIONS **

- Mean: **9.2 nm-rad **

**Emittance Dilution (nm)**

**Emittance Dilution (nm)**

**DFS**

**1:1**

- Mean: **6.9 nm **

- 90%: **13.1 nm**

- Mean: **471 nm**

- 90%: **941 nm**

****

****

**1:1**

**DFS**

**NO STEER**

**  ****Gradient : 30 MV/ m;  100 seeds**

**Projected Emittance Dilution = Emittance (Exit) – Emittance (Entrance)**

## FOR USColdLC NOMINAL CONDITIONS

**DFS**

| Tolerance | 1:1 | DFS |
| --- | --- | --- |
| Nominal | 470 | 6.9 |
| Wakes only | 1.9 | 1.9 |
| Dispersion only | 280 | 2.2 |
| Quad roll only | 2.1 | 2.1 |

**Average Normalized Emittance Dilution (nm)**

**Average Normalized Emittance Growth (nm) vs. s (m)**

**1:1**

** ****Wakes include only Cavity and CM offsets;   Dispersion includes Quad / BPM Offsets & Cavity / CM pitches**
** ****Nominal ****>Wakes+Dispersion+Quad roll (Why?– wakefields causing systematic errors ?)**

**Almost equal contributions**

## EFFECT OF QUAD OFFSETS / QUAD ROLLS VARIATION

**DFS**

** ****1:1**

**  ****Emittance dilution increases slowly with increase in Quad Offsets**
**  ****DFS: Just under the budget for 2x nominal values **
**  ****DFS: Emittance dilution increases more rapidly with increase in Quad Roll**
**  ****DFS: Goes Over the budget even for 1.5x nominal values**

** ****Keeping all other misalignments at Nominal Values and varied only the Quad offsets **

**DFS**

** ****1:1**

## EFFECT OF BPM OFFSETS / RESOLUTION VARIATION

**DFS**

** ****1:1**

**DFS**

** ****1:1**

**EFFECT OF *****BPM OFFSETS / RESOLUTION***** VARIATION**

** *****Advantage of DFS:***** Emittance dilution for 1:1 increases very sharply with BPM offsets **
**  ****DFS: Emittance dilution is almost independent of BPM offset**
**  ****DFS: Remains within the budget even for 5x nominal**
**  ****Emittance dilution for 1:1 is almost independent of the BPM resolution  **
**  ****DFS: Emittance dilution is sensitive to BPM resolution**
**  ****DFS: Goes Over the budget even for 5x nominal values**

## EFFECT OF STRUCTURE OFFSET / PITCH VARIATION

**DFS**

** ****1:1**

**  ****Emittance dilution for 1:1 is almost independent of the structure offset**
**  ****DFS: Emittance dilution grows slowly with structure offsets**
**  ****DFS: Goes Over the budget for 2.0x nominal values**
-  DFS: Emittance dilution is sensitive to Cavity pitch
-  DFS: Goes Over the budget even for 1.5x nominal values

**DFS**

** ****1:1**

## EFFECT OF CRYOMODULE OFFSET/ PITCH VARIATION

**DFS**

** ****1:1**

-   DFS and 1:1: Emittance dilution grows sharply with CM offset
-   DFS: Goes Over the budget even for 1.5x nominal values
-   DFS and 1:1: Emittance dilution is almost independent of the CM pitch
-   DFS: Remains within the budget for 3x nominal

**DFS**

** ****1:1**

## Effect of Including JITTER  

**Average Normalized Emittance Growth (nm) vs. s (m)**

**Quad Vibration**** **

**DFS**

**Beam–Beam + Quad Vibration**

**Beam – Beam**** **

## Dispersion Bumps

**It changes y-position**
**for structure or field**
** ****for y-corrector **

**Reads information **
**about vertical beam**
**size from wire monitor **
**at the end of linac **
**for a few times **

**Makes approximation**
**of data using parabola:**
**y=A (x**** ****- B) ****2 + C**

**Takes a minimal value of**
**vertical beam size which**
**corresponds to minimum**
**of parabola**

**Contributed by :N.Solyak + E. Shtarklev**

- Two y-correctors located 1800 apart in phase such that 1st one generates dispersion and the other one cancels it

- Beam size vs. corrector kicks

## Dispersion Bumps

**Two dispersion bumps applied for bad seed**

**Dispersion Bumps**

-   Inclusion of bumps can help in further minimizing the emittance dilution after steering, also important for bad seeds

**Contributed by :N.Solyak + E. Shtarklev**

- DFS only

- DFS + Dispersion bumps

**Average Normalized Emittance Growth (nm) vs. s (m)**

## QUAD CONFIGURATION

**Dispersion**

**Wakes**

**30 MV/m**
**TTF CM**
**8 Cavity / CM**

**Number of Quads (N****Q****)**

**Emittance dilution**

-  Projected emittance growth is dominated by dispersive sources
-  Large quad spacing seems to be an attractive choice (?)

**QUAD CONFIGURATION**

- 8 configurations with diff. quad spacing (from 1 Quad / 1CM  to 1 Quad / 8CM)
- Dispersion Case – Quad, BPM Offsets and Structure, CM Pitch
- Wake Case – Structure, CM offset, wakefields

**1:1**

- 1 Quad / CM

- 1 Quad / 6 CM

## EMITTANCE DILUTION – SOURCES

**1Q / 1CM;**** 36 segments**

**1 Q / 4 CM****; 9 segments**

**1Q / 2CM****; 18 segments**

**1 Q / 4 CM****; 13 segments**

## EMITTANCE DILUTION – SOURCES

**EMITTANCE DILUTION – SOURCES**

**1:1**

**DFS**

- DFS: 							             1Q/2CM is equilibrium optics with equal contribution from each source. Optics with larger quad spacing is wakefield dominated with the systematic wake-related contribution (Sum of all three contributions is smaller that the total calculated emittance growth).

**Wake**

**Dispersion**

**Dispersion**

## Status after

**Baseline Configuration Document (BCD)**

- Released at the Frascati GDE meeting in December, 2005

## ILC MAIN LINAC - BCD

**ILC MAIN LINAC - BCD**

- not to scale

**  ****TUNNEL -  ****“Until on-going beam dynamics simulations show otherwise, the *****linac will follow the curvature of the earth*****, unless a site-specific reason (cost driven) dictates otherwise.”**** **
** ****CAVITY -  ****“*****31.5 MV/m gradient****** *****and *****Q of 1×10******10****** *****would be achieved on average in a linac made with *****eight-cavity cryomodules*****.****”**
** **
** ****LATTICE –***** “Every fourth CM***** in the linac would include a cos(2*phi)-type *****quadrupole****** *****that also would contain horizontal and vertical corrector windings (this corresponds to a *****constant beta lattice with one quadrupole every 32 cavities*****). “**

## USColdLC vs. ILC BCD

**  ****Comparison of the  ****LASER STRAIGHT LINACs**** (ILC BCD vs. USColdLC)**
**  ****All nominal misalignments included;  No Jitter, No dispersion bumps; 100 seeds**

**A.) US Cold LC Lattice (1Q/24 cavity), TESLA wakes, E = 5 GeV, Espread = 125 MeV (2.5%)**
**B.) ILC BCD Lattice (1Q/32 cavity), TESLA wakes, E = 5 GeV, Espread = 125 MeV (2.5%)  **
**C.) ILC BCD Lattice (1Q/32 cavity), ILC wakes, E = 15 GeV, Espread = 150 MeV (1.0%)  **

|  | Mean dilution (nm) |  | 90% dilution (nm) |  |
| --- | --- | --- | --- | --- |
|  | 1:1                      DFS |  |       1:1                     DFS |  |
| USCold LC | 471 ± 38 | 6.9 ± 0.4 | 940 | 13.1 |
| ILC BCD ( 5 GeV) | 191 ± 16 | 8.9 ± 0.6 | 387 | 15.5 |
| ILC BCD (15 GeV) | 197 ± 17 | 5.7 ± 0.4 | 398 | 9.8 |

**Mean projected Normalized Emittance (nm) vs. Linac length (m)**

**1:1**

**DFS**

##   LIAR ADD-ONS

-  Earth curvature effect in simulation : can be done
-  using vertical S-bend magnets (requires significant work in LIAR particularly since it is meant originally for the laser-straight linacs)
-  by actually placing the beamline elements on  the earth curvature using offsets and pitch (some limitations as in LIAR Quads don’t have the pitch) –  Alexander Valishev + Nikolay Solyak
-  using an arbitrary “dispersion-free” geometrical kick (GKICK) which places beamline elements on the earth curvature by changing the reference trajectory
-  Didn’t exist in LIAR. Francois Ostiguy has helped in adding this feature.
** ****issue about the geometrical transformation - further checks are being carried out**
-  In LIAR, dispersion could not be used as initial condition and there was no provision for propagating it through the Linac
-  Francois has added this feature. The matched dispersion condition at the beginning of the linac can now be artificially introduced into the initial beam (w/o constructing any matching section)

## ILC BCD CURVED LINAC - SIMULATION

**  ****Length of CM w/o Quad  =  ****10.651 m****;  Length of CM w/  Quad  =  ****11.452 m**
** ****To place the beamline elements on the earth curvature, each of the CM is given two half kicks in y-direction using GKICK (one at the beginning and other at the end)**
**    ****ANGLE_CM =  L_CM / R_Earth / 2 =  ****0.8360 ********rad (or  0.8989 ********rad)**
**  ****Since YCORs are with the Quads (which are 1 / 4CM), so an equivalent kick is given to beam to launch it into the reference orbit set by earth curvature**
**    ****- (2 * ANGLE_CM_Quad + 6 * ANGLE_CM_NoQuad) =  ****-**** ****6.8139 ********rad**

- Linac

**8 CM**

**Quad package   = Quad, BPM, COR**

## ILC MAIN LINAC - BCD

**  ****Linac Cryogenic system is divided into CM, with ****8 RF cavities / CM**
** ****1 Quad / 4CM**** : Superconducting Quads in every fourth CM, **
**  ****FODO “constant beta” lattice, with phase advance of ****75****0**** / 60****0**** in x/y plane**
**  ****Each quad has a *****BPM***** and a *****Vertical & Horizontal Corrector***** magnet; **

**ILC MAIN LINAC - BCD**

-  Main Linac Parameters
**  ****~11.0 km**** length**
**   ****9 Cell cavities at 1.3 GHz; **
**  ****Loaded Gradient : ****31.5 MV/m**** **
**  ****Injection energy = ****15.0 GeV**** **
**  ****Initial Energy spread = ****1.07 %(~150MeV)**
**  ****Extracted beam energy = ****251.8 GeV**

-  Beam Conditions
**  ****Bunch Charge: ****2.0 x 10****10**** particles/bunch**
**  ****Bunch length = ****300 ********m**
**  ****Normalized injection emittance: ********Y**** ****= 20 nm-rad**

**Length (m) : 10417.20     **
**N_quad   :         240 **
**N_cavity  :       7680**
**N_bpms  :          241**
**N_Xcor    :         240 **
**N_Ycor    :         241**
**N_gkicks :       1920 **

## GKICK checks

-   GKICK provides the reference trajectory ( to incorporate earth curvature effect) so that all the beamline elements get placed on that reference.
-   YCOR launches the beam on to that reference trajectory

- Three cases are simulated
- A.) GKICK - OFF , YCOR - ON   => Terrible case
- B.) GKICK - ON ,   YCOR - OFF => Terrible case
- C.) GKICK - ON,    YCOR - ON   => Nominal case

****

****

****

**ILC BCD LATTICE**
**1****st**** 1000 meters**

## GKICK checks

**FULL ILC BCD LATTICE:  Measurements at the YCOR locations (matched dispersion)**

- ZOOM

- ZOOM

## ILC BCD Main Linac: Matched Lattice

**1****st**** 1600 m of  ILC  BCD  CURVED LATTICE: matched dispersion**

## ILC BCD: Curved Linac

** ****Matched initial beam conditions are used**

** ****Systematic**** offset of (maximum) ~40 ********m through the cavities  **
**      ****< **
**Expected 300 um RMS cavity and 200 um RMS CM alignments ****(Random)**** foreseen in ILC main Linac**** **

**Y-orbit only at YCOR locations (4****th**** CM)**

**FULL  Linac**

**Y-orbit (BPM at the centre of each CM)**

## ILC BCD: Curved vs. Straight Linac

**   ****Matched initial beam conditions are used ; 100 seeds; BPMs only at YCOR locations**
**   ****All nominal misalignments except that ****all errors in 1****st**** 25 CMs are reset to 0****; WAKES ON**

**1:1**

**DFS**

**CURVED**

**STRAIGHT**

- Mean: **11.9 nm**
- 90%: **16.3 nm**

- Mean: **2.7 nm**
- 90%: **4.7 nm**

- Mean: **132 nm**
- 90%: **229 nm**

- Mean: **143 nm**
- 90%:  **274 nm**

**1:1**

**DFS**

## ILC BCD CURVED: Matched vs. Unmatched

**  ****100 seeds; BPMs only at YCOR locations; WAKES ON**
**   ****All nominal misalignments except that all errors in 1****st**** 25 CMs are reset to zero**

**1:1**

**DFS**

**Mean projected Normalized Emittance (nm) vs. BPM index**

## Two different CURVED geometries

**   ****Compare ILC BCD curved linac with a design where GKICK and YCOR are placed together at the centre of every 4****th**** CM**
**   ****Matched beam conditions; 100 seeds; BPMs only at YCOR locations; WAKES ON**
**   ****All nominal misalignments except that all errors in 1****st**** 25 CMs are reset to zero**

**Mean projected Normalized Emittance (nm) vs. BPM index**

**1:1**

**DFS**

## BENCHMARKING / CROSS – CHECKING

- SINGLE  BUNCH  EMITTANCE  DILUTION  WITH  STATIC  MISALIGNMENTS

## BENCHMARKING

-  Differences in the emittance dilution predictions and sensitivity of the beam based alignments.
-  Thus, it is generally felt by LET community to understand these subtle differences carefully and hence various analyzers have agreed to cross-check results  and so far two exercises were attempted
-  Codes compared
- BMAD (TAO)   --    Jeff Smith (Cornell)
- PLACET          --    Daniel Schulte (CERN)
- MERLIN          --     Nick Walker (DESY) & Paul Lebrun (Fermilab) separately
- SLEPT            --     Kiyoshi Kubo (KEK)
- MATLIAR        --     Peter Tenenbaum (SLAC) and Kirti Ranjan (Fermilab)

**BENCHMARKING**

## BENCHMARKING Exercise # 1 

** ****In perfectly aligned LINAC (TESLA lattice), launch the beam with the initial y-offset of 5 microns (including TESLA wakes) **
** ****Half Linac is low energy section and half if the high energy section.**
** **

- Difference in the vertical orbit at the BPMs w.r.t. BMAD

- Kubo’s old version

- Kubo’s new version

**Paul’s MERLIN**

- BMAD’s vertical orbit

-   Paul’s new results are consistent with the Nick’s MERLIN results

## BENCHMARKING Exercise # 1 

**Diff. in QUAD STRENGTH **

**Diff. in  REFERENCE ENERGY **

**Diff. in  QUAD STRENGTH / REF. ENERGY **

**  ****Ref. energy and Quad. Strengths of PLACET is quite different**
** ****PLACET - because of the diff. in the interpretation of ELOSS**
** ****Differences in Quad strength/ Ref. energy is found in PLACET, beam trajectory doesn’t look significantly different.**
-  Paul’s new results are consistent with the Nick’s MERLIN results

- Daniel

- Paul’s MERLIN

## BENCHMARKING Exercise # 1 

**BENCHMARKING Exercise # 1 **

**Diff. in  PROJECTED VERTICAL EMITTANCE w.r.t. MATLIAR **

- 0.1 nm diff. for 1.2 nm emittance growth : 10% variation – are we close enough??

- BMAD’s projected vertical emittance

-   Paul’s new results are consistent with Nick’s MERLIN results

- Paul’s MERLIN

## BENCHMARKING Exercise # 2 

** ****Then he generated the vertical corrector’s setting for the DFS**
** ****Exercise:**** Include the misalignments and the vertical corrector’s setting and plot the emittance dilution**

**BENCHMARKING Exercise # 2 **

- Wakes on

- ~ 10% variation – are we close enough??

- BMAD results are somewhat different w/ wakes on

## BENCHMARKING Exercise # 2 

- BMAD results are also in agreement w/o wakes on

- Wakes off

- How close do we want to be? -  I would say that If we can show agreement among various codes at the 10% level w/ all the input ingredients then it would be REASONABLE agreement

## Summary

-   We have studied the single bunch emittance dilution for USColdLC Main Linac, compared 1:1 and DFS for static misalignments, and also studied the sensitivity of these algorithms
-   Studied various lattice configurations for the design of ILC BCD
-  LIAR has been modified to study the curved Linac
-   Preliminary results of the ILC BCD curved Linac show that the there is no significant impact on the achievable emittance from the linac which follows the Earth’s geometry as compared to the straight linac.
-    Different groups have been able to find some small bugs / differences in their code while doing benchmarking tests.
-    Most of the codes show agreement w/ each other now at the 10% level.
-    Recently Leo showed  the verification of exercise # 1 using CHEF...development is going on...seems like a promising simulation package !

## Plan

-   Close look at the ILC BCD curved linac  and perform various sensitivity studies and understand the tolerances
-   Understanding of the outstanding issues of the DFS (for ex. Improved Launch steering and wake related systematic effects)
-   Add Beam Jitter, Quad Jitter, Ground motion, Dispersion bumps
-   Bad seeds studies

##   SIMULATION: LIAR

-   Beam with a total charge Q is described as a train of Nb bunches
-  Each bunch is longitudinally divided into Ns slices that are located at different positions in z.
-  Each slice is divided into Nm mono-energetic beam ellipses
-  Vector X describes the centroid motion of thin longitudinal slice
-  With each slice, a beam matrix is also associated
-  Both the centroids X and the beam ellipses are tracked through the lattice
-  Beam emittance w.r.t. beam centroid is defined as

- where

- and so on

## ILC BCD – Baseline Parameters 

**Baseline Parameters**

**ILC BCD – Baseline Parameters **

## Emittance Dilution

**Emittance Dilution**