# Presentation: 270514

## Abatement of the beam emittance growth in the ILC main linac using dispersion and wake bumps

- Evgeniy Shtarklev
- Supervisor: Nikolay Solyak, TD

## USColdLC MAIN LINAC

**  ****USColdLC Main Linac Design**
-   Linac Cryogenic system is divided into Cryomodules(CM), with **12 RF structures / CM**
-  **1 Quad / 2CM** : Superconducting Quads in alternate CM, **330 Quads** (165F,165D)
-   Magnet Optics : FODO “constant beta” lattice, with β phase advance of **60****°** 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.
** ****Main Linac Parameters**
-   ~**11.0 km** length
-    **9 Cell** structures at **1.3 GHz** and **12 structures** per cryostat; Total structures : **7920**
-   Loaded Gradient : **30 MV/m**
-   Injection energy = **5.0 GeV** &  Initial Energy spread = **2.5 %**
-   Extracted beam energy = **250 GeV** (500 GeV CM)
-  Normalized injection emittance:

## Installation conditions and requirements to emittance

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

| 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 |
| Structure Offset w.r.t. Cryostat | 300 μm |
| Cryostat Offset w.r.t. Survey Line | 200 μm |
| Structure Pitch w.r.t. Cryostat | 300 μrad |
| Cryostat Pitch w.r.t. Survey Line | 20 μrad |
| BPM Resolution | 1.0 μm |

**10 nm (50%) Vertical emittance growth in USColdLC **

## BBA methods to reduce beam emittance growth: ONE-to-ONE correction and DFS-steering 

**Divide linac into segments of ~50 quads in each segment:**
**Read all Q-BPMs in a single pulse**
**Compute set of corrector readings and apply the correction**
**Iterate few times before going to the next segment.**
**Performed for 100 Seeds**

**Divide linac into segments of ~40quads**
**Vary energy by switching off structures in front of a segment (no variation within segment)**
**Two orbits are measured**
**Measure change in orbit (fit out incoming orbit change from RF switch-off)**
**Apply correction**
**Iterate twice before going to the next segment**
**Performed for 100 Seeds**

**1:1**

**DFS**

## Effects from using 1:1 and DFS

- Mean: **471 nm**

- 90%: **941 nm**

**1:1**

**Emittance Dilution**

- Mean: **6.9 nm **

- 90%: **13.1 nm**

**DFS**

**Emittance Dilution**

**Gradient : 30 MV/ m; No BNS Energy Spread ; 100 seeds**

##  Concept of bump and its realization

** ****Emittance bumps are trajectory oscillations that are excited      with a feedback at one point s****0**** and closed with another  feedback at some other point s****1****.**
** ****Minimizing the emittance means minimizing the  Courant-           Snyder invariant:**
**  ****with**

##  We express the slice positions yi  and divergences y ́i in terms of the setpoints x0 and x ́0 for the first feedback:

 Solving for the minimum        provides the following solution for the optimal setpoints: 

From last equation we obtain the following explicit expressions for the optimal setpoints:         

** ****Solving for the minimum        provides the following solution for the optimal setpoints: **
** **
**From last equation we obtain the following explicit expressions for the optimal setpoints:         **

## Location of dispersion and wake bumps in the ILC main linac

- _2 dispersion bumps_ (at energy 5 Gev; with β phase advance of **180****°** in each bump):
- _2 wake bumps_ (at energy 50 Gev; with β phase advance of **90****°** between bumps):

## How does bump work?

## Dispersion free steering: separately and in combination with bumps (60 seeds)

## Improvement of emittance after bumps for 60 seeds

## Bad seed

**             ****Effectiveness of dispersion and wakefield bumps**

## Bad seed

**Comparison of contributions from separate bumps**
**               ****to final improvement of emittance**

## Bad seed

**Influence of fractional error on beam size reporting**
**                              ****on final results**