# Presentation: 004593

## IR optics compensation

- Fulvia Pilat
- LARP Collaboration Meeting
- Danfords, September 16-18, 2003

***brookhaven - fermilab - berkeley***

_**US LHC Accelerator Research Program**_

## outline

**IR optics compensation** (introduction, motivation)
**Optics measurements**
**Local IR correction**
- 		RHIC and LHC IR correction systems
- 		Linear compensation (data RHIC Run 2000 and 2001)
- 		Non-linear correction methods
- 			IR bumps method  results RHIC run 2001
- 			IR bumps application  results RHIC run 2003
**Beta* knobs**
**Non-linear chromaticity**
**Dynamic aperture**
**LARP areas of activity**:	commissioning, IR upgrade

## IR Correction systems

**Motivation:**
- local correction of **linear errors** (**coupling**, **gradient**)
- Local correction of **nonlinear errors** ( IR magnets **field errors**)
**Beta squeeze**, **crossing angle**
- Beam control, luminosity
**Design:**
**Multi-layer corrector packages** installed next to IR triplet
-    quadrupoles
- Typically, dipole  dodecapole
- Independently powered
- RHIC  LHC  (VLHC)

## LHC inner triplet - correctors

- MQXA

- MQXB

- MQXB

- MQXA

- M

- C

- B

- X

- A

- a2

- M

- C

- B

- X

- M

- C

- B

- X

- B

- P

- M

- B

- P

- M

- LMQXB

- LMQXC

- LMQXA

- LQXB

- LQXC

- LQXA

- To

- IP

- 

- “Q3”

- “Q2”

- “Q1”

- MCBX: 	 b1 a1
- MCBX:	 b1 a1
- MQSXA:	 a2 a3 a4 b4
- 	 a2  +  a3 a4 b4
- MCBXA:	 a1 b1 b3 b6
- Optimization process:
- Magnet design – correction system

- a3
- a4
- b4

## RHIC IR’s - layout

- 6 o’clock IR
- 8 o’clock IR:
- Dipole correctors
- Skew quadrupoles
- Nonlinear
- Other IR’s:
- dipole correctors
- Skew quadrupoles
- (nonlinear layers
- exist but no PS
- yet)

## Run 2000  – IR correction linear

- IR bump method

- Action-jump method

- Determine local IR skew quadrupole correction strenghts (Cardona, Ptitsyn, Pilat)

## IR Correction - linear

- From Run 2000 **IR bump** data and **action jump** data, we had **predictions**
-    for the **12 IR skew quad correctors** in each ring
-  The results from the 2 methods **agree** (5-10%)
- The **predicted values** from the 2000 data analysis agree with the
-     corrector settings found **operationally in 2001**
-  The **residual coupling** in the machine (not arising from the IR triplets)
-      is corrected with **skew quadrupole families** by correcting the coupling
-      resonance (minimum tune separation)

| Configuration 2001 (blue ring) | Q(min) |
| --- | --- |
| Uncorrected  | 0.009 |
| Local correction IR8, IR10,IR2 | 0.019 |
| Local correction in all IR’s | 0.008 |
| Local correction + global correction | 0.0005 (tune meter resolution) |

## IR nonlinear correction methods

_**Dead reckoning**_:  	  _action-kick minimization_ (Wei)
-                                 	  order-by-order prescription, assumes field errors known
-                                 	  (off-line code – “IR filter”-  to set corrector strengths)
- _driving terms compensation_ (Farthouk)
- needs 2 knobs for each multipole to cancel selected DT for both beams:
**a2** (1,1) **a2**(1,-1) **b3** (1,2) **a3**(0,3) **b4**(4,0) **b4**(0,4) **a4**(1,3) **a4**(3,1) **b6**(6,0) **b6**(0,6)
**operational:**	beam based + off-line analysis
- _IR bumps_:	measure and fit **observables vs. bump amplitude**:
- (Koutchouk)	rms orbit	(BPM’s, linear, sextupole)
- (Ptitsyn, Pilat)	tunes** **	(Tune Meter, up to dodecapole)
- 	(tune spread)	(Schottky, octupole, dodecapole?)
- _frequency analysis_:	“better FFT”	detect and correct nonlinear
- (Schmidt, Tomas)		resonance driving terms
- SUSSIX

## IR bumps method - principle

**Closed local orbit bump (triplet)**
- Observable as function of bump amplitude:
**rms orbit outside the bump**
- z=(x,y)  cn=(an,bn) zba=bump amplitude

- The orbit perturbation depends on the **plane of the bump** (H,V)
- And the **parity of the multipole order**
**tune shift**
- Arises from normal gradients (Q) or repelling effect of linear coupling (measured by c)

- Selection of one or the other effect depends on the **plane of the bump**, whether the multipole
- is **skew or normal** and on the **parity of the multipole order**

## IR bumps: simulation, performance 

- Use MAD to compute orbit and tune response to H and V orbit bumps in the
- LHC IP5, assuming:
- 0.1% gradient error (****~20%), 1 mrad roll (c~0.04)
- Multipoles set to 10 units in Q2B.
**Orbit response:**
- (assuming 20 data points)
**Tune response:**
- Assuming 20 measurements and tune resolution of 2 10-4
-  resolve multipoles up to b6 (dodecapole)
**DC offset of BPM** can be eliminated by subtracting 2 orbits
**Accuracy** can be improved by increasing the number of measurements

| Perturbation | BPM resolution |
| --- | --- |
| roll 0.1 mrad | 15 m rms |
| b3 = 7.6 10-4 | 8 m rms |
| b4 = 7.2 10-4 | 3.5 m rms |

## Run 2000–IR correction nonlinear

- RHIC IR bumps – beam experiment
- Bump data at IR2, IR6, IR8, blue & yellow
- Mostly H bumps, some V bumps
- Tune resolution run 2000: 0.001
- Bump amplitude typically to **6s**
- Orbit linear, sextupole
- Tune 5th order polynomial

- Tune resolution 2001 (0.0002) decapole
- 			     dodecapole?

| triplet | b3 | a3 | b4 | b5 | a5 | b6 |
| --- | --- | --- | --- | --- | --- | --- |
| YO5 |  0.94 | -0.55 |  0.03 | -0.08 |  0.11 | -0.01 |
| YI6 | -0.95 |  0.14 |  0.36 |  0.03 | -0.06 | -0.03 |
| YI7 |  1.01 | -0.22 |  0.81 |  0.36 | -0.17 | -0.15 |
| YO8 |  3.81 |  | -0.47 | -1.85 |  |  0.06 |
| YO1 |  0.32 | -0.14 |  0 |  |  |  0 |
| YO2 |  1.51 |  |  0.76 | -0.75 |  | -0.21 |

## IR corrections: run 2003

- Orbit bumps at triplets and across IR
- rms **orbit** and **tunes** vs. bump amplitude
_**PLL ~10**__**-5**__** resolution**_

- _Motivation_:
**Dynamic aperture**
**Operations** (closure of steering bumps)

## IR bumps application

-       IR bump application:
**set-up** and **ramp-up** of IR and triplet bumps in specified time (1-2 minutes)
- Tune and power supply monitoring
- Plot orbit rms and **tunes as a function of bump amplitude**
**Polynomial fitting** up to 5th order of tunes versus amplitude  **coefficients**nonlinear **corrector settings**

## Run 2003: sextupole correctionyellow ring 

- Yellow – IR6

- Yellow IR8

- after
- correction

## Run 2003: octupole correctionblue ring

- Blue – IR6

- Blue IR8

- small effect
- left uncorrected

## Run 2003:  *=2m vs. 1m

- Yellow
- IR8

- before
- sextupole
- correction

- after
- sextupole
- correction

*****=2m

*****=1m

**Sextupole correction** at **IR6** and **IR8** – blue and yellow rings beta*=1m and 2m
- test of **octupole correction** at **YIR8** (2 octupoles allow individual triplet correction)
- 	feed-down octupolesextupole, to be repeated: octupole first, then sextupole
**Current dependence** of field harmonics (left 5000A, right ~2000A)

## IR correctors - results

| IR | plane | Sextupole BC  | Sextupole AC | Octupole BC | Octupole AC |
| --- | --- | --- | --- | --- | --- |
| Y IR8 | H | 0.22209 | 0.01347 | 0.00535 | 0.00093 |
|  | V | -0.33559 | 0.00595 | -0.00388 | 0.00119 |
| Y IR6 | H | -0.23338 | -0.02673 | -0.00968 | -0.00051 |
|  | V | 0.41028 | -0.00042 | -0.00745 | -0.00251 |
| B IR8 | H | -0.03204 | -0.03204 | -0.00557 | -0.00557 |
|  | V | 0.07865 | 0.07865 | 0.00646 | 0.00646 |
| B IR6 | H | -0.06853 | 0.02713 | 0.00536 | -0.01491 |
|  | V | 0.12877 | 0.01121 | -0.00176 | 0.00002 |

- Fit coefficients (x10-3) before and after correction – beta*=2m

- Similar tables for beta*=1m
- Full set of measurements taken in IR10 and IR2
-    (to evaluate ***** options at Phobos and Brahms )

## IR corrector strengths  2m vs 1m

| Sextupole
corrector | Strength *=2m
~5000 A | Strength *=1m
~2000 A |
| --- | --- | --- |
| yo5-sx3 | -0.014 | -0.003 |
| yi6-sx3 |  0.004 |  0 |
| yi7-sx3 |  0.003 |  0.007 |
| yo8-sx3 | -0.01 | -0.038 |
| bi5-sx3 |  0.012 |  0.001 |
| bo6-sx3 | -0.004 | -0.003 |
| bo7-sx3 |  0.0 | -0.003 |
| bi8-sx3 |  0.0 | -0.0005 |

- Difference in strength due mainly to the current dependence of the
-    triplet field errors (if the effect is local).
- The *******=2m strengths** can be used as a **starting point for correction**
**   ****next year Au-Au run** + readjustment when needed (*******=1m at ~5000A**)

## IR bumps – tune shift vs.crossing angle

- Test of using the IR bump application to speed up the measurement of **tune shift vs. crossing angle** at the IP. (compare **cogged vs. un-cogged beams**)
- Promising – to be repeated with beams better centered in the triplets

## Model predictions

- Started comparison of experimental data with RHIC model (including measured individual field errors in triplet cold masses and alignment errors)
- R.Tomas working on RHIC modeling with beam-beam and IR errors (working point)

## Nonlinear chromaticity

- Correct **linear chromaticity** to 0
**Separate tunes** (reduce coupling effects)
- Compare radial steering shift to bpm
- Tried various radial steering ramps
**Radial steps (chrom app)**
**5 and 10 steps**
**Radial modulation (PLL)**
**0.4mm amplitude at 1Hz**
**1mm amplitude at 0.4Hz**
**2mm amplitude at 0.2Hz**

- Prediction from model:

## Nonlinear chromaticity - 2

- Residual linear
- chromaticity

- Radial
- modulation

**PLL FFT**
**Signal**
****

## Nonlinear chromaticity - results

| Ring | * | run | date | 2x | 2v |
| --- | --- | --- | --- | --- | --- |
| blue | 2m | d-Au | Feb 5   2003 |  999 +/- 158 | 212 +/- 202 |
| yellow | 2m | d-Au | Feb 26 2003 |  271 +/- 179 |   81 +/- 463 |
| blue | 1m | p-p | May 23 2003 |  884 +/- 179 | 988 +/- 79 |
| yellow | 1m | p-p | May 23 2003 | -720 +/- 218 | 743 +/- 281 |

- analysis of
- PLL and Artus data

## (Dynamic) aperture measurements

_**Goal**_: collect data to compare with (up-to-date) model
_**Method**_ used:
- ramp **6 bunches** (avoid possible emittance blow-up), **nominal tunes**
- use **scrapers** to confirm **halo beam size** (PIN diodes) and **core beam size** (DCCT and WCM, beam intensity)
**increase H emittance** of bunches selectively via **tune meter kicks (1 Hz)**
- measure continuously emittance with **IPM** and **Schottky**
- emittance **‘saturation’** defines **aperture**
- use scrapers to confirm beam size
- check **loss** pattern and use **orbit** to _discriminate __**physical **__**from **__**dynamic**__** aperture  **_**(physical typically at the abort, and triplets)**
- repeat procedure for **vertical emittance**
- repeat procedure for horizontal _**tune close to the 0.25 resonance**_

## Dynamic aperture, blue, *=2m

- kicking

- Qx=.235
- (nominal)

- Qx=.247
- (resonance)

- “fresh bunch”

- kicking

- Dynamic aperture
- (nominal tune) ~**4.5 sigma**
- By rescaling the emittance
- To the initial one

- Dynamic aperture
- (resonant tune) ~**3.6 sigma**

- data to compare
- with simulation

- Blue ring -  *******=2m** in IP6 and IP8

## * tuning “knobs”

- For *******< 2m** we  ***** tuning “knobs” are desireable
**Tuning knobs** = (quasi) **orthogonal** quadrupole vectors able to produce
**matched** changes in **b*** in a range of about **+/-20%**
_**Necessary:**_
- Find the appropriate orthogonal knobs
- Verify **orthogonality** and **matching** (offline)
**Online model** with beta, dispersion, coupling in order
- Implementation in RE (**online matching** capability – cfr. JVZ talk)
**Optics measurements** with 5-10% resolution
- Existing work for LHC (“Correcting the LHC ***** at collision – Wittmer
- Verdier, Zimmermann, PAC2003)
- Calculation & matching
- Tested orthogonality
- Tested performance in simulation (with errors)
**They have the RHIC lattice with 2m and 1m beta star and agreed to**
**repeat the study for RHIC, possible ****test in run 2003**** if study is**
**successful.**

## LARP-related IR activities

**LARP-related IR activities**

- IR optics compensation is necessary for the **IR upgrade** and
- to enhance the **baseline machine performance**
- Development of _**operational IR correction techniques**_** **capabilities
-    for the LHC (application, analysis) – correction system testing at RHIC
-     1. IR bumps      2. Resonance driving terms
- _Test of__ __**LHC simulation IR filter**_ (compensation of selected driving terms)
-    at RHIC: apply filter in simulation and measure driving terms with
-    before and after correction (RHIC beam experiment)
_**Test of LHC **__****__*** tuning knobs**_ at RHIC
- Precise _**beta function measurements**_ with AC dipole
- Measurement techniques for _**non-linear and skew chromaticity**_
_**Dynamic aperture measurements**_
_**Test of **__****__*** squeeze 1m -> 0.5m optics at RHIC**_** **
**   ****(LHC IR upgrade also factor~2 in*********) – possible with p at 100 GeV without**
**   ****change in power supplies**