Optics measurements through K- MODULATION in LHC IR 4

1

Optics measurementsthrough

K- MODULATION in

LHC IR 4

Emittance Meeting05/12/2012

2 Emittance Meeting 05/12/2012

𝛿𝜀𝜀

=√( 𝛿𝜎2

𝜎2 )2

+( 𝛿 𝛽𝛽 )2

𝜀𝑥 , 𝑦=𝛾𝛽𝑥 , 𝑦

(𝜎 2−𝐷2(𝑑𝑝𝑝 )2)

Since :

Motivation:

Therefore:

Reducing the Uncertainty on the

beta.

negligible

Checked with sub % differences


Technique:

Far from integer and half integer tune resonances (our case)

• Inducing a change in the strength of the quadrupole (k)• Measuring the resulting tune change

Where:


• Injection @ 450 GeV

Interesting results, worth checking for changes at higher energy

• FlatTop @ 4000 TeV + Unsqueezed optics

• FlatTop @ 4000 TeV + Squeezed optics

ADT OFF+

INJECTION TUNES

(less coupling)

K Modulation in IR 4 was repeated at:

BEFORE THE SQUEEZE AFTER THE SQUEEZESQUEEZE

5

RQ6 R4 Beam 1 @450 GeV

Emittance Meeting 05/12/2012




IP 4

D3

ws

bsrt

MQ.5R4

.B2

MQ.5L4.B2

MQ.6L4.B2


INJECTION FLATTOP BEFORE SQUEEZE

FLATTOP AFTER SQUEEZE

MQY . 5L4 . B1MQY . 5R4 . B1MQY . 6R4 . B1MQM . 7R4 . B1



MQY . 5R4 . B2MQY . 5L4 . B2MQY . 6L4 . B2



LIST OF THE MODULATED QUADRUPOLES :

BEAM 1

BEAM 2

MQY errors in the transfer function

Bad measurement due to noisy tune steps




200 250 300 350 400 450 500 550 600 650 700

MEAS. after Squeeze

MEAS. before Squeeze

MEAS. at Injection

MODEL

RQ5 L4 B1 HOR

80 100 120 140 160 180 200 220 240 260

MEAS. after Squeeze


MEAS. at Injection

MODEL

RQ5 L4 B1 VER

BEAM 1


80 100 120 140 160 180 200 220 240 260 280

MEAS. after Squeeze


MEAS. at Injection

MODEL

RQ5 R4 B1 HOR

200 250 300 350 400 450 500 550 600 650

MEAS. after Squeeze


MEAS. at Injection

MODEL

RQ5 R4 B1 VER

BEAM 1


200 300 400 500 600 700

MEAS. after Squeeze


MEAS. at Injection

MODEL

RQ6 R4 B1 HOR

60 80 100 120 140 160 180 200

MEAS. after Squeeze


MEAS. at Injection

MODEL

RQ6 R4 B1 VER

BEAM 1


30 40 50 60 70 80 90 100 110

MEAS. after Squeeze


MEAS. at Injection

MODEL

RQ7 R4 B1 HOR

60 80 100 120 140 160 180

MEAS. after Squeeze


MEAS. at Injection

MODEL

RQ7 R4 B1 VER

BEAM 1


200 250 300 350 400 450 500 550 600 650 700

MEAS. after Squeeze


MEAS. at Injection

MODEL

RQ5 R4 B2 HOR

100 150 200 250 300

MEAS. after Squeeze


MEAS. at Injection

MODEL

RQ5 R4 B2 VER

BEAM 2


80 100 120 140 160 180 200 220 240

MEAS. after Squeeze


MEAS. at Injection

MODEL

RQ5 L4 B2 HOR

300 400 500 600 700 800

MEAS. after Squeeze


MEAS. at Injection

MODEL

RQ5 L4 B2 VER

BEAM 2


200 250 300 350 400 450 500 550 600 650

MEAS. after Squeeze


MEAS. at Injection

MODEL

RQ6 L4 B2 HOR

80 100 120 140 160 180 200 220 240 260 280

MEAS. after Squeeze


MEAS. at Injection

MODEL

RQ6 L4 B2 VER

BEAM 2


Transport MEASURED VALUES AT RQ TO WS + UND +D3

1) ANALYTICAL METHOD

2) MATCHING WITH MADX

ONLY WITH 2 QUADRUPOLES

WITH 3 QUADRUPOLES


1) ANALYTICAL METHOD

IP 4

UND

ws

MQ.5R4

.B1

MQ.6R4

.B1

MQ.7R4

.B1

MQ.5L4.B1

Transport Matrix between two point in the line is give by

Where

Depends only on: α,β,µ

SO ….


IP 4

UND

ws

MQ.5R4

.B1

MQ.6R4

.B1

MQ.7R4

.B1

MQ.5L4.B1

@6@UND

T UND6

@6@5

T 65

KNO

WN

FO

RM M

OD

EL

{𝜷𝑼𝑵𝑫=𝒂𝑼𝑵𝑫𝟔 .𝜷𝟔+𝒃𝑼𝑵𝑫𝟔 .𝜶𝟔+𝒄𝑼𝑵𝑫𝟔 .𝜸𝟔

¿𝜷𝟓=𝒂𝟓𝟔 .𝜷𝟔+𝒃𝟓𝟔 .𝜶𝟔+𝒄𝟓𝟔 .𝜸𝟔


2) MATCHING WITH MADX

IR 4

LINEIP 4

UND

ws

MQ.5R4

.B1

MQ.6R4

.B1

MQ.5L4.B1

Element 1

VARY

ConstraintsConstraints

β m

eas

σ meas


β ca

lc

σ cacl

ANALYTICAL METHOD

MATCHING

Q 1

Q 2

Q 1

Q 2

Q 3

β WS/UND x,y

Include Errors


RESU

LTSINJECTIONBE

AM 1

BEAM

2MODEL Beta-beating Best Analytical matching

WS X 165.484 158.83 ± 13 % 181.2 ± 6.45 % 183.7± 11.5%

Y 287.814 280.99 ± 12.3% 287.1 ± 4.22 % 286.9± 3.34%

Undulator X 178.144 174.93 ± 13.2% 199.9 ± 9.75 % 196.8± 13.3%

Y 192.094 188.1 ± 22.1% 189 ± 4.94 % 187.5± 3.24%

MODEL Beta-beating Best Analytical matching

WS X 123.512 126.43 ± 9.5% 124.2 ± 2.04% 125.3 ± 4.05%

Y 404.551 418.95 ± 8.5% 424.7 ± 3.33% 412.9 ± 2.78%

Undulator X 127.535 129.3 ± 16.2% 126.5 ± 3 % 172.7 ± 2.82%

Y 332.832 344.02 ± 7.4% 354 ± 2.72 % 351.2 ± 4.2%


RESU

LTS BE

AM 1

BEAM


WS X 165.484 151.74 ± 12.1% 159.2 ± 6.45% 173.3±12%

Y 287.814 292.0 ± 10.68% 288.2 ± 10.9% 284±6.82

D3 X 172.967 158.7 ± 8.76% 165.4 ± 5.35% 177.3±12%

Y 214.595 209.51 ± 0.75% 207.5 ± 3.1% 213 ±11%


WS X 123.512 122.91 ± 2.75% 118.7 ± 4.2%

Y 404.551 451.04 ± 23.11% 438.7 ± 4.1%

D3 X 127.090 124.96 ± 11.87% 122.1 ± 6.2%

Y 334.613 381.16 ± 23.37% 358.8 ± 3.9%

FLATTOP BEFORE SQUEEZE


RESU

LTS

FLATTOP AFTER SQUEEZEBE

AM 1

BEAM


WS X 165.484 159.27 ± 23.6% 161.7 ± 7.5 % 179.9±16%

Y 287.814 280.4 ± 7.13% 274.8 ± 5.72% 276.3±3.3%

D3 X 172.967 167.43 ± 24.5% 174.5 ± 7.77%

Y 214.595 203.65 ± 11.27% 206.5 ± 4.2%


WS X 123.512 127.52 ± 96.6% 114.3 ± 6.2% 119.1±8.3%

Y 404.551 413.24 ± 7.18% 410.4 ± 1.33% 413.6±1.6%

D3 X 127.090 126.34 ± 17% 126.2 ± 2.7% 122.3±9.5%

Y 334.613 358.9 ± 23.72% 340 ± 4.545% 344±2%


80 100 120 140 160 180 200 220 240 260

MEAS. after Squeeze


MEAS. at Injection

MODEL

WS B1 HOR

150 200 250 300 350 400 450

MEAS. after Squeeze


MEAS. at Injection

MODEL

WS B1 VER


60 80 100 120 140 160 180

MEAS. after Squeeze


MEAS. at Injection

MODEL

WS B2 HOR

200 250 300 350 400 450 500 550 600

MEAS. after Squeeze


MEAS. at Injection

MODEL

WS B2 VER


80 100 120 140 160 180 200 220 240 260 280

MEAS. after Squeeze


MEAS. at Injection

MODEL

SR Source B1 HOR

100 150 200 250 300

MEAS. after Squeeze


MEAS. at Injection

MODEL

SR Source B1 VER


60 80 100 120 140 160 180 200

MEAS. after Squeeze


MEAS. at Injection

MODEL

SR Source B2 HOR

150 200 250 300 350 400 450 500

MEAS. after Squeeze


MEAS. at Injection

MODEL

SR Source B2 VER


For meas. During ramp,beta values

are obtained from linear

interpolation of the 450GeV

values and 4 TeV values

Plots Courtesy of Maria Kuhn

Beta from model






Beta from beta beating







Beta from K mod



Preliminary results for the BGI:

MODEL Beta-beating4 TeV - Sqz

Analytical4 TeV - Sqz

Beta-beating4 TeV + Sqz

Analytical4 TeV + Sqz

BGI

Beam1

X 310.35 287.7 ± 1.8 % 281.1 ± 7.83% 318.7 ± 3.21% 305.9 ± 18%

Y 95.1 95.57 ± 3.9% 93.4 ± 5.97% 97.63 ± 15.6 % 95.89 ± 8.35%

MODEL Beta-beating4 TeV - Sqz

Analytical4 TeV - Sqz

Beta-beating4 TeV + Sqz

Analytical4 TeV + Sqz

BGI

Beam2

X 273.42 273.8 ± 14.5 % 262.8 ± 14% 271.1 ± 20.9% 277.1 ± 5.3%

Y 212.51 232.9 ± 17.7% 224.1 ± 3.6% 219.46 ± 16.8% 216.9± 1.89%


Preliminary results for the BGI:

THANK YOU FOR YOUR ATTENTION

Emittance Meeting 05/12/201236

Documents

Optics measurements through K- MODULATION in LHC IR 4