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f. Main Injector Slow Extraction Studies. Y. Alexahin, E. Gianfelice-Wendt, J. Johnstone (APC) D. Morris, M.-J. Yang (AD). MI Slow Extraction Group Meeting, June 29, 2012. Issues. 2. - PowerPoint PPT Presentation
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Main Injector Slow Extraction Studies
f
Y. Alexahin, E. Gianfelice-Wendt, J. Johnstone (APC)
D. Morris, M.-J. Yang (AD)
MI Slow Extraction Group Meeting, June 29, 2012
Issues
What are the optimal conditions for ½-integer resonance extraction?
The amplitude and phase of the quad harmonic?
Nonlinear tuneshift with amplitude?
Where we are:
Tune vs harmonic quad strength and amplitude of oscillations.
TBT optics measurements.
Nonlinear chromaticity
Optimum ES angle vs ES position
Plan of action
2
MI Slow Extraction Group Meeting, June 29, 2012
Theory
Best orientation ()?
Optimum parameters?
3
constrealG
iinGG
nQx
4
22 ),exp(||
,02/
)/(2/Im xxx xxa
observablesgn||4
0atdetuning
||||
||2
||2||
,/
02
220
20
20
2
2/
4
200
42
G
G
acr
eG
Ga
GGc
i
r
2-turn move for < 0: clockwise counter-clockwise
a0
/2
xxa 2/Re c
Model:
MI Slow Extraction Group Meeting, June 29, 2012
Theory - 2 4
For this reason, and to maximize the step size, 0 < < (better << )
orientation for maximum 2-turn step in x and maximum x and …
With orientation like that (or on the right) Ima < 0 for xES < 0 the extraction trajectory can be diverted from the axis, with the angle
maximum tangential2-turn step here
)/(2/Im xxx xxa
r
2-turn move for < 0: clockwise counter-clockwise
a0
/2
xxa 2/Re c
allowed ES position
axx xxESx Im/2/
+0.0011 for x=31m, x=1.72, xES=-2cm
MI Slow Extraction Group Meeting, June 29, 2012
Measurements 5
There was a few rounds of measurements:
03/21/12: TBT optics with harmonic quads: “nominal”; off; minimum Qx (QC206=+1.5A, QC328 = -2A); and QC206 = -3A Qx vs amplitude with harmonic quads for minimum Qx TBT optics with vertical kicks at QC206 = -3A (also gives Qx vs amplitude)
04/02/12: Qx vs amplitude with OF on and off (data not saved)
04/10/12: TBT optics and Qx vs amplitude at QC328 = -6.5A
04/25/12: TBT optics with individual harmonic quads offset by 12A from minimum Qx settings Extraction with QC328 = -6.5A attempted
Also, Ming-Jen and Denton measured 2nd order chromaticity with OF on and off
MI Slow Extraction Group Meeting, June 29, 2012
x - function @ HBPMs 6
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100
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500 1000 1500 2000 2500 3000
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500 1000 1500 2000 2500 3000
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125
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Q206=-3A, Q328=-2A,Qx=0.4895
- x @ HP520 goes down, not up!
design
Distance from HP624 (m)
HP520measurement
“Nominal” harm. quads,Qx=0.485627
Q206=+1.5A, Q328=-2A,Qx=0.484487
- John’s algorithm works!
MI Slow Extraction Group Meeting, June 29, 2012
QC206 vs QC328 7
500 1000 1500 2000 2500 3000
25
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125
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500 1000 1500 2000 2500 3000
40
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140
nominal
Distance from HP624 (m)
HP520
measurement
QC206=-1A, QC328=-4.5A,Qx=0.4899
- x @ HP520 goes up!
QC206=-4.5A, QC328=0,Qx=0.4895
- x @ HP520 goes down, not up!
x
x
Distance from HP624 (m)
MI Slow Extraction Group Meeting, June 29, 2012
Closer Look 8
2650 2700 2750 2800 2850 2900 2950 3000
25
50
75
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125
150
2650 2700 2750 2800 2850 2900 2950 3000
20
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MAD model
Distance from HP624 (m)
ES entrance
QC206=-1A, QC328=-4.5A,Qx=0.4899
- x @ ES larger while max x is smaller
QC206=-4.5A, QC328=0,Qx=0.4895
x
x
Distance from HP624 (m)
measurement
nominal
MI Slow Extraction Group Meeting, June 29, 2012
Phase Space @ ES 9
-2 -1 1 2
-4
-2
2
4
-2 2 4
-3
-2
-1
1
2
3
Design optics used to compute variables @ES from HP520 & HP522 data
QC206=-3A QC328=-6.5A
The ellipse tilt with QC206 is wrong: /2 = 108 > 90
With QC328 it is still wrong: /2 = 145
Inversion of QC206 polarity will give (-) = (+) - = 216 - 180 = 36
Still some contribution from QC328 may be helpful
“minimum Qx”
)(mmx
xx xx
)(mmx/2
xx xx
MI Slow Extraction Group Meeting, June 29, 2012
How it looks in ordinary coordinates 10
xx
From Ming-Jen’s I90 simulations
-2 2 4
-6
-4
-2
2
4
)(mmx
QC328=-6.5A
MI Slow Extraction Group Meeting, June 29, 2012
Harmonic Quad Strength 11
When QC206 is downshifted by 4.5A Qx=0.485 0.4885, so that 0=0.015 =0.0115that gives |G2|0.0052
One more way is to use the transfer function – would I have known it – to calculate K1QC206 for a given current.
The last necessary parameter is
x
x
dJ
dQG
2
14
To obtain the observed (by eye) beta-beat with MAD K1QC206 0.0011m-2 is needed that gives |G2|0.0055
Another way is to look at the tuneshift:
4||
2202
2
G
MI Slow Extraction Group Meeting, June 29, 2012
Effect of Octupoles
MAD8 with octupole components provided by D.Johnson seems to underestimate the effect, while I90 seems to overestimate it.
12
From 03/21/12 studies, harm. quads set for minimum Qx (QC206=+1.5A, QC328=-2A),
Action variable determined from all HBPM data by a special algorithm
0.05 0.15 0.2 0.25 0.3
0.4846
0.4848
0.4852
0.4854
Qx
Jx (m)
case measured MAD8 STATIC I90
“minimum Qx” 1.68103 1.03103 -
QC206=-3A 8.0103 3.4103 12.0103
QC328=-6.5A 10.8103 2.6103 -
Tuneshift with amplitude dQx/dCSI=1.68103 [1/m] (Courant-Snyder Invariant = 2J)
MI Slow Extraction Group Meeting, June 29, 2012
Tune vs Δp/p
May 02, 2012Harmonic quads?
04/28/12 studies by D.Morris & M.-J. Yang
2nd Order Chromaticity (/2) 13
OF (A) measured MAD8 STATIC I90
0 326.9 178.0 249.0 326.7***
+10 454.2 (+127.3) 311.9** (+133.9) 455.8 (+129.1)
–10 198.6* (-128.3) 44.2 (-133.8) 200.9 (-125.8)
*) using more points for p/p>0**) using transfer function 2.8 T-m/m^3/A (multiplied by 3!/LMRO)***) increasing the built-in octupole component by 32.5%
Correspondence between measured OF effect and I90 is amazing!
MAD8 underestimates built-in octupoles by a factor of 1.84 and exaggerates OF (slightly)With this factor in the MAD8 detuning will be dQx/dCSI=1.90103 [1/m] – not too far from the measured dQx/dCSI=1.68103 [1/m] G4=dQx/dJx/2=dQx/dCSI
G4=1.68103 [1/m]
MI Slow Extraction Group Meeting, June 29, 2012
Step Size 14
- this is just a half of the available ES aperture (14mm).To increase xmax we can increase |G2| (and 0/2) by up to 58%(or reduce G4 by a factor of 4?)
/2 = 18 (the same |G2|)
2-turn step =- 6.5mm @ xES=-1cm,x=-0.0003: x=-1cm -1.2cm over ES
With larger |G2| xES can be increased
mm7)(/824
)168(24Re24Re22/1
42/3
2
342max
GG
rGrGaax
x
xxx
At the stopband boundary (0=-2|G2|) and =0 (left pic.) the step size in x reaches its maximum:
0.030 0.025 0.020 0.015 0.010 0.005
0.004
0.002
0.002
0.004
0.006
x (m)
x
x (m)
/2 = 108
2-turn step =- 4.5mm @ xES=-2cm,x=+0.0007: x=-2cm -1.5cm over ES
0.015 0.010 0.005 0.005 0.010
0.006
0.004
0.002
x (m)
x (m)x
MI Slow Extraction Group Meeting, June 29, 2012
Central Separatrix Area 15
xc =1.7mm for /2 = 108 and xc = 5.1mm for /2 = 18 - no problem with xES=-1cm
Still, can be further optimized by mixing QC206 and QC328
0Re2 ax xc
From Leo & John:
...)||
||2||
10
11(
||
|)|2|(|
3
22
...)5
11(
||3
||8)sin(2
2
202/1
24
2/320
2
03
02
G
G
GG
G
c
a
c
arAc
To begin the squeeze of 95%N = 20 mmmrad out of the central separatrix
Ac < 95%N / |0| - 2|G2| < 0.0016 ( |a0/c| < 0.39 )
At this moment the separatrix extends to
MI Slow Extraction Group Meeting, June 29, 2012
Plans
Analyze measurement data from 03/21 - 04/25
extract BPM calibration errors
find -functions at important locations (harm. quads, septa)
fit the optics model to the data
Look for optimal harmonic quad configuration (, |G2|)
16-mult for resonance excitation?
Extracted beam transport? (Larger step-size larger emittance)
Simulate extraction with account of nonlinearities and space-charge
16
MI Slow Extraction Group Meeting, June 29, 2012