AP-SR-REP-0114 Further Modelling of the Results from Girder ...

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ESA Optics Measurements and Tuning During
April/May 2006 Beam Test




F.

Jackson




Accelerator Physics Group

ASTeC, Daresbury Laboratory, Warrington WA4 4AD, UK




Abstract

This report describes the process of beam focussing for the different
experim
ents in the End Station A test
-
facility at the Stanford Linear
Accelerator Center, California, USA, during the beam test in
April/May 2006. A brief overview of the A
-
line is given and beam
transport simulation studies are described. The beam set
-
up in the

April/May test is de
s
cri
bed, starting with an overview

of the steering
and dispersion matching

procedures
, followed by details of the
emittance and Twiss measurements performed.

Finally th
e beam
focussing results are described
.








1.

INTRODUCTION

End Sta
tion A (ESA) at the Stanford Linear Accelerator Center (SLAC)
provides a tes
t facility for various components

of the International Linear
Collider

and is described
in general

elsewhere
1
,
2
.

This report descri
bes aspects
of the ESA beamline
optics; in partic
ular the optics measurements and tuning
performed during the period 23 April until 9 May 2006.

2.

ESA BEAMLINE DESCRIP
TION

The
ESA beamline (from linac exit to experimental alcove entrance) has the
same configuration as
that
used for the most rece
nt experime
nt (E158)
,

except

the magnet strengths are scaled for a lower beam energy of 28.5 GeV. A
description of the A
-
line can be found elsewhere
3
. A brief overview is given
here.

The beamline from the linac exit
to the experimental alcove
is around 300
m
long, th
e first ~30m being shared with the other two
SLAC test beam lines

(FFTB and NLCTA). The
‘swivel point’ marks the beginning of

the unique
part of the A
-
line, and the components of this section are set out below.


Magnet Configuration

Two pulsed dipoles are
followed
by a string of dipoles which bend the beam
by 24 degrees. A quadrupole doublet at the bend
entrance
is used focus the
be
am at the bend mid
-
point Two more

quadrup
oles then
suppress the
dispersion at the bend exit.
The bending section
begins 100m af
ter the swivel
point and
is approximately 100m long.
The
four
focusing quadrupoles
(Q27,

Q28,

Q30,

Q38)
follow

over a distance of about
80
m.

Vertical and horizontal
cor
rector dipole pairs are located at swivel point, and just downstream of Q28
and Q30. Add
itional vertical correctors are situated
within

the bend.


Experiment
al Alcove

Apparatus

The experimental alcove
, from Q38 to the east wall is
approximately 80m.
The collimator wakefield box was located at
~
20m, followed by 2 energy
-
spectrometer
-
BPM tripl
ets
.

A diagram of the alcove apparatus is shown in
Figure
1


Figure
1
. ESA alcove apparatus.


Instrumentation



Beam
profile monitors are located
within the experimental hall, one just
upstream of the wak
efield box (PR2), one just beyond the east wall (PR4).
Two wire

scanners
approximately
20 m apart are also located in the alcove for
accurate beam

size measurements; one

just downstream of the wakefield box
(WS1) and one between the BPM triplets (WS2). Add
itional BPMs are
located along the length of the A
-
line and within the alcove itself.
The BPMs
crucial to the April 2006 experiments were BPM31
-
32, just downstream of
Q30, and BPMS1
-
2, 3
-
5, 7
-
9 in the alcove.
BPMs1
-
2 are also known as
BPMs41
-
42.


A synchro
tron light monitor
is positioned at mid
-
bend, and is used to monitor
beam energy spread. Two toroids in the
focusing section mo
nt
i
or the beam
current.
Diodes are installed to monitor
Bunch Length Monitor


Collimators

Momentum slits SL
-
19

at the bend mid
-
p
oint.
Two
protection
collimators are
located i
n the alcove; 3C1 (19mm radius)
, upstream of the wakefield box and
3C2 (8mm aperture radius), near the east wall.

3.

BEAM TRANSPORT SIMUL
ATION IN THE A
-
LINE

In this section the
transver
se beam dynamics in the A
-
l
ine

are

described;
longitudinal dynamics are not addressed.


Significant synchrotron radiation
(SR)
is emitted from the beam in the s
trong
horizontal
bending magnets
of the A
-
line. This particularly affects the
horizontal beam dynamics and thus linear opti
cs models are not sufficient to
describe the beam transport. The
transverse beam envelope will not

follow the
conventional
T
wiss

-
function
s

from linear
lattice
theory (such as the MAD
Twiss calculation). The particle tracking code ELEGANT includes the eff
ects
of synchrotron radiation and has been used previously to model the beam
transport in the A
-
line
5


I
n order to perform beam size tuning

for the various ESA experiments, the
beam
phase space (or
Twiss functi
ons
)

must be known at the entrance to the
final fo
cusing quadrupoles (Q27
-
Q38).

The beam phase space was

calculated
using both the MAD and ELEGANT programs. A nominal beam was
assumed with linac exit emittances


x

=2

10
-
5

m
-
rad,


y
=6

10
-
5

m
-
rad, and
mome
ntum spread of

p=0.2%. The initial Twiss parameters of the beam
were defined to be

x,y
=14m,

x,y
=0 at the swivel

point
.



For the

ELEGANT
simulation,
the initial particle distribution was
crea
ted at
the swivel

point using the Twiss parameters specified.
The nominal
emittances were taken as RMS values, creating Gaussian projections in the


phase space co
-
ordinates
x
,

x
’,

y
,

y
’. The particles were then tracked to the
Q27 entrance, where the emittance and Twiss parameters were computed
using the standard sta
tistical definitions

for
centred
beams.








)
'
,
'
cov(
)
,
cov(
)
'
,
cov(
)
'
,
'
cov(
)
,
cov(
2
x
x
x
x
x
x
x
x
x
x





()

Incoherent sy
nchrotron radiation was simulated

in each bending magnet.


For the MAD model

Twiss parameters were propagated from the SWIVEL
point to Q27 entrance.
No mechanism exists in MAD to compute the effec
t of
SR on the Twiss parameters, linear transport matrices are simply assumed.


Figure

2

shows the beam phase space ellipses calculated at Q27 entrance
using both the MAD Twiss calculation and ELEGANT particle tra
cking.
Table
1

summarises the comparison between the MAD and ELEGANT
results
.




Figure
2
. B
eam phas
e space at the entrance to Q27 for x
-
plane (top left) and y
-
plane (top
-
right, bottom left zoom).

The 2D
histogram shows the ELEGANT
tracked particle distribution. The solid line shows the ELEGANT phase space
ellipse, calculated statistically from the distribution. The dashed line shows the
MAD phase space el
lipse, computed using the Q27 emittance calculated
from
the ELEGANT simulation.

In the y
-
plane t
he solid (ELEGANT) and dashed
(MAD)
phase space ellipses co
-
incide, and cannot be distinguished.



Q27 Entrance Beam Par
a
meters

MAD

ELEGANT



x,y

(m
-
rad)



-
5

N
/
A

31.9, 2.0


x,y

(m)

231.3, 2020.5

83.
1,

1958.
3


x,y

-
14.4,
-
42.8

-
5.0,
-
41.5

Table
1
. Twiss parameters at Q27 entrance calculated with MAD and ELEGANT.




The conclusions from the MAD and ELEGANT studies of the A
-
line are as
follows:




SR has a significant effect on the
horizontal beam dynamics, including a
5
-
fold increase in emittance. The MAD Twiss calculation for the A
-
line
becomes invalid.



The vertical dynamics are not significantly affected by the SR. The MAD
Twiss calculation is valid in this plane.


It is interest
ing to use the ELEGANT simulation to predict the effect of input
conditions on the beam parameters at Q27. The input parameters bunch
length, energy spread, and emittance were varied in turn, keeping all other
parameters at the nominal values. Beam energy
spread and x
-
emittance were
found to have a significant effect on the Twiss parameters at Q27.


Figure
3
. Twiss parameters at Q27 as a function of input x
-
emittance (left) and energy spread (right).
Each parameter is normalised

to it’s nominal value. In each case the trends for

y
,


y

(green and blue
lines) coincide.


During the energy spread variation study, it was observed that the beam
distribution at Q27 becomes highly non
-
Gaussian

as the e
nergy spread
increases
, which in
fact makes the Twiss characterisation invalid.


4.

BEAM SET
-
UP

The detail
s of the final
steps of beam set up in

the April 2006 run are
described here; the preliminary A
-
line beam steering process and BPM set up
is not detailed.

The A
-
line beam runs parasitic
ally with the PEP
-
II storage
ring at 10Hz single bunch, except during PEP
-
II injectio
n, when it is limited
to 1 Hz. 10 Hz is required to take
beam size

measurements with the wire

scanners.


The
A
-
line magnet strengths
used for preliminary beam set
-
up were
those
from the E158 configuration,
scaled for a 28.5
GeV beam.




After preliminary steering was carried out, the beam was then centred on the
final focusing quadrupoles (Q27
-
Q38). The quadrupole centres
of Q27 and
Q30
wer
e found
with respect to BPM 2860 (j
ust downstream of Q28)
by use
of ‘bowtie’ BPM measurements
.

See Appendix A for details of this
procedure.

Q27 and Q38 were found to be well aligned in x but ~1mm
misaligned in y.
The beam was aligned

to the mean centre of Q27 and Q28.

The alignment feedba
ck maintains the aligned beam orbit during normal A
-
line operation.


The dispersion was then measured
at two BPM locations,
BPM
31

(just
downstream of Q30) and
BPM42 (just upstream of the wakefield box)
. This is
done by ditheri
ng the energy of the beam (by

~
100 MeV) while measuring the
beam positions
at the BPMs. For zero dispersion the BPM readings should not
change as the beam is dithered.

The actual dispersion values can be obtained
by measuring the correlation of these BPMS with an upstream BPM (1790) a
t
a high dispersion point.


Tuning knobs for first and second order dispersion
minimisation have
previously been
constructed from two quadrupoles strengths Q19
, Q20
.

The
correlations
between the high dispersion BPM
and those downstream are
minimized by tu
ning the knobs. The measured correlations
after dispersion
minimisation
in the April 2006 run are shown below.
The dispersion
mi
ni
mised config
uration

was saved as 454

on the SLAC control program
(SCP)
.



T
he energy spread of the beam measured by the

synchr
otron light monitor
,
and

is sensitive to the bunch charge, the phasing of the beam at the linac
entrance (‘phase ramp’) and the bunch compressor voltage, and also tends to
drift with time.


Figure
4

illustrates

the typical minimu
m achievable beam energy spread,
measured on the synchrotron light monitor. In this case

the parameters were
adjusted to 40 MeV phase ramp 42.5 degrees, charge
2e10 e
-

per bunch.







Figure
4
. Synchroton light monitor signal. Two
plots were obtained shifting the beam energy by 100
MeV to roughly calibrate the horizontal scale. The
width of the signal

is approximately

0.25% of
the
nominal beam energy.


5.

OPTICS MEASUREMENTS

This section describes the
measurement of the beam o
ptical f
unctions
(emittance and Twiss) at the end of the A
-
line in April 2006.
The goal was to
determine the
beam
optics at the entrance to Q27.
Fitting procedures
could
then be performed using Q27,Q28,Q30,Q38
to
obtain desired beam profiles in
the ESA alcove
.



T
he optics were

measured on three

occasions

(26
th
, 29
th
, 30
th

April)

u
sing the
q
uadrupole scan method (see for example

[
4
]
),

recording the beam

size
s with

WS1.

This method can be run automatically from the SLAC control system,
and the final calculations are

performed online, using a linear thick
-
magnet
model (i.e. no approximations other than linear transport between quadrupole
and WS1).




It is desirable to choose the quadrupole scanning ranges so that the beam

size
waists pass through WS1 during the scan.
I
n addition, care must be taken that
the beam
trajectory is not

altered
too much
by the scanning
quadrupole,
or it
may move out of the wire

scanner range, and/or hit downstre
am apertures
causing beam

trips
. This is possible even with the A
-
line
steering fee
dbac
k
turned on, since perfect simultaneous alignment of all quadrupoles with the
beam is never achieved in practice. However, it was possible to find
quadrupole scanning ranges for which the measurements could be performed
without re
-
steering.


Measureme
nts were carried out on three separate occasions, 26
th
, 29
th
, 30
th

April, using different Q27 and Q28 to perform the scans.
The initial Q27
-
Q28
strengths used were those giving small vertical beam size at WS1, found by
hand in the January A
-
line commission
ing.
To determine the Q27 entrance
optics from a Q28 scan, reverse linear transport was calculated.


The
measurements sum
mary is presented in
Table
2
.







Description


Linac
Emittance

(m
-
rad)

10
-
5

A
-
line
Emittance
(m
-
rad)

10
-
5

Q27 entrance Twiss

Figure
s



(m)



ELEGANT

prediction

x

6.0

31.9

83.1

-
5.0

N/A

y

2.0

2.0

1958.3

-
41.5

26

Apr
il
06

Q
28

x

not
m
easured

40.6

2.6

110.2

12.5

-
4.9

0.6

12

y

not
m
easured

4.5

0.2

258.8

28
.3

-
6.0

0.7

29
April
06

Q28

x

not
mea
sured

41.7

1.5

97.0

19.8

-
4.5


0.8

12

y

not
measured

1.3

0.1

180.1


1.2

-
2.9


0.3

30

Apr
il
06

Q27

x

not
measured

30.6

1.9

69.5

7.5

-
3.5

0.4

13

y

0.51


0.01

1.9

0.1

147

11

-
3.2

0.3

Table
2
.

Summary of A
-
line beam optics mea
surements using quadrupole scans.


It is no
ticeable that the emittance and Twiss measured on different days have
different values, even accounting for the errors on these values. This can only
be attributed to variation in linac beam properties
, since no

magnets were


altered in the A
-
line in this period
. For example beam energy spread is
expected to affect the beam optics. Unfortunately a detailed record of beam
energy spread and linac emittance was not kept during these me
asurements.


On the one occasio
n that the linac emittance was measured (30
th

April)
,

it is
noticeable that
y
-
emittance increases by a factor of 4 from the linac exit to the
End Station.
Simulations of the emittance growth effects such as b
eam
-
gas
scattering

or magnet misalignments have
not been performed.


Comparing the measured optics with the ELEGANT prediction, it is
noticeable the agreement is much better in the x
-
plane than the y
-
plane.
General sources of error in the simulation (perfect alignment and perfect
vacuum) would be expect
ed to cause disagreement in both planes, although
these have not been studied in detail.

6.

OPTICS TUNING

The optics measurement
s

in the pr
evious section were used as the input to
dete
r
mine

beam
focussing solutions fo
r the ESA experiments T480 and T474.
It
has

been seen that the
incoming
beam optics at the entrance
to the
focussing
section (Q27 onwards) is not stable on a day
-
to
-
day basis.
An optics solution
can be determined for current conditions, but the beamsize and waist location

of the solution
will dr
ift as the incoming beam properties alter.
One can try to
recover the conditions by linac emit
tance tuning
.


The program MAD was used for linear optics fitting.


T480

Collimator Wakefield Experiment
.

A small vertical beam waist (

y


100

m) wa
s desired at
the collimator jaws,
i.e. the centre
of the
collimator wakefield box,
~
100m downstream of the first
focussing quadrupole Q27.

The desired horizontal beam size at the collimator
was

x



1mm.


For the wakefield measurements, t
he beam t
rajectory was

to be me
asured
starting from BPMS 31 and 32 (just downstr
e
am of Q30)
.

Thus it was
desirable to use only the quadrupoles upstream of BPM 31 (Q27
-
Q30) for
focussing, to avoid quadrupole kicks to the measured beam trajectory
.


The

optics fitting was done on

26
th

Apr
il with the corresponding Q27 entranc
e
beam parameters (see
Table
2
)
. A solution was found for

y

= 70

m (waist)
and

x

= 700

m

at the wakefield box
centre.
The measured beamsizes at
WS1 were found to be

y

= 83

5

m (waist) and

x

= 982

41

m.
Figure
5

shows the
MAD
optics solution and the WS1 measurements.







Figure
5
.

(Left) MAD
T480 optics solution, x and y beamsizes
.
Q27 entrance at 0m, wakefield box

centre at 95 m.

(Right
) beam size measured on WS1.


T474

Energy Spectrometer BPM Experiment.


The T474 experiment involves a prototype energy spectrometer for the ILC,
which consists of a horizontal dipole chicane

with BPMs to measure the beam
trajectory. The stability of the E
SA BPMs is under test in 2006. For these te
sts
a narrow horiz
on
t
al beam waist

x




200

m

is required at the centre of the
proposed chicane location, at which another wires

canner WS2 is placed. The
vertical beam

size was required to be
~0.5 mm.


The optic
s fitting was done using the most recently measured Q27 entrance
beam parameters (at that time), which were those taken on 30
th

April. A
solution was found for

y

= 200

m (waist) and

x

= 590

m at WS2.

The
measured beam sizes at WS2 were found to be

y

=

241

12

m (waist) and

x

= 547

34

m.
Figure
6

shows the MAD optics solution and the WS2
measurements. The measurements were taken several days after the optics
was determined.





Figure
6
.

(Left)
MAD
T4
74 opt
ics solution, x and y beamsizes,

Q27 entrance at 0m
WS2 at 116.5m.

(Right) beamsizes measured at WS2.

7.

STABILITY ISSUES

As was seen in the optics measurements, the emittance and thus beam sizes in
the End Station varied quite noticeably on a day
-
to
-
day basis. The stability
and quality of the beam in the April 2006 test beam is discussed in this
section.


A recurrent feature observed was the deterioration in the beam profile

particularly in the y
-
plane
-

following a tuning period. The beam profile
q
uality can be improved by the phase ramp, the bunch compressor voltage,
and the linac beam position and angle feedback setpoints. However the
profiles usually deteriorate, becoming larger and/or non Gaussian.


Examples of this can be seen from scans taken

during the emittance
measurement and optics tuning shifts.
Figure
7

shows a highly non
-
gaussian
beam observed on WS1 at the beginning of a beam tuning shift, when it was
also noticed that the beam energy spread (SLM signal) was v
ery large. After
unsuccessful attempts to improve the energy spread with the phase ramp, the


beam current was turned down from 2.0


10
10
(e
-

per bunch) to 1.3


10
10
,
which noticeably improved both the energy spread and the beam y
-
profile.


Figure
7
.
(left
) y
-
beam profile taken with WS1 at beginning of shift on 29
th

April. (
right
) y
-
beam
profile after reducing the bunch charge from 2.0



10
(e
-

per bunch) to 1.3



10
.

A very similar observation was made on a later occasion

(2
nd

May), see


Figure
8
. (left) y
-
beam profile taken with WS1 at beginning of shift on 2
nd
May. (right) y
-
beam profile
after reducing the bunch charge from
1.7




10
(e
-

per bunch) to
1.2




10
.

The x
-
beam profile was in ge
neral more well behaved, apart from one
instance (29
th

April) where an unusual tail was observed on one side, see
Figure
9
. No remedy could be found for this, and it eventually disappeared.


Figure
9
. Un
usual x
-
profile observed on beam at WS1 on 29
th

April.




Instability in the vertical plane was observed in the E158 experiment
5
, and a
skew quadrupole was introduced (located just downstream of Q27) to couple
increase the vertical emittance by x
-
y coupling
, thereby reducing the vertical
sensitivity. The skew quadrupole was not
exploited during the April
runs as
very small vertical beams sizes
-

and thus
small vertical
emittances

-

are
required.



Beam instability from the SLAC may arise from temperature v
ariations which
affect the RF system, and

has been the subject of previous studies
6
,
7
.


8.

CONCLUSION
S

Experience with the beam optics at the End Station A has shown that they are
dominated by the linac beam conditions, which demonstrate considerable
variati
on on a day
-
to
-
day timescale.
However, the beam optics have been
successfully measured and used to tune the beam to the desired size in the
alcove, in combination with linac emittance tuning.


The beam transport simulations in ELEGANT are in reasonable ag
reement
with horizontal optics measurements. However the agreement is much poorer
in the y
-
plane and the reason for this is not clear. Effects such as lattice errors
and beam gas scattering have not been studied yet.


The beam optical parameters (emittance
, Twiss) of the beam at the end of the
A
-
line can be measured to ~10%, at a given period when the linac conditions
are stable.

Dispersion has been successfully controlled by the dispersion
suppression quadrupoles.


In beam tuning studies it was observed t
hat h
igh beam currents (2

10
10
e
-

per
bunch) are correlated with large energy spread and
non
-
Gaussian beam
profiles
.
Without resorting to linac tuning, the beam conditions can usually be
improved by simply reducing the beam current.


9.

ACKNOWLEDGEMENTS


This

report summarises the work of several people
who performed

the optical
set
-
up of the beam at End Station A, including C. Clarke (Univ. Oxford, UK)
R. Iverson, J. Nelson, T. Fieguth, M. Woods (Stanford

Linear Accelerator
Centre, USA)
.






APPENDIX A. BEAM
ALIGNMENT BY ‘BOWTIE

METHOD


When the beam passes through the magnetic centre of each quadrupole,
downstream BPM readings should not vary with the quadrupole strength. The
beam position in the quadrupole can be controlled using an upstream
corrector dipol
e (‘A4’ was used, ~200m upstream of Q27).


The beam position is read on two downstream BPMs;
one near

the quadrupole
exit, o
ne further away. See
Figure
10

corrector
bpm
-
A
bpm
-
B

Figure
10
. Illustration of ‘bow
tie’ beam alignment measurement in quadrupole
using
correcto
r and two downstream BPMs.

The beam position
in the quadrupole
is altered in steps; for each step the
quadrupole strength is set to two different values and the BPM readings
recorded. When the BP
M readings are plotted against each other, a ‘bow
-
tie’
distribution is observed. Two slopes corresponding to the two quadrupole
strength are seen; at the crossing point the beam is centred. The centre of the
quadrupole with respect to the adjacent BPM can
be read from this plot. The
beam can then be steered to the quadrupole centre.


The horizontal and vertical quadrupole centres were found for Q27 and Q28.
The BPMs 2860 (just downstream of Q28) and 4160 (a further 80m
downstream) were used for both quadru
pole centering measurements. The
results are shown in the figures below
.












The summary of the centred beams positions in Q27 and Q28 are given in
Table. The beam was steered to the average centre of the Q27 and Q28 on
BPM 2860.





BPM
-
2860
-
X
(mm)

BPM
-
2860
-
Y
(mm)

Q27

0.37

-
1.25

Q28

-
0.30

-
2.11



Average

0.03

-
1.68


The beam was steered to 0 mm and
-
1.7 mm on BPM 2860 X and Y
respectively.

APPENDIX B. DISPERSI
ON MINIMISATION


Figure
11
.
BPM correlation plots with beam en
ergy dither applied. Correlations

are plotted
between
the high
-
dispersion

BPM (1790) and downstream
BPM

3115 (
which is BPM 31
just downstream of
Q30) and
BPM
4170 (
which is BPM 42 just upstream of the wakefield box). The left (right) plots show
the correl
ations in the x (y) planes. The
correlation plot for BPM 4170 Y was not recorded.





10.

APPENDIX C. EMITTANC
E MEASUREMENT PLOTS


Figure
12
. Quadrupole scan beamsize plots taken using Q28 on the 26
th

April (left) and 29
th

April
(righ
t).






Figure
13
. Quadrupole scan beamsize plots taken using Q27 on the 30
th

April (top and middle). Linac
y
-
emittance measurement taken simultaneously.










1

M. Woods et al, ‘
Test Beam Studies at SLAC's End Station A, for

the International Linear Collider
’, EPAC
2006, Edinburgh, Scotland. Pre
-
publication

2

M. Woods et al, ‘
A Test Facility for the International Linear Collider at SLAC End Station A for Prototypes
of Beam Delivery and IR Components
’, PAC 2005, Knoxville, Ten
nessee, US, p 2461

3
R. Erikson et al, ‘SLAC A
-
LINE UPGRADE TO 50 GeV’, SLAC
-
PUB
-
5891

4

K. Ebihara et al, ‘Non
-
Destructive Emittance Measurement of a Beam Transport Line’, Nuclear Instruments
and Methods 202 (1982) p403
-
409.

5

M. Woodley et al ‘BEAM STABIL
IZATION IN THE SLAC A
-
LINE US
ING A SKEW
QUADRUPOLE’
,
EPAC 2002. Paris, France

6
F. J. Decker et al, ‘BEAM
-
BASED ANALYSIS OF DAY
-
NIGHT PERFORMANCE

VARIATIONS AT THE SLC LINAC’


7

F. J. Decker et al ‘STATUS OF THE SLAC LINAC’. EPAC 1998