Timing Constraints on ILC

Abstract

ILC(International Linear Collider) is a future project of the high energy physics as a partnership among the world countries. The baseline design of ILC, which has been de-veloped by ILC-GDE(Global Design Effort) in 2005, has various constraints on the beam handling and layout due to the inter-system dependencies. We discuss these con-straints and possible solutions.

Full text

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ILC-Asia-2006-03
August 2, 2006
Timing, Control









Timing Constraints on ILC


Presented at the Annual Meeting of Accelerator Society of Japan










M.Kuriki, K.Kubo (KEK), E.Ehrichmann (DESY), S.Guiducci (INFN-LNF),
A.Wolski (Cockcroft Inst.)

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Timing Constraints on ILC
M. Kuriki
H. Ehrlichmann, DESY, Hamburg, Germany
S. Guiducci, INFN-LNF, Frascati, Italy
and A. Wolski, Cockcroft Institute, Warrington, Cheshire, UK
?, K. Kubo, KEK, Tsukuba, Ibaraki, Japan
Abstract
ILC(International Linear Collider) is a future project of
the high energy physics as a partnership among the world
countries. The baseline design of ILC, which has been de-
veloped by ILC-GDE(Global Design Effort) in 2005, has
various constraints on the beam handling and layout due
to the inter-system dependencies. We discuss these con-
straints and possible solutions.
INTRODUCTION
ILC (InternationalLinearCollider) is aimingat electron-
positron collisions at 1 TeV center of mass energy. Be-
cause ILC is based on the super-conducting accelerator, a
long pulse of 1ms with 10mA average beam current must
be implemented. The all bunches in one pulse-train has to
be stored in DR, because the damping time is much longer
than the pulse duration, 1 ms. The bunch spacing has to be
compressed and expanded in the injection and extraction
respectively for a reasonable circumference of DR. This
complex injection/extractionscheme makes constraints not
only on the bunch spacing in DR and linac, but also the fill
pattern in DR.
Other aspects of the timing in ILCis comingfrom the e+
generation. In the current baseline design of ILC[1], e+ is
generated from the high energy gammas produced by the
undulator radiation with the e- beam before the collision.
The new e+ beam is then born during the collision and can
be conflict with the un-extractede+ bunches in DR. Comp-
ton based e+ production[2], which is an alternative method
of ILC, gives constraints on DR circumference (harmonic
number) and extraction and injection scheme.
Objective of this article is to discuss the constraints of
ILC system, which was originally considered for TESLA
project[3] and initiated by H. Ehrlichmann for ILC[4], and
identify possible solutions that provide good flexibility for
dealing with unexpected limitations in the performance of
particular components or subsystems.
DR FILL PATTERN
The bunch spacings in linac and DR has to be an inte-
ger of the linac and DR RF periods respectively. The base-
line configurationis 1.3GHz forlinac and 650MHzforDR,
which are in a simple harmonic relation[6]. The bunch is
handled independently with a fast kicker, which has 3ns
rise/fall time[5]. Table 1 defines parameters for the follow-
ing discussions.
is DR circumference. As general
conditions for the parameters,
?????
? must be a divisor of
? , i.e.
?
masao.kuriki@kek.jp
Table 1: Parameter definitions.
name
DR RF period
Bunch spacing in DR
Linac RF period
Bunch spacing in Linac
DR harmonic number
Harmonic relation
Possible number of bunches in DR
definition
?
???????
?
?????
???
???????
???????
???
?
?????
???
?
?????
???
?
?
???????????
?
?????????
?
?
?
?????
?
?
???
? ?
?
?
?
?
?
?
?"!$# , where
Uniform solution
There are two kinds of solutions for DR fill pattern and
extraction/injection scheme. One is Uniform solution, in
which the bunch spacing in linac is uniform. In that case,
the following propositions have to be true
#
means the natural number class, and
bunch spacing in Linac has to be an integer of that in DR,
?
?
?%!&# .
')(+*-,
?
,/.
!0#21?3?
?
*
?54
.76
(1)
8:9<;
!&#
,>= ?
;
?@.BA
A
A
ADC@E
and
?3?
;
!"#GF
.
;
!&#IHKJ
(2)
where
and number of remainder bunch position when all mini-
trains are filled. Fig. 1 shows an example of fill patterns.
Prop (2) means that
*
and
.
meannumberofmini-trainsinDRfill pattern
? ?
.
has no common divisors. It
1
.......
k positions (one mini-train)
repeated p times
e remainder
Figure 1: An example of fill pattern. Solid and open circles
are the filled and vacant positions , respectively.
can be understood by considering an example, which vio-
lates Prop. (2);
assume that extraction starts first with at the bucket posi-
tion 1 and continuesto the positive direction. The extracted
bunch train labeled by the bucket position is :
?
? =100,
*
= 12,
? =8, and
.=4. Let us
L
,NMO,
L+P
,RQSQRQB,NT7MO,NM
P
,>U?,
L)V
,RQSQRQW,NM
V
,
L
,RQRQSQ<,
(3)
where the extraction is back to the initial position after two
turns. At that time, only 25 of 100 bunches are extracted

Page 3

and other 75 bunches are never extracted. If the parameters
are := 11,
(2), extraction sequence is
?2? =100,
*
? =9, and
.=1, which satisfy Prop.
L
,
LSX
,
L
MO,RQRQSQW,>M
L
,
LSXYX
,>M?,
L
T?,SQRQRQO,NM7MO,NTO,RQRQSQZQRQSQ?,NMY=?,
L
,
(4)
where the extraction is back to the first position after 10
turns, whenall buncheshas beenextracted. In caseof Prop.
(1) and (2) are satisfied, all bunches are already extracted
whenever the extraction is back to the first position.
This is similar to considerations for the Weyl’s billiard;
when a ball is shot into an angle of a rational number in a
billiard table, the ball will return to the original position in
some period. In case of the irrational number, the ball will
never return to the original position and the orbit covers
everywhere in the table.
In Uniform solution, the bunch fill pattern does not have
any exact periods, because
mon divisors. In the second example shown in (4), the
bunch fill pattern has roughly 11 periods, but the period is
not exact due to the remainder,
solution has a limited flexibility because the parameters
? , andmust satisfy Prop. (1) and (2).
? ? and
.
do not have any com-
.. Once
? is fixed, Uniform
*
,
.
Step Solution
The second solution is Step solution. The condition for
Step solution is expressed as
'+(+*-,
?%!&# 1?2?
?
*
?
6?[
(5)
Please remember the first example, (3), which does not sat-
isfy the condition of Uniform solution. The extraction is
back to the first position after two turns. If we move to
the position 2 instead of the position 1 by stepping one
bunch spacing in DR,
be continued without hitting any vacant buckets. This is
Step solution. All bunches are extracted by making a step
whenever we hit a vacant bucket. Due to the step, the
bunch spacing in linac,
be.
In the step solution, the bunch fill pattern has exact
super-periodsdetermined by parameter
a fixed
exists comparing to Uniform solution.
???
???????
, the bunch extraction can
?
?\?????
???
is varied periodically to
?
???????
???
4G???
???????
*
. In addition, with
?
? , a wide flexibility changing parameters
? and
*
Boundary conditions and solutions
In addition to the general considerations for the DR pat-
tern, there are several boundary conditions coming from
the real accelerator system as follows:
]
The damping ring’s circumference is approximately 6
km. This was decided after a through set of studies
considering beam dynamics issues.
]
The maximum linac average beam current is 9.5 mA.
]
Thebeampulselength,
imately 1 ms.
^B_R`)acb?d
?
?3???
????? , is approx-
Table 2: ExamplesofUniformsolutionforDR fill patterns.
Units for
respectively.
?3e ,
3484
2752
5289
3074
2644
fRgihkj , and
1.61
2.03
1.06
1.82
2.12
^W_iacb are
9.5
9.5
9.3
9.3
9.3
L)Xml
eparticles, mA, and ms
noIp orqsktkuNv wyxkzD{
0.96
0.96
0.96
|}~
1434046011.22 9.50.95
0.95
0.95
2
3
4
2
1
4
107
81
64
123
71
61
67
59
56
59
203
59
1
1
1
114516
103
30
Table 3: Examples of Step solution for DR fill patterns.
Units for
ms respectively.
?€e ,
4032
2688
2520
fRgihkj , and
1.39
2.08
2.20
^W_iacb are
9.63
9.63
9.63
L)Xml
e
particles, mA, and
??2?3efRgZhkj^W_Za‚b
0.93
?
*
?
1440050401.109.630.93
0.93
0.93
2
3
3
3
120
96
64
60
60
50
75
80
]
Theminimumbunchseparationshouldbe3.08ns(two
damping ring RF periods) to allow for the kicker/rise
and fall time.
]
The maximum kicker reputation is 6 MHz, which is a
likely upper limit based on present tests[5].
]
Gapsofatleast 40nsshouldappearintheDR’s fill ap-
proximately every 50 bunches, for ion cleaning. This
is based on expectations from recent simulation stud-
ies of fast ion instability.
]
The number of particles per bunch should not exceed
e, andthelayoutshouldbe capableofaccom-
modating fills with bunch chargeas low as
This claim is basedon effectsat the interactionregion.
=?[D=/ƒ
The total number of particles in a train should be at
least
LSXyl
L
[
X
ƒ
L)X?l
e.
]
U?[„…ƒ
LSXyl\†, to achieve the required luminosity.
6.7 km circumferences, respectively. In this table,
bunch number actually filled,
a bunch, and
point is thatis almost half of
In these cases, separation of mini-trains (
(
because the extractin position is shifted by roughly half of
? value every DR revolution.
Examples of Step solution are given in Table 3 with
=6.6 km. The definition and units of the parameters are
same in Table 2. Those solutions have exact periodic pat-
tern, e.g. 10, 15, 32, etc. This characteristic is usable for
the positron production based on the Compton scheme as
described later.
Examples of Uniform solution are given in Table 2.
Those solutions with
? =14340 and 14516 have 6.6 and
?
 is
?
e is number of particles in
f
gZhkj is average beam current. An interesting
.
? for the last two solutions.
? ) is actually half
) is double (
‡ˆ?
?
=) and number of mini-trains (
*
‡
=Z*
),
?

Page 4

CONSTRAINTS FROM THE POSITRON
PRODUCTIONS
Self-reproduction Condition
E+ beam is generated by e- beam before the collision
by passing the undulator. Gamma ray is converted into e+
beam in a conversiontargetand transportedinto e+ injector
linac. The self-reproductioncondition,in which the e- gen-
erates the new e+, who is the collision partner in the next
pulse. Assuming this self-reproduction, the generated e+
can be accepted by DR with any DR fill patterns, because
the corresponding e+ bunch is already extracted. The path
length for the round trip from and to the e+ DR has to be
an integer of DR circumference.
e+ DR
∆2
∆1
IP
e- DR
L4
L2 L1L3
Figure 2: A schematic layout with the significant beam line
length.
A schematic layout is shown in Fig. 2. e+ production
target is at the junction of three sections,
l is the distance from the injection kicker to the extrac-
tion kicker in the positron DR.
bunch in the positron DR travels in the time between the
extraction of the electron bunch with which it will collide,
and the arrival of the positron bunch at the positron DR in-
jection kicker.
kicker timings; all other lengths are fixed in construction.
To ensure collisions at the IP:
‰
l,
‰?Š , and
‰?‹ .
Œ
Œ
Š is the distance that a
Œ
Š can be changed simply by adjusting the
‰
lŽ
‰
Š
?
Œ
l?
Œ
Š

‰
†
[
(6)
For the self-reproducing, the condition is:
‰
l

‰?‹
?
Œ
Š
?
?
,
(7)
where
inating
?
is the DRcircumferenceand
Š :
 is aninteger. Elim-
Œ
‰
‹

Œ
l?
‰
†
?
‰
Š
?
?
[
(8)
Assuming
the constraint 8 can be satisfied by adjusting (at the design
stage)
along the main linac is arbitrary; it may be adjusted simply
by increasing
vice versa.
‰
Š ,
Œ
l, and
?
are fixed early in the design,
‰
†
‰
‹ . We notethatthepositionofthepositronDR
‰
†, and reducing
‰
‹ by equal amount, and
Longitudinal separationof two interaction points
In the current baseline design of ILC[1], two interaction
points with a longitudinal separation is assumed. The lon-
gitudinal separation should be an integer of a half of the
linac bunch spacing for collisions. It is desirable allowing
several fill patterns and it could be implemented when pos-
sible bunch spacings are in a simple ratio to each other.
Greater flexibility is provided by the use of delay lines,
which is now a part of the baseline design.
Super-period in DR Fill Pattern
In Compton e+ production scheme, gammas, which will
be converted into e+, are produced by Compton scattering
between laser and e- beam.
Laser is operated in a mode-locked with 325 MHz,
stored, and stacked in an optical cavity, in which the laser
power is enhanced by the stacking. The laser burst wave
shuttles back and forth in the optical cavity with 325 MHz.
Electronbunchesare storedin CR with 3.08ns bunchspac-
ing to ensure the synchronous Compton scattering every
325 MHz cycle.
Because CR has circumferenceexactly1/10smallerthan
that of DR in the current design and positron bunches
generated in a period corresponding to 10 turns of CR,
will be filled into DR, the bunch fill pattern in CR must
be repeated 10 times in DR. At this moment, some
remainder is allowed, i.e.DR pattern can be
L)X
ƒ
???’‘”“k•
bucket 10 times. After some cooling period, this process
is repeated 10 times to achieve the full intensity.
Because the bunch fill patterns in CR and DR have to be
synchronized to each other over many turns, DR harmonic
number,
10 super-periods. Because this can be implemented only
with Step solution and not with Uniform solution, only
Step solution is possible when the e+ generation with the
Compton scheme is employed.

?
?
*B–
?—?
.)˜

?
š™S›
;
.œ.S
?
˜ž–
“Z•B?
?
.
?
™. However,
because the e+ intensity from one Compton scattering is
1/100 less than the requested, this process is repeated 10
times, so that positron bunches are stacked into a same
? , and the DR bunch fill pattern must have exactly
SUMMARY
Constraints of ILC system for the DR fill pattern, injec-
tion/extraction scheme, and the layout were discussed. We
have confirmed that various solutions exist, providing dif-
ferent flexibilities. The final solution should be obtained
as a result of a system-wide optimization by considering
technical detail of each components.
REFERENCES
[1] ILC Baseline Configuration Document (February 2006).
http://www.linearcollider.org/wiki/doku.php?id=bcd:bcd home
[2] S. Araki et al. “Compton based ILC positron source”, KEK-
Preprint, (September 2005).
[3] W. Kriens, Basic timing requirements for TESLA, TESLA
2001-10 (2001).
[4] H. Ehrlichmann, Bunch timing aspects for ILC presented in
ILC-GDE meeting at Frascati, Italy (December 2005).
[5] T. Naito et al., Annual meeting of PASJ, 21P056, (August
2005)
[6] A. Wolski, J. Gao, S. Guiducci (eds.), Configuration studies
and recommendations for the ILC damping rings , LBNL-
59449 (February 2006).