# 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.

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**ABSTRACT:**Positron generation is one of the most difficult technical challenges among ILC (International Linear Collider) sub-systems. In Conventional method, the positrons are gen-erated, via the pair-creation process in Electro-magnetic shower induced by electron beam in a target. In ILC, a pulse train contains 2625 (5120 for low Q parameter) 3.2 nC (1.6 nC) bunches and a fixed solid metal as the positron production target can not survive and a fast rotating target (more than 100 m/s tangential speed) is required. The cur-rent baseline design is based on Undulator radiation, which mitigates the thermal stress slightly, but not dramatically; 90 m/s tangential speed is still necessary. In this article, I propose an ILC positron source based on Conventional method with a liquid metal target system under develop-ment in Budkha Institute for Nuclear Physics, Novosibirsk, Russia. This concept resolves not only the technical dif-ficulty on the target, but also issues on system complex-ity introduced by the Undulator method: path length con-dition, inter-system dependency, commissioning scenario, problems associated with electron deceleration, etc. This scheme makes the whole ILC system much simpler and the system availability higher.

Page 1

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.)

Page 2

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

noIporqsktkuNvwyxkzD{

0.96

0.96

0.96

|}~

1434046011.229.50.95

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_Zab

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=/

The total number of particles in a train should be at

least

LSXyl

L

[

X

L)X?l

e.

]

U?[

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 (

?

?

=) 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

L2L1L3

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,

? , and

? .

is the distance that a

can be changed simply by adjusting the

l

?

l?

[

(6)

For the self-reproducing, the condition is:

l

?

?

?

?

,

(7)

where

inating

?

is the DRcircumferenceand

:

is aninteger. Elim-

l?

?

?

?

[

(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.

,

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

???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

??

.)

?

S

;

..S

?

ZB?

?

.

?

. 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).

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