THE NEXT LINEAR COLLIDER* 1. 1. Introduction - Semantic Scholar

SLAC-PUB-5406 February 1991 (A)

THE NEXT LINEAR COLLIDER* Ronald D. Ruth Stanford Linear Accelerator Center Stanford University, Stanford, California 94309

1. 1. Introduction There is now broad agreement in the high energy physics community that to continue exploring the energy frontier in e+e- interactions, we will have to abandon circular colliders and adopt linear colliders. This realization has led to active research throughout the world towards the next generation of linear colliders. The past few years have seen great strides in our understanding of both the accelerator physics and the technology of linear colliders. We are now at the point where we can discuss in fair detail the design of such a “Next Linear Collider,” or NLC. 11-51 The two key design parameters of the NLC are its energy and luminosity. A broad consensus has emerged over the past couple of years that the energy should be 0.5 TeV (total electron plus positron energy), upgradable to at least 1.0 TeV. One reason for this choice of energy range is the great potential of such a collider for significant high-energy physics research in the era of the SSC. Another is that this energy range is a natural next step; it is a factor of 5 to 10 beyond that of the present Stanford Linear Collider (SLC). In order to obtain a sufficient event rate to perform detailed measurements, the luminosity of the collider should increase with the square of its energy. For an NLC in the TeV energy range, a luminosity of 1O33- 1O34cm-2s-’ is required. A factor of 5-10 energy increase can be obtained in two ways: by increasing the collider length to 10-20 times that of the SLC (3 km), or by raising its accelerating field to 5-10 times the SLC gradient (20 MV/m). The present consensus is that we should first increase the accelerating field by about a factor of three to five-up to about 50 to100 MV/ m. To limit the RF power required, this field should be provided by structures similar to those used in the SLC but at a higher RF frequency of lo-30 GHz. At SLAC, the frequency choice for the NLC is 11.4 GHz, or four times the present SLC frequency. Of course, the ultimate tradeoff

* Work supportedby the Departmentof Energy,contract DE-AC03-76SF00515. Inviteo! talk at the 18th Annual SLAC Summer Institute on Particle Physics, Stanford, CA, July 16-27, 1990; and at the 1990 US-CERN School on Particle Accelerators: Rontiers of Particle Beams, Intensity Limitations, Hilton Head Island, SC, November Y-14, 1990.

-

between

length

and

upgradeability.

accelerating

A broad

(accelerating

structure,

field

optimum magnets,

is governed

occurs tunnel,

by the overall

at the point etc.)

equal

where

cost and the

the linear

costs

the cost of the RF powel

source. The choice of luminosity ear collider.

In principle,

the repetition

rate of the accelerator,

100-200

MW.

shrink

must

strahlung”

each machine

we get both

to the beam.

structure

Given

layout electrons

compressors

efficiency

With

factor

only transfer

t,hat direct]?.

tha.t can be stored

of beamstrahlung

a

a.dditional

of energy

another

on

radiation

in the

tha.t can be bunches.

each

we can now sketch

collide

a rough

and luminosity.

are two complete

linear

After

passing through

at a small crossing

with

particle

consisting

of a

A possible

accelerat,ors,

Each linac is supplied section

design

one for beams

of two bunch

the main linacs and final

angle inside

a large particle

like the SLD.

To illustrate through

the basic features the collider.

source and accelerated bunches

t.he

bunches

extract

st.ructure.

in each bunch,

by a preacceleration

and a 16 GeV linac. the beams

several

the desired energy

for positrons.

ring followed

focus system,

bunches

1. There

and the other

by a damping

detector

in Fig.

with

of particles.

able to achieve both

is shown

cross

of “beam-

interact

can, in practice,

by the RF energy

these goals and constraints,

collider

the amount

is to generat’e tra,ins of successive

number

is to

the beam

or positrons

and higher

and by the amount

moderate

fall in the range

In addition,

in the accelerating

of particles

solution

in direct

the luminosity

by acceler.ating

of particles

luminosity

is limited

The obvious

a fairly

linear

The number

the luminosity,

tolerated. with

greater

increases

should

to minimize

electrons

enhanced

available

(IP).

by raising

bunch.

A single bunch

of the energy

accelerating

point

as energetic

ca.n be further

cycle.

power

power

of the lin-

simply

the best way to increase

field of the opposing

The luminosity

affects

emitted

the design

the luminosity

the wall-plug

be kept flat at the IP in order

electromagnetic

bunches,

design,

size at the interaction

radiation

few percent

increase

influences

but the wall-plug

Given this constraint,

the beam

section

one could

In a reasonable

proportion.

.

range also greatly

is then injected

of the NLC operation,

A sequence of 10 bunches

up to about

let’s follow

or so is created

1.8 GeV in a. preaccelera.tor.

into a damping

ring that

2

some electron

This

at the

“batch”

serves to reduce the transverse

of

Compressor

.,: ...‘ .,.........I. .,,,,, ..:: ‘8: .,.:” ..:

F Pre-Accelerator

t

Compressor Damping

Ring

Main Linac

,,;:i’:;

J te-

Electron

Source

P

Beam Dump

Final Focus

Electron

Source

Positron

Source

Beam Dump

t es Main Linac

Pre-Accelerator

4

::,, ,..:.: w..,.

Compressor 7-90

4494A96

Fig.. 1. Schematic

diagram

3

of the NLC

and longitudinal proper

moment,

along their erated

phase space occupied these bunches

direction

linac.

magnets

in the final focus system

300 just

before

they

occurs when bunches

collide

of electrons

have followed

channeled

1.1

a similar

out of the detector

NLC

differently,

we have recently

down

reviewed

options:

Option

several options

the first

acceleration

2, a long linear

Option required

In both

of the 1ina.c while collider

debris is

short

This

keeping with

to Option

paths,

a reduced

an initially

longer

with

the increased

in the design process that

damping

ring.

To model

in Table

1. In addition,

the injection a reduced

the emittance

fixed.

13 In

gradient

somewhat. 2, but we are

for RF power The price is

construction.

it is very important

to realize

that

than those in the

to decrease as shown

at the final focus is assumed

4

with

and the required

gra.dient.

conventional

the

of power sources

gradient

ha.s been allowed

while

to Option

system

Option

at the final focus are quite different

this, the intensity

1 lists three

acceleration

than

acceleration

energy

is constructed

2, we relax the requirements

with

and emittance

collider

of the high acceleration

of four and begin

We have found

TeV. Table

the final focus must be modified

In Option

At SLAC,

has an initial

3 by the addition

by a factor

accelerator

which

can be upgraded

and may be less expensive

high peak power RF sources.

over the past few

are for 0.5 TeV in the CM,

is constructed

to face all the problems

the intensity

positron

their

considerably.

energy of 1.0-1.5

of 100 R/IV/ m.

upgrade

1 is quite

yet; however,

1, a short linear

This can be upgraded

to the linac.

that

dumps.

for an NLC

two columns

gradient

the length

of 50 MV/m.

these high-energy

the range of possibilities

is for 1 .O TeV. In Option

by doubling

of

Except

of particles

the beams collide,

are not definite

of 0.5 TeV in the CM and an upgraded

the full

a factor

of positrons.

the shower

area and into shielded

and foPrecision

down by about

target,

After

steered

in the linac.

bunches

from

hits a metal evolution.

for an NLC

years we have narrowed

final column

similar

to injection

PARAMETER OPTIONS

The parameters

parameter

is carefully

squeeze the bunches

they were created

a bunch

batch

up to full energy

at the IP with

At the

after which they are accel-

a second time just prior

The entire

are accelerated

in each bunch.

the ring and then compressed

by a bunch compressor,

high-gradient,

for the fact that

from

16 GeV and compressed

cused as the electrons

.

are extracted

of motion

up to about

into the main,

by the electrons

to be diluted

Table

NLC

1.

Parameter

Option

1

2

3

Energy

i + i TeV

$ + i TeV

$ + 4 TeV

2 x 1033

2 x 1o33

1 x 1o34

Luminosity Linac Accel.

14 km

I

Gradient

I100 MV/m

1 50 MV/m

I 100 MV/m

1 11.4 GHz

1 11.4 GHz

1 11.4 GHz

2 x lOlo I Linac I 1.8 x lOlo

1 1 x 1010 I I 9 x 10’

1 2 x 1010 I I 1.8 x lOlo

FF 1 1.5 x 10”

1 7 x 10’

1 1.5 x lOlo

I

I

# Particles/bunch:DR

# Bunches,

I

nb

10

10

1

14 km

10

Repet,ition

Freq.

120 Hz

180 Hz

180 Hz

Wall-Plug

Power

66 MW

50 MW

200 RIW

UY

4 nm

4 nm

2.5 nm

cx

320 nm

200 nm

220 nm

0.2

100 pm

100 /Lrn

100

IP Beam

Size:

pm

65%.

To discuss the NLC in more detail, parameters: obtain

1

7 km

Length

RF Frequency

by about

Options.

the energy

the energy

we divide the problem

and the luminosity.

into the two primary

In the next section

we discuss how t,o

in an NLC.

2. The Energy As discussed through

in the Introduction,

a combination

of length

where

&= is the acceleration

lation

is over-simplified,

the energy of the linear

a.nd acceleration

gradient

5

is obtained

gradient,

and L is the length

for reasons which

collider

we discuss later,

of the linac.

This

re-

in tha.t the average

acceleration

gradient

may differ from the peak and the length

for focusing

magnets,

etc.

The acceleration as shown

in Fig.

basically

is obtained 2.

a long copper

the center line.

Every

The

with

structure

cylinder

the use of radio shown

periodically

so often (every

may include

frequency

is a travelling interrupted

(RF)

space

structures

wave structure. by disks with

1.5 m or so), the structure

a feed for fresh RF power and a load to remove the depleted

It is

holes along

is interrupted

upstream

by

power.

Waveguide /

RF Power Source

-? Accelerator Structure

r-1 I I I I I I I I I I I I 1 II IIll I)! \ IIll 1 I I Load

Beam Axis

_ 12-90 6793A2

Fig. 2. Diagram

The RF power erating

structure

wave structure

is provided in a copper

is designed

enters the structure

continually

accelerated

is the rate at which envelope length

wave RF structure.

by the RF source and is transported waveguide.

The structure

and, as such, has a characteristic

The phase velocity electron

of a travelling

as it traverses the structure

is filled

For cases of interest,

with

energy;

velocity

is somewhat

6

then it will be

The group

velocity

it is the velocity

wave structure.

then the time to fill the structure

the group

velocity.

In this way, if a relativistic

structure.

the travelling

as a travelling

and group

phase for acceleration,

the entire

of the RF pulse as it traverses

of the structure,

phase velocity

to be the speed of light. at the correct

is designed

to the accel-

vg

of the

If L, is the

Tf is given by

less than

one tenth

of the

velocity

of light.

2.1

THE EXTRACTION OF ENERGY

The energy gain of a test particle

at the head of a bunch traversing

a structure

L, is

of length

AE = ~zL,cos~ , where 9 is the phase on the RF wave. The trailing supplied

by external

gitudinal

wakefield.

of oscillation

particles

sources, but also the field induced

by the bunch itself, the lon-

structure.

The field induced

Ewake = -2k q cos(w*/c)e-Az k is called

compared behind

the loss parameter:

to the wavelength the point-like

structure

walls.

causalit,y.

The total

The wakefield wakefield

This field induced The particles

)

(4)

q is the charge in a bunch

and X is the decay

constant

ahead of a speed-of-light induced

the dominant by the particle

which

z is the distance

vanishes

term

is given in Eq. (4).

bunch causes problems

reduced

by 2kq.

feel an accelerating

accelerated

on the crest of the RF, this causes a reduction

by the bunch,

and it also causes an energy

which

must be dealt

If the particles

while those are being

of the average energy

sprea.d:

AEwe = ((5 - k)L W)spread These effects induced

= fWs

are due to the extraction

by the bunch

due to

consists of a sum over all the syncl~ronous

at the head of the bunch feel the full accelera.tion, field

is short,

due to losses in the bunch

at the tail

gained

in the fundamental

of the RF, w is the RF frequency,

bunch,

modes of the structure;

with.

modes

mode is

. where

see not only the field

The bunch charge induces fields in all the synchronous

of the accelerating

accelerating

(3)

of energy

reduces the electric

(5)

. from

the RF wa.ve.

field in the structure

7

The field

an a.mount

which

corresponds energy

to the energy

extracted

from

extracted

by the bunch

a full structure

of pa,rticles.

by a bunch

The fraction

at the crest of the RF is

qo,= 1 _ (82 - 2w2 e N- 4kq - fz The reduction either

of the average

by increasing

to make up the lost energy. for by shifting little

variation

induced

a full width

Ay,

gain can be compensated

field &= or by adding

more accelerator

The spread of energy in a bunch

the phase of the bunch

loss of acceleration,

(6)

for small 70

value of the energy

the accelerating

on the RF wave.

it is possible

to obta.in

by the bunch wakefield.

can be compensated

In this way, with

a slope sufficient

For a. uniform

sections

particle

very

to cancel the

distribution

with

the phase offset is

2kq ‘lnyo Provided well.

In order

intensity into

that

variation

the pha.se offset

to achieve a small phase offset, the bunch can be lengthened

or the

With

very long bunches,

and can, in fact,

In the Introduction, order to improve From the analysis

the curvature

With

which leaves a residual than the energy

MULTI-BUNCH

this compensa.tion

be used to provide

of energy along the bunch.

must be kept smaller

which

is small,

(7)

’

works

can be cancelled,

2.2

= Ap&z

technique

reduced.

account

of

of the RF must be taken

compensation

short bunches, nonlinear

of the nonlinear

only the linear

energy va.ria,tion.

acceptance

variation

This residual

of the final focus syst’em.

ENERGY COMPENSATION6 we discussed the acceleration

the luminosity of the previous

by extracting section,

of a short train

of bunches in

more energy from the RF structure.

the second bunch

must have an energy

is lower by

AEz Once again, this is simply

= -2kqL,

,due to the extraction

8

. of energy from

(8) the RF wave.

This

problem

the two bunches. through,

can be sohved bl’ changing

the effective

If the structure

filled

and if the additional

of the second bunch second bunch

energy entering the energy

to compensate

areas of the external

the energy difference.

energy of the positrons

when

the first

the structure

extracted

prior

b!. the first

will have the same energy as the first.

the cross-hatched

the relative

matches

is partially

structure

bunch

for

pan”

to the pas5agt’ bunch.

This is illustrated

field and wakefield

This technique

length

must

then

tllo

in Fig. 3:

mat.ch in order

is used at the SLC to adjust

and electrons.

rl

(a)

LS

Ewake 12-90

6793A3

Fig. 3. The electric field profile iri tire structure (a) just before passage of bunch one and (1~) just before passage of bunch tn’o.

MULTIBLI\‘CH BEAM BREAKLP

2.3

Let us assume that

are still other

b1 a bunch of particles.

If the bunch

in the previous

wakefield

induced

the bunch.

This

tile energ!. of a sl~ort trail]

There

described

then it induces

Iye can match

a deflecting transverse

section.

force behind wakefield

it which

is similar

problems

is proportional in form

cause deflection,

where

mode.

of a particular

9

caused 1,~. tllc,

is offset in the structure’.

consists of the sum of many modes which

11’” is the strength

of bu11c11e.+a’

to the offset of

to the longitudinal

z is the distance

behind

alit1

a sl~~l:

bunch,

wn is the is the mode frequency

n. The transverse sine-like

while

wakefield

differs from

the longitudinal

The transverse

coming

the structure,

into

wavelength

of the coupling

To see this, consider the magnet

bunch’s

bunch

is also,focused

the transverse

is

as beam to bunch

breakup:” and also by

If these two are offset

causes them

to oscillate

with

freely down the linac according

a

to

(10)

P2 in addition,

is deflected

by the leading

wakefield

where N is the number The deflecting one oscillates oscillates

of particles

in bunch one and E is the energy of the bunches.

force is proportional in the focusing

and bunch

second bunch

grows linearly

one and bunch

at resonance.

The solution

is to eliminate, This

Therefore,

one. Because bunch hand side of Eq. (11) the amplitude

bunch three is driven

two and so on. The result

problem.

and is the subject

the force on the right

for many bunches:

can reach large amplitudes

together.

of bunch

of the

down the accelerator.

the train

the bunches

to the position

system,

two is driven

The effect is similar bunch

but,

bunch

just two bunches.

2n/3. The first bunch oscillates

second

known

from

focusing

d2xl z+s=o.

The

in that

can cause an instability

It is caused by the combination effect.

the longitudinal

for mode

is cosine-like.

wakefield

a resonance

and X, is the decay constant

is that

unless something to the extent

can be done by a special

of the next section.

10

on resona,nce b>

the bunches

at the end of

is done to ameliorate possible,

the

the force coupling

design of the RF structure

-

ACCELERATING STRUCTURES

2.4

As discussed

earlier,

As such, it is usually RF power.

optimized

In addition,

single bunch bunches.

the job of the RF structure to provide

the greatest

acceleration

the design can have a large impact

(to be discussed

field induced

of a train

by a bunch

of bunches,

on the stability

we would

as much as possible

the beam.

for the lowest

3.6.2) and on the stability

in Section

To assure the stability

deflecting

is to accelerate

of a

of a train

of

like to reduce the

before the passage of the

next bunch. This can be accomplished in Fig. 4(a), coupled

the cavity

to external

die out quickly The design

design is altered

so that

After

waveguides.

a,s they

shown

in two ways (see Fig. 4). In the first method,

a bunch

are propagated

in Fig. 4(a)

the deflecting

shown

fields are strongly

passa.ge, the fields in the calit)

out the waveguide

shows ra.dial wa.veguides

into

a matched

coupled

load.

via slots cut in

the irises of the accelerator? The _

second

deflections

from

technique, cell to cell.

so tha.t the deflecting deflection

in frequency.

This

oscillate

ie. 1ies on the cancellation

at different

effectively

The initial technique

is accomplished

in Fig. 4(b)

If the cells in a single short

modes

over the structure

ious cell wakefields.

quency

shown

frequencies,

then

are designed the average

da,mps due to the decoherence

decoherence is illustra.ted

with

structure

three radial

of the

of the var-

time is just the inverse of the spread in Fig. 4(b),

where

the change in fre-

slots of varying

depth

cut into the irises

of the structure. Damped

structures

similar

at SLAC

and have achieved

mode. “J

This

discussed The technique

damping

in the previous second which

to tha.t shown in Fig. 4(a) have been constructed

a qua.lity

is completely section.

technique is presently

factor

Q - S for the dominant

sufficient

to eliminate

higher-order

the beam

breakup

and possibly

simpler,

73

of detuning under

is an alternative,

investiga.tion

11

a.t SLAC.

(a) Beam

(W

12.90

6793A4

Fig. 4. Two methods of wakefield damping: (a) ra.dial waveguides transmit the energy out of the structure; (b) variation of cell construction causes decoherence and effective damping. 2.5

RF

POWER SOURCES

To achieve the desired power

sources

must

length

at the desired

acceleration

be provided

of 50-100

gradient,

it is necessary

of about

100 ns in length

AN/m

3 m in length.

which

yields an acceleration

increase

gradient

In t,he designs

to provide

tures

for the Kext

give the required

at an RF frequency about

is accomplished

of about

in such a structure

the RF peak power

about

with

12

energy

RF

and pulse acceleration

To achieve the larger in a pulse

1.5 m in length.

2.8 GHz accelerating

20 MV/m.

to 100 RIV/m,

and the stored

power

of peak RF power

Each of these is fed by a 40 MW gradient

Collider.

1 we find

of 11.4 GHz.

350 hlW

Linear

peak

in Table

to be fed into a structure

In the SLC, the a.cceleration

acceleration

which

frequency.

gradients

gradient

pulse

about

struc-

1 ,us long

In order to increase it would

by a factor

be necessary

of 25.

the to

At the higher increase

frequency

by a factor

of 25; however,

l/16.

Thus,

factor

of two, provided

changed

the energy

very little,

and feed a shorter

The first

approach,

pulsed

shown

a modulated

power

transformer,

is utilized.

The primary

the characteristics

in Fig. 5(a), pulse

to this

Although

This

from that at the

but shorter

in duration

for the RF power

described

above.

as outlined

in Fig.

by RF pulse compression

After

to the desired

With

5. this

by a conventional

pulse is converted

it can be compressed

by a

the energ!. is

uses RF pulse compression.

by some device such as a klystron.

higher

changes

of

challenge

problem

of the same duration

correspondingly

only

of m 1 ~1s is provided

a modulator.

once again

area drops by a factor

in peak power,

approaches

power

must

of the RF pulse is very different

structure.

two

density

in the RF structure

frequency

a source with

are basically

technique,

length

the higher

accelerator

the energy

the cross-sectional

RF pulses are higher

is to provide

There

per unit

the structure

SLC. The necessary

system

of 11.4 GHZ,

to an RF pulse the RF is created,

pulse length

with

a

peak power.

(a) RF Pulse Compression n

Klystron ---Modulator Pulse

Compress RF

IL RF

(b) Magnetic Compression

--

Modulator Pulse

Fig. 5. Two methods

The second technique, power

pulse

and then

pulse compression;

of producing

magnetic

compresses

short high peak power

compression,

is achieved

a technique

in parallel.

13

called

before the creation

by a device such as a relativistic

power sources driven

RF pulses.

begins with the same modulated

this pulse using

the time structure

this stage, RF can be created array of multiple

RF 12-90 67Q3A5

magnetic

of RF. After

klystron

or b). an

This second technique

has been

under

experimental

The relativistic This

investigation

klystron

t.echnique,

by a collaboration

achieved a power output

however,

source due to inefficiency.

is presently and cost.

of SLXC.

LLSL.

of 330 M\l’ with

not considered The remainder

and LBL.

a 20 ns pulse!’

a candidate

for the po\ver

of this section

is devoted

to

the first alternative.

2.5.1

The Klystron

A block diagram in Fig. 6.

of the RF power system with

The modulator

poiver

supply

RF pulse compression

is conventional

is shown

and is similar

in most

respects to those used at SL.4C for the SLC. Th erefore. we will begin the discussion with

the klystron.

/’ //

L-l

I I, Pnwpr

I

/ /’ ,/

/’

I

I

Klystron

1

12-90 6793A6

Fig. 6. Block

A schematic klystron

an electron

across the cathode 400 I(\’ with

frequency.

of a klystron high-gain

to the input

radio

The electrons

of about

magnet

is shown

in Fig.

frequent).

7.

Put

providing

cavity

Due to the induced

(5

\ver\. simpl>.. a To achie\,e thiy

anlplifier.

beam is created bx the voltage induced

and anode.

a current

a solenoid

applied

diagram

of RF po\ver s!.stem \\-ilh RF pulse compressiorl.

is a narroiv-band.

amplification,

with

diagram

by the modulator

are accelerated

to an energ!. of

500 .4: they are transported

dolvn a narrow

the focusing. 1 k\\‘)

velocity

modulates difference.

14

.4 small

amount

the beam

tube

of RF po\ver

energ?

the faster electrons

alJoUt

at the RI’ catch up I(!

RF Out

Cavity

12.9c

Fig. 7. Schematic those that

were decelerated.

diagram

6‘93A‘

of a kl!.stroll.

This creates a small densit!.

modulation

of the beall]

as it enters the first gain ca\.it!.. This

cavity

is resonantly

excited

b:. the RF electric

beam

to a field of approximatel!.

10 times

acting

back on the beam provides

much

reaches the second gain cayit!.. beam bunches

by the penultimate

This process continues

or more

standing

beam induces so that

it. This deceleration

it to the cavity

fields which

flows out the waveguide deposited removed

structure:

regioll.

by this process.

to an external

.and can be transported collector

the beam

This

compressed

This ma!. be

\vave structure.

this structure

CHIC

Thc~

is designed

the sequence of bunches

the RF energy in the bunches and transfer.\

are coupled

\\‘ith

is furtIler

structure.

however.

field

the final gain ca\.it!..

or it may be a travelling

extracts

in a water-cooled

\vith

the parameters

waveguide.

for further

approximatel!.

The RF power.

use.

The

bealn

i\

one half of its energ!.

given ab0L.e. tile kl!.stron

produce\

100 MU’ of RF power.

Klystrons SLAC

in the final drift

a field in the output

This

b!. as much as 30% of its \.aluc.

and then enters the output

\vave cavities.

ca\-ity.

h!. the time

until

the phase of the RF field is such as to decelerate

entering

about

strongly

cayit!.

in the input

deeper bunching

where the energy of the beam is modulated modulated

that

field of the modulated

similar

in all respects

and have achieved

of this writing13

to the one just

75 11\\* in short

described

pulses and 50 \I\\.

have been built

in long pulses a-

The design goal is to achieve a 100 1I\\‘ kl>,stron

15

a~

at 11.4 C;ll~

with

a pulse length

directly

of about

in the acceleration

2.5.2

1 ps. This pulse length

process; we need RF pulse compression.

RF Pulse Compression

The object

of RF pulse compression

power into a short pulse length

RF pulse with

could yield a factor

(SLAC

Doubler)

by about storage

a factor cavities

effectively

to allow

cavities.

spiked

For an NLC

energy

before

used at SLAC

powering

the RF to build

flat-top

method,

called

leading

Due to inefficien-

to boost

up.

system

SLED

the klystron

power

linac.

This

system

A phase switch

from

the klystron

this

dtie to the exponential

system

uses

gives a pulse

shape

decay of the fields in the storage

it is useful to have a flat-top

pulse

This

yields

pulse to control

to about

compression

(BPC),

an RF pulse which

multibunch

dia.gram

two power inputs

relative

In this way phase shifts

a multiplication

sufficient

100 MV/m.

first

lines to delay

in time

with

the

the tra.il-

is one half as long, but with

nearly

in a sequence to achieve more and and waveguides,

of a two-stage

system,

factor together

the method

One disadvantage

system

of 5.5 while reducing with

two lOO-MW with

of the BPC

method

long delay lines. The waveguides

output

is

at SLAC

would

an acceleration

upon

RF switches.

the pulse length klystrons,

was

device

port depending

and has

by a factor produce

gradient

RF

of about

system are continuing.

of pulse compression

is that

which a.re used ha.ve a group

they are only used once as transmissive

16

which

in Fig. S is a four-port

design has been constructed

tests of this three-stage

close to the speed of 1ight;and

BPC

can be used as high power

for a 5-m long accelerator

High-power

shown

into one or another

system of analogous

of eight?’ This

The

three compressions.

which combines

A three-stage

methods.

uses delay

Due to losses in components

at SLAC. ‘*-I6 The 3db hybrid

phase.

different

so tha.t it is coincident

8 shows a schematic

constructed

achieved

by two

This process can be repeated

more multiplication.

Figure

pulse

of an RF pulse

twice the power.

limited

can be obtained

binary

portion

ing portion.

rather

of five decrease in

spread.

This

power

a factor

the SLAC

Unfortunately,

releases the energy.

is sharply

Ideally,

less. The RF pulse compression

is p resently

of three

a long RF pulse of moderate

of five increase in peak power.

is always somewhat

Energy

is to convert

high power.

cies, the factor

which

is much too lorig to be used

it uses

ve1ocit.y very dela,y lines.

2 STAGE BEC SCHEMATIC --f-

78 ns

156ns-j

-i

j--

3 db +--I 90” 4 Hybrid jrnL Hl

I

I

8.9

Fig. 8. Schematic This problem

diagram

has led to the development

of a BPC

except

that

for storing

input

pulse length

buildup which

range of four to eight. example

of a SLED

Measurements

from

shown excellent

a flat-top

II pulse compression

with

SLED

scheme called

system at SLAC

by resonant

delay lines.

equal to the output

pulse

in the lines takes place during

number

output

a low-power

to the SLED

delay time

stored

is an integral

agreement

Reannant

of energy

A phase reversal

stored energy to produce

system.

the RF are replaced

Each of these delay lines has a round-trip A resonant

‘nput

of a new pulse compression

II.‘” The system as shown in Fig. 9 is similar the cavities

Power

I

SLED

length.

312 I--

I ns I Jll

of delay periods,

of the input

pulse effectively

pulse during by a factor II system

typically

an

in the

releases the

the final delay period.

An

of four is shown in Fig. 10.

with

a power gain of four have

theory.

K = Klystron

3db Hybrid

nhu

I

l-91 6793A14

Accelerator Fig. 9. A block diagram

Comparing

SLED

a similar

compression

reflective

nature

builds

II with BPC, is reduced

the amount

of SLED

II.

of waveguide

by more than a factor

delay line to achieve

of five. This is due to the

of the scheme; the delay lines are used repeatedly

up. In addition,

this method

can be staged by placing

17

as the RF Lva1.e

the SLED

II s\‘stems

5

I

4-

: ;

I

I

S20

1 I

..*...-....-

1 2

0

4 TIME (Tf)

Fig. 10. SLED even larger

collider:

compressions

\ve discussed

depends

if necessary.

the basic la!.out

SLED

I1 this

we must trace this influence

however,

let’s examine

the luminosit!.

is the same as for a circular

collider

due to the mutual

and how to obtain

we discuss how to obtain

depend upon beam d!xamics

factor

A high-po\ver

at SL.I\C in 1991 to in\.estigate

upon beam properties

therefore,

enhancement

8

II pulse compression.

in this section.

the luminosit,,

those properties

I

further.

In the first two sections.

Although

I 6

6793A’5

system nil1 be constructed

technique

energy in a linear

I I I .

1

1.9:

promising

I

Input

l.--...-..-

pulse compression

I

output

3 2-

in series to provide

1

I

throughout

throughout formula. except

that

pinching

tlltx

the luminosit!..

at the interaction

point.

the entire linear collider:

the collider. Luminosit!.

Before doing that. for a linear

there is an additional of the beams.

collider tern].

all

The luminosit!,

i,

given b>

where

R*

frequency,

is the number

of positrons/electrons

nb is the number

HD is the pinch enhancement

of bunches accelerated factor.

and final]!..

18

per bunch.

.frep is

the repetition:

on each c\.cle of the accelerat 01. ur and oy are the rms bean] >i,t,

of the gaussian with

spot at the interaction

only one other The object

range

bunch

To do that

decrease the denominator the number

of bunches power

in the opposing

per bunch,

is in the range of 100-200

3.1

the numerator

we have at our

rate,

the constraint

gZ and oy, but

we discuss each term

and the number

that

the wall-plug

we can decrease the

to do this we must

in the luminosity

into severa.l sections.

keep the

formula.

The

In the next section

we

of Eq. (12).

let’s discuss the single bunch

From conservation

where

power

system

This is a fairly which

new ideas which

could

shown in Section

2.5, q7j is about

For somewhat 2%.

is induced

compensated

power

ra,te frcP.

is the total

efficiency,

were discussed

qrf,

estimate

775is the wall-plug

is about

including

in the first

section.

30-40%, however,

with

20%

all of the There

are

the system

20%.

reasons,

the single-bunch

In Section

2.1, we discussed

by longitudinal

wakefields.

the RF phase to obtain

to compensa.te.

to RF power,

and P,,lr

realistic

raise this to perhaps

different

by shifting

effects are difficult

wall-plug

The wall-plug-to-RF

RF system.

in the power

to about

I’Jh and the repetition

by a single bunch,

to the linacs.

for the projected factors

for converting

of the energy extracted supplied

intensity

of energy, we must have

qrj is the efficiency

fraction

which

of Eq. (12) and

INTENSITY AND REPETITION RATE

First

ited

the repetition

For the denominator,

of beam size is subdivided

begin with

the numerator

for the energy

For the numerator,

satisfy

to collide

beamstrahlung.

In the next few sections discussion

MW.

area by decreasing

beam flat to control

to 1033-1034 cmP2s-l,

as much as possible.

of particles

is assumed

train.

increase

on each cycle, but we must

cross-sectional

_

we must

Each bunch

bunch

is to increase the luminosity

$ to 1 TeV.

disposal

point.

This

a few percent.

19

limits

extraction

efficiency

is lim-

energy

spread

the single-bunch Although a linear

the linear

part

can be

slope, the higher

single bunch

energy

extraction

order to

For the purpose for an E,,

of this discussion,

necessary

the required

to control

for this feedback

an important

bunches

their

system

source of bunch motion,

It could

number

the sample

must

as low as 120 Hz; however,

the previous

parameter

motion

is

drops off rapidly than

60 Hz.

frequency

60 Hz is probably

to 180 too low.

values in Eq. (13), we find that the maximum

is iV* N 2 x lOlo.

THE NUMBER OF BUNCHES

As discussed eration

in the Introduction,

of many

of course, If there

bunches

to increase

is quadratic

the luminosity

a small

relative

consistent

with

transverse

3.7.1).

Thus,

with

into

energy stability

the quadratic

by increasing

because

As discussed

It turns

out that

3.6.2)

A large number

of bunches

of these were discussed means that the structure The energy presented

spread in Section

earlier.

This

intensity

must

limits

the number

must

it can extract

while is also

and wit.11 beam-beam

effects

by these bounds;

however,

it. is possible to continue

be stable

complications.

Some

transversely

which

2.3 and 2.4).

be controlled.

the solution

spread

introducing of bunches

can be tra.ded off somew1~a.t with

20

section,

in a special wa,y (Sections

2.2 does keep the energy without

in this case there

of bunches.

The bunches

bunch-to-bunch

by plac-

this intensity

along a host of other

must be designed

the energy can be extracted techniques.

brings

of bunches.

in the previous

of energy

gain is stopped

the number

of this is,

be obtained

since there is about 98% of the energy left in the structure, to gain linearly

The purpose

would

one bunch

(Section

the a.ccel-

number

by the amount spread.

include

increa.sing

luminosity

intensit,y.

is limited

retaining

(Section

train

increasing

intensity

linearly

the largest

in the bunch

ga,in with

the single bunch

the designs for the NLC

on each cycle of the collider.

were no constraints,

ing all the charge

bunch

be at least six

be greater

we set the repetition

it is

In order

Because ground

and because the spectrum

greater,

per bunch

system.

rate must

is changing.

be dropped

of particles

3.2

of 150 MW

dimension,

a feedback

rate of the accelerator

to have it sufficiently

transverse

with

efficiently,

the beam centroid

above 10 Hz, the repetition

Substituting

have a very small

offset pulse-to-pulse to work

times the rate at which

Hz.

power

= 1 TeV.

Because

In order

let’s select a wall-plug

Although small,

only

more complicated

about

compensa,tion

to about, 10; although the number

20% of

the single

of bunches.

The RF pulse must be of rather variations

over the bunch

not unrealistic

with

train

rings

which

without

on the same trajectory so that

subsystem

position

the distant

2% (such tolerances

Because a significant

a precision

the bunches

crossings

of bunches

of

the intensity

be able to accelerate

changes

the same energy.

fraction

less than 2%. The damping

must

or energy

bunches,

are

occur,

them

a compensation

enter the final focus system The final

focus system

do not disrupt

must

the primary

point.

the addition that

with

of bunches

and with

phase and amplitude

are due to the leading

to assure that

at the interaction

use energy

bunches

If small

system must be developed

Although

about

these trains

instability.

collisions

must be less than

must be controlled

produce

be designed

Systematic

the power sources discussed).

the fields felt by the trailing of the bunch train

high quality.

of many bunches appears

would

normally

be wasted,

of the entire

collider.

The benefit

to be “free” in that we simply

it introduces

complexity

is an order of ma.gnitude

into

every

increase

in

the luminosity. 3.3

THE BEAM SIZE

The transverse parameters:

size of a beam

the emittance

The emittance beam distribution

in an accelerator

c and the beta function

is a parameter in transverse

that

is determined

by two basic

,D,

is proportional

phase space (~,p~).

to the area occupied It is defined

by the

by

cy-- ;i < x2 >< pz > - < xp, >“]i ) where z is the transverse and po ‘is the central Eq. (15) indicate the quantity synchrotron the bunch

position,

momentum

pz is the corresponding of the bunch

an average over the distribution

in the square radiation), in a linear

brackets

the emittance

.

21

momentum,

The angle brackets

of pa.rticles invariant

decreases inversely

accelerator.

transverse

of particles.

is an adiabatic

(15)

with

in a bunch.

in

Because

(in the absence of the momentum

of

The longitudinal

emittance

in a similar

z is the longitudinal

deviation

from

a central

and Ap is the deviation

of the particle

Once again,

in the square brackets

the quantity

causes er to decrease inversely In the special

way,

< .z2 >< Ap2 > - < ZAP >2]+ ,

ez =

where

is defined

with

position

momentum

from

a central

is an adiabatic

the beam momentum

case of a high-energy

electron

and the bunch

length

speed of light.

In this case, the fractional

within

linac,

in a linear

all travel

momentum

momentum.

invariant,

the longitudinal

are fixed because the particles

the bunch,

which

accelerator. distribution

at essentially

spread varies inversely

the with

the beam momentum. The

beta

description

function

of the alternating

not only determines instantaneous

region,

focusing

by Courant of particle

beam size through

of the oscillations

the focusing

The beta function

introduced

gradient

the particle

wavelength

as they traverse

magnet-free

,B was first

magnets

also plays an important it has the particularly

beamst9

The para.meter

within

= 37r,B).

p* is the minimum

the IP in this case. point

value of /?( s ) and SO is the location

According

to Eq. (14),

point.

In a

form

P(s) =p*+csp2 ) where

the

the beam envelope

role a.t the interaction

simple

in their

Eq. (14), it also determines

of particles

(wa.velength

and Snyder

(17) of that

minimum,

the b earn size near the interaction

is therefore

02(s)= ep*+ ;(s - so)2. From this form,

it is obvious

increases

when s - so = ,L?*. Thus,

by fi

roles a.t the IP-it

determines

that

both

p* is the depth

of focus because the beam size

the beta function

plays two important

the spot size and dept,h of focus.

22

THE DAMPING RING*“”

3.4

The damping

ring serves to reduce the emittance

in all three degrees of freedom. features tion.

to the storage rings used for colliding The particles

their

It is an electron

in an electron

storage

energy on each turn--energy

the process of radiation, dom, but it is restored is supplied to damping

beams or synchrotron

light produc-

lose energy

a substantial

fraction

of

by RF accelerating

cavities.

In

from

only along one, the direction

in all three

Crete quanta,

in all essential

ring radiate

at a single RF phase for a particle

however,

introduces

stocha.stic

all three

of motion;

with

The fact

dimensions.

of particles

storage ring similar

that is restored

the particles

of the bunches

degrees of free-

the proper

amount

the design energy, which

that

radiation

is emitted

noise that causes diffusion

leads as dis-

of particle

trajectories. The competition librium

between

these damping

value for the emittance

designed

to enhance

those in wiggler transverse storage

focusing

emittance

two orders

of magnitude

many

designs.

and operates

a.t an energy

than

the vertical microns,

that

Another

of a beam

inject

10 batches

a new “young”

damping

from

is the simultaneous

fields

are

(such as

by the special design of the fea.ture of electron bending,

than the horizontal-typically flat bea.ms are a. key feature

ring is about than that

a factor

of

of five larger

of the SLC clamping

leads to much

smaller

this da.mping

ring

damping

rings

sizes. In fact, would

those in their

undisturbed.

23

point.

whereas

all at once. This feature

because we can extract

batch while leaving

be a few

of many batches of bunches.

are da.mped simultaneously,

of 10 bunches

time for any given bunch,

rings

of the beam is more than an order of magnitude

emerging

In the SLC, at most two bunches

damping

magnetic

equal to the final spot size at the SLC interaction

key difference

ring will damp

higher

of the SLC beams, which

extent

or about

damping

50 percent

Damping

Due to the lack of vertical

Such nat,urally

design for a future

ring.

there is a unique

of the beam is much smaller smaller.

effects lea.ds to an equi-

strong

the diffusion

In addition,

(see Fig. 11). Th e fi na 1 emittance smaller

storage

using

can be used to advantage.

the vertical

One possible

effects

while limiting

in the ring.

rings that

NLC

of an electron

the damping

magnets),

and diffusion

this NLC

allows a longer

the “oldest”

“adolescence”

batch and to continue

-

Injection Extraction e

g and Magnets 7-93 4494A95

Fig. 11. .A design of an NLC Because the bunches forget upon

emerging

are entireI>.

This places special emphasis and extraction 3.3

Although

shortens

emittance

an RF accelerating

that

structure

disperses

paths.

travel

a longer

bunch

can therefore

path

the cost of a greater

transverse

will

wakefields

so that

in the damping

in the damping

ring. ring

with

ring is small

in a linac.

higher

In the SLC

called bunch compression.

the trailing

particles

particles

of different

momentum

than those of lower momentum

\vhich

Each bunch passes througll emerge

Then the bunch passes through

the beam so that

Particles

\vith

a sequence

momenta

tra\.el

(at the head of the bunch) (at the tail).

catch up \vith the head. producing

a shorter

The tail of the buncll-but

at

energy spread.

type of bunch

bunches

obtained

its energ!. spread.

phased

compression

bunches 5 mm long are compressed shorter

conditiorl>

in the damping

of the magnets

is sol\.ed 1)~. a technique

lower energy than the leading particles.

This

ring. their

beha\.ior

is still much too long for acceleration

the bunch while increasing

on different

by their

on the stabilit!-

the longitudinal

this problem

of magnets

in the damping

CO~!PRESSI~S//PRE-.~C.CELERATIOS'~~

the bunch

and YLC.

determined

ring.

s~.st em.

BI.SCH

enough.

their origins

damping

be required

has been used routinely

in the SLC.

\vllere

to 0.5 mm for acceleration

in the linac.

hluc11

in the NLC.

Short

in the linac. and the!. permit

24

bunches a smaller

will suffer less frorrl depth of focus at t II~J

IP (about

100 microns

in compression approach that

could

would

would

provided

lead to other

the bunch

the beam

of the beam

length

two discrete

deleterious

with

energy.

operating

acceleration,

but

The compression

is so vital great,

the emittance

and the potential

Injection

After

necessary

along with any offset

is about

factors

upstream

in length

the bea.m must

process

resulting

in a

process

into

continuously va.rious effects

Because

and beam

the linac

size increase

is so

in the next few subsections.

All of the offsets

of the fina. focus system, means that divergence

at some location

miss at the interaction

magnetic

point.

be small

component

along

to the size shown or a.ngular

however,

kicks

the

in Table

of the beam

get demagnified

the accelerator,

to avoid

right

kick.

If

and if the beam

this problem,

these pulse-

to the local 1~ea.m size. Equivalently, amplitude,

to the beam divergence

25

To obtain

to the beam size, then the beams

has a varying

kick must be small compa.red

long.

sets the scale for any angular

In order

compared

the high-gradient

the local beam size sets the scale for

pulse to pulse is large compared

offsets must

and as it enters

be demagnified

motion

angular

this

2 /em high, 20 /lm wide a.nd 100 /m

and the local beam

a particular

spread

spread small throughout.

dilution

the beam

to-pulse

spread

energy

As the beam is almost

we examine

will

longitudinal

the relative

During

contributing

the beam size. This

from

The

the compression

energy

for emittance

is compressed

luminosity,

occur

energy.

unless specia,l care is taken.

1, uY x uZ = 4 nm x 320 nm. which

is

Errors

the bunch

lina.c, the bunch

compression

is then repeated,

By separating

transversely.

we will discuss various

3.6.1

spread

PRESERVATION’~

it is also focused

to dilute

at a higher

this

as in the SLC to 0.5 mm in length,

The linac is the heart of the linear collider.

conspire

however,

the extra

16 GeV.

steps, we can keep the relative

accelerated,

of magnitude

effects due to the large energy

to about

as low as 50 microns.

order

in practice,

For this reason,

is accelerated by this

another

stage;

is first compressed

LINAC EhurTmcE

3.6

in a single

compressor

is unaffected

decreases linearly

In p rinciple,

in the beam.

by a second bunch

which

bunch

be obtained

be induced

In the NLC, after

for the NLC).

the variation at that

point.

if

of the

The

emittance

entrance

can also be destroyed

to the linac.

If there is bending with

different

by initial

errors

The beam size in an accelerator

occupying

different

size at the

was discussed in Section 3.3.

or if the beam is offset in quadrupoles,

momenta

in beam

positions.

the beam is dispersed

In this more general

case,

the beam size is

(19)

u2 = q3 + D2S2 , where

D is called the dispersion

the beam prior section,

to the bending

function field.

in emittance

flat beam parameters

For example,

dilution

the tolerance

vanish.

in the acceleration

on dispersion

variation

in

at the end of the compression

to the 1ina.c D should

6 21 0.01. At the entrance

in beam size results

and S is the momentum

If not, this error

process.

For typical

D given by

D, < 0.2 mm (20)

D, < 2 mm . The dilution plicative lattice.

effects due to the mismatch If the beam

and could

dilution

spread,

dispersion

at any point

this mismatch

to the linac,

and provided

is additive.

of the beta function

were mono-energetic,

be compensated

cant energy entrance

caused by residual

There

of the magnetic

these mismatches along the linac.

must be avoided. the filamentation

are also multi-

would

focusing

not fila.ment’

Since there is a signifi-

For a small error is complete,

in /3 at the

the emittance

is given by

For incomplete

filamentation,

the emittance

26

dilution

will be somewhat

less.

3.6.2

and BNS Damping

Wakefields

Wakefields

are a key problem

tors and storage rings. wakefield

forces until

compensation

The standard

can be used, either live within

bunch

small.

sufficiently

In Sections

the limits

beam

breakup

modes in the RF structure;

on the stability

in Fig.

will

wake is shown

a frequency

be in an NLC

wakefield.

This

of beam

the number

parameters

of particles

the effects of the long range by damping

Then in the

wakefield.

the undesirable

Now we examine

the effect of the short

can be expressed again as a sum of modes; however,

short which

fields.

of a single bunch.

to include

with

external

or modification

can be controlled

in this case it is necessary then oscillates

is to first reduce the

to the applied

by keeping

the first bunch.

The short range wakefield

range

but for all accelera-

this reduces the long range wake at the second bunch

effect within

range wakefield

colliders,

to this problem

feedback

2.2 and 2.3 we discussed

multibunch

but has little

solution

they are small compared

or we can simply

The

not only for linear

modes

12.

It rises from

determined

are so short

is sometimes

at very high

they

A typical

zero, has a large peak and

by the dominant

that

approximated

frequency.

fall

mode.

The bunches

on the initial

as a linear

rise (shown

rise of the a.s the dotted

line in Fig. 12). The

transverse

dimensions

wakefield

increases

rapidly

with

increasing

frequency.

If a.ll

are scaled, then

W(z) = ( 2 >3W~(*X,,X) ) where X is the scaled wavelength

and X, is a reference

varies inversely

power

with

comes only

from

short

wakefield

range

a structure.) increasing

size with with

the proximity must

possible

of the distance

to reduce

range

one must balance the transverse

the increased

RF power

necessary

iris size.

27

benefit

to achieve

the

wall of

wakefield

reduces

wakes, but it also decreases the effectiveness

Therefore,

causalit,y

to the outer

This

slope

of this variation (By

the short

to the wavelength.

The initial

Most

of the iris hole to the beam.

the iris hole size relative

the larger

wavelength.

of the wavelength.

be independent

It is, therefore,

range transverse structure.

the fourth

(23,)

by

the short

of the accelerating of increasing

a. given

a.cceleration

the iris field

20

‘0 1-91

80

40 60 z (mm)

100 6’Y?A16

Fig. 12. The short range transl’erse nakefield at tile SLC. T11e upper graph shows a detail of the beha\Aor 5 mm behind a point buncll.

Even with induced

within

The situation in Section

the reduced

\vithin

the buncll.

a bunch due to the coupling is completely

analagous

2.3; the same t\vo-particle

bunch,

particle

growth

is initially

model

wakefield

of the head and tail by the wakefield.

to that for multibunch model

suffices.

one, drives the tail of the bunch. linear

with

there is still an instatilit\.

distance

but

instabilit!.

discussed

In this case the head of tllc

particle

becomes

tlvo. on resonance.

exponential

TII(~

as tile simpl(~

breaks down.

Fortunately, compensate

there is a technique,

the instabilit\T!5

where a two particle the structure.

model

the wakefield

add to this the external

called BSS damping.

The problem is shown.

and solution

If the t\vo particles

force deflects the tail particle

fields due to the focusing

28

magnets:

\vhich cau be used tu

are illustrated

in Fig. 1:j

are offset to one side vf‘ a\va!. from the axis. \\‘(a on the average there i* Ii

focusing

force in the opposite

by inducing controlled a stronger adjusted

an energy

direction.

correlation

along the bunch

by the phase offset discussed earlier). force than

move coherently

Finall}..

the head particle.

to cancel the wakefield

correlated

If we reduce the energ!. of tail of the buncl~

together,

occurs

and the growth

natural]!.

and i>

then the tail particle

experiences

if the additional

force cali IX

force, then the two particles, is completely

the head and tail.

eliminated.

The

BKS

energy spread is given b>

G EBSS =

E2Aw&7;)3,,

4E,

BNS

where A’ is the number evaluated

(this

of part.icles in a bunch,

at oz, and ,~3~is the $-function

lZ’l(az)

(23)

* is the transverse

\val;efield

at energ!. E,.

I I I /I/ I \\\ I I I -------------~----------~-----------\\ / I I /I I I \ \ \ I I \\ \\ I/ I \\ \\ /I l’ \ \

External Focusing

1-91

6793A17

Fig. 13. Illustration of BXS damping. The additional focusing force on the lower energy trailing particle (dotted line) exactl!. cancels the wakefield force of opposite sign.

If the wakefield rather

is large, then one can still satisf!. Eq. (23) 1)~.using RF focusing

than energy variation.to

var!. the focusing

29

strength.

In this case. how\er.

trajectories

can filament

the alignment

rapidly.

and trajectory

to 1 pm alignment

To avoid emittance

tolerances

tolerances

can be avoided

by keeping

tolerances

are dominated

by chromatic

wakefield

regime,

linac. 28 In this case the tail growth order of magnitude. configuration 3.6.3

related

position Thus,

with

energy.

oscillation

has since been adopted

leads

these tiny

weak wakefields,

at the SLC

was reduced

as the normal

the overall

an effective

energy

damped,

increased

one with

has about

by an

running

this relative between

constant

design from

spread

spread decreases energy

Table

The first chromatic

spread

energy

effect to consider

of the phase advance

is much greater

than

unity,

amplitude

must

be less than

chromatic

phase advance

oscillation

of size 2, is

energy

After

sprea.d remains

when projected along the injected

the bunch emitconsta.nt

unless

For this reason it is useful to consider and one with

damping

energy

t,wo

spread.

but also the value for

0.5 TeV in the cent,er of mass. is that of a coherent

with

momentum

the oscillation

filaments.

the bea.m size to avoid

is small

of the RF.

of the damping

we give not only the formula

1 with

and bunch

At any location

of energy along the bunch.

energy

below,

spread.

is a combination

the rela,tive

a 1% uncor-

wake and the curvature

energy

by phase changes.

In all cases considered

If the variation

bunch

in phase space becomes a wavy line which,

axis, yields

is sufficiently

the compressed

due to the longitudinal

energy spread and the variation

the first

With

has been tested

At the same time a correlation

the distribution

models;

damping

As the beam is accelerated,

is introduced

deliberately

size. This

effects.

due to a coherent

into the linac,

spread.

on the energy

tance

weak.

wakes,

Effects

energy

accelerator,

the beam

strong

for SLC.

injection

inversely

the wakefields

BNS

BNS damping

Chroma.tic

Upon

are less than

with

As we shall see in the next sections,

tolerances?”

In the weak

dilution

(Sll, tot < l),

30

betatron

(chromatic

oscilla.tion.

phase advance)

In this case t,he oscillation emittance

then the tolerance

dilut,ion.

If the

on a coherent

where S, = 2x 10e3 is the constant advance

per cell and total

relative

phase advance

quadrupoles.

For the case of a damping

the tolerance

is

For the case of a corrected of random alignment

trajectory

momentum,

GCeu and &,t

respectively,

and Nq is the number

energy spread with

trajectory

let us consider

In this

case the tolerance

bumps.

are the phase

initial

of

value Si = 0.01,

the model

of a sequence

on the trajectory

or

is (A4rms




ce

(26)

9

< 30pm

spread 6,. For an initial

damped

energy

spread 6;, we ha\:e

ap (LJ2 (zL)3’4) (Ax)rms < WkeIl

(Ax)

rms < 30pm

3.6.4

.

Misaligned

BNS damping in the linac; linac,

Accelerator

misalignments

kicks are not cancelled growth

between the strength

on random

of wakefield

the trajectory

locally

by adjacent

tails

misalignments

(Axstructure

> rms
yc,tl

in Section 3.3, the beam size is just proportional

to the square root of j*.

‘Ihi,

is shown as the dotted line in Fig. 16. If the bunch has finite energ!. spread a],~1 with no correction,

this linear decrease is modified by chromatic

that the beam size reaches a minimum Finally,

if the chromatic-correction

aberrations

so

of about 1 pm (the solid line in Fig. 16).

sextupoles are powered and if the system is

properly tuned and adjusted, the vertical beam size follows the linear optics do\vll to a size of about 60 nm before other high-order

effects spoil the compensatiorl

(the dashed line in Fig. 16).

1

t?

0.1

0.01

1 0.01

0.1

1 P;

32.90

10

100 67:931'C

(mm)

Fig. 16. Beam size versus optical tuning for uncorrected (solid), corrected optics (dashed) and linear optics (dotted).

The FFTB

will not achieve the beam size necessary for NLC due to the lack

of a suitable low-emittance

source.

In fact. to achieve such 10~ emittance.

need the KLC damping ring and linac. The FFTB demagnification

optics

will: ho\ve\.er. test the optical

necessary. for an NLC. In fact. the design 3’ for FFTB is identical

to that for NLC. In addition

to this primar!. goal. the collaboration

facility

stabilit)!

to test the alignment,

and instrumentation

\vill use tlli*

requirements

need(s,l

to achieve such small spots. The Final Focus Test Beam is a ke!. component the worldwide

w(’

research effort towards the NLC.

37

of

3.7.1

Beam-Beam

When magnetic

Effect.s3g-44

two oppositely-charged field

generated

leads to disruption

this enhancement

are attracted which

are misaligned,

disruption

yields substantial

designs.

photons

(2

In extreme

This

of the luminosity.

actually

This

to each other,

For round however,

helps the collision

each other

of synchrotron

and collide

radiation

process; if the bunches partially

known

ranges from

can strike detector

instability

anyway.

fields and high particle

cases, many of these photons

particles

the centroids

leads to a two-stream

pairs in the intense electromagnetic

or charged

them.

5); for flat bunches,

relative

loss due to beamstrahlung

electron-positron

focus

enhancement

of very high electroma.gnetic

amounts

average energy

large

passage.

they bend toward

The combination

NLC

and to a pinch

are misaligned

the bunch

for moderate

to mutually

electro-

(S 2) b ecause the pinch only occurs in one dimension.

the bunches during

tends

can be quite

reduced

If, in addition,

at the IP, the intense

Ho was given in Eq. (12) for the luminosity.

factor

it is considerably

collide

by the bunches

of the bunch

The enhancement bunches,

bunches

energj

as beamstrahlung.

1 to 30 percent

in various

can subsequently fields present.

components,

The

generat’e

The radiated

causing

undesirable

backgrounds. The train In order

of bunches

on each cycle also presents

to have a separate

take place at a small angle. the field from sequence trailing

those bunches

of bunches bunches

In practice,

cha,nnel for the outgoing As the bunches which

can induce

a multibunch

these beam-beam

above, with

the luminosity moderate

luminosity

while

total

limit charge.

keeping

instability

This

effect

beam-beam

by using

approach

impose

a short

allows

effects under

38

collisions

point,

they feel

collided.

which

This

can cause

can be controlled

bar

angle.

thus on the luminosity.

is bypassed This

the collision

kink

effects are what

the possible charge per bunch-and

bunch,

and have alrea.dy

point.

or by the crossing

at the final focus.

disrupted

approach

are exiting

to miss the interaction

the charge per bunch

a problem

the ultimate

on

In the design described train

of bunches,

us to maintain

control.

limits

ea.&

the desired

4. Summary and Concluding Remarks In the previous design

sections

of a Next

conventional

Linear

means,

we have outlined The

Collider.

with

the basic issues important

energy

the use of RF accelerating

high peak power RF sources-klystrons-which in the SLC.

The key difference

the structures

designed.

option

(option

proper

pulse length

2) in Table

compress

of the Next Linear

is forced within

upon

spot

reasonable

ances can be brought applied. Final

Many

The klystron

necessary

a.s theory

is perhaps

square

to achieve the

would

prob

it is necessary

nanometers.

the wall-plug

This

power many

spots will

to

situation

must

values when compensa.tion small

indicate.

the more difficult

In spite of the small size required,

of the issues of producing

be kept

of the toler-

techniques

be addressed

are

by the

Focus Test Beam. The second major

of many collider

bunches but

Experience

component

bunches which

also introduces has been gained

on each cycle.

would

preclude

To conclude, Generation

on the power

to the luminosity

on each ma.chine many

This

cycle.

complications

linacs which

the outlook

accelerate

Linear

of trains

for obta.ining

Collider

source is successful,

is bright. an NLC

mid 1990s.

39

increases

is the acceleration the efficiency

both

sometimes

problems

of the

all the subsystems.

a.ccelera.tes three bunches

Thus fa.r, no fundamental the acceleration

increase

throughout

at the SLC which

cycle, and also at all long-pulse

Next

Collider

of energy;

to conventional

or

enough power for the lower gradient

to a few hundred

bounds.

at 11.4

have been built

levels of 1O33 - 1O34 cm-‘secW1,

us by conservation

with

of 4. For

Structures

source is very close to realization.

has been tested and has behaved

the beam

by a factor

structures

1. The RF pulse compression

To reach the desired

combined

to those used presently

no problem.

and detuned

2.5.1 could easily provide

The luminosity lem.

damped

The power

discussed in Section

are similar

presents

by essentially

structures

is the change of frequency

this change of frequency

GHz have been constructed; are being

can be obtained

in the

on each

thousands

of

ha.ve been discovered

of bunches. the energy

Provided

that

design could

and luminosit,y the engineering

become

a reality

of a effort by the

Acknowledgements I would Perry Wilson thank

like to thank

Tanya

for his careful

the members

reading

Department

NLC;

effort

their

and good suggestions.

of the Accelerator

and the Accelerator without

Boysen for help in preparing

Theory

at SLAC

and Special

for their

the manuscript Finally, Projects

continuing

like to

Department

work on SLC and

this paper could not have been written.

40

I would

and

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43. V.N. Baier, V.M. Katkov and V.M. Strakhovenko, Proc. 14th International Conf. on High Energy Particle Accelerators, Tsukuba, Japan, 1989. 44. M.S. Zolotarev, E.A. Kuraev and V.G. Serbo, “Estimates of Electromagnetic Background Processes for the VLEPP Project,” Inst. Yadernoi Fiziki, Preprint 81-63, 1981; English Translation SLAC TRANS-0227, 19S7.

43