1.) I’m a Physicist At CERN We’ve Done Something We Shouldn’t Have Done= entered another Dimension via 40 TEV tearing our Universe.

https://www.youtube.com/watch?v=Ckvs5HHUl4k CERN “NOW” not 40 TEV but– breaking International Laws regarding 100 1000 TEV RANGE

 

2.)  PROOF of Point 1: MANDELA EFFECT IS ACTUALLY CERN QUANTUM EFFECT= Causing Mandela Effect whereby History is changed.

https://www.youtube.com/watch?v=m5NVS6z8S_U

 

ACCELERATOR FACILITIES IN THE 100-1000 TEV R NG W A Wenzel Lawrence

Berkeley

Laboratory Berkeley,

California

Summary

The

Application of current

technologies

to

proton-antiproton

colliders

of

20,100and1000

TeV

is

studied.

The

maximum

field

in

the

superconducting

magnets

is

2

or

5

Tesla.

The

facility

also

includes

a

conventional

ring

ror

electrons

and

positrons

with

two

tothree

orders

of

magnitude

less

energy.

 

unique

injector

employsa

rapid

cycling,variable

tunesuperconducting

ring

to

accelerate

particles

from

10

GeV

to

the

minimum

operating

momentum

ofthestorage

accelerator.

The

scaling

of

costs

with

momentum

is

minimized

in

several

ways.

Extensive

beam-beam

feedback

for

orbit

control

permits

the

use

of

small

apertures.

The

very

longmagnets

are

produced

on

a

linear

assembly

line.

Finally,

the

accelerators

are

combined

into

a

threering

circus

maximus

within

a

single

neutral

buoyance

cryostat

supported

in

a

water-pipetunnel

of

small

diameter.

The

creation

with

current

technologies

of

1001000

TeV

accelerators

may

not

be

completelyincon

ceivable;

but

some

significant

departures

from

current

design

philosophies

are

needed.

For

example,

1.

The

fabricationof

verylong,small

aperture

superconducting

magnets

requires

a

linear

assembly

line

approach.

2. Smart

detectors

and

processors

must

use

beam

position

information

for

on

lineorbit

correction

and

to

damp

instabilities.

3.

Amodest

but

selective

site

development

is

required.

In

particular

elaborate

tunnels

mustbe

avoided.

In

addition

some

priority

among

scientific

goals

is

needed

so

that

design

compromisescan

be

compared

realistically.

High

energy,high

luminosity,

good

duty

cycle

and

efficient

beam

extraction,for

example,

createadditive

 if

not

multiplicative

problems

affecting

both

feasibility

and

cost.

In

what

follows

we

suggest

an

approach

to

P-P

colliders

which

is

intended

to

explore

the

implica

tionsof

a

single

very

large

step

beyond

current

facilities

Some

of

these

may

be

useful

for

amachine

inthe

20

TeV

rangel,

for

which

parameters

are

also

included.

I.

General

Plan

The

proton

and

antiproton

sources

use

Tevatron

like

10

GeV

ringsfor

accumulation,

cooling

and

preliminary

acceleration.

Figure

1shows

thestorage

accelerator

ring

carriedin

a

single

cryostat

with

a

superconducting

injection

ring

of

lower

field

anda

conventional

magnet

ringto

help

with

injection

and

for

e±

storage.

At

intersection

regions

therings

are

separated

radially

using

straight

sections

whichoccupya

verysmall

part

of

the

circumference.Short

straight

sections

betweenlongmagnets

alternate

infunction

between

cryogenic

and

warm

services

 Figure

2 .

At

several

dozen

stations

beam

position

and

phase

information,received

just

ahead

of

beam

arrival,

is

used

for

fastorbit

corrections.

Relatively

slow

site

movementand

atmospheric

changes

are

monitoredusing

microwave

interferometry

across

radii

and

sectors,optical

registration

of

beam

line

elements

within

the

cryostat

andmeasured

beam

position.Site

development

is

minimal.

There

are

several

experimental

intersection

regions,

a

dedicated

gigawatt

power

station,

a

ring-oriented

network

of

ac,

dcand

radio

frequency

power,communicationandcomputing

equipment,

refrigerators

and

correction

magnets.

The

magnet

ring

follows

smooth

elevation

changes

inthesurface.

The

neutral-buoyancy

cryostat

is

suspended

in

water

inside

a

pipeburied

at

modest

depth Figure

1 .

Relativelylarge

 ~lOmm

transverse

displacements

ofthe

cryostat

can

be

carried

out

within

minutes.

For

thestorage

accelerator

two

values

of

the

magnetic

field,

2Tand5T,and

three

energies,

20

100and1000

TeV

areconsidered.

Because

the

avail

ability

ofsuitable

sites

on

land

is

obviously

limited,

especially

at

1000

TeV

the

examination

of

alternative

designs

for

the

ocean

orouter

space

is

an

appropriateexercise

for

the

reader.

II.

MagnetandRingDesignand

Construction

A

General

Features

In

severalrespectsthe

superconducting

magnet

design

departs

from

conventional

approaches.1.All

normal

lattice

magnets

are

idential.

Thenumber

is

minimizedbymakingthem

long.

2.

Full

length

separately

powered

 Figure

3

current

elements

of

simple

shapes

give

complete

flexibility

in

the

azimuthal

current

distribution.

The

required

multipole

distri

bution

of

the

magnetic

field,

therefore,

is

readily

achieved

at

all

levelsof

excitation.

3.

The

use

of

wedge-shaped

conductors

in

the

high

field

storage

accelerator

 Figure

4

permitsnecessary

stress

loading

from

theoutside

radius.

4.

The

magnet-core

assembly

line

is

linear;

the

fabrication

technique

is

independent

of

magnet

length.

5.

The

cryostat

for

the

small

aperture

magnet

uses

a

very

light-weight

support

system

to

minimize

heat

losses.

6.

 

unique

injector

is

proposed

for

considera

tion.

Thisuses

spiral

quadrupole

windings

 Figure

4

toobtainshortbetatron

wave

lengths

at

lowmomenta.

B

SuperconductingCoil

1.

Superconductor

We

assume

that

the

superconductor

is

a

commonly

used

monolithic

intrinsically

stable

Cu-NbTi

matrix

with

10

 

diameter

NbTi

filaments

anda

twistpitchof

O.Olm.

For

a

Cu/SC

ratio

of

1.8

the

critical

currentsare

0.6xl0

9

A/m

2

at

5T

and

1.2xl0

9

A/m

2

at

 T

The

conductorshapes

vary

froml3mm-deepwedges

at

5T

to

millimeter

stripsat

2T

andeven

thinnerlayers

for

the

injector.

Table

I

gives

approximate

superconductorrequirements

for

the

storage

accel

erator.

-322-

 

For

simplicity

we

have assumed

that

all

magnet

apertures are the

same. Because

of the strong

dependence

on

radius

of

some

transverse

beam

instabilities,

it

is

likely thatat  2T the aperture would have

to

be

larger

than

at

ST.

This

offsets

to

some

extent

the

advantages

of

low

fields

in

theoverall

magnet

hardware

requirements.

At

ST

some

savings

in

the

amount

of

superconductor

couldbe

made

with

a

double

layer dotted

line

in

Figure

4)

of

wedges

operated

with

different

current

densities

or

superconductor

ratios.

For

fields

above

ST

this

alternative

would

probably

be

necessary.

2.

Magnet

Current

Figure

3shows

schematically

how

the

magnets

-are

powered.A

central

facility

distributes

as

a

functionof

time

digital

signals

specifyingthe

magnet

currentsin

all

windings.

The

required

number

of

combinations

of

dipole,

quadrupole

and

sextupole

components

is

small.

Local

corrections

can

beadded

for

non

planarity

of

orbit

and

those

misalignments

which

cannot

beremovedby

adjustingthe

cryostatposition.

3.

Stored

EnergyandQuench

Protection

The

stored

energy

inside

the

inner

coil

radius

a

is

given

by

 1

In

the

absence

of

any

magnetic

shielding,the

total

stored

energy

is

larger

bya

factor,

1+2b/3a+b

2

/3a

2

whereb

is

the

coil

outer

radius.

For

the

ST

field,

where

the

steel

helps

only

a

little

thestored

energy

exceeds

10

MJ/km.

At

2T

it

is

approximately

1MJ/km.

For

internal

quench

protection

the

coil

configura

tion

proposed

here

has

some

advantages

over

the

familiar

pancake

design,

because

current

elements

occupying

only

smallazimuthal

intervals

are

sep

arately

powered.In

the

event

of

aquench

the

increase

in

terminal

voltage

effectively

disconnects

the

power

source

ofthe

quenching

element,

shifting

current

tothe

neighboring

elements

and

leaving

the

stored

energy

distributionessentially

unchanged.

Because

each

power

supply

is

current

regulated,these

additionalcurrents

are

supplied

through

the

terminal

resistors.

Whether

or

not

the

neighboring

elements

quench

immediately,

all

the

terminal

resistors

share

inthedissipation

ofthestored

energy.

The

beam

tube

also

will

carry

axialcurrent.

Its

heating

will

both

absorb

energy

and

helpspread

the

quench.

C

MagnetCore

In

operation

the

magnet

steel

and

the

beam

tube

arecold.

The

full

length

insulated

conductors

are

assembled

radially

against

a

thin

beam

tube,then

squeezed

bya

laminated

steel

core

which

providesnecessary

hoop

stress,

confines

the

magnetic

flux

and

permits

axial

displacement

to

accommodate

the

differ

ential

thermal

contractionof

one

partin

1000between

superconductor

and

steel.

Because

the

magnet

has

relatively

little

axial

stiffness,

the

assembly

line

terminates

with

a

large

drumonwhich

the

core

is

wound

like

a

cable.

Ina

relatively

conventional

approach

pairs

of

stamped

laminates

couldbe

stacked

around

the

coil.

The

coolingtubes

could

serveas

stacking

guides

and

then

squeezed

to

apply

radial

force.

Because

of

the

relatively

small

coil

diameter,

the

hoop

stresses

even

at

ST

are

relatively

small.

 t

mightbe

sufficientto

glue

 rather

than

weld)

the

structure

together.

-323-

Figure

4showsan

alternative

approach

whichmight

be

well

suited

to

long

assembly

lines.

The

conductor

is

wrapped

with

steel

wire

or

narrow

strips

in

helical

layers

of

alternating

helicity.

 t

remains

to

be

learned

how

well

the

azimuthal

wrapping

forces

and

the

resultant

twists

can

be

cancelled.

Small

residual

twists

can

be

controlled

using

gravity

and

the

positioningof

the

cryostatinside

its

waterbed.In

spite

of

their

great

lengths

the

magnets

are

thin

lenses,

so

that

average

values

for

coil

position

and

axis

alignment

are

most

important.

For

simplicity

Figures

1and4show

circular

apertures

forthe

magnets.

For

thestorageaccel

erator

an

elliptical

cross

section

is

probablyappro

priate

and

is

consistent

with

the

fabrication

procedure.

For

the

low

field

superconducting

injector

the

circular

aperture

is

necessary,

so

that

twoquad

rupole

 cos

 

current

distribution)coils

can

be

spirally

wrapped

to

produce

many

shortalternating

gradient

magnet

elements

within

each

long

cryostat.

Because

circular

symmetry

is

required

for

these

quad

rupole

windings,

careful

keying

is

needed

to

preserve

theorientation

ofthedipole

windings.

D

Tunnel

and

Cryostat

Support

 Figure

1)Eachmagnet

cryostat

is

supported

in

a

water

filled

pipe

buried

2 3m

deep,

as

required

forradia

tion

safety

and

to

achieve

asmooth,

not

necessarily

planar,

orbit.

Deep

cutting

and

tunnellingare

needed

only

for

locally

steep

terrain

orto

avoid

population

centers

and

other

immovable

objects.

Both

water

pipe

and

cryostat

shell,

including

separate

sets

of

rails

for

warm

and

cold

inserts,

are

assembled

in

situ

from

short

 ::SOm-long)

sections.

These

are

joined

withvery

short

 ::

O.lm-long)

transition

sections

which

hold

the

pulleys

and

cables

which

support

the

cryostat.

The

cables

run

insidethe

water

pipe

to

the

ends

of

each

magnet

section

where

they

can

be

used

to

adjustthe

transversepositionsofthe

magnets.

At

each

end

of

each

magnet

thecryostat

and

water

pipearejoined

with

a

bellows

which

provides

severalcentimetersof

relative

transverse

motion.

The

tolerances

on

this

assembly

are

obviously

very

loose.Nevertheless,

the

magnet

can

be

aligned

precisely

by

opticalsighting

through

the

 cold

part

ofthe)

cryostat.

E.Assembly

into

Cryostat

Eachmagnet

core

is

insertedinto

its

cryostat

in

situ

using

a

mini-assembly

line

at

the

warm

service

straight

section.

As

it

is

unwoundfrom

thestorage

drum

the

core

ofthe

storage

accelerator,

withcoolingtubes

and

injector

ring,

is

clamped

atintervals

of

~

andwrapped

with

superinsulation

andan

inter

mediate

heat

shield.

Rollers

which

ride

ontwo

rails

on

thecryostat

wall

are

each

attached

with

two

fiberglass

stringsto

the

coolingtubes

near

the

clamps.Other

rails

on

the

cryostat

inner

wall

are

used

to

support

the

third

 conventional)

magnet

ring

and

to

carry

warm

services

such

as

distributed

vacuumpumps.Duringmagnet

installation

the

empty

cryostat

rests

on

the

bottom

of

the

empty

water

pipe.

Longitudinal

forces

ofthe

orderof

a

ton,

necessary

to

overcome

roller

friction

and/or

gravity,

are

provided

by

pulling

on

the

cooling

tubes.

Themagnet

elements

will

recede

at

cooldownfrom

the

warm

service

stations

by3

partsin

1000

of

their

lengths.

Duringwarmup,

tension

may

beneeded

to

keep

the

core

from

buckling.

 

u

is

also

related

to

the

focal

length

F

per

cell

and

the

field

gradient

B

byWith

the

magnet

installed

the

supportpipe

is

filled

with

water.

The

cryostat

support

interval

can

be

made

aslargeas

sOm

by

carefully

adjustingthecryostatdensity.Ballast

tubes

filled

with

air

or

water

could

be

used.

The

densityof

water

changes

by

only

one

part

in

1000

for

a

4°C

change

in

temperature.

F.

Cryogenics

u=

 2L/F ~

=

2L

2

B /

V 3BR,hence

Bq/B

=

2Y3

aQ2/RuwhereB

=

aB

is

the

quadrupole

field

at

theinner

coil

ra~ius

a.

 5) 6)

Refrigeration

may

be

the

largestsingle

expense.

The

proposed

magnet

support

system

is

intended

to

minimize

this,

but

it

will

be

hard

to

get

the

lossesto

the

wall

of

the

cryostat

below

100W

per

km.

In

thelongestringconsidered

here

(1000

TeV

at

2T

this

would

require

~l

of

cold

power.The

effi-

ciency

of

the

refrigeration

system

must

be

examined

carefully.

Heat

exchangers

within

the

cryostat,

for

example,

couldbeused

to

precool

helium

coming

intothe

refrigerators.

Another

source

of

heating

is

from

thecycling

of

the

superconductors,

which

produces

a

hysteresis

loss

given

by2A

similar

relationship

applies

to

separatedfunction

lattices

provided

that

the

ratio

of

field

strengths

is

multiplied

by

the

ratio

of

quadrupole

to

dipole

magnet

lengths.

With

this

correspondence,

the

Fermilab

MainRing,

with

quadrupole

aperture

a=

O.Osm,

R=lkm,Q=20,u=

1.25gives

aQ2/Ru=0.016

or

LB

/LB

=

0.055.

TheMainRing

has

approximately

tWic~~his

ratio

of

magnet

length

devoted

to

quadru

poles

because

the

circumference

factor

is

appreciably

less

than

unity

and

because

the

poletipfieldsare

smaller

forthe

quadrupolesthan

forthe

dipoles

 1.2

T

vs

1.8

T

at

400GeV).

3.

Magnet

sagitta

 2)

The

sagitta

S

of

each

magnet

is

given

bywhereic

is

the

critical

current,df

is

the

filamentdiameter,

fiB

is

the

field

changeandA

is

the

fraction

of

superconductor

in

thematrix.

Takingic

fiB

=

2.4xl0

9

ATm-

2,A=0.36,df=lO

~m,

we

find

Go=8640J/m

3

cycle.

Theamount

of

superconductor

in

the

(sT)

storage

accelerator

is

at

mosta

cubicmeter

per

km,

soeven

for

a

relatively

short

1000

sec

ramping

time,

the

hysteresis

power

is

<lOW/km,

much

smaller

than

the

assumed

total

loss

of

100

W/km.

For

the

injector

the

fields

are

lowerbymore

than

an

order

of

magnitude.

Because

the

requiredareaof

superconductor

goes

inversely

asthe

square

of

the

field

strength,

the

injector

cycle

time

may

be

as

low

as

afew

seconds.

 7)

For

aQ2/Ru

~

0.016u,

therefore,

it

is

possible,

inde

pendent

of

designenergy,

tosight

through

theapertureof

each

magnet.

Usually

the

phase

shift

per

cell

is

limited

to

the

range

rr/3

~

u

~

rr/2.

In

any

case

the

cold

part

ofthe

cryostat,

as

shown

in

Figure

1,

provides

plentyof

width

for

optical

alignment.

4.Dispersions

of

orbit

radius

and

frequency

From

the

relationship

between

the

momentum

compaction

factor

aand

Q,

i e

III

Orbits

and

Optics

a

=

 dR/R)/

(dP/P)

 

Q-2

 8

)

The

factor

aQ2/R,

therefore,

determines

also

the

effect

of

fractional

field

errors

on

the

relative

 toaperture)

orbit

displacement.

A.

General

The

momentum

P,

dipole

magnetic

field

Band

radius

R

are

related

byP=

0.3

 R

 Table

I

We

assume

the

circumference

factor

is

unity,

agood

approximation

in

view

of

the

design

featuring

relatively

few

combined

function

magnets

separated

by

short

straight

sections.

the

radial

displacement

fiR

associated

with

momentum

width

fiP

is

given

by

fiR

=

RfiP/PQ2

=a(fiP/P)/(aQ2/R)

 9)

1.

Orbit

corrections

The

frequency

dispersion

D

is

relatedto

aby

Table

Ishows

the

number(2rr/lji)

of

independent

feed

back

arcs

per

revolution.

We

have

used

fit=100

nsec

to

accommodate

amplifier

delays

and

signalrouting

to

andfrom

thetransmitters

and

receivers.

2.

Betatrontune

and

relative

quadrupole

strength

ThemagnetnumberNand

length

L,

the

tune

Qand

the

phase

shift

u

per

alternating

gradient

cell

of

length

2L

are

related

by

Fast

beam-beam

feedback

canbe

used

tocorrect

orbits,

damp

instabilities

and

perhaps

to

reduce

emittance.

The

differential

elapsedtime

fitbetween(beam)

arc

and

 signal)

chord

routesfor

angular

width

 

is

given

byfit=R[lji-2

sin

 lji/2 ]

/c

or

~ (24cfit/R)

1/3

(3)

 10)

where

w

=

vIr.

Phase

transition

occurs

at

y=

Q.C.

Injector

B.

Storage

Accelerator

Table

I

gives

parameters

for

thestorage

accelerator.

We

take

Us

=

1,

as

=

l3mm,

asQs2/R=0.013.

In

all

cases

thestorage

accelerator

operates

above

transition

energy.

From

equation

9

the

closed

orbitsensitivity

is

given

byfiR/as

=

80fiP/P,

indicating

that

field

errors

must

be

corrected

to

better

than

one

percent

ofthe

injection

field.

Injectionintothe

storage

accelerator

could

follow

current

practice

of

successive

injectioninto

and

extraction

froma

series

of

relatively

high

field

synchrotron

rings.

For

the

verylarge

overall

momentum

ratio

required

here

several

such

rings

wouldbe

required.

Although

the

sum

of

the

circumferences

oftheserings

wouldbe

much

less

than

forthe

(

4)

u/2Q

 

=

2rrR,

Nu

=

4rrQ,

or

L

-324-

 

to

becompared

with

a

P-~

dependence

for

fixed

Q

accelerators.

The

transverse

slope

is

damped

according

to

<y~>

aQ

<y>

The

transverse

emittance,

therefore,

goes

as

storage

accelerator,

the

relative

costofthe

injec

tion

system

would

not

necessarily

be

smallbecause

comparableeconomies

of

scale

would

not

apply.

Furthermore

the

gymnastics

of

manybeam

transfers,

although

persumably

straightforward,

could

be

time

consuming.

<y>

<y~>

a

QP-~

a

liP

 15)During

acceleration

thetune

may

have

to

bejumped

over

harmonics

associated

with

magnetand

cell

lengths

Land

2L.

These

occur

for

For

 ll

cases

considered

here

 Table

I),

PI

< 

Pt

< 

Pz.4.

Orbit

stability

From

equation

10,

phase

transition

forthe

injector

occurs

at

 17

0.0063and

the

same

as

for

fixed

Q

accelerators.

Qi

=

 rrQ

s

 u

s

and

 rrQ

s

 u

s

or,

given

Qz=Qsand

Us

=

1,

at

Pi/P2

0.025,

respectively.

1.

Quadrupole

strength

Proceedingas

in

III.A.

above

we

find

that

as

a

function

of

momentum-dependent

injector

parameters

 subscript

i)

For

injection

we

propose

to

consider

an

unusual

alternative

--

a

full

radius

variable

tune

ring

to

carry

particles

from

preinjection

at

Po

=

10

GeV

to

storage

accelerator

injection

at

Pz.

To

offset

the

effect

of

fixed

field

errors,

a

very

largebetatron

tune

is

required

at

low

momenta.

Short

lenses

for

this

purpose

use

spiral

windings

with

acos

2~

current

distribution

 Figure

4).

The

superposition

of

opposite

helicity

windings

gives

a

field

gradient

that

variessinusoidally

along

the

orbit

with

an

effective

strength

that

is

two-thirds

the

maximum.

The

alter

nating

gradient

cell

length

2L

o

is

equal

to

half

the

winding

pitch.

IV.

Injector

Operation

Generally

the

orbitcharacteristics

of

thevar

iable

Q

injector

differ

invery

important

waysfrom

those

ofthe

conventional

fixedtune

machine.For

the

l tt r

thebetatron

amplitude

producedbya

periodicperturbation

is

bounded,

throughphase

closure,

bya

value

inverselyproportional,for

example,

to

the

phase

difference

from

thenearest

harmonic

resonance.

In

thevariable

Q

injector

on

theother

hand,

steady

state

operation

is

impossible

at

low

energies,

whereQ

is

so

large

that

the

chromatic

effects

cannot

be

sufficiently

corrected

to

avoid

such

resonances

and

stop

bands.

During

acceleration

these

effectsdon t

matter

directly,

because

Qchangesso

rapidly

that

for

each

particle

the

betatron

phase

at

any

point

on

thering

is

effectively

randomfrom

cycle

to

cycle.

A

local

perturbation,therefore,

creates

a

seriesof

randomchanges

inbetatron

amplitude.

Although

average

effects

are

readily

corrected

by

using

beam-beam

feedback,

the

random

nature

of

individual

particlehistories

can

lead

to

some

stochastic

increase

inemittance.

Note

that

forthe

fixed

tune

accelerators

a

similar

problem

exists

if

there

are

random

perturba

tions

from,

say,

groundmotion

with

frequenciesnear

or

larger

than

the

orbital

frequency,

a

range

of

more

than

two

orders

of

magnitude

for

the

facilities

considered

here.

At

Pi

=P,where

we

set

Q2

=

Qs

the

injector

could

presumabfy

operate

as

a

storage

accelerator,

although

it

will

be

desirableto

avoid

paying

too

much

for

field

quality.

For

theintenseantiproton

source

the

injector

wouldbe

cycled

very

rapidly

 >1

Hz

to

provide

protons

of

afewhundred

GeV,

optimum

for

producing

antiprotronsin

the

10

GeV

range.

Similarly,therapidaccelerationof

small

electron

bunches

to

fill

the

conventional

ring

for

e±

collider

operation

will

avoid

overloading

the

cryogenic

system

withsynchro

tron

radiation.

The

latter

goal

will

also

be

achieved

by

injecting

somewhatbelowe±

operating

energy.

For

theseapplications

only

theshort

lens

system

is

needed.

 11

14

12)

for

ao=

13mm,

Note

that

for

Lo=

Ruo Q~

RUi/2Qi

and

Bqi/Bi

=

3V3

aoQiz/RUi

From

equation

9

we

inferthat

PiQi2=

const.

is

the

appropriate

scaling

law

for

injector

tune.

This

gives,

2.

Two

stage

injector

Table

Ishows

injector

parameters

Uo

1,P2=0.05PsaneQ2=Qs.Uz=

us

L/Lo=

 P2/Po ~.

At

thehighestenergies

considered

here,

B

z>B

z•

The

total

field,

B2

 

B2,

is

still

small

enougR

to

avoid

saturation

 

the

magnet

steel,

an

effect

that

would

seriously

jeopardize

the

field

quality.

Nevertheless

the

total

amount

of

steel

and

super

conductor

can

bereduced

if

an

additional

setof

quad

rupole

windings

is

added.Thesewould

give

a

stronger

lens

of

length

L,

for

use

whenPI

~

Pi

~

P2•

The

initi l

lens

of

length

Lowouldbe

used

for

Po

 

Pi

 

Pl.

The

quadrupole

field

is

minimizedby

choosing

PI

=

 o

P2)~

anduI=uo•

This

gives

LIlLo=

 P?/Po ~.

In

this

case

the

quadrupole

field

at

PI

obtaInedwith

lenslength

Land

at

P

with

length

LI

are

equal

and

are

given

°by2Bq2/B2=3

 

Q

 

/Ruo 

Pz/Po)l: 13)

 

smaller

bya

factor

 Pz/Po ~

than

forthe

one

lens

injector

design.

For

this

choice

of

Pi

the

two

stage

injector

parameters

are

also

given

in

able

I.

Alternatively,

and

with

littl

difference,

PI

could

bechosen

equal

to

theelectron

momentum

for

the

conven

tional

third

ring

discussed

below.

3.Betatron

dampingand

phase

transition

For

the

variable

Q

injector

thetransverse

amplitude

y

is

damped3

according

to

<y>

a

 PQ)-~

a

p-l:

-325-

 

 22) 26) 25)

Independent

of

refrigeration

problems,

thestored

energiesin

the

proton

beams

are

terrifying,

primarily

because

the

magnetcan

be

destroyedunless

d

(Power)/ds

 

1.98 10-

22

B3E/M

4

 W/m

23)

VII.

Conclusions

A

particularly

significant

cost

factor

for

very

high

energy

superconducting

facilitiesis

refrigera

tion.

If

synchrotron

radiation

mustbe

absorbed

inthe

magnet

the

circulating

beam

will

be

limited

significantly

in

intensity.

The

alternative

of

absorbing

the

synchrotron

radiation

on

warm

surfacesrequires

amore

elaborate

magnet

structure

and

support

system

and

implies

a

much

larger

ambient

heatload.

Improvements

in

refrigerationefficiencies

can

help.

This

is

an

application

where

the

development

of

a

highertemperature

superconductor

wouldbe

especially

welcome.

From

the

wide

range

of

momentaand

field

strengths

consideredhere

some,

certainly

not

all

of

the

problems

of

applying

present

technologies

to

much

larger

facilities

are

perceived.

Itis

at

best

sobering,

and

at

worst

impossible,

to

conceive

theconstructionof

a1000

TeV

facility

in,

say,

five

shift-years

 104

hours),

during

which

the

assembly

line(s)will

have

to

produce

and

install

almost

everything

at

a

rate

of

1

km

perhour.

Table

II

shows

that

synchrotron

radiation

can

provide

useful

damping

for

P-P.

If

the

number

of

stored

protons

is

large,

refrigeration

losses

in

thecryostat

canbea

problem.

A

possiblesolution

is

to

make

theaperture

wider

radially

in

order

to

insert

warm

absorbers

at

regular

intervals.

The

critical

energies

are

low

enough

for

absorption

ofthe

synchrotronenergy

in

short

lengths

of

heavy

metal.

The

radiated

power

per

particle

is

In

the

Table

we

show

the

radiation

loss

for

Np

 

10

15

•

At

the

higherenergies

the

power

gradientfor

radiationlossgreatly

exceeds

the

total

assumed

forthe

support

structure

 lOOW/km .

This

implies

either

a

smaller

circulating

beam

or

a

design

in

which

the

synchrotron

radiation

can

be

collected

on

warm

surfaces.

The

critical

energy

is

For

theelectronsthe

radiation

determinesboth

the

operating

energy

Eeand

the

number

 

e

orcurrentIe.

For

the

collider

to

function

as

a

synchrotron

we

assume

that

the

energy

loss

per

turn

is

amodest

fraction

ofthe

total

energy.

Arbitrarily

we

set

The

radiated

power

gradientper

particle

is

Thisdetermines

the

energy

and

gives

a

critical

energy

that

is

independent

ofBand

E,i.p-.

Itis

apparent

thatrefrigeration

forthe

protons

and

r f

power

forthe

electrons,

together

with

the

stored

beam

energy,

placestrong

limits

on

the

numbers

of

circulatingparticles

and,

therefore,

on

the

achievable

luminosities.

 21) 19)

l3mm

andue

=

1,

we

find

Q

eT

=

2E/(dE/dt)

=

0.77 10

11

M4/B2

E

(sec)

V.

Conventional

Third

RingVI.

Synchrotron

Radiation

For

n

inTesla

and

both

MandE

in

GeV,

the

energy

lossperturnper

particle

is

The

electron-positron

collider

ring

is

made

of

conventional

materials

because

of

both

theintense

synchrotron

radiation

and

the

very

low

dipole

field

strength.

Its

alternative

use

inproton-antiproton

injection

is

described

above.

Because

theoperatingdipole

field

Be

is

very

low

for

the

facilities

studied

here,

a

careful

magnet

design

using

severallayers

of

magnetic

shielding

is

needed.

Also

the

betatron

tune

should

be

as

large

as

possible.

If

both

magnetpowerand

conductor

volume

are

doubled,

the

quadrupole

and

dipole

fields

canbe

made

equal.

Assuming

forsimplicity

of

comparison

that

a

conductor

configuration

like

that

of

the

injector

is

used,

the

tune

is

determined

byTakingae

For

picture-frame

dipoles

the

powerand

conductor

volume

are

related

to

the

momentum

P

 GeV

,gapg

 m

and

resistivity

p

 ohm-m

byPowerx

Volume

 Wm

3)

=

10

10

pp2g

2/9

 18)

U

 

4nrpMp

y

4/3R

1.81.10-

 

BE3/M

4

 GeV

20)whererp

 

1.53.10-

 

mand

 

0.938

GeV

The

damping

time

T

is

given

by

The

two

stage

injector

is

especially

well

suited

to

preliminary

stacking

before

injectioninto

the

storage

accelerator.

Fedby

the

injector

at

momentum

PI the

third

(conventional)

ring

would

accumulate

and

stack

small

bunches

of

protons

or

antiprotons.

The

larger

(stacked)

buncheswould

then

be

accelerated

from

PI

to

P2

usingthe

second

lens

system.

This

process

would

not

onlyavoid

changing

between

injector

lens

systems

during

a

singleacceleration,

but

it

would

save

r f

power

by

reducing

the

number

of

 trips

to

P

Also,

by

involvingthe

conven

tionalring,

thfs

procedure

wouldminimize

lossesin

particle

transfers

to

the

cryogenic

system.

Forcos¢

dipoles

with

thin

coils,

multiply

byn2

/8.

Independent

of

ring

circumference,

therefore,

the

metal

inthe

Fermilab

MainRing

could

inprinciple

be

reshaped

to

provide

a1

TeV

third

ring

at

the

samepower

levelpresentlyrequired

at

500

GeV

for

twice

our

third

ring

vertical

aperture.

For

R~1 6m

the

coil

thickness

wouldbe

only

~lmm

The

steel

wouldbe

very

thin

and

the

cycle

rate

could,

if

necessary,

be

large.

In

summary,

the

variable

Q

injector

is

used

at

low

energies

like

alow

gradient

 ~three

orders

of

magnitudelower

than

SLAC s)

linac.

Relative

tolinear

linacs

its

advantages

are

that

the

hardware

is

recycled

and

that

thering

canbe

made

 smart

because

ofthecurvature.Relative

to

fixedtune

injection

synchrotrons

its

advantages

include

anenourmous

momentum

range

in

one

ring,

plus

the

factthat

it

is

matched

to

otherwisenecessary

character

istics

of

the tunnel

and

cryostat.-326-

 

beam

extraction,

emergencyand

otherwise,

is

100

per

cent

efficient.

It

isessential,

therefore,

that

experimenters

and

theorists

continue

to

examine

beam

requirements.

A

given

number

of

particles

will

provide

higher

collider

luminosity

if

the

number

of

bunches

is

small.

But

the

dutycycle

will

then

beworse

for

both

collider

and

fixed

target

experiments.

This

trade-off

alone

justifies

considerable

effort

on

both

detector

developmentand

simulation

studies

to

help

extractsignificant

results

from

junk-dominated

hadron

interactions.

One

advantage

of

studying

theimplicationsof

very

large

extrapolations

is

thatbetter

approaches

to

relatively

modest

steps

may

also

beencouraged.

At20

TeV,

for

example,most

ofthe

problems

consideredhere

are

relatively

small.

Departure

from

current

practices

fortechnical

reasons

seems

unnecessary,but

the

effort,

time

and

costofbuilding

even

this

small

facility

may

dicate

otherwise.

References

I.

ICFA

Workshops;

FNAL,

April

1979;Les

Diablerets,

October,

1979.2.

M.A.

Green,Ph.D.

thesis;

May,

1977,LBL-5350.

3.

Henri

Bruck,

Accelerateurs

Circulaires

de

Particles.

Presses

Universitaries

de

France.

Storage

Accelerator

TABLE

I-MagnetRing

Parameters.

Po

=

10GeV,

Q

2

=

Qs

as

=

ao

=

ae

=

13

mm,

Us

=

Uo

=

ul

=

ue

FIGURE

I.

Cross

sectionoftunnel.

The

cables

supporting

the

neutral

buoyancy

cryostat

at

~ m

intervals

are

controlled

from

the

ends

of

the

longmagnet

sections.

e±

RING

f

O.5m

 

1.

5

670

61

0.225

816

408

103004450

13

0.722

363140106

0.707

35

142068604950

3.1

2500

11940

0.5

16957700

5.8

1000

0.980

20

4970

168

SO

4.2

10004780

0.2

67.5

91300

9.1

2

1670

83

0.090

129064516200860

1.30.707

145701090077

5

0.66

2500

3780

5

1695770

5.8

5

6728

0.225

258129324044513

0.336

168

990

34

 224

112

800

1220

27

100

0.456

91

1570

53

5

0.90

10001510

2

67.5

9130

9.1

2

16739

0.090

408

204

5130

86

L

0.224

45

320

1930

43

1

0 23

2500

1690

25

1691160

5.8

5

13.3

17

0.225

116

5B

1450

B9

13

0.196

490

440

IS

0.100

250

53036518

20

1

0.31

100067510

67.5

1830

9.1

2

33.3

23

0.090

1B3

91

2300

17

1,3

0.266

266700

24

0.100

100

210

57729

Ini

2nd

stage

Electron

Ring

P

s

 IeV

B

s

 T

R km)

2n/1j.I

 feedback)

B

qs

 T

Q

s

 tune

L m

N

 magnet

no.

S

coil:

Vol

 

3)

 b-a

mm

P

e

 TeV)

Be

•Bqe G

Q

e

 e

 m

Electron.

Posi

t

ronProton-

Antiproton

TABLE

II

-

Synchrotron

Radiation.

Np

=

 ~;

Ue

=

0.05

Pe;E

ce

=

1.25

MeV.

Electron

radlated

power

=

100

MW

NpandNe

include

twobeams.

WARM

SERVICES

ACCELERATINGR.F.CORRECTIONMAGNETSCONVENTIONALRINGPOWER

VACUUM

SYSTEMBEAMDETECTORSOPTICALEQUIPMENT

L

CRYOSTAT

COLDSERVICES

REFRIGERATIONMAGNETCURRENTS

 BE M {

20100

1000

252525

33.313.3

16767

1670

667229573

46

115

4.6

11.50.037

 94

4,7

11.7

468011700

8.6

1.4

1,7

0.280.170.0280.086

0.215

2.155.4

215

540

0.0086

0.0540.2141.

34

21.4

134

0.0410.640.2053.202.0532.03.23.2

16

16160160

Ps

 IeV

B

s

 T)

R

 km

I

p

 rna

Up

 MeV/turn)

T

p

 days)

~iSi~~ ~

Power

 MW

Power

gradient

 I i/rn)

Beam

Energy

 GJ)

P

e

 TeV

Be

 G

N

e

 10

13 

Ie

 rna)

Ie

 sec

Power

gradient

 W/m)

Beam

Energy

 MJ)

0.2660.1960.4560.3360.9800.722

 ~

·490

91

168

20

36

3.31.89.55.2

4424

7.510.2

4,45.92.0

2.80.028

0.011

0.140.156

L4

0.56

480120096240

9.6

24

1.4

0.56

6.92.8

69

28

FIGURE

2.

Schematic

of

normal

ring

segmentation.

11agnetsand

related

services

are

fed

intothe

long

cryostats

from

the

warm

service

straight

sections.

Values

of

L

are

given

in

Table

I.

-327-