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
1001000
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
relatively
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
accelerated
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-