Beambeameffectforcollisionwith LargePiwinskiangleschemeand - - PowerPoint PPT Presentation

Beam‐beam
effect
for
collision
with
 Large
Piwinski
angle
scheme
and
 high
frequency
crab
cavity
in
LHC


K.
Ohmi,
KEK
 CARE‐HHH,
LHC
beam‐beam
and
beam‐beam
 compensation
 28
Aug.,2008
 Thanks
to
F.
Zimmermann,
J.P.
Koutchouk,
O.
Bruning,
 R.
Calaga,
R.
Tomas,
Y.
Sun,
A.
Morita,
M.
Aiba

F.
Zimmermann,
PAC07,

J.P.
Koutchouk,
EPAC08

LPA‐II
 2808
 2.5
 25
 1.22
 3.75
 Gaussian
 7.55
 0.14
 786

LPA
or
crab
cavity

• For
a
target
Luminosity,
there
are
choices
for
keeping
ξ,
β


and
Ι.

• 1. Design
with
the
head‐on
collision
condition
using
well‐

known
formula



• 2. Increasing
Piwinski
(crossing)
angle
and
bunch
population


can
keep
ξ.
To
keep
Ι,
bunch
repetition
is
decreased.



• The
choice
depends
on
other
conditions
for
βxy>σz,
if


crossing
angle
does
not
affect
the
beam‐beam
 performance.
For
example,
a
large
bunch
spacing
is
gain
for
 avoiding
parasitic
interaction
depending
on
arrangement
of
 separation
magnet
and
wires.
Electron
cloud…



• Both
scheme
are
examined
with
simulations.

L = Iγ rpeβ ξN

Simulations
for
LPA

• Weak‐strong
and
strong‐strong
simulations


were
performed.


• A
bunch
is
sliced
many
pieces
(15)
for
LPA


scheme.


• The
calculation
time
linearly
increase
for
the


number
of
slices
in
the
weak‐strong
 simulation.


• While
it
is
square
of
the
number
of
slices
in


the
strong‐strong
simulations,
.

Simulation
for
LPA
‐I


Np=4.9x1011


• 10
• 5

5 10 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 !L/L0 (x10-3) turn (x103) L0=0.71x103 LPA1

Np=6.
x1011


• Weak‐strong
(strong


beam
is
uniform)


• strong‐strong,
miss‐

matching
is
seen.


• Emittance
growth
due
to


parasitic
interaction
is
seen
 in
high
bunch
population
 (WS).

Large
Piwinski
angle
option‐II


J.P.
Koutchouk
et
al.

• N=2.5x1011
/bunch
,
β*=14
cm,
σz=7.5
cm,
,
θh(half
xangle)

=393
µrad,
Piwinski
angle
=
3.5,
HV
crossing,
no
parasitic
 









Weak‐strong







































Strong‐strong


 






























































(design
bunch
population)

• 10
• 5

5 10 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 !L/L0 (x10-3) turn (x103) L0=0.50x1035 cm-2s-1 LPB1

Noise
tolerance
in
LPA

• For
LPA‐II,
the
noise
tolerance
is
δx=0.1%σx.
• 40
• 30
• 20
• 10

10 0.2 0.4 0.6 0.8 1 !L/L0 (x10-9/turn) "x/#x (%) 0.994 0.995 0.996 0.997 0.998 0.999 1 1.001 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 !L/L0 turn (x106) 1% 0.2% 1% 0.5%

2
IP

Emittance
growth
in
LPA

• Weak‐strong
simulations
did
not
show
any
emittance


growth
and
halo
formation
for
the
design
bunch
 population.


• The
emittance
growth
for
5x1011
population
is
10‐9
or


slightly
higher
than
the
requirement
(1day
life
time).



• Fluctuation
of
luminosity
is
larger
than
the
nominal
case.


Miss‐match?


There
was
no
fluctuation
in
a
low
population.


• The
accelerator
lattice
should
be
included.
A.
Morita
can
do


it
with
SAD.


• Simulations
of
5000‐10000
turns
is
limit
for
the
strong‐

strong,
where
the
number
of
slice
is
15.
The
prediction
 power
for
the
emittance
growth
is
poor
in
the
present
 computers.


• Tolerance
for
fast
noise
is
similar
as
the
nominal
LHC.

• There
were
no
clear
problem
in
LPA
scheme
as
far
as
these


simulations.

Crab
cavity
scheme
in
LHC

• Choice
of
cavity
frequency,
800
MHz
or


400MHz.


• σz=7.5
cm,
ωσz/c=1.25
or
0.63.
• The
voltage
slope
may
not
be
negligible.
Beam


distributes
with
snake
shape.


• Study
of
collision
of
snake
shape
beams.

Effective
Hamiltonian
of
crab
cavity


• H
at
crab
cavity

• H
at
collision
point,
horizontal
betatron
phase


difference
between
crab
and
IP
is
chosen
π/2.

Hc = θ k px sin(kz + φ)

Hc = Vc E0 xsin(kz + φ) p

x = px − Vc

E0 sin(kz + φ)

δ = δ −θpx cos(kz + φ)

k = ωc c

x = x + θ k sin(kz + φ)

θ = ωc c Vc E0 βx,cβx

*

δ = δ − Vc E0 kxcos(kz + φ)

Weak‐strong
beam‐beam
simulation
 with
the
crab
cavity

• Weak
beam
is
transferred
with
Hc.

• Beam
envelope
of
the
strong
beam
is
sliced
in


longitudinal
direction.


• 4x4
beam
envelope
is
kept,
but
the
dipole
moment
is



Rij = xix j

c

x(z) = θ k sin(kz + φ)

Crab
kick
for
two
frequencies












400
MHz




























800
MHz

• 40
• 30
• 20
• 10

10 20 30 40

• 0.2 -0.15 -0.1 -0.05

0.05 0.1 0.15 0.2 x (µm) z (m) 800MHz crossing

• 40
• 20

20 40

• 0.4 -0.3 -0.2 -0.1

0.1 0.2 0.3 0.4 x (!m) z (m) !x=17!m

• 40
• 20

20 40

• 0.4 -0.3 -0.2 -0.1

0.1 0.2 0.3 0.4 x (!m) z (m) !x=17!m

Beam
distribution
of
the
weak
beam

• 400MHz
















800MHz

Outside
of
Crab
cavity

• 50
• 40
• 30
• 20
• 10

10 20 30 40 50

• 0.3
• 0.2
• 0.1

0.1 0.2 0.3 0.4 x (µm) z (m)

• 80
• 60
• 40
• 20

20 40 60 80

• 0.3
• 0.2
• 0.1

0.1 0.2 0.3 0.4 x (µm) z (m)

• 30
• 20
• 10

10 20 30

• 0.3
• 0.2
• 0.1

0.1 0.2 0.3 0.4 x (µm) z (m)

Simulation
results
of
weak‐strong

• Luminosity
evolution
for
LHC
nominal











2
crab




































1
crab






































• 80
• 60
• 40
• 20

20 40 60 80

• 0.5
• 0.4
• 0.3
• 0.2
• 0.1

0.1 0.2 0.3 0.4 x (µm) z (m)

• 0.4
• 0.2

0.2 0.4 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 !L/L0 (x10-3) turn (x106) L0=1.31x1034 cm-2s-1 nominal, Fcrab=400MHz

• 0.4
• 0.2

0.2 0.4 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 !L/L0 (x10-3) turn (x106) L0=1.18x1034 cm-2s-1 nominal, Fcrab=400MHz in a ring(w)

ΔL/L=(5.3+‐73)x10‐13 ΔL/L=(4.2+‐91)x10‐13

Simulation
results
of
weak‐strong

• Early
Separation
scheme

• Emittance
growth
is
negligible
ΔL/L0<10‐9.
• 1
• 0.5

0.5 1 0.05 0.1 0.15 0.2 0.25 0.3 !L/L0 (x10-3) turn (x106) L0=1.37x1035 cm-2s-1 ES, Fcrab=400MHz

• 1
• 0.5

0.5 1 0.05 0.1 0.15 0.2 0.25 0.3 !L/L0 (x10-3) turn (x106) L0=1.10x1035 cm-2s-1 ES, Fcrab=800MHz

• 3
• 2
• 1

1 2 3 0.05 0.1 0.15 0.2 0.25 0.3 L0=0.84x1035 cm-2s-1 ES, Fcrab=800MHz in one ring

ΔL/L=(10+‐410)x10‐13 ΔL/L=(10+‐430)x10‐13 ΔL/L=(70+‐1900)x10‐13

Luminosity
for
crab
in
Early
Separation
 scheme

• L
vs
Crab
angle

(2
crab
cavity)

1.1 1.12 1.14 1.16 1.18 180 200 220 240 260 280 300 L (x1035) crab angle (µrad) ES

Luminosity
for
single
crab
cavity

1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 0.05 0.1 0.15 0.2 0.25 0.3 L (x1034) cm-2s-1 crab kick (mrad) nominal

• nominal
Np=
1.15e11,
β=0.55m,


θ=280
µrad


• upgrade

Np=1.7e11,
β=0.25m,


θ=280
µrad


• upgrade

Np=1.7e11,
β=0.25m,


θ=440
µrad

4.1 4.2 4.3 4.4 4.5 4.6 0.05 0.1 0.15 0.2 0.25 0.3 L (x1034) cm-2s-1 crab kick (mrad) !=0.25m 3.2 3.3 3.4 3.5 3.6 3.7 3.8 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 L (x1034) cm-2s-1 crab kick (mrad) !=0.25m, "=440!rad

Np=
1.15e11 Np=
1.7e11 Np=
1.7e11

Strong‐strong
simulation

• Both
beams
are
transferred
with

• A
bunch
is
sliced
into
10
parts.
Sliced
beam


interacts
with
another
sliced
beam
10x10
 times
in
one
collision.


• Number
of
revolutions
is
limited
in
the
strong‐

strong
simulation,
30000
turns.

Hc = θ k px sin(kz + φ)

Simulation
results
(strong‐strong)

• Luminosity
evolution
for
nominal
LHC
• 80
• 60
• 40
• 20

20 40 60 80

• 0.5
• 0.4
• 0.3
• 0.2
• 0.1

0.1 0.2 0.3 0.4 0.5 x (µm) z (m)

• 5
• 2.5

2.5 5 5 10 15 20 25 30 !L/L0 (x10-3) turn (x103) L0=1.15x1034 cm-2s-1 nominal, Fcrab=400MHz

• 5
• 2.5

2.5 5 5 10 15 20 25 30 !L/L0 (x10-3) turn (x103) L0=1.06x1034 cm-2s-1 nominal, Fcrab=400MHz one ring

ΔL/L=(1.14+‐0.53)x10‐9 ΔL/L=(0.91+‐0.55)x10‐9

Simulation
results
(strong‐strong)

• Early
Separation
scheme
• 5
• 2.5

2.5 5 1 2 3 4 5 6 7 8 9 10 !L/L0 (x10-3) turn (x103) L0=1.04x1035 cm-2s-1 ES, Fcrab=800MHz

• 5
• 2.5

2.5 5 1 2 3 4 5 6 7 8 9 10 !L/L0 (x10-3) turn (x103) L0=1.20x1035 cm-2s-1 ES, Fcrab=400MHz

• 5
• 2.5

2.5 5 1 2 3 4 5 6 7 8 9 10 !L/L0 (x10-3) turn (x103) L0=0.76x1035 cm-2s-1 ES, Fcrab=800MHz in a ring

ΔL/L=(1.2+‐2.4)x10‐9 ΔL/L=(‐0.76+‐2.9)x10‐9 ΔL/L=(‐2.9+‐4.2)x10‐9

Tolerance
for
fast
noise
 weak‐strong

• For
800
MHz
crab
cavity,

0.1%
noise
is
limit.

• The
tolerance
is
a
little
severe
than
LPA.


Considering
the
higher
beam‐beam
parameter,
 it
is
reasonable.

0.988 0.99 0.992 0.994 0.996 0.998 1 1.002 0.05 0.1 0.15 0.2 0.25 0.3 !L/L0 turn (x106) 0.1% 0.2% 0.5% 1%

• 40
• 30
• 20
• 10

10 0.2 0.4 0.6 0.8 1 !L/L0 (x10-9/turn) "x/#x (%)

2IP

Summary

• Any
problem
was
not
found
in
both
of
LPA
and


crab
cavity
schemes
even
high
crab
cavity
 frequency,
800
MHz.


• Only
geometric
effects
are
seen
in
these


simulations
for
the
design
population.



• Tolerance
for
fast
noise
is
similar
level
as
the


nominal
LHC
(~0.1%).

• Ultimate

• The
luminosity
decrements
for
al
cases
are


very
small
in
the
weak‐strong
simulation.


• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 !L/L0 (x10-3) turn (x106) L0=2.5x1034 cm-2s-1 ultimate, no crab

• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 !L/L0 (x10-3) turn (x106) L0=3.1x1034 cm-2s-1 ultimate, Fcrab=400MHz

ΔL/L=(0.53+‐230)x10‐13 ΔL/L=(4.4+‐120)x10‐13

• Ultimate
• 5
• 2.5

2.5 5 5 10 15 20 25 30 !L/L0 (x10-3) turn (x103) L0=2.08x1034 cm-2s-1 ultimate, no crab

• 5
• 2.5

2.5 5 5 10 15 20 25 30 !L/L0 (x10-3) turn (x103) L0=2.5x1034 cm-2s-1 UT, Fcrab=400MHz

ΔL/L=(1.7+‐0.62)x10‐9 ΔL/L=(2.9+‐0.58)x10‐9

Local
crab
or
global
crab

• Local
crab

• Global
crab

e:Hc :exp(− : Hbb :)e−:Hc : e−:Hc :e−:Harc :e:Hc : = e−:Hc :e:exp(−:Harc :)Hc :e−:Harc : exp(− : Hbb :)e−:Hc :e−:Harc :e:Hc :