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 L = I γ r p e β ξ N • 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
 β xy > σ z ,
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.

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 
 10 LPA1 5 L 0 =0.71x10 3 ! L/L 0 (x10 -3 ) 0 -5 -10 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 turn (x10 3 ) • Weak‐strong
(strong
 beam
is
uniform)
 N p =4.9x10 11 
 N p =6.
x10 11 
 • 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=2.5x10 11 
/bunch
,
 β *=14
cm,
 σ z =7.5
cm,
,
 θ h (half
xangle) =393
 µ rad,
Piwinski
angle
=
3.5,
HV
crossing,
no
parasitic
 









Weak‐strong







































Strong‐strong


 






























































(design
bunch
population) 10 LPB1 L 0 =0.50x10 35 cm -2 s -1 5 ! L/L 0 (x10 -3 ) 0 -5 -10 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 turn (x10 3 )

Noise
tolerance
in
LPA • For
LPA‐II,
the
noise
tolerance
is
 δ x=0.1% σ x . 1.001 10 1 0 ! L/L 0 (x10 -9 /turn) 0.999 -10 0.998 ! L/L 0 0.997 -20 2
IP 0.996 1% 0.2% -30 0.995 1% 0.5% 0.994 -40 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0 0.2 0.4 0.6 0.8 1 turn (x10 6 ) " x/ # x (%)

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
5x10 11 
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.
 • 
 σ z =7.5
cm,
 ωσ z /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
 x = p x − V c p sin( kz + φ ) H c = V c E 0 x sin( kz + φ ) E 0 δ = δ − V c k = ω c kx cos( kz + φ ) E 0 c • H
at
collision
point,
horizontal
betatron
phase
 difference
between
crab
and
IP
is
chosen
 π /2. H c = θ x = x + θ k p x sin( kz + φ ) k sin( kz + φ ) V c θ = ω c δ = δ − θ p x cos( kz + φ ) * β x , c β x c E 0

Weak‐strong
beam‐beam
simulation
 with
the
crab
cavity • Weak
beam
is
transferred
with
H c .
 • Beam
envelope
of
the
strong
beam
is
sliced
in
 longitudinal
direction.
 R ij = x i x j c • 4x4
beam
envelope
is
kept,
but
the
dipole
moment
is

 x ( z ) = θ k sin( kz + φ )

Crab
kick
for
two
frequencies 40 800MHz 30 crossing 20 10 x ( µ m) 0 -10 -20 -30 -40 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 z (m) 










400
MHz




























800
MHz 40 40 20 20 x ( ! m) x ( ! m) 0 0 -20 -20 ! x =17 ! m ! x =17 ! m -40 -40 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 z (m) z (m)

Beam
distribution
of
the
weak
beam • 














400MHz
















800MHz 50 80 40 60 30 40 20 20 10 x ( µ m) x ( µ m) 0 0 -10 -20 -20 -40 -30 -60 -40 -50 -80 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 z (m) z (m) 30 20 10 x ( µ m) 0 Outside
of
Crab
cavity -10 -20 -30 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 z (m)

Simulation
results
of
weak‐strong 80 60 40 20 x ( µ m) 0 -20 -40 -60 -80 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 z (m) • Luminosity
evolution
for
LHC
nominal
 








2
crab




































1
crab




































 0.4 0.4 nominal, Fcrab=400MHz nominal, Fcrab=400MHz in a ring(w) L 0 =1.18x10 34 cm -2 s -1 L 0 =1.31x10 34 cm -2 s -1 0.2 0.2 ! L/L 0 (x10 -3 ) ! L/L 0 (x10 -3 ) 0 0 -0.2 -0.2 Δ L/L=(4.2+‐91)x10 ‐13 Δ L/L=(5.3+‐73)x10 ‐13 -0.4 -0.4 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 turn (x10 6 ) turn (x10 6 )

Simulation
results
of
weak‐strong • Early
Separation
scheme
 • Emittance
growth
is
negligible
 Δ L/L 0 <10 ‐9 . 1 1 ES, Fcrab=400MHz ES, Fcrab=800MHz L 0 =1.37x10 35 cm -2 s -1 L 0 =1.10x10 35 cm -2 s -1 0.5 0.5 ! L/L 0 (x10 -3 ) ! L/L 0 (x10 -3 ) 0 0 Δ L/L=(10+‐410)x10 ‐13 Δ L/L=(10+‐430)x10 ‐13 -0.5 -0.5 -1 -1 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0.05 0.1 0.15 0.2 0.25 0.3 turn (x10 6 ) turn (x10 6 ) 3 ES, Fcrab=800MHz in one ring L 0 =0.84x10 35 cm -2 s -1 2 1 0 -1 Δ L/L=(70+‐1900)x10 ‐13 -2 -3 0 0.05 0.1 0.15 0.2 0.25 0.3

Luminosity
for
crab
in
Early
Separation
 scheme • L
vs
Crab
angle

(2
crab
cavity) 1.18 ES 1.16 L (x10 35 ) 1.14 1.12 1.1 180 200 220 240 260 280 300 crab angle ( µ rad)

Luminosity
for
single
crab
cavity 1.08 4.6 1.07 4.5 L (x10 34 ) cm -2 s -1 L (x10 34 ) cm -2 s -1 1.06 4.4 1.05 1.04 4.3 Np=
1.7e11 Np=
1.15e11 1.03 4.2 1.02 nominal ! =0.25m 1.01 4.1 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0.05 0.1 0.15 0.2 0.25 0.3 crab kick (mrad) crab kick (mrad) 3.8 • nominal
Np=
1.15e11,
 β =0.55m,
 3.7 θ =280
 µ rad
 L (x10 34 ) cm -2 s -1 3.6 upgrade

Np=1.7e11,
 β =0.25m,
 • 3.5 θ =280
 µ rad
 Np=
1.7e11 upgrade

Np=1.7e11,
 β =0.25m,
 • 3.4 θ =440
 µ rad 3.3 ! =0.25m, " =440 ! rad 3.2 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 crab kick (mrad)

Strong‐strong
simulation • Both
beams
are
transferred
with
 H c = θ k p x sin( kz + φ ) • 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.