High%Intensity%Beams%Issues%in% …...Rise%Cme% Ê Ê Ê Ê Ê Ê Ê Ê ÊÊ ÊÊ Ê ÊÊÊ Ê ÊÊ Ê Ê ÊÊ Ê Ê Ê Ê ‡ ‡ ‡ ‡ ‡ ‡ ‡ ‡ ‡ ‡ ‡ ‡‡ ‡ ‡

High Intensity Beams Issues in the CERN Proton Synchrotron

S. Aumon EPFL-‐CERN

Aumon Sandra -‐PhD Defense 1

Contents •  Context-‐IntroducCon

•  TransiCon Energy

•  TransiCon Studies

a. Fast VerCcal Instability Measurements b. Macro parCcles SimulaCons c. Conclusions TransiCon Studies

•  InjecCon Studies a. Loss experiments with BLMs b. Turn by turn losses c. Monte Carlo SimulaCon with Fluka d. Coherent Tune ShiM Measurements e. Conclusions InjecCon Studies


Context-‐IntroducCon •  Intensity increase limited by aperture restric+on, collec+ve effects (instabili+es, space charge)

•  Here, studies of two intensity limitaCons on high intensity beams

-‐ at injecCon (aperture restric+on + space charge), more than 3% of the beam is lost, causing high radiaCon doses outside the ring -‐ at transiCon energy, fast ver+cal instability causing large losses or large transverse emiSance blow up, even with gamma transiCon jump (good method to cure the instability).

•  TransiCon Studies -‐ Extensive measurements of the dynamics of the instability, with and without gamma transiCon jump. -‐ Benchmark of the measurements with macro-‐parCcle simulaCons with HEADTAIL. -‐ Deduce a effec+ve impedance model (EsCmate the real part of the broad-‐band impedance). -‐ Find possible cures.

•  InjecCon Studies -‐ Measurements of proton losses with Beam Loss Monitors (BLMs) to idenCfy when the losses occur -‐ Losses when the beam goes through the injecCon septum (exactly at injecCon) AND then turn by turn at the minimum and maximum of the bump (orbit distorCon at during 1/2ms) -‐ Space charge is making worth the losses. -‐ Tune shiM measurements with intensity : deduce the imaginary part of the effec+ve broad-‐band impedance.

•  Studies important in the framework of the PS Upgrade for LHC Injector Upgrade (High Luminosity LHC beam)


TransiCon Energy


5.6 5.8 6.0 6.2 6.4 6.6 6.8 7.0-0.010

-0.005

0.000

0.005

0.010

Relativistic g

h

unpert.h»h»-jumph-jump

•  ParCcle oscillate around (ΔΦ,δ) in the bucket, the equaCon of moCon for small angle is the one of a spring. ParCcle oscillate with a angular synchrotron frequency ωs

•  Close to transiCon energy, the longitudinal moCon is frozen, ωsà0, non-‐adiaba+c regime

•  η defines the distance in energy from transiCon energy •  Stable phase shiM to keep the longitudinal focusing on

both side of transiCon energy •  In the PS, the use of a gamma transiCon jump is

necessary to cross faster transiCon energy

d2��

dt2+ !2

s�� = 0

Chapter 1. Basic concepts of Beam Dynamics

1.3 Transition Crossing

The CERN Proton Synchrotron is the first accelerator in which transition energy was crossed.Two months after the first turn of the beam in the PS, the 16 of september 1959, a bunch withan intensity of about 1010 protons per pulse was accelerated through the critical transitionenergy [10]. The idea was to use the radial position signal from the beam to control the RFphase instead of the amplitude. The sign of the phase had to be reversed at transition energy.Since then similar phase control system are used in the AGS in the Brookhaven NationalLaboratory a few months later and in all synchrotron where transition has to be crossed. Thischapter is focused on the description of the longitudinal particle motion around transitionenergy since the synchrotron motion is no longer adiabatic and the usual equation of Chap. 1.2breaks down.

1.3.1 Transition Energy

In synchrotron, a relative energy error can be related to a relative change in revolutionfrequency. Many medium and high energy synchrotron have to cross an energy at whichthis derivative of the revolution frequency ¢ f / f with respect to the momentum error ¢p/pchanges sign and has to cross zero. This energy is called transition energy noted Etr .

Crossing transition energy changes the sign of the slip factor which related the frequencyspread in the beam to its momentum spread given by,

¢ ff

= ¥¢pp

with ¥= 1∞2 ° 1

∞2tr

(1.64)

with ∞tr is the relativistic mass factor at transition energy ∞tr = Etr /E0. Let remind the defini-tion of the momentum compaction factor which determines ∞tr ,

1

∞2tr

=Æp = dC /Cd p/p

= 1C0

ID(s)Ω(s)

d s (1.65)

where Æp is the momentum compaction factor , C0 is the path length in meter of a particulewith a nominal momentum p0 on the reference orbit, D(s) is the dispersion function in meterat the longitudinal position s, Ω(s) is the bending radius in meter in the magnet at the locations. Æp depends on the machine optics and a rough estimation of the relativistic transitionenergy mass factor ∞tr is given by,

Æp = 1C0Ω0

ID(s)d s

8<

:Ω = Ω0 in dipoles

Ω =1 anywhere else(1.66)

24

Stable phase shiM at transiCon

Tc non-‐adiabaCc Cme~2.2ms |t|>Tc adiabaCc regime |t|<Tc non-‐adiabaCc regime

ParCcle are turning round in the RF bucket

Fast VerCcal Instability ObservaCon

-‐  InstrumentaCon: Wide band pickup, bandwidth 1GHz -‐  Travelling wave along the bunch with a frequency 700MHz. -‐  OscillaCon close to peak density, short range wake field. -‐  Strong losses in few 100 turns, less than a synchrotron period.

Instability behavior similar to Beam Breakup (Linac), Transverse Microwave (coasCng beam), TMCI (bunched beam) Favorable condi+ons to develop the instability: •  Slow synchrotron moCon: no exchange of parCcles between

head and tail stabilizing instabiliCes •  No chromaCcity: no tune spread. •  Lose of longitudinal and transverse Landau damping

80 100 120 140 160 180!2

0

2x 10

4

Ver

tica

l D

elta

sig

nal

[U

.A.]

Time[ns]

80 100 120 140 160 180!4

!2

0x 10

4

Longit

udin

al b

eam

den

sity

sig

nal

[U

.A.]

Vertical Delta signal

Longitudinal beam density

Loss of parCcles


Vert. Delta signal Hor. Delta signal Longitudinal signal

20ns

A.U.

200 300 400 500 600 700 8000

50

100

150

Inte

nsity

[1010

pro

tons

]

Time[ms]200 300 400 500 600 700 800

−5000

0

5000

10000

Mag

netic

Fie

ld [G

auss

]

Goals of Measurements •  Characterize the mechanisms of the instability by varying chromaCcity, intensity,

longitudinal emiSance (εl) etc. •  Study behavior of instability versus intensity to compute rise Cme •  Measurement of intensity threshold •  Momentum compacCon factor threshold (ηth) to idenCfy the longitudinal regime: adiaba+c/

non-‐adiaba+c and define ηth as done for the longitudinal microwave instability (1)

•  First mechanism is the beam interac+on with transverse impedance, for the PS, unknown, here assumed to be (BB) broad-‐band (resonator).

•  Find an effec+ve transverse impedance model with the support of macro-‐parCcle simulaCons.

•  IdenCfy mechanisms able to damp the instability: chromaCcity, longitudinal emiSance, use of the gamma jump

Defines BB model


Beam CondiCons Beam parameters

TransiCon Energy ~ 6.1 GeV

Number of bunches 1

Harmonic h=8

Transverse tunes (Qx-‐Qy) ~ 6.22-‐6.28 (Set by PFWs)

VerCcal ChromaCcity (2 different sets) around transiCon ξy

0 and ~ -‐0.1 (Set by PFWs)

RF cavity voltage around transiCon

145 kV

Full bunch length around transiCon

20-‐30 ns

Longitudinal emiSance (εl) at 2σ(1)

1.3 -‐2.5 eVs

Beam intensity 50e10 to 160e10 protons

Transverse EmiSance (εx,ynorm 1σ)

1.17 to 2.33 mm.mrad

(1) Measured at the beginning of the acceleraCon Aumon Sandra -‐PhD Defense 7

ReconstrucCon of the longitudinal phase space for longitudinal emiRance measurements

AcceleraCng bucket

δz

δE

Rise Cme

Ê

ÊÊ

Ê

Ê

Ê

Ê

ÊÊ ÊÊÊ

Ê ÊÊÊ

Ê

ÊÊÊÊ

Ê ÊÊÊÊ

Ê ÊÊÊ

ÊÊ

ÊÊ

ÊÊ

Ê

‡

‡

‡

‡

‡

‡

‡

‡

‡‡

‡ ‡‡ ‡

‡

‡

‡ ‡‡‡‡‡‡

‡

‡‡‡

‡‡‡

‡

‡ ‡‡ ‡ ‡‡ ‡‡‡‡‡

‡‡‡

‡‡‡

‡‡‡

‡‡‡

80 100 120 140 16050

100

150

200

250

300

350

400

Intensity @1010protonsD

Risetime@Tur

nsD

1.9eVs-xy<01.9eVs-xy~0

limI!Ith

⌧ = +1

linear/saturated

non-‐linear

•  Rise Cme measurements performed for different longitudinal emiSance and for 2 different sets in verCcal chromaCcity.

•  Closer the beam is from transiCon energy, less reliable is the measurement of the chroma+city •  Weak reproducibility of the machine in terms of longitudinal emiSance (20%) •  Surprisingly, rise Cme faster in linear part for the case with chromaCcity.

Ilinear/Ith ' 1.3

ÊÊ

Ê

ÊÊ ÊÊÊÊÊ Ê Ê

Ê

Ê ÊÊ

Ê

‡ ‡

‡

‡‡

‡

‡‡

‡‡

‡‡ ‡

-20 -15 -10 -5 0 5

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

Time x=têTc

VerticalChromaticityxy

xy<0

xy=0

C h r om a C c i t y measurements n o t r e l i a b l e around transiCon


Tc: non-‐adiabaCc Cme 2.2ms in the PS

Threshold in Intensity

Ê

Ê

Ê

Ê

Ê

‡

‡

‡

‡

‡

‡

‡

1.2 1.4 1.6 1.8 2.0 2.2 2.440

60

80

100

120

140

160

elH2sL

Ithreshold@101

0protonsD

Fitted Ith xv~0Ith xv~0Fitted Ith xv<0Ith xv<0

•  Instability with threshold in intensity

•  Ith increases linearly with the longitudinal emiSance (here peak density), predicted by the coasCng beam theory by E. Metral for zero chromaCcity

Ith

Ith =32

p2

3

Qy0|⌘|✏le�2c

⇥ fr|ZBB

y |•  ChromaCcity (or the working point) increases

the instability threshold: changing chromaCcity in the PS means a change of tune and non linear chromaCcity

•  Non-‐linear chromaCcity components in measurements are nevertheless small

•  Rise Cme are faster than synchrotron period (no headtail instability)

•  According to the coasCng theory (microwave-‐TMCI), a beam crossing transiCon is always unstable, because ηà 0

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!!!

!

!

!

!!

!

!

!

!

!

!

!

!

!!

!

!!!

!

""

"" ""

""""

"

" "" ""

"" " """ ""

"

""""

""

"

"

"""

""""""

"

"

""

"""

""""""

1.0 1.2 1.4 1.6 1.8

0.005

0.010

0.015

0.020

0.025

0.030

I!Ith

!!T

s

"1.9eVs"#v$0

!1.9eVs"#v%0Curves constant

once normalized by the longitudinal emiSance

Minimum due to synchrotron period Ts Aumon Sandra -‐PhD Defense 9

Eta threshold !!

!

!

!

!!

!

!

!!

!

!

!

!

!!

!!

!

!

!

!

!

!

!

!

!!

!

!!

!

!

! !!

!

!

!

"

""

""

"

"

"

"

"

"

"

"

"

"

""" "

""

"

" "

"

"

"

"

"

"

"

"

"

"

"""

# #####

#

##

##

## ##

#

#

#

#

#

#

#

###

#

##

#

#

80 100 120 140 160

!0.0010

!0.0005

0.0000

0.0005

Intensity !1010protons"

"th

# 2.3eVs

" 1.9eVs

! 1.5eVs

#v$0

!!

!

!

!

!!!

!

!!

!

!

!

!!!

!!

!

!

!

!

!

!

!

!

!!

!

!!

!!

! !!!

!

!

"

""

" "

"

"

""

"

""

"

"

"

""" "

"""

" ""

"

"

""

"""

"

""""

# ##### #

###

######

##

#

#

#####

###

#

#

1.0 1.2 1.4 1.6 1.8 2.0

!0.0010

!0.0005

0.0000

0.0005

I!Ith"th

# 2.3eVs" 1.9eVs! 1.5eVs#v$0

!

!!

!

!

!!

!

!

!

!!

!

!!

!

!

!

!!! !

!!!

! !!

!

!

!

!!!!

!

!!!!

""

"" ""

""

""

"

" "" ""

"

" " """""

"

""""

""

"

"

""""

"""""

"

"

""

"""

""""""

80 100 120 140 160!0.0015

!0.0010

!0.0005

0.0000

0.0005

0.0010

Intensity !1010 protons"

"th

" #v$0

! #v%01.9eVs

•  Instability is triggered at different η, namely ηth for each intensity.

•  ηth linear with beam intensity.

•  Minimum ηth : -‐ Meas. 0.0004 , zero chromaCcity -‐ Meas. 0.001, negaCve chromaCcity

•  Resul+ng η is right only if the es+ma+on of transi+on +me is good.

•  With chromaCcity, possibility to accelerate more intensity for the same ηth

Error bar contains the possible error on the transiCon Cming

Offset


Threshold in Intensity with gamma jump

Ê

Ê

Ê

Ê

ÊÊ

Ê

‡ ‡

‡

‡‡

‡

‡‡

1.4 1.6 1.8 2.0 2.2 2.4 2.6200

300

400

500

600

700

Longitudinal Emittance elH2sL

ThresholdinIntensity@101

0protonsD

Linear Fit R2=0.979

xy Set 2Linear Fit R2=0.994

xy Set 1

Ê

Ê

Ê

ÊÊÊÊÊÊ

Ê

Ê

ÊÊÊÊÊ

Ê

‡ ‡

‡

‡

‡‡

‡‡‡

‡

‡‡‡‡

‡ ‡ ‡

4.0 4.5 5.0 5.5 6.0 6.5 7.0

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

Relativistic g

VerticalChromaticity

‡ xy Set 2

Ê xy Set 1

5.6 5.8 6.0 6.2 6.4 6.6 6.8 7.0-0.010

-0.005

0.000

0.005

0.010

Relativistic g

h

unpert.h»h»-jumph-jump

•  Use of a gamma jump allows to increase considerably Ith

•  Instability appears around ηth~0.005 •  Frozen synchrotron moCon for a shorter Cme

allows to increase by a factor 3 and up to 10, Ith according to the working point.

•  NegaCve large chromaCcity before and posiCve chromaCcity aMer transiCon helps to increase intensity threshold.

•  Threshold in η are also increased by a factor 10.


ηth~0.005

Conclusions of Experiments •  First +me that extensive measurements are done for this instability: instability measurements for zero and

small negaCve verCcal chromaCcity varying the longitudinal emiSance (peak density) and the beam intensity.

•  Instability is easily developed for zero (small) chroma+city (not a head-‐tail kind) and for slow synchrotron mo+on (BBU or coasCng beam), and high peak density (coasCng beam).

•  Chroma+city is a way to increase threshold in intensity and in η. •  Increase synchrotron mo+on (η) with the gamma jump, here close to a factor 10 with a good set in

working point. •  ηth ≠0 for the set zero-‐chromaCcity, could be due to an error in esCmaCon of the transiCon Cme (~300

turns is definiCvely possible), need to be check with macro-‐parCcle simulaCons. •  It appears that fast synchrotron moCon (large η) + jump in chromaCcity from large negaCve value to large

posiCve value is a way to cure the instability. •  Need of macro-‐parCcle simulaCons to benchmark the measurements and understand beSer the dynamics

of the instability. -‐ Check the raCo -‐ threshold in η and in intensity. -‐ Possibility to have a predicCve model

Ilinear/Ith ' 1.3


0 1 2 3 4 5 6!2

0

2

4

6

8

10

Position z behind the source !m"

Wak

efu

ncti

on!1

015

V#C#m"

Macro-‐parCcle SimulaCons (HEADTAIL) •  Use of a transverse broad-‐band impedance model

(resonator) •  I modified the code to adapt it as close as possible as

the measurement condiCons

ω angular revoluCon frequency ωr resonator frequency Rs shunt impedance (MΩ/m) Q quality factor

ICAP, Chamonix, 02.10.2006 Giovanni Rumolo 4/30

R&D and LHC Collective Effects Section

Interaction with animpedance

s

∫W(z-z‘)ρ(z‘)dz‘z

W

Z? =!r

!

Rs

1 + iQ⇣

!r! � !

!r

⌘

Simula+on parameters

RF bucket acceleraCng

Momentum rate 46 GeV/c/s

Twiss <βx,y> 16/16 m

Qx,y 6.22/6.28

Gamma transiCon ~ 6.1

Vacuum chamber flat

Impedance model broad-‐band

Quality factor Q 1

Resonator frequency 1 GHz

Shunt impedance Rs To be matched

Useful outputs to consider through transi+on •  Turn by turn Δy signal •  VerCcal normalized emiSance •  VerCcal centroid


SimulaCon with HEADTAIL

14

HEADTAIL Instability at ηth

HEADTAIL

HEADTAIL, Instability well above ηth

Measurement

OscillaCon Starts at the maximum peak density as the measurements

Tc: nonadiabaCc Cme ~2.2ms

ξv =0

Aumon Sandra -‐PhD Defense

Measurements

Simulated Rise Cme 1.9 eVs

Ê

ÊÊÊ

Ê Ê

Ê Ê Ê

ÊÊ

ÊÊ Ê Ê ÊÊ Ê

Ê

Ê

ÊÊ

Ê

Ê

Ê

Ê

ÊÊÊ

ÊÊ

ÊÊÊÊ

Ê

ÊÊÊÊ

Ê Ê

ÊÊ

ÊÊ ÊÊÊ

ÊÊ

ÊÊ

ÊÊ

Ê

50 100 150 2000

50

100

150

200

250

300

350

Beam Intensity @Nb protons 1010D

RiseTimet@Nb

turnsD

Asymptote y=31.36

f2HxL=81.6 - 1417.3

76.6 - x

Measurements

fHxL=14.63+ 10719

31.36 - x

Simulations Rs=0.7MWêm

2.3 eVs

Ê

Ê

Ê

Ê

ÊÊÊÊÊÊÊ

Ê

ÊÊ

Ê

Ê

Ê

ÊÊÊÊÊÊÊ Ê

Ê

ÊÊÊ

ÊÊ

Ê

Ê

Ê ÊÊÊÊÊ

‡

‡

‡

‡

‡‡

‡

‡‡

‡‡‡‡ ‡‡‡ ‡

‡ ‡‡

‡‡ ‡ ‡

‡ ‡‡ ‡ ‡ ‡ ‡

Ï

Ï

ÏÏÏ

ÏÏ

ÏÏÏ

Ï

Ï

ÏÏÏ

ÏÏÏÏÏÏÏ

ÏÏ

Ï

Ï ÏÏ Ï Ï Ï

Ï

50 100 150 200 250 300

100

200

300

400

500


RiseTimet@Nb

turnsD

el = 1.5eVs

Headtail-Rs=0.5MWêmHeadtail-Rs=0.7MWêmMeasurements

Ê

Ê

Ê

Ê

Ê

Ê

Ê

Ê

Ê

Ê

1.2 1.4 1.6 1.8 2.0 2.2 2.4

40

60

80

100

120

140

160

elH2sL

Ithreshold@101

0protonsD

1.5 eVs Measurements SimulaCons

fr=1GHz Rs=0.7MΩ/m Q=1

Ê

Ê Ê

Ê

Ê

Ê

ÊÊ Ê Ê Ê

Ê ÊÊÊ Ê Ê Ê

Ê Ê Ê Ê ÊÊ

Ê Ê Ê Ê Ê

‡

‡‡‡

‡

‡

‡

‡‡

‡

‡‡‡‡‡

‡

‡‡‡‡ ‡‡‡‡‡ ‡‡‡‡ ‡

100 150 200 250 300

100

200

300

400

500


RiseTimet@Nb

turnsD

el = 2.3eVs

Headtail-Rs=0.7MWêmMeasurements

Ilinear/Ith ' 3� 5


Dynamics with chromaCcity

•  ImplementaCon in the code of a chromaCcity change with acceleraCon

•  Delta verCcal signal shows that the oscillaCon of the instability is dumped with chromaCcity compared to the same profile with the same energy with zero chromaCcity.

•  Not the same dumping at the intensity threshold as in the measurements for the same chromaCcity .

•  EffecCve impedance between 0.5 and 0.7 MOhm/m


ÊÊ

Ê

ÊÊ

Ê

ÊÊ

Ê

Ê

Ê Ê Ê

4.0 4.5 5.0 5.5 6.0 6.5

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

Relativistic g

VerticalChromaticityxv

Headtail

Measurements

Ê Ê Ê

Ê

ÊÊ Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê

‡

‡

‡

‡ ‡‡ ‡

‡

‡‡ ‡

‡‡ ‡ ‡ ‡ ‡

ÏÏ Ï Ï

Ï ÏÏ Ï Ï

Ï ÏÏ Ï Ï Ï ÏÏ Ï

ÏÚÚÚÚÚÚÚÚ

ÚÚÚÚÚÚÚ

Ú

Ú

Ú

Ú

Ú

Ú

Ú

Ú

ÚÚÚÚÚÚ Ú

Ú

ÚÚÚ ÚÚÚ ÚÚ

Ú

ÚÚÚÚÚÚ

Ú

Ú ÚÚÚÚÚÚÚ

80 100 120 140 160 180 2000

100

200

300

400

500

600

Intensity@1010protonsD

RiseTimet@N

bturnsD Ú Measurements-xv~-0.1

Ï Rs=0.7MWêm-xv=0‡ Rs=0.5MWêm-xv~-0.1Ê Rs=0.7MWêm-xv~-0.1

Threshold in Eta No Chroma+city

Ê Ê Ê Ê ÊÊ Ê

ÊÊ Ê Ê

ÊÊÊ Ê Ê

‡ ‡ ‡‡

‡ ‡

‡‡

‡ ‡

‡ ‡‡ ‡ ‡ ‡

‡

‡‡ ‡

‡ ‡ ‡‡ ‡

ÏÏ Ï Ï

Ï Ï Ï Ï Ï Ï Ï Ï

Ï ÏÏÏ Ï Ï

ÏÏ Ï

Ï ÏÏ Ï

ÏÏ

Ï

Ê

ÊÊ

ÊÊ

Ê

Ê

Ê

Ê

Ê

Ê

Ê

Ê

Ê

Ê

ÊÊ

Ê Ê

Ê

Ê

Ê

Ê Ê

Ê

Ê

Ê

Ê

Ê

Ê

Ê

Ê

Ê

Ê

ÊÊÊ

0.5 1.0 1.5 2.0 2.5 3.0-0.0010

-0.0008

-0.0006

-0.0004

-0.0002

0.0000

0.0002

0.0004

IêIth

h

Measurements

el=2.3eVs

el=1.5eVs

el=1.9eVs

Small Nega+ve Chroma+city

ÊÊ Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê

‡ ‡ ‡‡ ‡ ‡

‡ ‡ ‡ ‡‡ ‡ ‡ ‡ ‡ ‡ ‡

‡ ‡ ‡ ‡ ‡ ‡ ‡ ‡

ÊÊ

ÊÊ ÊÊ

ÊÊ

ÊÊ

Ê

ÊÊÊ ÊÊ

Ê

ÊÊÊÊÊÊÊÊ

ÊÊÊÊ

ÊÊ

Ê

Ê

ÊÊÊÊÊÊÊ

0.5 1.0 1.5 2.0 2.5 3.0

0.0000

0.0005

0.0010

0.0015

IêIth

h

Measurements -xv<0

el=1.9eVs -xv=0

el=1.9eVs -xv<0

Agreement with measurements: •  ηth increases with chromaCcity, allows to

accelerate more intensity with non zero ξy •  Offset between ηth(ξy=0) and ηth(ξy<0) •  Linear behavior eta th with intensity

Disagreement with measurement and simulaCons: •  Not the same ηth close to the intensity threshold •  Not the same linear behavior about the slope •  Offset in η of 0.0002 in simula+ons , 0.0006 in

measurements

≠ ηth ≠ ηth

Offset

Best impedance model found Rs=0.7MΩ/m Q=1, short range wake field Fr=1GHz


Not Same Scale

Conclusions a)  Conclusions of the study

-‐ Equivalent broad-‐band impedance found Rs=0.7MΩ/m, fr=1GHz, Q=1 -‐ Intensity threshold predictable at 50% -‐ Possible cure of the instability: adequate chromaCcity (working point) + gamma jump. Limita+ons -‐ Impedance model is the biggest unknown of the study. -‐ Ilinear/Ith ~ 1.3-‐1.5 (Measurements) versus Ilinear/Ith ~ 3-‐5 (HEADTAIL) -‐ ηth close to the threshold in intensity are very different, partly explained the sezng of the transiCon Cming in measurements. -‐ Different offset in ηth , but behavior comparable to coasCng beam theory -‐ The effect of chromaCcity is less important in the simulaCons than in the measurements (strong effect !) -‐ Not presented here, but the simulaCons with gamma jump show travelling wave frequency higher than in the measurements. -‐ Influence of space charge not included in simulaCons. -‐ Non-‐lineariCes generated by PFWs. -‐ linear and non-‐linear coupling not included in simulaCons. Outlooks – Future works -‐ Complete impedance model -‐ Studies of ChromaCcity jump -‐ CollaboraCon with GSI: similar studies are carried out at GSI and measurements at the CERN PSBooster and PS will be made in June. -‐ Octupoles


Studies of losses at InjecCon

0

500

1000

1500

2000

2500

3000

3500

4000

4500

1959

19

60

1961

19

62

1963

19

64

1965

19

66

1967

19

68

1969

19

70

1971

19

72

1973

19

74

1975

19

76

1977

19

78

1979

19

80

1981

19

82

1983

19

84

1985

19

86

1987

19

88

1989

19

90

1991

19

92

1993

19

94

1995

19

96

1997

19

98

1999

20

00

2001

20

02

2003

20

04

2005

20

06

2007

20

08

2009

Prot

on In

tnes

ity [E

10]

Year

PS Proton Intensity Evolution Over 50 Years

Typical Intensity [E10]

Peak Intensity [E10]

Record Intensity [E10] PS Booster

1 GeV

PS Booster 1.4 GeV RF change h=5 to h=1

For LHC Beam Production

Double Batch Injection 4.2E13 inj. 3.55E13 ej.

PS Shutdown Magnet

renovation


Facts •  Large losses of proton while the beam is injected into the PS. •  Strongly dependent of the beam intensity, therefore high intensity beams most concerned

(ToF, CNGS), at least 3-‐4% of losses. •  High radiaCon dose outside the ring (the so-‐called Route Goward) •  Later moCvaCon, injec+on energy upgrade from 1.4 to 2 GeV kine+c, the radiaCon dose will be

increased by a factor ? (1) with the same scenario of losses.

Aims: find the mechanisms of the protons beam losses.

(1) Work of S. Damjanovic

Beam intensity conCnuously increases since its commissioning

Single Turn InjecCon System Septum

BSM40 BSM42 BSM43 BSM44

x’

xs xsbump

!k

"#

$s

s

Transferline

Fast Kicker

Closedorbit

Bump

%s

$k

%k


BSM40 BSM42 BSM43

BSM44

Kicker

230 240 250 260 270 280

!0.03

!0.02

!0.01

0.00

0.01

0.02

0.03

Longitudinal position s!m"

X!m"

Booster 4 superposed rings

Cross SecCon InjecCon Septum

InjecCon bump

Possible opCcs mismatch?

Aperture restricCon?

Loss Experiments •  BLMs located at the maximum (SS42) and minimum

(SS43) of the bump, i.e. where the available aperture is minimum.

•  Measurements done while the beam is injected (first turn) on single bunch ToF and mulC-‐bunch CNGS beam.

•  Losses while the beam is going through the injecCon septum, the beam is injected at the maximum of the bump.

•  The BLM are able to disCnguish the losses bunch to bunch.

Conclusions: Losses occur while the beam is going through the septum and then turn by turn


InjecCon, transit through the septum

BLM at minimum of the bump

BLM at maximum of the bump

Beam composed by 8 bunches

Beam from Ring 2

1 turn

1turn 2turn 3turn

0 10 20 30 40 50 60 700

2

4

6

8

10

12

14

s@mD

VerApertureêVe

rEnvelop 3sigma

RMS

!!

!

!

!

!

!

!

!

!

!

!

!

! !

!!

!

!

!

!

!

!

!

!!

!

!!

!

! !

!

!

!!

!

! !

!

0 100 200 300 400 500 6000

1

2

3

4

5

6

Longitudinal position s!m"

Hor.Dispersion!m"

Periodic DxMADX Dx

! Meas.Dx BT1

Septum losses •  Betatron and dispersion matching measurements in order

to idenCfy a possible mismatch between the injecCon line and the PS: determinaCon of iniCal condiCons, in parCcular for the horizontal dispersion.

•  Good agreement with the opCcs model computed with PTC-‐MADX: -‐ No large mismatch was found expect on dispersion for Ring 3. -‐ Beam size measurements right at injecCon: tail of the beam are cut on the septum blade (~1%)

•  It was found that the beam is pushed as close as possible of the septum blade to decrease the angle given to the beam by the injecCon kicker: compromise between losses and kicker strength.


�x(s) = D(s)�p/p

Losses due to the incoming beam

ToF beam full intensity800e10eHor(RMS)=12mm.mrad

MD beam100e10eHor(RMS)=5mm.mrad

1% of the beam

3% of the beam

Septum Aperture [A.U] [A.U]Horizontal Beam Profile Septum Aperture

Horizontal Position[m] Horizontal Position[m]

Thursday, April 5, 12

0 10 20 30 40 50 60 700

2

4

6

8

10

12

14

s@mD

HorApertureêHo

rEnvelop 3sigma

RMS

Turn by Turn losses


0.0 0.1 0.2 0.3 0.4

0.0

0.5

1.0

1.5

2.0

Time !ms"

Sig

nal!V"

BSM44BSM43BSM42BSM40

Friday, April 6, 12

•  Turn by turn losses while the injecCon bump is decreasing.

•  The losses occurs at the maximum and at the minimum of the bump: tails of the horizontal distribuCon are cut around 3 sigma.

•  Presence of direct space charge at injecCon •  Preliminary tune footprint simulaCon with PTC-‐

Orbit show the possibility that parCcles cross the integer resonance

•  It can cause emiSance blow up and high amplitude oscillaCon which hit the vacuum chamber at the first aperture restricCon

ArCficial offset to disCnguish the different signal

Integer tune

Fluka SimulaCons

Dose equivalent (pSv /lost proton)

Z (cm)

Y (cm)

Injection septum

PS magnet

Beam direction

BLM source

Z(cm)

X(cm)

SS41 SS42 SS43 SS44


0 1 2 3 4 5 60

20

40

60

80

100

120

140

Measured

Fluka

BLM41

BLM42

BLM

Nor

mal

ized

resp

onse

BLM43

BLM44

BLM45

Goal: Reproduce the signal of the BLM at injecCon (Supervision of a student)

Chapter 5. High intensity beams issues at Injection

5.6 FLUKA simulations of beam losses at injection

As explained earlier in Sec. 5.2, beam losses are observed when the beam is injected in themachine. In order to verify that the high radiation levels observed at Rue Goward, which arecorrelated with the PS BLMs, are related directly to the injection losses, a shower simulationwith the code FLUKA [61, 62, 95] has been performed.

FLUKA is a Monte Carlo code that tracks a given distribution of source particles, called primary,through a geometry programmed by the user. Interactions between the primary particles andthe different materials in the geometry are sampled and all secondary particles are tracked.Both the hadronic and the electromagnetic shower are simulated. The simulation output aredifferent quantities specified by the user, for example the energy deposition. in given parts ofthe geometry or a full record of all particle tracks and interactions.

A geometry of the region around the injection septum has already been implemented inFLUKA [96]. The existing input file has been adopted for this particular study through theaddition of BLMs. The FLUKA geometry is shown in Fig. 5.40. The BLMs, of the type ACEM,are described in detail in Sec. 5.2

The primary particles are started at the surface of the inside of the beam pipe at the longitudi-nal locations with the smallest normalized aperture as calculated with MAD-X. These locationscorrespond approximately to the maximum and minimum of the PS injection bump and theyare shown in Fig. 5.40. Several simulations were performed, and the relative weights of thelocations of the source particles were empirically adjusted in order to fit with the measure-ments. This was done to see if the loss locations are compatible with the aperture restrictions.The different positions with their relative weights are also described in Table 5.9. The particlesare assumed to be at their maximum amplitude and therefore have a zero angle towards thelongitudinal beam axis. An example of a starting distribution in the transverse plane is shownin Fig. 5.41.

Injection 30% At Septum 42, an electrostatic dipole in the straight section 42 to deflect theincoming beam form the PSB into the PS. The tail of the beam is hitting onthe inside at the end of the septum

Maximum ofthe bump

10% At the beginning on the outside of Septum 42, the tail of the beam is cut atthe blade

Minimum ofthe bump

60% On the inside on the first metre of Magnet 43. Spread on three equally spacedspots (30%,20%,10%)

Table 5.9: Location of the different sources in FLUKA

In order to gain in CPU time, 33 simulations were launched in parallel on a cluster and the

234

Coherent tune shiM measurements

25

-3¥ 1010 -2¥ 1010 -1¥ 1010 1¥ 1010 2¥ 1010 3¥ 1010w

-1.5¥ 106

-1.0¥ 106

-500000

500000

1.0¥ 106

1.5¥ 106Zt

Im(Z?) Re(Z?)

Real Tune shie measurements Es+ma+on of this part

Instability rise +me measurements (Transi+on study)

Aumon Sandra -‐PhD Defense

MoCvaCon •  Impedance effects (wall, space charge) are

important issues at injecCon •  First step toward a more complete PS impedance

model

ï150 ï100 ï50 0ï2

ï1.5

ï1

ï0.5

0

0.5

1

1.5

Time[ns]

Hor

izon

tal D

elta

Sig

nal [

U.A

.]

AD

2.5! 10"7 3.! 10"7 3.5! 10"7 4.! 10"7 4.5! 10"7 5.! 10"7

"0.02

"0.01

0.00

0.01

0.02

Time!s"

#x$U.A.

HI-‐LHC

Coherent tune shiM at injecCon

26 Aumon Sandra -‐PhD Defense

Injection

Extraction

Measurements

0 200 400 600 8000

500

1000

1500

Time @msD

Mag

net

icFiel

d@Ga

ussD

Ê

Ê Ê

Ê

ÊÊ

1.0¥ 1012 1.5¥ 1012 2.0¥ 1012 2.5¥ 1012 3.0¥ 1012

0.208

0.210

0.212

0.214

Nb

qx

R2=0.9396QxHNbL=-2.2145 10-15Nb+0.2149FitMeas

Ê

ÊÊ

Ê

Ê

Ê

1.0¥ 1012 1.5¥ 1012 2.0¥ 1012 2.5¥ 1012 3.0¥ 10120.225

0.230

0.235

0.240

0.245

0.250

0.255

Nb

qy

R2=0.9935

QyHNbL=-7.6024 10-15Nb+0.2559FitMeasurements

•  KineCc energy 1.4GeV •  Tune measurements all along the energy

plateau

Beam parameters at LHC extracCon energy

•  Almost no coherent tune shiM in the horizontal plane.


ÊÊ

Ê Ê

Ê

Ê

Ê

1¥1012 2¥1012 3¥1012 4¥1012 5¥1012

0.258

0.260

0.262

0.264

0.266

0.268

Nb

qy

R2=0.9532QyHNbL=-1.0545 10-15Nb+0.2674FitMeasurements

Ê

ÊÊ Ê

ÊÊ

Ê

1¥1012 2¥1012 3¥1012 4¥1012 5¥10120.2280

0.2285

0.2290

0.2295

0.2300

Nb

qx

R2=0.750QxHNbL=-1.1635 10-16Nb+0.229FitMeasurements

�Qx

coh

' 0

EffecCve Impedance

KineCc Energy K 1.4 GeV

Bunch length ~ 180 ns

βrel 0.91

γrel 2.47

ω0 2728 e3 rad.s-‐1

Horizontal Zeff 3.5 MΩ/m

VerCcal Zeff 12.5 MΩ/m

(1) From Sacherer formula (CERN/PS/BR 76-‐21)

Momentum p 26GeV/c

Bunch length ~ 50 ns

βrel 0.9993

γrel 27.729

ω0 2996 e3 rad.s-‐1

Horizontal Zeff < 1 MΩ/m

VerCcal Zeff 6.1 MΩ/m



5.8.3 Effective generalized inductive impedance estimation

The detailed of the theory of transverse bunched beam instabilities and the beam-impedanceinteraction developed by Sacherer can be found in Ref. [23, 104].

The beam-impedance interaction generates a complex tune shift¢! of the betatron frequency.The real part of¢!measured at injection and extraction energy corresponds to the interactionof the beam with the imaginary part of the transverse impedance Z? that is supposed broad-band. Chap. 4 has shown that the measurements of the fast transverse instability rise timescan be compared to HEADTAIL simulations assuming a broadband impedance. However,growth rates are the interaction of the beam with the real part of the impedance, meaningthat Re(Z?) measuring at transition energy can be considered as broadband. With tune shiftmeasurements, Im(Z?) is evaluated and as it will be seen this paragraph, this value is notabsolute. This is why we defined Ze f f , the effective impedance, i.e. the impedance weightedby the transverse bunch spectrum h(!) centered at the chromatic frequency !ª as shown inFig. 5.54,

Ze f f =

1Pp=°1

Z (!0)h(!0 °!ª)

1Pp=°1

h(!0 °!ª)

8>>><

>>>:

!0 =!0p +!Ø!ª = ª!Ø/¥

h(!) = e°!2æ2/c2

(5.49)

with !0 the angular revolution frequency, ª the chromaticity, !Ø the betatron frequency, ¥ themomentum compaction factor, h(!) the bunch spectrum, which a line spectrum within theenvelope h(!0°!ª) and then for a single bunch!0 = (p+Q)!, with p is an integer °1< p <1.Since the beam is assumed Gaussian, h(!0) is also a Gaussian spectrum. Im(Z?) is assumedconstant all over the spectrum of the oscillation mode at least for the lowest mode consideredherein (m=0). Such simplification is generally valid for long proton bunches. The real tuneshift is related to the effective generalized impedance developed by the Sacherer for a bunchedbeam [104]

¢Qm =° 11+m

j

2Q0!20

eØI∞m0øb

Im

0

BB@

1Pp=°1

Z (!0)h(!0 °!ª)

1Pp=°1

h(!0 °!ª)

1

CCA (5.50)

with m the oscillation mode, Q0 the transverse tune,!0 the revolution frequency, e the electroncharge in Coulomb, Ø and ∞ the relativistic parameters, m0 the proton mass in kg, I theintensity in A and øb the full bunch length in meter. The computation gives an effectivegeneralized transverse impedance. Effective since its value is not absolute and might changedaccording the energy and the length of the beam.

For asymmetric structures as in the PS and as explained in Ref [105] and briefly in Sec. 1.4.1,the impedance is transformed as a Taylor expansion and can be expanded into a power seriesin the offset of the trailing particles behind a source particle, which then normalized to a

252


5.8.3 Effective generalized inductive impedance estimation

The detailed of the theory of transverse bunched beam instabilities and the beam-impedanceinteraction developed by Sacherer can be found in Ref. [23, 104].

The beam-impedance interaction generates a complex tune shift¢! of the betatron frequency.The real part of¢!measured at injection and extraction energy corresponds to the interactionof the beam with the imaginary part of the transverse impedance Z? that is supposed broad-band. Chap. 4 has shown that the measurements of the fast transverse instability rise timescan be compared to HEADTAIL simulations assuming a broadband impedance. However,growth rates are the interaction of the beam with the real part of the impedance, meaningthat Re(Z?) measuring at transition energy can be considered as broadband. With tune shiftmeasurements, Im(Z?) is evaluated and as it will be seen this paragraph, this value is notabsolute. This is why we defined Ze f f , the effective impedance, i.e. the impedance weightedby the transverse bunch spectrum h(!) centered at the chromatic frequency !ª as shown inFig. 5.54,

Ze f f =

1Pp=°1

Z (!0)h(!0 °!ª)

1Pp=°1

h(!0 °!ª)

8>>><

>>>:

!0 =!0p +!Ø!ª = ª!Ø/¥

h(!) = e°!2æ2/c2

(5.49)

with !0 the angular revolution frequency, ª the chromaticity, !Ø the betatron frequency, ¥ themomentum compaction factor, h(!) the bunch spectrum, which a line spectrum within theenvelope h(!0°!ª) and then for a single bunch!0 = (p+Q)!, with p is an integer °1< p <1.Since the beam is assumed Gaussian, h(!0) is also a Gaussian spectrum. Im(Z?) is assumedconstant all over the spectrum of the oscillation mode at least for the lowest mode consideredherein (m=0). Such simplification is generally valid for long proton bunches. The real tuneshift is related to the effective generalized impedance developed by the Sacherer for a bunchedbeam [104]

¢Qm =° 11+m

j

2Q0!20

eØI∞m0øb

Im

0

BB@

1Pp=°1

Z (!0)h(!0 °!ª)

1Pp=°1

h(!0 °!ª)

1

CCA (5.50)

with m the oscillation mode, Q0 the transverse tune,!0 the revolution frequency, e the electroncharge in Coulomb, Ø and ∞ the relativistic parameters, m0 the proton mass in kg, I theintensity in A and øb the full bunch length in meter. The computation gives an effectivegeneralized transverse impedance. Effective since its value is not absolute and might changedaccording the energy and the length of the beam.

For asymmetric structures as in the PS and as explained in Ref [105] and briefly in Sec. 1.4.1,the impedance is transformed as a Taylor expansion and can be expanded into a power seriesin the offset of the trailing particles behind a source particle, which then normalized to a

252

(1)

Important Conclusions

�Qx

coh

' 0

�Qx

coh

' �Qx

dip

+�Qx

quad

�Qx

coh

' 0 ! Zx

dip

+ Zx

quad

= 0

Increase by a factor 2 with respect to measurements done in 1990 and 2000

From the measured tune shiM with intensity, the effecCve impedance can be deduced from the Sacherer formula of the interacCon of the bunch spectrum in frequency with a broad-‐band impedance: Zeff

Zeff depends of bunch length

Space Charge Tune ShiM EsCmaCon

1.0! 1012 1.5! 1012 2.0! 1012 2.5! 1012 3.0! 1012

"0.020

"0.015

"0.010

"0.005

0.000

Nb protons

Ver

tica

lT

un

esh

ift#

Qv

#Qv SC 26 GeV!c

#Qv SC 1.4 GeV

Total Vert. #Qv



5.8.4 Estimation of the Tune Shift due to Space charge

The measured tune shift at injection and extraction energy is the sum of a the contributionfrom space charge ¢Qsc and from the impedance ¢Qz . Let consider the vertical effectiveimpedance at the two energies. If the coherent tune shift due to space charge is assumednegligible at 26 GeV, it does not mean that the value of the imaginary part of the broadbandimpedance is the difference between Z e f f

y (26 GeV )°Z e f fy (1.4 GeV ) = 13°6.1 = 6.9 M≠/m,

since the bunch length at the two energies were different.

Very small coherent tune shift at 26 GeV were measured, assuming that the contribution fromthe space charge is negligible,

¢Qxcoh ' 0 (5.53)

It does not mean that Z e f fx , the horizontal impedance is zero. As explained previously, the

tune shift is the sum of the dipolar part and an incoherent part

¢Qxcoh =¢Qx

di p +¢Qxquad

in term of impedance,

¢Qxcoh ' 0 ! Z x

di p +Z xquad = 0

therefore the dipolar part compensates the quadrupolar part of the impedance in the horizon-tal plane. In the case of a vacuum chamber assume to two parallel conductive infinite plates,the force seen by a tralling particle behind a source particle will not depends neither on theposition of the source nor the position of the test particle. The coupling term are neglected.The vacuum chamber of the PS is elliptical with the half width being twice the half height.With such dimensions, the results of the two parallel conductive plates is found in the PS. Thedifferent contributions of the dipolar and quadrupolar parts of the impedance in the PS arenot known. 2-wire technique is required to obtain the dipolar part of the impedance [105, 107].

Z xdi p =°Z x

quad (5.54)

Concerning the vertical plane, the space charge has be taken into account

¢Q ycoh =¢Qsc

coh + (¢QZy

di p +¢QZy

quad ) (5.55)

The coherent tune shift due to space charge depends on the magnetic and electric contributionwith the environment, here the wall. It can be evaluated thanks to the Laslett coefficients

¢Qcoh =° NbRr0

ºQy∞Ø2

µ≤1

h2 + ≤2

g 2 + ª1

h2

1°Ø2

B 2

∂(5.56)

256


5.8.4 Estimation of the Tune Shift due to Space charge

The measured tune shift at injection and extraction energy is the sum of a the contributionfrom space charge ¢Qsc and from the impedance ¢Qz . Let consider the vertical effectiveimpedance at the two energies. If the coherent tune shift due to space charge is assumednegligible at 26 GeV, it does not mean that the value of the imaginary part of the broadbandimpedance is the difference between Z e f f

y (26 GeV )°Z e f fy (1.4 GeV ) = 13°6.1 = 6.9 M≠/m,

since the bunch length at the two energies were different.

Very small coherent tune shift at 26 GeV were measured, assuming that the contribution fromthe space charge is negligible,

¢Qxcoh ' 0 (5.53)

It does not mean that Z e f fx , the horizontal impedance is zero. As explained previously, the

tune shift is the sum of the dipolar part and an incoherent part

¢Qxcoh =¢Qx

di p +¢Qxquad

in term of impedance,

¢Qxcoh ' 0 ! Z x

di p +Z xquad = 0

therefore the dipolar part compensates the quadrupolar part of the impedance in the horizon-tal plane. In the case of a vacuum chamber assume to two parallel conductive infinite plates,the force seen by a tralling particle behind a source particle will not depends neither on theposition of the source nor the position of the test particle. The coupling term are neglected.The vacuum chamber of the PS is elliptical with the half width being twice the half height.With such dimensions, the results of the two parallel conductive plates is found in the PS. Thedifferent contributions of the dipolar and quadrupolar parts of the impedance in the PS arenot known. 2-wire technique is required to obtain the dipolar part of the impedance [105, 107].

Z xdi p =°Z x

quad (5.54)

Concerning the vertical plane, the space charge has be taken into account

¢Q ycoh =¢Qsc

coh + (¢QZy

di p +¢QZy

quad ) (5.55)

The coherent tune shift due to space charge depends on the magnetic and electric contributionwith the environment, here the wall. It can be evaluated thanks to the Laslett coefficients

¢Qcoh =° NbRr0

ºQy∞Ø2

µ≤1

h2 + ≤2

g 2 + ª1

h2

1°Ø2

B 2

∂(5.56)

256 •  “Non penetraCng field” •  LasleS coefficients for ellipCcal

chamber a centered beam in the vacuum chamber valid for h/w < 0.7 (B. ZoSer CERN ISR-‐TH/72-‐8)

EsCmaCon: ΔQ-‐Space charge ~ ¼ Total measured ΔQ at injecCon. Space charge for beam used for

measurement 29

✏V1 = �0.156

✓h

w

◆2

+ 0.21

✏V2 = 0.41⇣ ⇢

R

⌘

⇠V1 = �0.10

✓h

w

◆2

+ 0.617

Conclusions InjecCon Studies •  Large beam losses were measured on high intensity beams (more than 3%), which induce also high radiaCon

outside of the ring. The goal of this study was to idenCfy the loss process, limited an intensity increase. •  BLM experiments measuring the proton losses while the beam is going through the injecCon septum+ matching

measurements: -‐ combinaCon of large beam size for high intensity beam, aperture restricCon. -‐ the beam is placed close to the septum blade to save some strength of the injecCon kicker. -‐ tails of transverse distribuCon are cut at least at 3 sigma, explaining 1-‐2% of losses.

•  Turn by turn losses while the injecCon bump is decreasing: measured losses at the maximum and minimum of the bump (minimum of available aperture).

•  Direct space charge repopulated the transverse phase space extending the duraCon of the losses. •  Tune shiM measurements with intensity in order to evaluate the imaginary part of the impedance and esCmate the

LasleS tune shiM due to space charge (about ¼ of the total tune shiM)

•  Possible cures -‐ For space charge: increasing the injecCon energy to 2GeV is a gain of 63% in the tune spread (PS-‐LIU Project) -‐ 2GeV injecCon energy is a gain in beam size due the shrinking of the transverse emiSance. -‐ New opCcs in the transfer line to make a small beam size at the injecCon point in both x,y planes-‐(2 different opCcs for LHC and for high intensity beams) -‐ The PS opCcs has to adapted (QKE opCcs) to avoid opCcal mismatch -‐ Impedance model also needed to predict instabiliCes at injecCon, mostly head-‐tail kind


Documents

High%Intensity%Beams%Issues%in% …...Rise%Cme% Ê Ê Ê Ê Ê Ê Ê Ê ÊÊ ÊÊ Ê ÊÊÊ Ê ÊÊ Ê Ê ÊÊ Ê Ê Ê Ê ‡ ‡ ‡ ‡ ‡ ‡ ‡ ‡ ‡ ‡ ‡ ‡‡ ‡ ‡