Transcript MEIC e-ring instabilities

Beam Dynamics and Instabilities
in MEIC Collider Rings
Byung C Yunn
Jefferson Lab
Newport News, Virginia, USA
Outline
• MEIC e-ring
– Impedances
– Single-bunch instabilities
– Coupled-bunch instabilities
– Intrabeam scattering and Touschek scattering
– Beam-gas scattering, ion trapping
• MEIC p-ring
– Single- and coupled-bunch instabilities
– Intrabeam scattering and Touschek scattering
– Beam-gas scattering
– Electron clouds
• Summary
Impedances
• For the overall longitudinal broadband impedance of the MEIC e-ring,
0
Z
 3
n BB
is assumed. This is equivalent to assuming roughly the same amount of
impedance in e-ring as in PEPII ring.
• Transverse impedance is estimated to be about 1 MΩ/m from
2c
Z T BB  2 Z BB
b
• With the help of existing B-factory designs with comparable beam
parameters a first cut on impedance budgeting has been made. Estimation
of the total inductive component of impedance at MEIC e-ring is 0.2 Ω.
The MEIC inductive impedance budget
Component
No. of items
Inductive part of
Z/n(Ω)
Bellows
128
1.3 102
Flanges
1024
2.8 103
Valves
10
1.0 102
BPMs
256
4.6 104
Vacuum ports
256
9.0 105
8
2.0 102
Tapers
6.0 102
DIP screens
IR, injection, crotches
Feedback pickups,
kickers
2
5
2.2 102
1.2 102
• Total loss factor in e-ring is estimated to be 25 V/pC.
Ring components
1000 m resistive walls
Four 5-cell cavities
Loss factor (V/pC)
3.25
1.5
20
• The beam power lost to higher order modes (i.e. HOM loss) is given by
2
kloss I avg
PHOM 
kB f0
where kB is the total number of bunches and f0 is the revolution frequency
in the ring. Note that HOM loss will be less with more bunches for a fixed
amount of total charge in the ring.
• The total HOM loss for 5 GeV electron beam at the design current of 3
Ampere is only 150 kW.
Single bunch instabilities
• e-ring parameters
Energy E
Circumference C
Bunch charge N e
Bunch length  l
Bunch current Ib
Beam current
Energy spread  
Momentum compaction
Synchrotron tune  s
RF voltage V
5 GeV
1000 m
1.25 1010
7.5 mm
0.6 mA
3A
0.0007
0.003
0.045
4.8 MV
• Longitudinal microwave instability limits the bunch peak current. For the
Gaussian bunch the threshold current is given by
Single-bunch instabilities
100hV coss  l3
Ib 
Z
C3
n BB
• For the broadband impedance seen by the short MEIC bunch the Spear
scaling law
Z
n
BB
Z

n
l 
 
BB  b 
0
1.68
is assumed.
• With 3 cm of beam pipe radius assumed longitudinal microwave instability
threshold bunch current is estimated to be 3.1 mA for MEIC e-ring.
• Transversely the mode coupling instability is to limit the single bunch
current. The threshold current is estimated to be 4.2 mA from
E
16   s l
e
Ib 
ImZ T BB  av C
• The average beta function of 20 meter has been assumed.
• MEIC e-ring is not expected to suffer from single bunch instabilities. This
was expected because the bunch current is rather low considering very
large beam current in the ring by filling every bucket at 1.5 GHz RF
frequency. Broad band impedance requirements in MEIC e-ring are less
demanding compared to other existing and/or proposed rings of
comparable beam parameters.
Coupled-bunch instabilities
• Narrow band impedance in a storage ring, typically from the higher order
modes of RF cavities can induce coupled bunch instabilities as wakefields
generated by a bunch ring long enough to interact with the following
bunches.
• In MEIC effectively all HOMs of CEBAF cavity can cause the coupling of
successive bunches leading to a possible instability problem. Damping for
a HOM Q may be estimated from
 HOM
Q  2
 RF
Q of only about 10 will make inter-bunch interaction possible for MEIC.
• For N bunches in the ring there are N coupled bunch modes. A coherent
mode is specified by one index specifying the phase shift between
bunches and another index describing its motion in synchrotron phase
space.
• Instabilities are counteracted by Landau damping from the synchrotron
frequency spread within the bunch.
• Longitudinally a growing mode is Landau damped when
Z
n
eff
330 h 3V cos  s   l 

 
Ib
C
5
• Transversely a growing mode is Landau damped when
ZT
eff
1380ah2 Q Qs E   l  3

 
I bC
eC
• For MEIC e-ring longitudinal Landau damping condition will be satisfied if
the longitudinal impedance is less than 7.1 mΩ. Therefore, it is not likely
to get a help from Landau damping. Situation is similar in transverse
oscillations.
• The total number of particles in e-ring is 6.25 1013 (to be compared with
9.8 1013 in PEPII LER). MEIC will be expected to suffer from coupled-bunch
instabilities as these instabilities are driven by this total charge in the ring
and cavity impedance is much higher presently compared to PEPII .
• Calculations of ZAP with CEBAF cavity data show unstable longitudinal
modes (from Shahid Ahmed)
Mode
Growth time (µs)
a=1
42.8
43.5
45.8
409.7
414.2
439.8
a=2
• Coupled-bunch instabilities induced particularly by cavity resonances will
limit the total current in MEIC e-ring both in longitudinal and transverse
phase spaces. In storage ring these instabilities are routinely controlled by
the feedback system. Obviously, damping of higher order modes of CEBAF
cavity for use at MEIC rings would require a major R&D effort in controlling
resonant modes. A detailed study on the design of the feedback system
will be required with upgraded cavity modes.
Intrabeam scattering and Touschek scattering
• Multiple small-angle Coulomb scattering causes diffusion in both
longitudinal and transverse phase space resulting in a degradation of
beam emittances in both spaces. The intrabeam scattering growth rates of
emittances depend on beam parameters as follows
re2 cNe logc
1
i 
3
8    x  y l 
• Compared to PEPII transverse phase space volume is about 10 times
smaller. But the number of electrons in a bunch is smaller by a factor of 5.
Consequently, IBS growth rate is expected to be worse by a factor of 2 for
the same energy electron. PEPII design study concluded that no significant
emittance growth from intrabeam scattering was to be expected even for
the 2.5 GeV beam operation in the low energy ring. It is safe to say that
intrabeam scattering will not be a problem at MEIC for the 5 GeV beam.
• One needs to confirm this conclusion with a detailed numerical study
when the design of MEIC optics is advanced sufficiently to allow such a
study.
• Large-angle single scattering events during intrabeam collisions can
change the momentum sufficiently to make it fall outside the momentum
acceptance of a ring. The momentum acceptance may come from the RF
system or by the dynamic and physical aperture of the accelerator.
• Touschek half-lifetime for a flat beam is given by

1
1/ 2

re2 cN e
3
8 2 aperture
  aperture
F 
 x y l   x '
1



average _ around _ the _ ring
• where F is a very slow varying function of its argument. For the 5 GeV
electron beam the momentum acceptance from the RF system is 0.42 %.
With this RF aperture I have estimated the half-lifetime of MEIC electron
beam to be 12 hours. The momentum acceptance associated with
dynamic aperture is also needed to complete. Currently MEIC design team
is studying the dynamic aperture of the machine with several optics codes.
Beam-gas scattering, ion trapping
• Electron beam-gas scattering with residual gas nuclei results in the loss of
beam particle either from the excitation of betatron oscillation or from a
momentum change exceeding the dynamic and/or the momentum
acceptance of the ring. Two processes of particular interest are elastic
scattering on nuclei and the bremsstrahlung on nuclei of which the latter
is more dominant for the 5 GeV electron beam in MEIC.
• The total cross section for the bremsstrahlung is given by
 Bremsstrah lung
4re2 Z 2 4  183 
5

ln 1/ 3  ln  apertue  
137 3  Z 
8
where Z is the atomic number of the residual gas species.
• The lifetime (hour) is related to the gas pressure P (N2 equivalent). I get
43/P (nTorr) hours for the MEIC electron beam. The beam lifetime from
beam-gas scattering is about 8 and a half hours at a gas pressure of the 5
nTorr.
• The overall beam lifetime from gas and Touschek scattering is 4 hours.
• The trapped ions resulted from beam interactions with residual gas
molecules in the vacuum chamber degrade the performance of electron
storage rings. For any ring there exists a critical mass Ac such that ions with
mass greater than the critical value. An expression for the critical mass
from linear theory is given by
Axc, y
I avg me

34090m p
2
 2R 


 k B   x, y
1

x
 y

• Critical masses are much less than one with MEIC design beam
parameters. In other words all ion species will be trapped and stable. In
order to avoid ion trapping there will be a gap (or several gaps) in the
MEIC electron bunch train and the total length of the gap will be about 5
to 10% of the ring circumference. Note that clearing electrodes are also
necessary in addition to the gap.
• Single turn ions though unstable can affect the beam. They can produce a
betatron tune spread between bunches and also induce a two beam
instability known as the fast beam-ion instability, for example. The growth
rate for the beam-ion instability is given by the linear model as (Lsep is the
bunch spacing)
 1

n

2


L
Ne
B sep

     L

y
sep
 y x




3/ 2
• The strength of this instability is about the same as that of B-factories
when the machine is operated under a similar vacuum pressure. MEIC
may need a feedback system like those used at B-factories.
Outline
• MEIC p-ring
– Single- and coupled-bunch instabilities
– Intrabeam scattering and Touschek scattering
– Beam-gas scattering
– Electron clouds
• Summary
MEIC p-ring
• MEIC ion complex consists of several rings and instability issues only in the
final proton storage ring are discussed here.
• It is assumed that
Z
n
 5 ~ 10 
BB
for the overall broadband longitudinal impedance of the MEIC p-ring. A
detailed impedance counting is yet to be carried out.
• This implies
ZT
BB
 1.8 ~ 3.5M / m
Single- and coupled-bunch instabilities
• p-ring parameters
Energy E
Circumference C
Bunch charge N e
Bunch length  l
Bunch current Ib
Beam current
Energy spread  
Momentum compaction
Synchrotron tune  s
RF voltage V
60 GeV
1000 m
0.415 1010
10 mm
0.2 mA
1A
0.0003
0.0047
0.0215
8 MV
• Maximum acceptable impedances for p-ring required to run design beam
current are obtained.
• From the microwave instability threshold formula
2  ( E / e)( ) 2
Ip 
Z
n BB
p-ring can tolerate the longitudinal impedance up to 14 Ω.
• From the transverse mode coupling instability
E
16   s l
e
Ib 
ImZ T BB  av C
follows the limit on the transverse impedance
ImZT BB av  3.7G
• Assumed impedances are well within the above limits. As expected proton
beam in p-ring is not likely to suffer from single-bunch instabilities.
• Coupled-bunch instabilities were observed in several proton rings at about
1013 protons. Instabilities are also expected in MEIC p-ring. The total
number of protons in MEIC p-ring is 2.1 1013
• Calculations of ZAP with CEBAF cavity data show unstable longitudinal
modes (from Shahid Ahmed)
Mode
Growth time (µs)
a=1
668.5
679.5
714.2
1633.5
1655.8
1745.7
a=2
• We will need feedback systems to control as in e-ring.
Intrabeam scattering and Touschek scattering
• Scaling e-ring results from
re2 cNe logc
1
i 
3
8    x  y l 
growth time for emittance in p-ring is estimated to be about the same as
for the electron beam.
• Scaling from e-ring results based on

1
1/ 2

re2 cN e
3
8 2 aperture
  aperture
F 
 x y l   x '
1



average _ around _ the _ ring
Touschek half-lifetime for 60 GeV proton beam is estimated to be about
two order of magnitude larger than that of 5 GeV electron beam in e-ring.
Momentum aperture assumed is 0.2 % provided from the RF system.
Beam-gas scattering
• Beam-gas scattering with residual gas nuclei which is critical to the lifetime
of electron beam as we saw in the first half is not critical anymore . Both
the bremsstrahlung and elastic scattering on nuclei provide completely
negligible contribution to the beam loss rate.
• Angular scattering of the proton beam by multiple Coulomb scattering in
the gas can cause an emittance degradation. This effect may be estimated
from
d n
P(Torr)
 0.14  
dt
 2
• For 60 GeV beam at 5 nTorr (room temperature) the growth time is
estimated to be about 30 minutes.
• Electron trapping may be a problem due to very short bunch spacing. It
may be necessary to provide a gap in the bunch train. Such a gap in p-ring
may lead to a slight reduction in luminosity due to a likely beam-gap
collision.
• Background rates of secondary particles reaching the detectors due to
beam-gas scattering will be taken into account later in selecting the
operating vacuum pressure in p-ring.
Electron clouds
• Very short bunch spacing in MEIC makes forming electron clouds through
the multipacting mechanism rather complicated. One may use the
following relation to estimate the resonance
h y2
N b re Lsep
1
which gives hy = 1.5 mm. This indicates multipacting is unlikely.
• Electron clouds once formed can produce both single- and coupled-bunch
instabilities for the proton beam (and the positron beam in e-ring). Single
bunch transverse mode coupling instability is possible when the density of
electron clouds is greater than the threshold density
2Qs
 thresh 
Cre  y
• For both p-ring and e-ring the electron cloud threshold density is
estimated to be about 5 x 1012 /m3. Numerical study is necessary to
determine whether such a cloud density can be reached in MEIC rings.
• The growth rate of coupled-bunch instability caused by electron clouds
may be estimated from
2
2
r
c
Ne
e
 1 
 hx hy Lsep
• A rough estimate gives the growth time of this instability in p-ring at about
a few millisecond.
• Numerical study is necessary to find out whether MEIC rings will suffer
from these instabilities. If necessary, MEIC will consider various measures
(solenoid coils, coating the vacuum chamber with TiN, etc) which have
been taken at B-factories to avoid electron cloud problems.
Summary
• As long as the design of vacuum chamber follows the examples of ring
colliders, especially B-factories, we will be safe from the single-bunch
instabilities. No bunch lengthening and widening due to the longitudinal
microwave instability is expected and no current limitation from the
transverse mode coupling instability.
• The performance in MEIC collider rings is most likely to be limited by
coupled-bunch instabilities. Feedback system able to deal with the growth
has to be designed.
• All ion species will be trapped at the e-ring. Total beam current limitation
and beam lifetime will depend upon the ability of the vacuum system to
maintain an acceptable pressure, about 5 nTorr in the presence of 3 A of
circulating beam.
• The following problem areas require special attention for the MEIC design
team:
a) HOM damping of CEBAF cavity
b) Feedback system
c) Vacuum system
d) Dynamic aperture