Transcript Beam-beam R&D for eRHIC - Stony Brook University

Beam-beam R&D for eRHIC
Linac-Ring Option
Yue Hao
Collider-Accelerator Department
Brookhaven National Laboratory
Dec. 7, 2007
Outline
• Main consideration in eRHIC beam-beam R&D
study.
– Electron Disruption effect and mismatch
– Aperture of energy recovery path
– Proton beam transverse instability with
interaction with electron bunch.
– Electron beam jitter
• Countermeasure
• Conclusion
eRHIC parameter
High energy setup
Low energy setup
p
e
p
e
Energy (GeV)
250
10
50
3
Number of bunches
166
Bunch spacing (ns)
71
71
71
71
Bunch intensity (1011)
2.0
1.2
2.0
1.2
Beam current (mA)
420
260
420
260
95% normalized emittance
(π·mm·mrad)
6
115
6
115
RMS emittance (nm)
3.8
1.0
19
3.3
β*(cm), x/y
26
100
26
150
Beam-beam parameters, x/y
0.015
2.3
0.015
2.3
RMS bunch length (cm)
20
1
20
1
Polarization(%)
70
80
70
80
Peak Luminosity (1.e33 cm-2s-1)
166
2.6
0.53
Beam-Beam field
For a transverse Gaussian distribution,
𝑛𝑒
𝑥2
𝑦2
𝜌 𝑥, 𝑦 =
exp − 2 − 2
2𝜋𝜎𝑥 𝜎𝑦
2𝜎𝑥 2𝜎𝑦
Bassetti-Erskine formular
𝐸𝑥 − 𝑖𝐸𝑦 =
−𝑖𝑛𝑒
2𝜖0 𝜋𝜎𝑥−𝑦
[𝑊
2
2
𝑥 + 𝑖𝑦
𝑥
𝑦
− exp − 2 − 2
𝜎𝑥−𝑦
2𝜎𝑥 2𝜎𝑦
(+/-4 sigma cut-off)
𝑥𝜎𝑦 𝑖𝑦𝜎𝑥
+
𝜎𝑥
𝜎𝑦
𝑊
]
𝜎𝑥−𝑦
For round beam case, the field have simple form
2
𝑛𝑒
𝑟
1
−
exp
−
2𝜋𝜖0 𝑟 2
2𝜎 2
Near axis, the field is linear.
2
𝐸𝑥
𝑛𝑒 1 + 𝛽
=
𝐸𝑦
2𝜋𝜖0 𝜎𝑥 + 𝜎𝑦
𝑥/𝜎𝑥
𝑦/ 𝜎𝑦
𝑟
0.4
Field Amplitude(Any Unit)
𝐸𝑟 =
0.5
0.3
0.2
0.1
0.0
0
2
4
Transverse position r (in r)
6
4
8
Electron Disruption
The nonlinear
beam-beam force
will cause the
electron beam
geometric
emittance growth.
The focusing force
will attract the
electron to center
and form the
effect so called
‘pinch effect’
Mismatch
The mismatch due to
beam-beam effect also
plays a important role.
It can enlarge the
effective emittance in
additional to the
geometric emittance
growth.
Need 4e-7 m-rad
admittance to ensure all
electron from losing in
design optics. Average
electron beam size is 19
microns. Minimum
electron beam size is 8
microns.
Vary the electron emittance,
the optics (beta alpha
function) at IP point before
collision
Compromise to get higher
luminosity, smaller emittance
after collision, and larger
average electron beam size.
After Optimization
Graph shows the case
that electron waist offset
is zero.
Need 1.7e-7 m-rad
admittance to ensure all
electron from losing in
design optics.
And the average
electron beam size at
interaction region is 24
microns and minimum
electron beam size is 16
microns.
Power Loss calculation
Courtesy of V. Ptitsyn
With assumption beta=50m
The revised parameter table
High energy setup
Low energy setup
p
e
p
e
Energy (GeV)
250
10
50
3
Number of bunches
166
Bunch spacing (ns)
71
71
71
71
Bunch intensity (1011)
2.0
1.2
2.0
1.2
Beam current (mA)
420
260
420
260
95% normalized emittance
(π·mm·mrad)
6
460
6
565
RMS emittance (nm)
3.8
4
19
16.5
β*(cm), x/y
26
25
26
30
Beam-beam parameters, x/y
0.015
0.58
0.015
0.47
RMS bunch length (cm)
20
1
20
1
Polarization(%)
70
80
70
80
Peak Luminosity (1.e33 cm-2s-1)
166
2.6
0.53
Beam-Beam effect on Proton beam
• Tune shift and tune spread
– Need proper working point.
– (0.672, 0.678) is used in simulation.
• May introduce single bunch transverse
instability (Kink instability).
– Beam-beam force acts as wake field.
– Threshold
– Possible way to suppress the emittance growth
Kink instability
Use 2-Particle model to illustrate kink instability, The two particles have same
synchrotron amplitude but opposite phase. Let T be the synchrotron period.
p
p
p
e
p
e
p
p
e
e
p
p
p
e
p
p
p
e
p
e
e
p
p
p
After T/2, the head and tail exchange there positions
Unstable
p
3/6/2007
p
Stable
p
e
Candidacy Seminar
p
e
12
Proton emittance growth due to
kink instability
Threshold and modes
For fixed electron intensity (1.2e11 per
bunch), the threshold of proton
intensity for kink instability is about
1.6e10 proton per bunch.
The longitudinal snapshot shows mode 1
pattern.
Increase tune spread to
suppress emittance growth
With Energy
spread 1e-3
Electron parameter fluctuation
Assuming beam-beam force is linear, the electron beam can be considered as a
thin special quadrupole which focuses in both transverse directions. The shot to
shot noise of electron beam will cause proton beam size to grow exponentially.
d  1/ f 
d x2
dt

x

4T
 *2 2
 d
4
*
 *2 d x 2
d 2
2T
d2
d2
 d 
2

T
d2
4 2 2
 d 
Courtesy of E.Pozdeyev
2
Conclusion
• From the beam-beam study, the Linac-ring
option of eRHIC is a promising scheme.
• The aperture of electron energy recovery path
required by beam-beam interaction is
achievable.
• The kink instability can be suppressed by
proper chromaticity.
• The fluctuation of Electron beam parameter
must be controlled within certain level.
Histogram of electron beam after beam-beam interaction
Optimum Waist Position.