Beam performance for pEDM at BNL

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15 Νοε 2013 (πριν από 3 χρόνια και 10 μήνες)

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A. Fedotov, Trento, Italy, October 1
-
5, 2012

1






Beam performance for
pEDM

at BNL





Alexei
Fedotov


Collider
-
Accelerator Department


Brookhaven National Laboratory




Trento, Italy, October 1
-
5, 2012





A. Fedotov, Trento, Italy, October 1
-
5, 2012

Outline


Injector complex at BNL’s Collider
-
Accelerator
Department (C
-
AD) and available beam parameters


Beam parameters needed for
pEDM

ring


Collective effects and beam parameters



Attempt is made to stay mostly with baseline parameters (used in 2011
proposal submitted to DOE) and scenarios,
however it may not
necessarily reflect the latest thinking.
A variety of other approaches
(including cooling ) and choice of parameters were studied but will not
be discussed here.

2

A. Fedotov, Trento, Italy, October 1
-
5, 2012


RHIC


NSRL


LINAC


Booster


AGS


Tandems


STAR


6:00 o’clock


PHENIX


8:00 o’clock


10:00 o’clock


Jet Target


12:00 o’clock


RF


4:00 o’clock


(AnDY)


2:00 o’clock

Relativistic Heavy Ion Collider (RHIC) &


Collider
-
Accelerator complex (C
-
AD) @ BNL

Operated modes (beam energies):

Au

Au 3.8/4.6/5.8/10/13.5/19.5/31/65/100 GeV/n

d

Au* 100 GeV/n

Cu

Cu

11/31/100 GeV/n

p


p



11/31/100, 250 GeV

Planned or possible future modes:

Au


Au

2.5 GeV/n


U


U

100 GeV/n

p




Au*

100 GeV/n


Cu


Au*

100 GeV/n

(*asymmetric rigidity)


EBIS

A. Fedotov, Trento, Italy, October 1
-
5, 2012

4

Injector complex @ C
-
AD

Booster

AGS

Linac

TTB

NSRL

pEDM


100 m

AGS will be used

just as transport line

possible locations

of pEDM ring

A. Fedotov, Trento, Italy, October 1
-
5, 2012

5

Available proton beam parameters in BNL’s
Booster/AGS



Booster: injection energy


200MeV, typical extraction 1417MeV


For
pEDM

we will need a little bit of acceleration in the Booster:


from 200 to 232MeV.


AGS will be used just as transport line (if pre
-
cooling in AGS is not
needed)

Beam parameters in Booster:


e
n95,x,y
:

e
10, 5
m
洠⠹㔥Ⱐ湯牭慬楺i搩d慴楮i散e楯i


牭r


⽰㕥
-
4


偯污物穡瑩潮㨠㠰
-
㠵┠⡵瀠瑯㤰┠慦瑥爠潮杯o湧佐偉匠楮i敮獩t礠異杲u摥d


No loss of polarization from the source is expected


Intensity:

3e11 (or more) per bunch
at Booster injection

Notation: Emittance_95%=6*
Emittance_rms

Emittance_normalized
=
bg
*
b浩瑴慮m敟畮湯e浡汩穥m


bg
㴰⸷㐵=景爠
灅䑍

物湧.




A. Fedotov, Trento, Italy, October 1
-
5, 2012


6

A. Fedotov, Trento, Italy, October 1
-
5, 2012

Parameters needed for injection in pEDM ring

Single

bunch intensity

2e10

Horizontal

emittance

[mm
mrad
]

2.2 (95%,

normalized
)

3 (95%,
unnormalized
)

Vertical
emittance

[mm
mrad
]

4.5

(95%, normalized)


6 (95%,
unnormalized
)

Rms

momentum spread

2e
-
4

7

small horizontal emittance
: requirement from distance between plates

small dp/p
: requirement from injection and to have long Spin Coherence Time (SCT)

bunch intensity
: chosen to provide satisfactory beam lifetime

due to basic collective effects (IBS, space
-
charge, etc.).

This is for baseline
without cooling.

A. Fedotov, Trento, Italy, October 1
-
5, 2012

8

Getting needed beam parameters for pEDM ring

1.
Horizontal emittance:


To have distance between plates in EDM ring of 30mm, beam emittance
should be decreased to
e
n95,x
=2
m
洠⠹㔥Ⱐ湯m浡汩穥搩m


卣牡灩湧r楮⁴桥⁂i潳瑥爺


坥捡c瑯汥t慴攠慢潵琠a湥牤敲r浡m湩畤攠楮⁢i湣栠楮i敮e楴礠汯獳
瑯t
摥d牥慳攠敭楴瑡湣攠瑯′t
m
洠⠹㔥Ⱐ湯(浡汩穥搩m


丽㍥ㄱ爠浯牥r⡡琠䉯潳瑥爠楮橥j瑩潮⤠
-
㸠丽㉥㄰
慴⁅䑍⁩湪散瑩潮t


䕄䴠b楮机㉥㄰⼱〰2
-
㸠丽㉥㠠灥爠獨潲琠扵t捨楮⁴桥⁅䑍⁲楮朮


䵯M敮瑵洠m灲敡搠☠剆捡c瑵牥t


呷漠汯湧⁢畮捨敳e晲潭䅇A睩汬w扥⁣慰瑵牥搠楮⁢慲t楥爠i畣步琠剆
獹獴敭e楮i䕄䴠b楮朮周敮桩杨⁦牥煵敮捹c剆睩汬w扥⁴畲湥b潮o
resulting in short bunches rotating CW and CCW.


Presently rms dp/p is about 5e
-
4 in Booster/AGS bunch.


Smaller dp/p can be obtained with scraping (with intensity reduction)


or cooling techniques


One needs to make sure that momentum spread remains small during
adiabatic capture into high frequency RF.



(pEDM ring, p=0.7GeV/c:
g
=1.25,
bg
=0.745, Kinetic energy: 232 MeV)

A. Fedotov, Trento, Italy, October 1
-
5, 2012

9

mw006 response to the three
methods of reducing the intensity.

Note the relatively weak
dependence of emittance on the
length of time on the foil (chopper),
and some weak dependence of
the “plane not scraped”

emittance mw006 chopper
0
2
4
6
8
10
12
0
5
10
15
20
intensity (mw006 area)
pi mmmr
hori
vert
emittance mw006 vert scrape
0
2
4
6
8
10
12
0
5
10
15
20
intensity (mw006 area)
pi mmmr
hori
vert
emittance mw006 hori scrape (dumpbump)
0
2
4
6
8
10
12
0
5
10
15
20
intensity (mw006 area)
pi mmmr
hori
vert
L. Ahrens et al: example of

Scraping in Booster (2009)

Horizontal scraping

vertical scraping

A. Fedotov, Trento, Italy, October 1
-
5, 2012

10


March 18, 2011 scraping studies in the Booster by


Kieth Zeno

Unscraped

Scraped

Booster
Input intensity

31e10

31e10

Booster
Late intensity

26e10

3.5e10

Horizontal
emittance
,
95%,normalized

[mm
mrad
]

15

1.9

Vertical
emittance

95%,normalized

[mm
mrad
]


7

6.5

Longitudinal

emittance

[
eV
-
s]

0.8

0.25

(
dp
/p=4e
-
4
rms
)

Achieved parameters

similar to those

needed for pEDM ring.

A. Fedotov, Trento, Italy, October 1
-
5, 2012

11

Requirement on beam momentum spread dp/p





1) For electric field dependence between plates E
-
>1/r there is a
notion of “infinite dispersion”
(however, correct definition is
with respect to change in the total energy).


2) Curvature of the plates which almost removed radial
dependence was also considered.
For the present baseline, field
configuration is very close to 1/r (E
-
field plates will be nearly
cylindrical). Small momentum spread
dp
/p is needed both for
injection and long SCT.




A possibility of getting very small
dp
/p with Electron Cooling
in AGS was considered.


Summary: It is possible, but will result in strong IBS in EDM
ring without additional cooling directly in EDM ring.




-

rms

dp
/p=2e
-
4
looks satisfactory for injection and seems to be
achievable without pre
-
cooling in AGS. Thus, cooling is not
included in the baseline at this point.


-

whether 2e
-
4
dp
/p is sufficiently small for long SCT time is
being evaluated.




A. Fedotov, Trento, Italy, October 1
-
5, 2012

12

Requirement on synchrotron tune, RF



-

69MHz (h=100)
-
90 MHz (h=135) RF;

-

rms bunch length (
s
s
) = 40cm

-

rms momentum spread (
s
p
)=2e
-
4

-

Q
s
=0.01 (few kV RF voltage)



p
s
r
s
Q
L
s


s
2

-

RF frequency sets a limit on initial rms bunch

length: at a minimum one wants to fit into RF bucket

-

for a fixed bunch length and fixed dp/p one gets required value for
synchrotron tune Q
s

q
mc
V
h
Q
rf
s
/
2
2
2
g
b




If dp/p is not very small, large Q
s

is required

A. Fedotov, Trento, Italy, October 1
-
5, 2012

13

Beam size and aperture




Rms

dp
/p=2e
-
4


Horizontal
emittance

(95%, normalized): 2.2 mm
mrad


Vertical
emittance

(95%, normalized): 4.5 mm
mrad


s
x
=3.74mm; (Ax=3cm


plates),
b
x,max
=28m


s
y
=15mm; (Ay=8cm


polarimeter
),
b
y,max
=240m


Horizontal beam size with
dp
/p :
s
H
=6.2mm


Ax/2=2.4*
s
H


Ay/2=2.7*
s
y


Short single bunch intensity: N=2e8


100 such bunches moving CW and 100 CCW


total beam
-
beam parameters
x
㨠W⸰ㄵ

†
獰慣s
-
捨慲来c瑵湥獨楦s
D
Q
x,y
: 0.008, 0.014


synchrotron tune: Q
s
=0.01










95%

Needed aperture will

be further optimized

A. Fedotov, Trento, Italy, October 1
-
5, 2012

14

Working baseline beam parameters in EDM ring


Intensity of injected long bunch: N=2e10 (2 such bunches)



Rms dp/p=2e
-
4 (without pre
-
cooling in AGS)


Horizontal emittance (95%, normalized): 2.2 mm mrad


Vertical emittance (95%, normalized): 4.5 mm mrad





two such bunches are injected CW and CCW



captured with barrier buckets or low
-
frequency RF; de
-
bunched.



then high
-
frequency 69
-
90MHz RF is turned on



results in 100 such bunches moving CW and 100 CCW


N=2e8 single bunch intensity; synchrotron tune: Q
s
=0.01










“Polarized low
-
energy hadron collider”.

A. Fedotov, Trento, Italy, October 1
-
5, 2012

15

Beam parameters for EDM ring

1.
Need small horizontal emittance


to fit beam between plates and
to have reasonable beam lifetime.

2.
Need small momentum spread


for long spin coherence time
(SCT).

3.
Need short bunches


to get large synchrotron tune.



Each of these effects increases beam density and thus increases
collective effects.


As a result, bunch intensity in EDM ring was decreased
compared to available intensity from AGS.

A. Fedotov, Trento, Italy, October 1
-
5, 2012

Collective effects and pEDM ring beam parameters


During the last few years we considered various scenarios for
EDM experiment.



In all these scenarios beam parameters/intensity were chosen to
provide sufficiently long beam lifetime consistent with the length
of requested experimental store of 1000 s (IBS, space
-
charge
effects, beam
-
beam, etc.).



The thinking behind designed beam parameters was that EDM
ring should NOT be the ring where we have to worry about
collective effects. “Let’s worry about EDM instead.”

16

A. Fedotov, Trento, Italy, October 1
-
5, 2012

17

Intra
-
beam Scattering (IBS) simulations


IBS
-

multiple small
-
angle Coulomb scattering of particles within
the beam.




IBS simulations were done using BETACOOL code for various
versions of EDM ring lattice and various RF parameters.


Optimization depends on tolerable longitudinal losses from RF
bucket, transverse loss on the target, etc. This resulted in baseline
bunch intensity with 2e8 particles per short bunch (90MHz RF).



Simulations were done for “all
-
electric” lattice as well.
However, possible dynamic aperture limitation (if any) like in
ELISA (attributed to dynamic aperture limitation due to nonlinear
fields of electrostatic deflectors) was not included.
Subject for
present studies and discussions.




A. Fedotov, Trento, Italy, October 1
-
5, 2012

18

Approximate scaling of IBS (for
g


g
t
)

2
2
2
2
1
||
1
p
s
y
x
i
i
p
p
cN
r
dt
d
s
s
e
e
s
s





longitudinal diffusion:



more important for heavy ions
than protons due to Z
4
/A
2




more important for electrons

than protons due to m
2




becomes more important for
higher beam densities



Ring lattice is important

2
2
2
2
2
1
1
1
p
s
y
x
i
i
x
p
x
x
x
x
x
x
cN
r
D
dt
d
s
s
e
e
b
s
s
e
e
e

b





transverse diffusion:

In EDM ring


operation is below transition energy.

This allows for some optimization between beam
parameters, RF and ring lattice.

A. Fedotov, Trento, Italy, October 1
-
5, 2012

19

N=2e8


target & RF loss

(black


target & RF;
blue



only target loss with 500 sec beam lifetime)

Example of IBS
simulations with
optimization of losses
from RF bucket and on
target (not for latest
lattice).

A. Fedotov, Trento, Italy, October 1
-
5, 2012

20

Space charge

Transverse
emittance

(95%,
unnormalized
):
e
x
,
e
y
,
m
m

㌬6

卥慲慴a楸敮i瑨tm

ㄮ9

Initial rms bunch length, m

0.4

Rms momentum spread

2.5e
-
4

Bunch intensity

2e8

Ring circumference C
r
, m

240

01
.
0


D
x
Q
s
r
y
y
x
x
x
y
y
x
p
b
y
x
C
Q
Q
A
r
Z
N
Q
s

e
e
e
g
b

2
1
1
3
,
,
,
3
2
2
,











D
014
.
0


D
y
Q
Such incoherent tune
shifts/tune spread are still
small enough for needed
beam lifetime. Also, these
values quickly decrease
due to intensity loss.

Walls (effect of images):

first order effect is correction

of incoherent tune shift and coherent

tune shift


both are sufficiently small.

Self
-
fields (maximum, incoherent tune shift):

A. Fedotov, Trento, Italy, October 1
-
5, 2012

21

Space
-
charge effects


For present beam parameters, space
-
charge tune shift is
sufficiently small.


This allows to think about pre
-
cooling to smaller momentum
spread (to increase SCT), for example.
Electron cooling directly in
EDM ring was considered in the past.


Or operate with higher bunch intensities, provided that resulting
beam loss due to IBS is tolerable and other intensity
-
dependent
effects are carefully taken into account.

A. Fedotov, Trento, Italy, October 1
-
5, 2012

22

Beam
-
Beam


Since in present approach CW
and CCW bunches will be
circulating in the same ring, one
will have beam
-
beam effects.




Starting point for estimate of
beam
-
beam effects is linear tune
shift on particles in one bunch
from space
-
charge forces of
incoming bunch.


For beam parameters with N=2e8
per bunch, 100 CW and 100 CCW
bunches , total
x
㴰=〱0

睨w捨楳i
獵晦楣i敮瑬礠獭慬氠景爠r敡洠
汩晥瑩l攠潦楮i敲敳琮



b
b
e

x
2
1
1
4
2
,
2




D

rms
n
p
b
b
b
A
r
Z
N
Q
Beam
-
beam simulations were done

by Y. Luo for 2009 “magnetic” lattice

(no problems were found). One would

need to repeat with sextupoles and

other multipoles for present design.

Beam
-
beam & space
-
charge together:

this is something to watch. We know it
from low
-
energy RHIC operations.

A. Fedotov, Trento, Italy, October 1
-
5, 2012

23

Boris Podobedov (NSLS)

Just a single
example of

wakefield effect.

A. Fedotov, Trento, Italy, October 1
-
5, 2012

24

A. Fedotov, Trento, Italy, October 1
-
5, 2012

Effects which may not cancel “completely”


Self
-
fields (bunches and their intensities are not identical).


Fields from counter
-
rotating beams.


RF fields if there is substantial energy loss per turn.


Wakefields/impedances.



Rough estimates of some effects were done. However, detailed
study of each effect is required, including realistic beam dynamics
tracking eventually.


25

A. Fedotov, Trento, Italy, October 1
-
5, 2012

26

Small dp/p issues:

1.
How to get small dp/p?

-
by momentum scraping with additional intensity loss

-
by cooling without intensity loss

2. Beam stability for small dp/p.



A. Fedotov, Trento, Italy, October 1
-
5, 2012

27

Small dp/p and beam stability


If we are talking about small bunch peak current (0.013A for
baseline parameters), it looks like rms dp/p as small as 5e
-
5 could
be OK (300
W

汩m楴).


Longitudinal space
-
charge impedance is large (500
W
⤬扵琠楴b摯d猠
湯琠汥慤a瑯楮獴慢ali瑹t批b楴獥s昮f卭慬摰d瀠獥瑳t愠汩浩m潮o
業灥摡湣攠扵摧b琠晲潭f潴桥爠獯畲捥献



Rms momentum spread of 5e
-
5 becomes 8e
-
5 (rms) after adiabatic
capture.




Getting momentum spread as small as 5e
-
5 rms will require
cooling. Would need to watch other effects simultaneously.



A. Fedotov, Trento, Italy, October 1
-
5, 2012

28

Summary

Beam parameters:

Needed beam parameters can be produced with existing complex at BNL:

-
Some scraping will be needed to produce small horizontal
emittance

(but
we have plenty of intensity to spare).

-
Careful RF manipulation will be needed to maintain small momentum
spread.

-
Having cooling in EDM ring was considered (in case it would be needed)

Collective effects:

-
Bunch intensity was chosen to provide reasonable beam lifetime time
due to IBS and space charge, including loss on target and from non
-
linear
RF.

-
Investigation of other effects such as wakes, beam
-
beam, etc. , were done
only at a very preliminary level. Detailed study and simulations will be
needed as design proceeds.

Collective effects determine beam parameters consistent with required

beam lifetime for the experiment.


Thank you.