Chapter 4. Booster synchrotron

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Nov 15, 2013 (3 years and 8 months ago)

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59


Chapter

4.
Booster

synchrotron


Contents


Chapter 4. Booster synchrotron

................................
................................
................................
.....

59

4.1. General parameters of the Booster

................................
................................
.....................

60

4.2. Lattice & beam dynamics

................................
................................
................................
...

62

4.3. BOOSTER magnets

................................
................................
................................
............

63

4.3.1. Normal conductin
g magnetic system

................................
................................
..........

64

4.3.2. Superconducting magnetic system

................................
................................
..............

65

4.3.2.1. Dipole Magnet

................................
................................
................................
......

66

4.3.2.2. Quadrupole Lens

................................
................................
................................
..

69

4.4. Injection and extraction

................................
................................
................................
......

69

4.5. Collimation

................................
................................
................................
.........................

71

4.6. Beam acceleration. RF system
................................
................................
............................

73

4.6.1. Adiabatic trapping

................................
................................
................................
.......

73

4.6.2. First stage o
f acceleration

................................
................................
............................

75

4.6.3. Beam bunching at 1
st

harmonics and electron cooling

................................
................

76

4.6.4. Second stage of acceleration
................................
................................
........................

76

4.6.5. Acceleration system

................................
................................
................................
.....

77

4.7. Tune shift at injection and at extraction

................................
................................
.............

78

4.8. Emittance growth after crossing the stripping foil

................................
.............................

79

4.9. Electron cooling system
................................
................................
................................
......

80

4.9.1. Ion energy choice for e
lectron cooling application

................................
.....................

80

4.9.2. Recombination in the cooler section

................................
................................
...........

82

4.9.3. Design of the Booster electron cooler

................................
................................
.........

84

4.9.4. Stabilization of the ion beam emittance with electron cooling

................................
...

85

4.9.5. Simulation of cooling process with BETACOOL

................................
.......................

87

4.10. Schedule of the works. Estimated cost

................................
................................
.............

89

4.11. References

................................
................................
................................
........................

89



60


4.1.
G
eneral parameters of the
B
ooster


The

main functions of the intermediate heavy ion synchrotron,
the Booster

of the Nuclotron
, are
the
following
:



Accumulation of
4
∙10
9

U
3
2
+

ions

in the
Booster;



Acceleration of the ions up to energy of 400 MeV/
u that is
sufficient
for
stripping of the
U
ranium ions up to
the
charge state of 92+
;



Simplification of
the requirements to the
vacuum conditions in the Nuclotron
owing to

high
er

energy and charge state of the ions injected into the Nuclotron
;




D
ecrease
of

the
ion beam longitudinal emittance at the energy
of

100 MeV/u

approximately

by application of
the
electron cooling.


The present layout
of the
Nuclotron and existing injectio
n and extraction
systems
make it
possible to place the
Booster having
216 m circumference and four fold symmetry inside of the
Synchrophasotron

yoke (see Fig.
4.1.
1 and
4.1.
2).



Four large straight sections will
be used for
injection from the linac, one t
urn extraction to
transfer the beams into the Nuclotron,
placing of the
acceleration cavity and electron cool
er

(
Fig.

4.1.
3
)
.




Figure

4.1.
1. Fragment of the
Synchrophasotron iron yoke
.

Figure
4.1.
2. Booster position inside of the
Synchrophasotron yoke

(cross section).



We considered two versions of the
Booster

lattice
-


DFO and FODO
periodicity
.
DFO lattice
provides
more efficient collimation of charge exchanged ions
whereas the
FODO one
has

other
well
-
known advantages. Low initial intensity level (
about
4∙
10
9

particles per pulse) allows us to
install small
number

of collimators to
clean

out the
U
33+

ions

from the U
32+

beam
. That is why
the FODO lattice is
considered as
more preferable for further consideration.
Main
Booster
parameters are listed in
the Table 4.1.1.

The Booster cycle diagram is shown in the Fig. 4.1.4.


61


Figure
4.1.
3. Booster
location
in the Synchrophasotron yoke


Table 4.1.1.

Basic Booster parameters.

Ions

U
32+

Circumference, m

216

m

Fold symmetry

4

Quadrupole periodicity

24

Injection/extraction energy U
32+
,
M
eV/u

6.2/
4
00

Magnetic rigidity,

T∙m

2.
4



㈵⸰



楰潬e⁦楥汤
,

T

〮ㄷ0


ㄮ1


畬獥⁲
e灥瑩瑩潮

牡瑥Ⱐz

〮㈵

䵡gne瑩c⁦楥汤⁲a浰m

启T

ㄮ1

Bea洠I湪散瑩潮⁴灥

瑷楣⁲pea瑥

獩sg汥⁴畲渠

B
ea洠e瑲c瑩潮⁴灥

楮i汥⁴畲n

I湪nc瑩潮⁳o潲o⁤畲a瑩潮Ⱐ獥c

〮㠠

噡c畵洬

呯Tr


-
11


U
32+

beam intensity
, ions
p
er
p
ulse

6×10
10


Transition energy, GeV/u

3.9



Figure 4.1.4. Booster cycle diagram

The Booster R
ing

The Electron


Cooler


62

4.2. Lattice & beam dynamics


The chosen lattice (
Table

4.2.1 and
Fig.

4.2.1, 4.2.2
) contains 4 arcs. Each arc consists of 5
regular FODO cells with dipoles and one without them. One regular cell includes focusing and
defocusing quadrupoles, one sector dipole and small drift section used for location

of m
agnetic

correctors, beam position monitors, collimators and so on. The equipment of injection, ejection

and acceleration are placed in the four large straight sections. The possible position of the
working point for this lattice version is given in the res
onance diagram 4.2.1. There are only two
systematic betatron difference resonances of the forth order: 3
Q
x



Q
y

=12 and 3
Q
y



Q
x

=12.
Both are quite distant from the working point
Q
x,y

≈ 5.8.


Table 4.2.1.

Lattice parameters of the Booster.

Fold symmetry

4

Number of the FODO lattice cells per arc

6

Length of lattice cell, m

9.0

Length of large straight sections per cell, m

4.1×2

Length of small straight sections, m

0.65

Betatron

tunes

5.
8
/5.85

Phase advance per cell

1.51

Amplitude of
β
-
晵湣瑩潮o
I
=
m
=
ㄷ⸰N
=
䵡x業畭⁤楳灥i獩潮⁦畮s瑩潮Ⱐo
=
㈮2
=
䵯Me湴畭⁣潭灡o瑩潮⁦ac瑯t
=
〮〳M
=
C桲潭h瑩c楴y
=
-
㜮T
=
䡯e楺潮瑡氠occe灴慮ceI
=
π∙mm∙mrad
=
㐰〠
=
噥牴楣a氠lcce灴慮peI
=
π∙mm∙mrad
=
㜰T
=
=
=
=
c楧u牥=
㐮㈮ㄮ4Be瑡瑲潮=牥s潮o湣e猠楮⁶楣楮楴y映瑨f⁷潲歩湧⁰潩湴
.
=
=

63



Figure

4.2.2. B
etatron and dispersion functions for one FODO arc.



4.3. BOOSTER magnets


The magnetic system of the booster consists of 4 quadrants. There are 10
dipole magnets, 6
focusing and 6 defocusing lenses in each one. The multipole correctors are also used to
compensate the errors of both main (dipole, quadrupole) and higher (sextupole, octupole)
harmonics of the magnetic field. The needed magnetic field in
duction in aperture is 1.
5

T at
maximum rigidity

(Table 4.3.1)
. The large aperture of both lattice dipole and quadrupole
magnets is one of the
main design features.


Table 4.3.1.

Lattice magnets.

Dipoles

Number of dipoles

40

Maximum magnetic field, T

1.
51

Effective field length, m

2.6

Bending angle, deg

9.0

Curvature radius , m

16.55

Vacuum chamber, mm
2

150 x 62

Q
uadrupoles

Number of quadrupoles

48

Field gradient, T/m

20

Effective field length, m

0.4

Vacuum chamber aperture, mm
2

150 x 62



The requirements for dipole and quadrupole magnets of the Booster can be met using eith
er


normal conducting or
super
conducting

windings. In this report we consider the normal
conducting version of the magnets as a base line for the Booster design. Th
e Nuclotron
-
type
magnets are discussed as a reserve option.



64

4.3.1. Normal conducting magnetic system


The normal conducting booster was designed for the fist project of the heavy ion accelerator
complex at the JINR [4.3.1]. As an example the quadrupole le
ns design is presented in the
Fig.

4.3.1.1.


Figure 4.3.1.1. Drawing of the quadrupole lens designed for heavy ion booster in [4.3.1].


Other

close
prototypes of the Booster magnets
are
the magnets used in IHEP and ITEP boosters
.


Presently technical desi
gn of the Booster magnets is in progress. Preliminary drawings of the
dipole magnet are shown in the Fig. 4.3.1.2 and its parameters are listed in the Table

4.3.1.1.
Total electric power required for supply the Booster magnetic system is less than 3 MW.


F
abrication of the Booster magnetic system can be performed in the JINR machinery workshop.
Estimated cast of one dipole magnet is about
30
k
$.


65


Figure 4.3.1.2. Preliminary design of the Booster dipole magnet.


Table 4.3.1.1.

Parameters of the Booster dip
ole magnets.

Weight, kg

2915


Iron

yoke


а

摩de湳楯ns


=
=
††††
b

睥ig桴Ⱐhg
=
=
㐰〪㜳〪ㄳ〰
=
㈶㄰2
=
††††
t楮摩湧
=
††††
а

睥ig桴


=
††††
b

汥lg瑨Ⱐt
=
††††
c

摩de湳楯n猠潦⁴桥⁣異灥爠灩灥Ⱐ浭
=
††††
d

湵浢敲映瑵=湳
=
=
=
㌱〠
=
ㄳ〠
=
ㄸ⸵⨱㠮㔪

㤮9

ㄶ⨲1㌲


††††
Re獩s瑡湣eⰠ佨,

0
⸰〸㐹

††††
I湤nc瑩癩Ⱐ浈

㘮㜵

††††
C畲ue湴⁡n

1.6 Т
ⰠI
=
㌳ㄲ⸵
=
††††
䵥a渠n畲牥湴Ⱐn
=
1657 А
=

4.3.
2
. Superconducting magnetic system


The magnetic system based on superconducting magnets is considered as
an
alternative.
The
Nuclotron
-
type de
sign based on a
window
-
frame iron yoke and a single
-

layer saddle
-
shaped

66

superconductor winding
can be

chosen for the
Booster

[4
.3.2
]. Nevertheless, a further
development of the technology was proposed [
4.3.3
] to increase the efficiency of the magnetic
sy
stem. In accordance with this proposal the cold mass of the magnet, consisting of a SC
-
winding, a beam pipe, a reinforcing shell and correcting windings (if needed)
are

fabricated as a
common rigid unit separated from the iron yoke. The last one is kept at

a temperature of 80 K. A
small vacuum gap between the outer surface of the cold mass at 4.7

K and the internal surface of
the yoke is used to avoid a direct heat infiltration from the iron to the SC
-
winding. The cold mass
having a substantially lower weig
ht and surface and the cooled iron yoke are suspended inside
the cryostat, for example, by suspension parts similar to those used at the Nuclotron. The main
characteristics of the magn
etic system are given in Table 4.3.2.1
.


T
able

4.3.
2
.1
.

Main Characteris
tics of the Magnetic System
.

Circumference

216

m

Max m
agnetic rigidity

27 Tm

Feld ramp

1.5

T/s

D
IPOLE MAGNETS

Maximum magnetic field

1.
5

T

Number

40

Effective length

2*1.3

m

Aperture

160 mm x
70

mm

Mass

1
5
00

kg

Q
UADRUPOLE LENSES

Maximum gradient


20

T/m

Number
of quadrupole

24

Effective length

400

mm

Mass

220 kg



4.3.
2
.1. Dipole Magnet


Main dynamic forces in the magnet winding are compensated by the bandage of glassfiber tape
and synthetic thread (see

Fig. 4.3.2.1
). Dynamic forces due to a non
-
symmetrical position of the
cold mass in the magnetic gap are compensated by
76

horizontal and
26
vertical thermal
insulating spacers. The magnet is of demountable construction. The yoke consists of two
symmetric
al parts connected to each other by means of bolts. The half
-
yokes are assembled of
laminated steel 0.5 mm in thickness. The laminations are clamped together by means of steel
angles 10 mm thick and end
-
face steel plates 12 mm thick.


Two copper pipes are
intend
ed for liquid nitrogen circulation and cooling the yoke. Two copper
plates soldered to the nitrogen pipes are connected to the iron yoke. A high precision of half
-
yoke assembling is provided by means of 8 pins which are placed on both end
-
faces of th
e yoke.
The winding is made of a hollow superconducting cable.



67


Fig. 4.3.2.1

Cross
-
section of the dipole magnet. 1


iron yoke, 2


SC bus, 3


bandage of the
winding, 4


winding, 5


beam pipe, 6,7


helium headers, 8


liquid nitrogen tube, 9


therma
l
insulating spacer.


The cable (see Fig. 4.3.2.2
) is a 5 mm diameter copper
-
nickel tube wrapped with 27
superconducting strands. The strands are decoupled into 9 banks with 3 strands in each by means
of 9 fishing
-
lines 0.45 mm in diameter. The cross
-

sect
ion of the strand is shown in Fig. 4
.3.2.3
.
The twist length of the strands is 55 mm. Each strand contains 8910 NbTi filaments 4.5x10
-
6
m
in diameter in the copper matrix. The twist pitch of the filaments is approximately 3 mm. A
0.2

mm diameter synthetic
thread is spirally wound with tension around the superconducting
strands. The copper
-
nickel tube with a 4 mm diameter helium cooling channel is wrapped with
two layers of 0.04 mm

thick
K
apton tape
. The cable is wrapped with one layer of 0.1 mm thick
glassf
iber tape impregnated with epoxy compound. The basic characteristics of the
superconductor are given in
the
Table
4.3.2.2
.



Fig. 4.3.2.2
. Cross
-
section of the cable. 1


copper
-
nickel tube, 2 and 5


K
apton tape
, 3


SC
strand, 4


insulating fishing
-
li
ne, 6


synthetic thread,
7
-

glassfiber tape.



68



Fig. 4.3.2.3

Cross
-
section of the s
trand.


The saddle
-
shaped winding
has 10 turns of cable or 90 (10

turns x 9 banks) turns of current. All
banks of 3 strands in each are connected in series. Three strands

of each bank connected in
parallel conduct an operation current of
10
00

A
.


The beam pipe in the dipole magnets is made of stainless steel 0.3 mm in thickness. The needed
mechanical rigidity is provided by gluing it to the winding and the bandage. After a
ssembly the
cold mass is placed inside the half yokes and pressed by them over the thermal insulating
spacers.


T
able

4.3.
2
.2

Basic Characteristic of the Superconductor

S
TRAND

superconductor

50% Nb

=
㔰R⁔椠
=
湵浢敲映千⁦楬=浥湴猠
=
㠹㄰

diameter of SC f
ilaments

4.5

m

瑨攠潰灥爠瑯⁴桥⁓C⁲瑩o

1.39/1

twist pitch of filaments

3 mm

nominal current at 1.
5

T

333

A

short sample critical current at 1.8 T
and 4.5 K

540 A

C
ABLE

cable type

hollow composite

helium cooling channel diameter

4 mm

copper
-
ni
ckel tube diameter

5 mm

insulation
K
a
pton tape thickness

0.04 mm

number of banks with strands
triplet

9

number of strands

9 x 3

number of insulation fishing
-
line

9

twist pitch of strands

55 mm

banding kapron thread diameter

0.2 mm

insulation glass
fiber tape thickness

0.1 mm

external cable diameter

7.14 mm








69

4.3.
2
.2. Quadrupole Lens


There are 24 focusing (F) and 24

defocusing (D) quadrupole lenses
4
00 mm long in the magnetic
system
of the Booster
. The cross
-
section of the quadrupole lens wit
h hyperbo
lic poles is
presented in Fig. 4.3.2.4
. The yoke of the lens consists of four symmetrical parts assembled of
laminated steel 0.5

mm

in thickness. The production, assembling and cooling of the dipole and
quadrupole magnet
s are similar. The quadrupo
le and
dipole windings, connected in series, are
supplied with an equal current of
10
00 A.




Fig. 4.3.2.4

Cross
-
section of the quadrupole magnet in its cryostat.


The superconducting cable of focusing and defocusing lenses comprises only 4 active banks w
ith
a triplet of strands. The quadrupole lens winding has only one turn of cable per pole or 4 turns of
operation current per pole.


Total electric power required for supply the superconducting magnetic system is less than
1

MW.



4.4. Injection and extrac
tion


The
twice repeated

single
turn
injection

has
duration of
7
µ
sec
per
pulse
with
a
betatron stacking
in
the
horizontal plane
. The injection
scheme includes
three

bump magnet
s

BM 1


3

a
nd one
septum magnet

SM

(Fig.

4.4.1
). The bump magnets
form

the
nec
essary
local distortion
of the
closed orbit
that

decreases
by two steps
during injection time
.

The
time interval
between
injection pulse
s

is
of
0.1 sec.


Fast (single turn) extraction is planned to transfer the beam into the Nuclotron and,
when
necessary,
to the experimental hall

for
a
fixed target experiment performance
. It consists of a
kicker and a septum magnet
s

(
Fig.

4.4.2
)
.


The parameters
of the beams
at injection and extraction
and the magnets
are listed in the
Table
s

4.4.1
,

4.4.2.




70


Figure 4.4.1
.

Injection
system
layout and
beam orbits and envelopes:

red


injected beam,

violet


‘bumped” one,
blue


circulated beam after first turn injection,
green

after
accumulation
;

QD, QF


quadrupole lenses, DIP


dipole magnet,
BM 1


3


magnets for the
b
ump formation,

SM



injection
septum

magnet.




Figure 4.4.2
. Fast (one turn) beam extraction
from the Booster

(green

before acceleration, blue


after acceleration and cooling
, red

the extracted beam)
.



Table 4.
4.1.


Parameters of the i
nject
ed

and ex
tract
ed

beams
.


Injected beam

Horizonal /vertical emittance of injected beam
,

π

mm∙mrad
=
㄰⼱N
=
䡯e楺潮瑡氯癥o瑩ca氠敭楴瑡湣e映c畲c畬慴楮u=
beam
I
=
π

mm∙mrad
=
㄰N
⼱L
=
䡯e楺潮瑡氯癥o瑩ca氠湯牡浬楺e搠d浩瑴a湣e
I
=
π

mm∙mrad
=
㄰⼱
=
oe污瑩癥
潭敮瑵洠獰牥ad
=
±5∙10
-
4

Extract
ed beam

Horizontal/vertical emittance
,

π∙mm∙mrad
=
㜮㔠
=
oe污瑩癥
=
m
潭敮瑵洠獰牥a搠
=
넱–
-
4




71

Table 4.4.2.

The
parameters of the injection and extraction
magnet
s


Deflection a
ngle
,
mrad

Magnetic f
ield
,
T

Length
,
m

Injection

system

ВМ1
=
㘮S
=
〮M
㌴P
=
〮M
=
ВМ2
=
V
=
〮M
㌴P
=
〮M
=
ВМ3
=
㘮S
=
〮M
㌴P
=
〮M
=

=

=
〮M
㤴V
=
N
=
Extraction

system

Kicker

6

0.125

1.2

SM

10

0.25

1
.2


4.5. C
ollimation


Vacuum conditions in the Booster define significantly ion losses during storage and acceleration.
Considering requirements
to the vacuum system one has to distinguish among static vacuum (in
absence of the ion beam) and dynamic one, when
the
ion beam circulates in the ring. Ions being
lost during injection, storage and acceleration bombard the vacuum chamber walls and knock ou
t
atoms (molecules) absorbed by the chamber surface. This process forms the
dynamic vacuum

condition.


Ion loss occurs due to several reasons:

-

imperfect beam dynamics in the ring,

-

ion scattering on residual gas atoms,

-

ionization or recharge of circu
lating atoms in collisions with rest gas atoms.


Two last ones depend on vacuum conditions. The ion scattering process plays a minor role in
limitations of multicharge ions life time. Main reason of
the
ion loss is the last process


ionization on
the
rest

gas species. One can estimate the ion life time roughly by
the formula


v
n
1
0
gas
rest




,







(4.5.1)


w
here
and


is the cross
-
section of the ions ionization

in collisions with rest gas atoms of the
density
n
0
,
v

is
the ion velocity. The cross
-
section


depends on

the

ion velocity (energy) as well


it decreases with the energy growth. For estimates one can accept



(
E
ion
)

~ 10
-
16

cm
2

at
E
ion

~
6

MeV/u.




(4.5.2)


Then at the rest gas pressure 10 pTorr (
n
0

= 3.53*10
5

atoms/cm
3
)
the f
ormula (4
.5.1) gives



rest gas

= 8 s .


This estimate does agree with experimental data for Pb
54+

(15 s at P = 5 pTorr).


The U
33+

ions appear in the Booster as a result of charge exchange interaction of the circulating
U
32+

ions with residual gas atoms. One needs

to collimate the 33+ ions to keep proper vacuum
conditions.


72

A

layout of U
33+

separation in
the
horizontal plane and absorption is illustrated in Fig.
4.5.1

in

the

phase and geometrical spaces.


Fig
ure 4.5.1..

Illus
tration of the

ion
U
33+

collimat
ion

in the phase space

(a) and
the
collimator

geometry

in
the
horizontal plane (b).

1



x co
-
ordinate of collimator entrance,

2



thickness of
the
collimator,
the
line
colors in
the
Fig. b)

correspond to color
in
the
Fig. a)
.



To obtain the 100% absorption
of the U
33+
ions

only on
the
collimators
, it takes at the least
eleven
collimators per arc. The location of
the
collimators and distribution of
the
ion absorption
are shown in the Fig.
4.5.2
.

The lower part of Figure shows the arc lattice, the location of
eleven
collimators (markings C1,…C11), the horizontal envelope of
the
beam of ions with Z

=

32 (dark
color) after injection and horizontal envelope of trajectories of ions with Z

=

33 (sky blue color).
The figure shows the process of absorption of ions wit
h Z

=

33 on
the
collimators. They are
located on the inner part of chamber and ratio of
the
collimator edge co
-
ordinate
X
colim

to
the
beam envelope
X
env

at the collimator azimuth is 1.2. The following markings are adopt
ed

in the
Figure
. Focusing and defocu
sing quadrupoles are marked
QF

and
QD
, the number after this
marking shows period number in the arc. The label
Dip

is adopted for
the
dipoles
.



Figure 4.5.2. Ion absorption distribution for
eleven

collimators (the 100% collimation efficiency
).
Percent
ag
e

shown with upper and bottom lines indicates
losses on the
lattice magnets and
collimators
.

b)

a)


73


This figure indicates as well, that the each of the collimators C5, C7, C9 and C11 absorbs a small
quantity of the U
33+
ions (about 3% each). If these collimators

are removed, the collimation
efficiency is equal
98.6%
. The additional removal of the collimator C1, which catch 6.3% of the
U
33+
ions, reduces the collimation efficiency to 94.9%. The further decreasing the number of
collimators reduces the collimation e
fficiency strongly. The variant with 6 collimators per arc
and the collimation efficiency
of
94.9% is shown in
the
Fig.
4.5.3
.



Figure 4.5.3. Ion absorption distribution for
six

collimators
and
the 94.9% collimation efficiency.


On this figure the deal
of ions with Z=33 is absorbed by lattice elements QF1, QF2, QF4, QF5
and QF6. The

total

part

of

these

ions

is

5.1% (
losses
=5.
1%)




4.
6
. Beam acceleration. RF system


The Booster RF cycle is composed of four parts
:


-

the adiabatic trapping at fixed frequenc
y (flat bottom),

-

the beam acceleration at the forth harmonics of the revolution frequency

up to
100

MeV/u and debunching,

-

the beam bunching at the first harmonics of the revolution frequency

together with
the
electron cooling,

-

the beam acceleration
at the

first harmonics of the revolution frequency

up to 400 MeV/u
.


4.6.1. Adiabatic trapping


The unbunched beam from linac (Δφ

=

360
0
) is trapped with the use of the adiabatic trapping
process

[4.6.1]
. The process is called adiabatic when its duration is long compare to the
synchrotron period
T
s
. At
the beginning
of the process the small RF volta
ge
V
i

is

established.
V
i

is small enough for the correspondent bucket area
A
i

to be (much) smaller then the initial beam
emittance. The special coefficient for the trapping process

c

is defined

as
:



c
s
dA dt
A T


.

(4.6.1)


This coefficient

should be much smaller than 1 for the adiabaticity condition to be approached.


74


When the RF voltage is raised from
V
i

to its final value
V
f

keeping α
c
constant (so called
isoadiabatic law) the voltage variation is given by:



2
( )
f
i s
f
V
V T
V
V t
t


 

 
 
.

(4.6.2)


The parameters for the trapping process are chosen to satisfy the following criteria: the capture
efficiency has to be near to 100%.

The longitudinal emittance increase (the beam dilution) has to
be minimum. The duration of the trapping process should have reasonable limits.


The following parameters of trapping were chosen:

α = 0.38 ,

V
i


=

50

V,

V
f


=

2000

V
.
The
simulation

results o
btained with ESME program [4.6.
2
]
under conditions

listed in the Table

4.6.1

show a theoretical 100% efficiency (see
F
ig
. 4.6.
1
, 4.6.2
).




Figure
4.6.
1. Distribution of particles in phase space during adiabatic trapping at the start and at
the end
of the process.


75



Figure
4.6.2.

rms bunch length during adiabatic trapping.



Table
4.6.
1
.


Adiabatic trapping, main parameters

Number of injected particles

4
·

9

Injection energy (MeV/u)

6

Revolution frequency (MHz)

0.160

Revolution period (μs)
=
㘮㤶
=
B畮u栠牭猠e浩瑴a湣e(es猩
=
㇗4
=
䡡牭潮楣r浢敲
=
4
=
p瑡扬t⁰桡獥
=
M
=
V
i
/
V
f

(kV)

0.05/2

dp/p at injection

±0.0005

dp/p after capture

±0.0013

Trapping time (ms)

2
5

Synchrotron period T
s
at end (ms)

0.5

Adiabaticity coefficient α
=
〮㌸
=
=
=
=

4.6.2. First stage of acceleration


The first stage of acceleration begins just after adiabatic trapping and finishes at the energy
suitable for
the
e
lectron
cooling (100 MeV/u)
. The variation of the magnetic field is chosen to
be composed of lineal ramp of 1

T/s and two parabolic parts 40

ms each


transitions from
the
flat bottom and to
the
flat top for debunching and e
lectron
cooling. The starting value for
the
voltage variat
ion during transition from
the
flat bottom to
the
lineal magnetic field ramp is
defined by
the
previous trapping process. The final value is suitable to choose so that the stable
synchronous phase is near 30
0
(sinus wave) i.e. approximately 7

kV
. Computer
simulations show
good results even for
the
lineal voltage variation from 2

k
V to 7

k
V. Similarly deceleration is
accompanied by lineal voltage decrease from 7

k
V to 1

kV just before
the
debunching.

During
the first stage of acceleration
the
RF
frequency
is

varied from 640
k
Hz at
the
injection up to
about 2.4 MHz.

Main parameters of the ion beam and the Booster RF system are summarized in
the Table 4.6.2.



76



Table
4.6.
2.

Characteristic parameters for the fist stage of acceleration in
the B
ooster

Number of p
articles

6·10
9

E
nergy

(MeV/u)

6/100

Momentum
(MeV/s)

105/440

Magnetic rigidity
(Tm)

2.85/11.7

RF frequency
f
RF

(MHz)

0.640/2.400

Bunch rms emittance

(eVs)

1×4

Harmonic number

4

Stable phase (lineal ramp)

27.5

Vmax/Vmin (kV)

7/1

Freq. swing

4

Bdo
t
max

(T/s)

1

A
cceleration
duration

(s)

0.64



4.6.3. Beam bunching at 1
st

harmonics and electron cooling


The process of
the
electron cooling is discussed in details in
the chapter 4.9.



4.6.
4
. Second stage of acceleration


In
the
collider
the
longitud
inal rms emittance must not exceed 3 eVs so after
the electron
cooling
it has to be no more th
a
n 2 eVs to make allowance of
the
inevitable emittance growth (factor 1.5)
on
the
stripping foil, during beam matching in
the
Nuclotron and collider and due to th
e various
other reasons.
The
RF frequency varies from 600

k
Hz up to 1

MHz.
The m
agnetic field variation
has two parts
:

40

ms parabolic part and
the
lineal ramp at 1

T/s.
The
RF voltage is assumed to
vary lineally from 1

k
V to 7

k
V during
the
parabolic vari
ation of the magnetic field and
to
be
the
constant 7
kV
(maybe less) during
the
lineal magnetic field ramp

(Table 4.6.3)
.


Table
4.6.
3.

Characteristic parameters for the second stage of acceleration in
the B
ooster

Number of particles

6·10
9

Energy (MeV/u)

100/400

Momentum (MeV/s)

440/950

Magnetic rigidity (Tm)

11.7/25.2

RF frequency f
RF

(MHz)

0.600/1.00

Bunch rms emittance(eVs)

2

Harmonic number

1

Stable phase (lineal ramp)

27.5

Vmax/Vmin (kV)

7/1

Freq. swing

1.66

Bdot
max

(T/
s)

1

acceleration time (s)

0.92




77

4.6.
5
.
Acceleration system



Nearest prototype of the Booster acceleration system is that one for SIS
-
100 designed by GSI in
collaboration with BINP (Novosibirsk). Due to cost and reliability consideration the optimum is

to use a ferrite loaded cavity for the acceleration.
The
cavity consists of two coaxial quarter
-
wave resonators, working in push
-
pull mode onto a common accelerating gap

(Fig. 4.6.3)
. The
resonant frequency of the cavity is controlled by DC biasing of the

air cooled ferrite stack.
In the
frequency range from 0.6 to 2.4 MHz the accelerating voltage of 7 kV is necessary due to beam
dynamic requirements.

The
parameters of the cavity based on ferrite rings produced by Russian
industry are listed in the Table 4
.6.4.



Fig. 4.6.
3
. Schem
atics

of
the cavity and
RF generator. 1


phase discriminator, 2


biasing
amplifier.


Table 4.6.4.

Parameters of the Booster accelerati
on

RF system
.

Harmonics number

4/1

Frequency range, MHz

0.6

=
㈮2
=
䵡x業畭⁶u汴ageⰠ歖
=
T
=
乵浢k爠潦⁣a癩v楥i
=
N
=
ieng瑨映瑨f⁣a癩vyⰠI
=
㌮P
=
cer物瑥⁲楮g⁰=ra浥瑥牳
W
=
f湮e爠摩r浥me爬r
=
併瑥爠摩r浥瑥爬r
=
t楤i栬h
=
me牭ra扩b楴y
=
f湩n楡氠灥牭楴r楶ity
=
䕱畩癡汥湴ⁱ畡汩ty⁦ac瑯t
=
=
ㄵN
=
㈰2
=

=

=
㈰2
=
8
=
m潷o爠r潮獵o灴p潮Ⱐ歗
=
ㄮㄵ
=
C潯汩湧映=楮g⁣o

=
䅩爬⁤楲ict
=
†=
N
=
††††=
2
=

78


The RF power supply can be designed on the basis of GU92
-
A electronic tube. Due to relatively
small heating power in the ferrite the air cooling can be applied. The inner cylinder of the cavity
can be designed as a double wall pipe (Fig. 4
.6.4). The air flux moving through the halls in the
outer wall cools the inner and side surfaces of the ferrite rings.




Figure 4.6.4. Air cooling of the ferrite stack.

1


air flux, 2


ferrite rings.



4.
7
. Tune shift at injection and at extractio
n


The incoherent space charge

tune shift can be estimated

by well
-
known
f
ormula



b
sc
n
p
F
F
N
A
r
Z
Q


2
2
4



,

(4
.
7.1
)


w
here
Z

and
A

are the ion charge and mass number
s

correspondingly,
r
p

is the proton classic
radius,
N

is the total number
of the ions
in t
he ring,

n

is
the

normalized rms
beam
emittance
,

F
sc



image force correction factor
,
F
b

-

t
he bunching factor

that is

equal

to

the
ratio

of

peak

bunch

current to

the mean one:



s
Ring
b
2
h
/
C
F




,

(
4
.
7.2
)


C
Ring

is the Booster ring circumference
,
h

is harmonics number
,

s

is the rms bunch length.
Assuming

F
sc

~ 1

one can estimate acceptable
normalized
beam emmitance at the injection into
the
B
ooster:



max
2
2
4
Q
F
N
A
r
Z
b
p
n





.

(4.
7.3
)


We need to store in the booster up to 4

10
9

of
U
32+

ions at t
he energy of
about
6

MeV/u.
At

Q
max



0.05 and
F
b

= 2

one has to provide
the
normalized
beam emittance

n



0.74



mm

mrad.
This value is slightly larger than that one expected at the exit of the linear injector

and
1

1

2


79

corresponds to the
unnormalized
95%
(6
-
sigma)
emittance




39



mm

mrad
.


T
hat is
a
few
times smaller than the Booster acceptance

(Table 4.2.1)
.


The reserve option

of the injection chain operation presumes storage in the Booster of 2

10
9

U
64+

ions. In this case the tune shift of 0.05 corresp
onds to the emittance value of

n

= 1.5



mm

mrad,

or
95%
unnormalized

emittance

of about 78


mm

mrad
.
This value is comparable with the
vertical booster acceptance and

corresponds to the limit value

if a larger tune shift value can not
be reached due to
the beam instability.
One should note that in this case t
he electron cooling time
will be shorter because of its Z
2

dependence.


At the energy of the electron cooling application (
about
100 MeV/u) the emittance of the U
32+

can be decreased to the value of
about

n



0.16



mm

mrad

limited by the tune shift at this
energy
. So small emittance is not acceptable for the experiment
because of very high bunching
factor

in the collider
:
minimum
unnormalized
emittance value required at 3.5 GeV/u of the
experiment e
nergy is equal to about 1.3


mm

mrad
. T
herefore one needs to take a care about
stabilization of the emittance during the cooling. It can be
done
, for instance, by the cooling with
misaligned electron beam

(see chapter 4.9).


To avoid a sufficient increase

of the bunch longitudinal emittan
ce

at

crossing the stripping foil

the bunch length
after acceleration to the maximum
Booster
energy
has to be as small as possible
.

The
bunch intensity
at the injection into the Nuclotron
decre
a
se
s d
ue to
partial

ion loss
in
the
stripping
foil
and
will be slightly larger than 10
9
. For the fully stripped uranium ions at the rms
normalized emittance of 1.3


mm

mrad the rms bunch length has to be larger than about
6

m to
keep the tune shift in the Nuclotron below 0.05.




4.
8
.
Emittance growth after crossing the stripping foil


As a prototype of the stripping target design the RHIC stripp
i
ng foil was chosen. At the RHIC
two types of the foil were tested for the gold ion stripping at 70 MeV/u

[4.8.1]
. In routine
operation the c
arbon foil of the thickness of 120

m is used. The foil thickness is larger than the
optimum one
:

such a value
was chosen to provide
a
long life
-
time of the foil.


The
ion
interaction
with the target
leads to an increase of
both
-

transverse

and

longitudi
nal beam
emittance
s. The first one
increases

due to
ion
multiple scattering
on
the target atoms.
The second
one
grow
s

up

due to
two effects: the fluctuations of the ionization energy loss (

the
energy
straggling

) and non
-
uniformity of the foil thickness
p
rovoking

variation of the ionization loss
with the ion position at the target. The rms non
-
uniformity of the carbon foil is about 5% and the
growth of the longitudinal emittance due to this effect is about t
h
ree times larger than due to the
energy straggli
ng. The situation can be sufficiently improved by using of silica foil
of
precise
thickness (
of
the non
-
uniformity below 0.5%). The experimental investigations
done at BNL

[4.8.1]

show that the longitudinal emittance of the gold beam after crossing the sil
ica foil of the
thickness of 100

m is about three times less than after crossing the carbon foil.


Here we analyze the transverse and longitudinal emittance growth of the uranium beam at
400

MeV/u after crossing of both types of the foils: carbon foil of
the thickness of 125

m and
silica foil of 100

m. The ion charge state chang
es

inside the foil and for an accurate calculation
of the emittance growth one needs to integrate the ionization loss and multi
-
scattering cross
-
section over the ion
trajectory in

the target. However
one can calculate
the upper estimat
e

for the
maximum charge state only. Therefore we present
here
the results for the emittance
growth
of

80

the U
92+

ions that slightly overestimate real situation.

The rms parameters of the scattering
pro
cess were calculated in accordance with [4.8.2].
The expected longitudinal and transverse
emittance growth after crossing the
foils of
two
kind
s
is presented in the Table 4.
8
.
1.


Table 4.
8
.
1.


Change

of the U
92+

beam emittance after crossing the stripping
target


carbon

silica

Thickness,

m

ㄲ1

㄰1

F潩o
R浳mn
-
畮楦潲浩

t

, %

5

0.5

Ionization energy loss

E
BB
, MeV

320

397


t

E
BB
, MeV

16

1.99

Rms

ion

energy straggling
E
str
, MeV

3.76

4.38


E
, MeV

16.4

4.81

Rms
ion multi
scattering angle

1.22


-
4

2.0
2


-
4

Longitudinal emittance growth at

s

= 7 m, eV

s

ㄮ㘹

〮㐹0

乯N浡汩me搠瑲湳癥牳re浩瑴a湣e⁧牯瑨⁡琠

t

= 1 m,




浲m

㜮㜶


-
3

2.13


-
2


As shown above t
he minimum normalized transverse emittance required at the experiment is
about 1.3



mm

mrad

and the emittance growth after the foil crossing is negligible at the beta
function
at
the foil position of a few meters.


The longitudinal emittance required for
a
successful
bunch
compression
in the Nuclotron is
about 3

eV

s. At the large foil non
-
u
niformity the increase of the longitudinal emittance after
crossing the target has to be taken into account. The required longitudinal emittance value after
the electron cooling can be estimated using the following expression for the final emittance

||,f

:


2
||
2
0
||,
||,






f
,


where

||,0



2.5 eV

s.



4.
9
. Electron cooling system


The main goal of the Booster electron cooler is the decreasing of the longitudinal emittance from
the injection value
of about
7.5

eV

s to the necessary value
of
2.5

eV

s.

Cooling time is limited
by the operation cycle of
the
Booster and can not exceed the
value of 1 sec
. For the transverse
plane the cooling sy
s
tem has to keep the value of the normalized transverse emittances
at

the
level
of

1



mm

mrad (rms). For the stabi
lization of the transverse emittance the misalignment
of

electron and ion beam ax
e
s is proposed on the level
of
about
1 mrad

in both transverse planes.


4.9.1. Ion energy
choice
for electron cooling
application


Ion energy in the Booster ranges from 6 MeV/
u to 400 MeV/u that corresponds to the electron
energy range 3.27


217.86 keV. Choosing an optimal energy value for electron cooling one has
to account the following effects:

1) beam lifetime limitation due to interaction with the rest gas ;

2) beam life
time limitation due to recombination on the cooling electrons;

3) space charge effects appearing due to ion beam shrinking at cooling;


81

4) sufficiently short cooling time (

1 sec);

5) space charge effect of electron beam on ion cooling;

6) an optimal use
of the RF

station

(see this section, below)
;

7) cost of
the
electron cooler.


In the range of so called large ion velocity
the
electron cooling time increases with
the
ion
(electron) energy as following [4.9.1]:


e
2
/
3
i
2
ecool
J
C






,






(4.9.1)


w
here
C

is
the
constant depending of the cooler design (electron beam and magnetic field quality,
etc.),


and


are
the
Lorentz factors,

i

is
the
normalized ion
beam
emittance,
J
e

is
the
electron
current density. “Theoretically” reasoning the last one can

be increased with energy as energy in
power 3/2 (the Child
-
Langmuir law). However, as practice of electron coolers shows, in the
electron energy range quoted above one can have an effective cooling with
J
e

~ 10 mA/cm
2

at
2.5 keV (LEAR electron cooler) and

with
J
e

~ 100 mA/cm
2

at 70 keV (COSY electron cooler).
That scales with energy much slower
-

as (
E
e
)
0.7
, or

1/3
.

Thus, one can believe the cooling time
dependence on ion energy is given (in the quoted energy range) by the following
f
ormula:



ecool





2
/3



(
E
ion
)
1/3

.






(4.9.2)


Now we can begin the choice of the electron cooler energy based on
the
effects mentioned above.


1) Ion lifetime is sufficiently long even at injection energy (paragraph 4.5). Therefore
thr
limitation by

interaction with the
rest gas does not play a significant role in the choice of electron
cooler energy.


2) Ion recombination on the cooling electrons is almost independent of
the
energy (when
neglecting with Lorentz transformation for time: 1 <
γ

< 1.4 in
the
ion energy range for the
Booster). Therefore, this effect does not define a choice of the cooler energy (nevertheless, it is
critical for

the

ion life time


see section 4.9.2).


3) Space charge tune shift grows up when

the
ion beam emittanc
e decreases at cooling (see
Formula 4.
7
.
1
). Due to this reason we can not use
the
electron cooling at injection energy when
the
ion beam intensity is near
the
limit by tune shift. However, we need to cool
the
beam later to
obtain a sufficiently small ion m
omentum spread for formation of short bunches after
acceleration in
the
Nuclotron (section 5.3.2). Therefore, one has to cool the ion beam at certain
acceleration when
the
factor


2

decreased tune shift by two times at least. It gives us




cool

>

2

inje
ction
,

or
E
cool

> 4

E
injection

= 24 MeV/u .

(4
.
9.
3)


4) Provision of a sufficiently short cooling time (

1 sec) can be done in all the energy range
because of rather slow dependence of cooling time on energy (4.9.2).


5) The space charge effect of the elec
tron beam plays an important role when its space charge
parabola produces electron energy shift across the beam larger than the energy spread of the ion
beam. Such an energy shift (difference of electron energy on the beam axis and its border) is
given by
the f
ormula


82






]
A
[
e
]
eV
[
e
I
30
E




.





(4.9.4)


So, for
the
electron energy of 54 keV (


= 0.427) and electron beam current of
about
1 A it gives

E




70 eV (

E
/
E




1.3×10
-
3
) that may have an essential impact on the cooling process.


6) Ion accelerati
on in the Booster is proposed to be performed in two steps (Paragraph 4.6): on
4
th

harmonics of the revolution frequency up to
the
cooler energy and on the 1
st

one after
the
cooling. It would be convenient to use the same RF system on both steps of the acc
eleration.
That would be possible if the cooler energy
(E
i
on
)
cool

is sufficiently high. At the Booster
parameters such an opportunity appears if
(E
i
on
)
cool


100 MeV/u.


7) The cost of the electron cooling system has rather smooth dependence on the electron

energy
for the standard scheme of the cooler. The price of the
B
ooster cooler can be estimated on the
level 1÷1.2 M$.


A cooler of electron energy of 50 keV planned for the Booster can be constructed by a
conventional (“standard”) scheme. As a prototype o
ne can consider the cooler (Fig.

9.4.1)
designed and constructed at Budker Institute of Nuclear Physics (Novosibirsk) for Institute of
Modern Physics (Lanzhou, China) [4.9.2].



Fig.4.9.1
.
Electron cooler EC
-
35 (BINP, Novosibirsk)

1


electron gun, 2


el
ectrostatic plates for compensation of centrifugal drift, 3
-

toroidal
solenoid, 4


straight solenoids, 5


magnetic shield, 6


collector, 7


ion beam orbit magnetic
correctors, 8


ion beam channel
.



4.9.
2
.
R
ecombination in
the
cooler section


At

the
e
lectron cooling

of

heavy ions
the
recombination
-

i.e. capture of cooling electrons
by ions
-

result
s

in loss of
the
ions due to change of their charge

and deformation of
the
ion closed orbit
.
The theory of the electron
-
ion

recombination is well elaborated

for fully stripped ions

[4.9.3]
. In
the case of partially charged ions the

recombination rate can be interpolated from the
experimental data.


83


Measurements of electron recombination rates for Pb
52+
, Pb
53+

and Pb
54+

ions were done at
LEAR (Fig.4.9.2 [4.9.4
]). The ion energy in these experiments was of 4.2 MeV/u,
the
ring
circumference of 78.54 m,
the
vacuum pressure
of
2×10
-
11

Torr.



Fig.4.9.2. The dependence of the recombination rates on the electron beam current for different
charge states of lead ions.


For the charge state Pb
54+

the number of electrons on electron shells is 28 and the electron
structure is 1s
2

2s
2
2p
6

3s
2
3p
6
3d
10
, which corresponds to three closed electron shells
.

For the
charge state Pb
5
3
+

one electron stays on the forth shell that decr
eases the recombination time very
significantly. The lifetime for the charge state Pb
5
2
+

(two electrons on the fourth shell) is
comparable with the charge state Pb
5
4
+

(Fig.4.9.
2).

The recombination coefficient

rec

is defined
usually by the
f
ormula


e
ion
rec
rec
n
n
dt
dn





.





(4.9.5)


Then the recombination time is equal to

e
rec
rec
ion
rec
n
dt
dn
n
1










(4.9.6)


Here
n
rec

is density of recombined ions,
n
ion

,
n
e

are the densities of recombining ions and
electrons. Table 4.9.1 gives experimental values of

rec

[4.9.4] and theoretically estimated ones
with Bell's formula [4.9.3]. One can see a great discrepancy of experiment and theory that
demonstrates a complexity of the problem.





84


Table 4.9.1.

Experimental and theoretical recombination coefficient valu
es,

ion energy 4.2 MeV/
u
, transverse electron temperature 0.2 eV.

Ions kind

Experiment

10
-
8

cm
3

s
-
1

Bell's formula

10
-
8

cm
3

s
-
1

Pb
52+

11

2.25

Pb
5
3
+

60

2.29

Pb
54
+

9

2.32

U
2
8
+

10

1.8

Au
2
5
+

10

1.3



The U
32
+

ions assumed to be cooled in the Booster hav
e the electron shell structure
4s
2
4p
6
4d
10
4f
14
. That corresponds to 4 closed electron shells. According to LEAR experimental
results (Table 4.9.1) one can expect the recombination coefficient



rec



10

10
-
8

cm
3
/s .


An electron beam of 1 cm radius, of 1 A

current and electron energy of 54 keV has
the
electron
density
n
e



1.5

10
8

cm
-
3
. This gives us according (4.9.6)



rec

= 15 s .


That is sufficient for our goal.



4.9.3.
Design of
the Booster
electron cooler


Parameters of the proposed
electron cooling
system
are very close to those ones of the existing
cooling system EC
-
35 presented above (Fig. 4.9.1 and Table 4.9.2). It
consists of the following
main subsystems: electron beam formation system including the electron gun (p
os
.1)
;
electron
collector (p
os
.
6
); magnetic system
contain
ing straight solenoid (p
os
.
4
), toroidal solenoids (p
os
.3),
bending field
coils and
electrostatic plates
for drift compensation in bending toroids

(pos.2),
coils

for
the
electron beam position
correction; vacuum system, which cons
ists of vacuum chambers
and vacuum pumps, as well as of
tools

for vacuum chamber heating and for pressure
measurement
; diagnostics system including two pairs of pickup stations at the entrance and the
exit of the cooling section; water cooling system provi
ding cooling of the solenoids,
the
collector,
the electron
gun anode

and the radiators of air cooling and distillate
water
cleaning system; high
voltage power supplies; mechanical supports.
Two pairs of dipole magnets will be installed in
the cooler sectio
n of the Booster to correct
the
ion beam trajectory displacement produced by
vertical components of the cooler toroid field (pos.7).


For simulation of the optics of the electron guns and electron collectors both BINP and JINR
electron cooling groups use
mostly the special code SAM [4.9.5]. The code allows to simulate
the electron trajectories taking into account the geometry of electrodes, the longitudinal
magnetic field and the field of the electron beam space charge. As result of a simulation one can
o
btain distribution of the electron beam density and variation of the electron transverse velocity
across and along the beam. Two examples of such simulations are presented in the Fig.4.9.3.



85


Table 4.9.
2
.

Main parameters of electron cooler.

Maximum electr
on energy, keV

60
.0

Beam current, A

0


ㄮ1

潷o爠r潮獵o灴p潮Ⱐ歗

㄰1

Be瑡晵湣瑩潮猠o渠n潯汩湧⁳
ec瑩潮
Ⱐ洠

㠠⼠8

䑩獰牳楯渠r畮u瑩潮

楮⁣i潬o湧⁳
ec瑩潮
Ⱐ洠

0

C潯汥o
潶o牡汬
汥lg瑨Ⱐ

㐮4

䕦晥c瑩癥eng瑨映瑨攠o潬o湧⁳c瑩潮Ⱐ洠

㈮2

䵡gne瑩c⁦
楥汤⁩渠i桥⁣潯汩湧⁳c瑩潮Ⱐ歇

ㄮ1

䵡gne瑩c⁦楥汤潮
-
桯浯genei
⁩渠桥c潯汩湧⁳ec瑩潮o

1


-
4

Electron b
eam radius in the cooling section, cm

1.0

Transverse electron temperature, meV

200

Longitudinal electron temperature, meV

0.5





Fig.4.9
.3. Simulation of electron
trajectories in the
gun and collector

for EC
-
35
performed
with
the
SAM program [4.9.6]. Red


electrodes and electric field
equipotential lines, blue


electron trajectories, green


magnetic shield and magnetic field
distributi
on along the collector axis.



4.9.
4
.
S
tabilization
of the ion b
eam emittance
with electron cooling


Electron cooling applied to the ion beam in the Booster has a specific feature. As said above, it
has to decrease ion momentum spread and to keep (almost)
constant the ion beam emittance to
avoid increase of the space charge tune shift (Paragraph 4.7).
A few different methods
are known
for stabilization of the emittance at required value

when
the
electron cooling is applied
:

-

use of a “hollow” electron beam

w
ith a special
electron density

distribution across the
beam: it

is
very low near the beam axis and

grows up in the
outer part,

-

application of white noise in transverse degree of freedom in order to
shift

equilibrium
between cooling and heating into
the
re
gion of larger emittance

value
,

-

misalignment of the electron beam (introduction of some angle between electron
and
proton
beam
axes
in the cooling section).


86


The “hollow” beam application

[4.9.7]

is
suppose
d to be very efficient for ion beam storage
using
cooling
-
stacking procedure. In this case low electron density in the stack region

(near
the
electron beam axis)

permits to avoid

overcooling


the stack and decreases (for heavy ions)
recombination rate in the cooling section.
However, main restriction on
the “hollow” beam
application is related to the fact that significant part of the ions are crossing the cooling section in
the region of non
-
linear electric field of the electron beam outer part. That can provoke
additional
ion

loss due to “electron heatin
g” effect.


The heating of
the
transverse degree of freedom by additional noise were used at a few rings to
suppress
a
coherent instability of the cooled
ion
beam. However it was shown that the transverse
heating decreases the beam life
-
time

as well

and le
ads usually not only to increase
of
the
emittance, but the momentum spread also.


As it
is
shown in many experiments the electron beam misalignment is a powerful tool to control
emittance of the ion beam
[4.9.8].

However, at small angles the misalignment l
eads to decrease
of the cooling efficiency only, but the beam emittance is determined by
an
equilibrium between
cooling and heating
due to
intrabeam scattering. When the misalignment reaches a certain
threshold value a qualitatively different situation
tak
es place: t
he amplitude
of the
ion betatron
oscillat
ions grow up to

certain value

that

depends on
the
misalignment angle
.

Therewith,
the
beam emittance value (independently o
f

an
additional heating

presence
) correspond
s

to
the
oscillation amplitude. In abs
ence of another

heating


effects the beam profile has specific
double
-
peak structure
. The
sudden appearance of this structure at
increase

of
the
misalignment
angle
was

called “
mono
chromatic instability”

observed in first experiments at NAP
-
M [see, for
ins
tance, 4.9.1]
.

Simulations with

the

B
ETACOOL

program
demonstra
te

also

development of
the mono
chromatic instability

(see section 4.9.4 below)
. However,
as
the
experiments at S
-
LSR
cooler ring
(Kyoto University)

have shown,
the measured beam profiles have pr
actically
Gaussian shape up to very large misalignment angle (Fig.
4.9.4
)
[
4.9.
8
].

It can be explained by
peculiarities of
the intrabeam scattering

process, which leads to very fast relaxation of the
distribution function to
the
equilibrium Gaussian shape.




Fig.

4.9.4
. Transverse beam profiles measured by the ionization monitors on S
-
LSR storage ring
,

proton energy is of 7 MeV, t
he electron current
is of
25.5

mA, horizontal misalignment angles

[
mrad
] are
:
-
1

(red)
,
-
0.5

(blue)
, 0

(green)
, 0.5

(cyan), 1

(pink), 1.5

(violet), 2

(yellow),

dash
curve is the Gaussian extrapolation.





87

4.9.
5
.
Simulation of cooling process with BETACOOL


BETACOOL software
[4.9.9
]
was
developed

for
simulation

of ion beam parameters in a storage
ring taking into account peculiari
t
ies

of electron, stochastic and laser cooling, intrabeam
scattering

(IBS)
,
ion
beam interaction with residual gas, internal target

and

colliding beam
(
in a
collider mode of the ring operation
)
.

General goal of the BETACOOL program is
the
simulat
ion

of
lo
ng (compar
atively to
the ion revolution period)

processes
, which

lead to variation of the ion
distribution function in 6
-
dimensional phase space. The ion beam motion inside a storage ring is
supposed to be stable and it is treated in linear approximation.


BETACOOL code
is

being
developed by JINR Electron Cooling group since 1995 in the frame
of collaborations with different scientific centers: BINP (Novosibirsk, Russia), ITEP (Moscow,
Russia),

CERN,

RIKEN (Japan),
FZJ (Germany),
NIRS (Japan), Kyoto Univ.
(
Japan),
BNL
(USA), Fermilab (Batavia, USA),
GSI (Darmstadt, Germany), Erlangen Univ.
(Germany),
Uppsala Univ. (Sweden). The program was
and is being
used for optimization of the cooling
process of the existing cooling device
s

and design of the new electron

coolers
[
4.9.1
0
].


The simulation of
the electron
cooling
of
238
U
32+

ions in the Booster at the parameters listed in
Table
4.9.3 does demonstrate the effect of
misalignment of the electron beam
(
Fig.

4.9.5
-
4.9.6)
.



Table
4.9.3
.

Main parameters of simula
tion

of the electron cooling process in the Booster

Ion energy, MeV

100

Ion kind

238
U
32+

Particle number

2
×10
9

Initial transverse emittance,


浭牡

ㄮ1

I湩n楡氠浯ie湴畭⁳灲a

㗗㄰
-
4

RF voltage, kV

10

Initial bunch length, m

14

Electron beam cur
rent, A

1.0

Electron beam temperature long/trans, meV

200 / 0.5

Misalignment
of

ion and electron beams

axes

5×10
-
4



One can see that a
fter
1

sec of cooling the transverse emittance (Fig.
4.9.5
a) and momentum
spread (Fig.
4.9.5
b) reach the equilibrium bet
ween
the
cooling and
IBS
heating. The necessary
longitudinal emittance
of
about 2.5

eV

s can be reached
in less than

1

sec of the cooling process
(Fig.
4.9.5
c).


a) b) c)




Fig.

4.9.5
. Evolution of
the
bunched ion
beam parameters during
the
cooling process

with
misalignment angle
of
5×10
-
4
.
a
) horizontal
(r
ed)
and vertical

(blue)

emittances, b)
ion
momentum spread, c) longitudinal emittance
.


88

The beam profile
at cooling with misaligned
electron
beam
has a well pronounced double peak
structure and most of the particles oscillate with
equal

amplitude
s

in the ho
rizontal plane.
(Fig.4.9.6a)
. Due to misalignment the transverse
cross
-
section

of
the cooled
ion beam
has

a
rectangular
form
(Fig.

4.9
.
6
b)
, but

their
transverse phase space looks as
elliptical one

(Fig.

4.
9
.
6
c).


a)

b)


c)



Fig.
4.9.6
.
Ion beam density

distribution after 2 seconds of
the
cooling: a
-

h
orizontal
(red) and
vertical (blue)
profile
s
,
b
-
t
ransverse plane and
c


horizontal
tr
ansverse phase space

of
the
cooled
ion beam


The optimum regime can be found from the dependence of the cooling time on

misalignment
angle when the longitudinal emittance decreases from 7.5 eV

s to necessary value
of
2.5 eV

s
(Fig.

4.9.7). The cooling time has to be less than 1 sec and the transverse emittance has to be
about 1


mm mrad. For the misalignment angle 0.5 mra
d the cooling time does not decrease too
much and the transverse emittance is sufficiently large to avoid a tune shift resonance.


0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0.E+00
2.E-04
4.E-04
6.E-04
8.E-04
1.E-03
misaligment, rad
cooling time, sec .
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
emittance, pi mm mrad .
cooling time
emittance

Fig.4.9.7. The dependence of
the
cooling time and transverse emittance after th
e

cooling process
on the misalignment angle

between electron and ion beams axes; “the cooling time” is defined as
a time interval when the longitudinal emittance decreases from 7.5 eV

s to 2.5 eV

s (see
Fig.4.9.5).


Summary


The electron cooling can not be applied at the ion injection energy of 6 M
eV/u due to large tune
shift that appears under an action of the cooling. The proposed cooling energy of 100 MeV/u
allows to avoid this problem and provides the cooling time
of
about 1 sec. For the electron cooler
of the electron energy of 54 keV the stand
ard design can be used.


89


4.1
0
.

Schedule of the works. Estimated cost


The Booster Technical Design Report preparation is scheduled for 2008
-
2009.

Due to the
application
of the magnet design developed for IHEP and ITEP boosters the TDR
does not
require

a
l
ong R&D stage.


The disassembling of the Sinchrophasatron coils will be performed during the same period.


Manufacturing of the Booster magnetic, vacuum and RF systems will be provided during 20
09
-
201
0
.


The assembly and commissioning are scheduled for 20
1
1



2013.


The
cost of the Booster magnetic system fabrication in the JINR machinery workshop is
estimated preliminary as
2.6


3.6 $M.

Other

more expensive subsystems are the vacuum, RF
and extraction ones. Their cost will be estimated accurately at the
technical design stage.


The nearest prototypes of the Booster electron cooling system are the
EC
-
35

cooler constructed
by BINP and ITEP cooler designed by the JINR electron cooling group. The cost of the first one
was slightly below
1 M€, estimated cost of the second one was about
0.
85 $
M


The estimated cost of the Booster construction including the electron cooling system is about
8

$M.

4.1
1
. References


4.3.1.
A.M.Baldin et. al.,

Heavy ion accelerator complex, JINR preprint 9
-
11796,

Dubna 1978.

4.3.2.

N.N. Agapov, A.M. Baldin, H.G. Khodzhibagiyan, A.D. Kovalenko, V.N. Kuzichev, V.A.
Mikhailov, and A.A. Smirnov, «Low field cold iron SC
-
magnet technology: New aspects of
application,»
IEEE Trans.
Appl. Supercond..
vol. 10, N 1, pp.280
-
283
, 2000.

4.3.3.
A.D. Kovalenko, «The concept of an intermediate temperature iron SC
-
magnets,»
VLHC
Magnet Workshop,
Batavia, USA, May 2000
,

submitted for publication.


4.6.1.
1. A.V.Eliseev, I.B.Issinsky, A.D.Kovalenko, V.I.Volkov. Investigations of possibi
lities of
Nuclotron’s beam intensity Increase by optimization of capturing into acceleration. Proc. of
the 7
-
th International Workshop. Stara Lesna, Slovak Rep., “Relativistic Nuclear Physics
from Hundreds of MeV to TeV”, 2003. pp. 91
-
96.

4.6.
2
.
http://www
-
ap.fnal.gov/ESME/


4.8.1.
C. Montag, L. Ahrens, P. Thieberger, T
omographic measurement of longitudinal
emittance growth due to stripping foils,
Proceedings of 2005 Particle Accelerator Conference,
Knoxville, Te
nnessee
.

4.8.2.
F. Hinterberger, D.Prasuhn, Analysis of internal target effects in light ion storage ring,
NIM A 279(1989), 413
-
422
.


4.9.1.

K. Kilian and D. MShl,

Lecture Notes in Physics 178 (
1983) 163.

4.9.2.

X.D.Yang
, V.V.Parkhomchuk, et al.
,

Commissi
oning of Electron Cooling in CSRm
. Proc.
of COOL'07 (2007).
http://www.cool07.gsi.de


90

4.9.
3
. S. Baird, J. Bosser, C. Carli, I. Meshkov I, D. Möhl, et al.
Measurement of the lifetime of
Pb52
+
, Pb53+ and Pb54+ beams at

4.2 MeV per nucleon subject to electron
cooling. Physics
Letters B 361 (1995) 184
-
186.

4.9.
4
.

X.D.Yang
, V.V.Parkhomchuk, et al.
Commissioning of Electron Cooling in CSRm
. Proc.
of COOL'07 (2007).
http://www.cool07.gsi.de

4.9.
5
. B.Fomel, M.Tiunov, V.Yakovlev. SAM


an interactive code for evaluat
ion of electron
guns. Preprint BINP 96
-
11, Novosibirsk (1996)

4.9.
6
.

A.Ivanov. PhD Thesis. BINP, Novosibirsk (2007).

4.9.
7
. A.Bubley, V.Parkhomchuk, V.Reva. Advantages of electron cooling with radially varying
electron beam density. Nucl. Instr. and Meth.
A532 (2004) 303
-
306.

4.9.
8
. A.Smirnov, I.Meshkov, A.Sidorin, A.Noda, et.al. Investigation of ordered proton beams at
S
-
LSR. Preprint NIRS, HIMAC
-
126 (2007).

4.9.
9
. I.Meshkov, I.Seleznev, A.Sidorin, A.Smirnov, E.Syresin, G.Trubnikov. BETACOOL
program for si
mulation of beam dynamics in storage rings. Nucl. Instr. and Meth. A 558
(2006) 325
-
328.

4.9.1
0
.
A. Sidorin: Cooling Simulations with the BETACOOL Code
. Proc. of COOL'07 (2007).
http://www.cool07.gsi.de