Limitations of Ion Beam Brightness with
Electron Cooling - Theory and Experiment
V. Parkhomchuk
BINP, Novosibirsk, Russia
Abstract. Electron cooling is used for damping both single particle and coherent oscillations of ion beams. The
extremely high phase space density of the cooled ion beam can become a source of stability problems ("electron
heating"). For storage rings such as CELSIUS, COSY and the Indiana Cooler, this is a serious problem that limits the
use of the electron cooling in physical experiments. Proper design of the electron cooler can improve the stability of the
cooled ion beam.
SINGLE PARTICLE APPROACH
The cooling rate is determined by the cooling
force - the friction force of an ion moving with
velocity V with respect to an electron beam with
density ne. A longitudinal magnetic field is used to
counteract the deflection caused by the space charge of
electron beam. This field magnetizes the transverse
thermal motion of the electrons. The cooling force can
be calculated using the following equation [1,2]:
For an ideal magnetic field in the cooler, 0B = 0. The
ion beam emittance is ex.
The cooling rate is
maximized at a given electron current Je with
ne=(Je/e)/(27C8x px), <x2 >=ex px, V=cpy (ex /px )1/2). The
cooling rate can be written as:
Acool = MV ~
nfp
(4)
/ Anax
+
Anin
+
L
PL ^
Pr^+PL
-)
(1)
where the impact parameters can be written in their
simplest form as:
It is easily seen that maximum cooling is achieved
when the electron current is :
(5)
2
(2)
(Vie)
PL =
me
eff=C
_2reri(B/e)7jec
eB
27ienex
~~g
V2
The maximal cooling rate is:
^max - ^3/2
Here, Z is the ion charge, (Ob is the electron beam
plasma frequency, T is the time of flight in the cooling
section (all quantities are evaluated in the beam
reference frame), B is the longitudinal magnetic field,
Ve_L is the thermal velocity of the electrons in the
cooling section. Veff is the effective velocity of the
center of the electron Larmor orbits but is not the
electron velocity. Veff is determined by the electrical
field from space charge of the electron beam and the
transverse component of the magnetic field in the
cooling section:
V
^,= (£x I mm * mrad)(B / kGs)p f (
(3)
3/2gl/2
A
(6)
/^max + Anin + Pi ^
,3/2
Prn*+PL
For example, accumulation in the SIS synchrotron
[3] for 8X =150 mm*mrad, B=0.6kG, E = 11.4 MeV/n
, Jemax=0.7A., and ?W=0.5 1/s. Figure 1 shows the ion
beam accumulation in multiturn injection, with
injection at every 0.5s and simultaneous cooling. The
time interval of 0.5 sec is not enough to cool all ions, a
small fraction of the beam at the edge of the
acceptance is lost at the moment of the next injection.
(The first step is higher than the following ones.)
where 0B is the deflection of the direction of the
magnetic line from the center of the ion beam orbit.
CP642, High Intensity and High Brightness Hadron Beams: 20th ICFA Advanced Beam Dynamics Workshop on
High Intensity and High Brightness Hadron Beams, edited by W. Chou, Y. Mori, D. Neuffer, and J.-F. Ostiguy
© 2002 American Institute of Physics 0-7354-0097-0/02/$ 19.00
325
+67
SIS Bi +67
accumulation
+67
SISBiBi
accumulation
accumulation
Je=400SIS
mA
Je=400mA
mA
Je=400
beam
current
(mA)
ionion
beam
current
(mA)
ion beam current (mA)
0,2
0,2
0,2
0,4
0,40,4
beam
current
(mA)
Bi Bi
beam
current
(mA)
Bi beam current (mA)
0,0
0,00
0,0
00
0,3
0,30,3
0,2
0,20,2
1
11
2
2
22
3
3
time3 3
(s)
time(s)
(s)
time
(s)
time
4
4 44
5
555
0,1
0,10,1
6
666
0,0
0
0,00,0
0 0
FIGURE
1. Ion
FIGURE
Ionbeam
beamaccumulation
accumulationin
inthe
theSIS
SISsynchrotron
synchrotron
FIGURE1.1.
1.Ion
the
SIS
synchrotron
FIGURE
beam
accumulation
inin
the
SIS
synchrotron
GSI.
GSI.
GSL
GSI.
10
10 10
20
20 20
30
30 30
time (s)
time
time
(s)(s)
time
(s)
40
40 40
FIGURE
Accumulation and loss of Bi beam at SIS
FIGURE3.
Accumulationand
andloss
lossofofBiBibeam
beamatatSIS
SIS
FIGURE
3.3.Accumulation
Accumulation
and
FIGURE
3.
synchrotron.
synchrotron.
synchrotron.
synchrotron.
0,5
0,5
0,5
invers cooling
time (1/s)
invers
invers cooling
cooling time
time (1/s)
(1/s)
A(1-exp(-t/t )) Je=0.4 A
A(1-exp(-t/t
)) Je=0.4 A
A(1-exp(-t/t
———A(1-exp(-t/t
Aexp(-1/t
) ))t Je=0.4
=8.1 s A
Aexp(-1/t
t =8.1
Aexp(-1/t
)) ) t =8.1
s s
———Aexp(-1/t
+67
Bi +67 +67
beam accumulation
Bi beam
beam
accumulation
Bi
accumulation
———
Bi+67
beam
and
stop
injection
after 15 s
and
stop
injection
after
and
stop
injection
after
15
s s
and
stop
injection
after
1515
0,5
0,5
0,5
Number
ofof
Number
ofofthe
the
storage
saturation
Numberof
thestorage
storagecycles
cyclesfor
forsaturation
saturationof
Number
of
the
storage
cycles
for
storage
current
is
estimated
as:
storage
current
isisestimated
estimated
as:
storagecurrent
currentis
estimatedas:
as:
storage
0,4
0,4
0,4
0,3
0,3
0,3
N stor = λ cool × τ rec ≈
λ
N*Nstor
λ
τ τrecrec≈ ≈
star
">co
stor= =
cool× ×
cool
×
T
8500
<<n
n (r) >
1
e
⊥
8500
× TeT⊥e⊥
8500×x,
8500
< <neeen(r)>
(er()r>) >
11
A(γβε nx / β x ) 33// 232 / 2(1 + ( Je / Je max ) 22 )233// 223 / 2 n e (0)
:)
)
(V)
n
n
(
A
+
Je
Je
(
/
)
(
1
(
/
)
)
γβε
β
A(γβε nxnx/ β x )x (1 + ( Je / Je maxmax)
ee e0()0) (7)
(7)(7)
=
0,2
0,2
0,2
0,1
0,1
0,1
0,0
0,0
0,0
0,0
0,0
0,0
theory
theory
theory
+67
SIS Bi +67+67cooling measuring
SISBiBi cooling
coolingmeasuring
measuring
SIS
0,5
0,5
0,5
0,5
1,0
1,0
1,0
1,0
1,5
1,5
1,5
1,5
Electron beam current (A)
Electronbeam
beam
current
(A)
Electron
Electron
beamcurrent
current(A)
(A)
where
Te⊥iisis the
electron
temperature measured in
eV,
where
the
electron
ee⊥isisthe
where
whereTTT
theelectron
electrontemperature
temperaturemeasured
measuredinineV,
eV,
e⊥
ε£nx=P7£x
the
normalized
ion
beam
emittance,
<n
(r)>
nx=βγεx is
e
is
the
normalized
e
εnx
is
the
normalized
ion
beam
emittance,
<n
(r)>
εnx=βγε
=βγε
is
the
normalized
ion
beam
emittance,
<n
(r)>
xx
e e
isis the
average
electron
beam over tcross section of
the
the
average
electron
isisthe
theaverage
averageelectron
electronbeam
beamover
overtcross
tcrosssection
sectionofofthethe
electron
beam
and
nnee(0)
is
the
electron
beam
density
at
electron
beam
and
(0)
is
the
electron
beam
density
electron
atat
electronbeam
beamand
andnen(0)
theelectron
electronbeam
beamdensity
densityat
e(0)isisthe
the
center
of
beam
where
storage
ion
beam.
A
cooling
the
center
of
beam
where
storage
ion
beam.
A
cooling
the
thecenter
centerofofbeam
beamwhere
wherestorage
storageion
ionbeam.
beam.AAcooling
cooling
system
with
a large
expansion
of
electron
beam
system
with
large
expansion
ofofthe
the
electron
system
the
beam
systemwith
withaaalarge
largeexpansion
expansionof
theelectron
electronbeam
beam
from
the
gun
to
the
cooling
section
obtains
a
low
from
the
gun
totothe
the
cooling
section
from
obtains
low
from the
thegun
gunto
thecooling
coolingsection
sectionobtains
obtainsaa alow
low
electron
beam
temperature
(T
/expansion),
e⊥i =
electron
beam
temperature
(T
==T
Tcathode
h0de/expansion),
e e⊥=
catcathode
electron
beam
temperature
(T
T
/expansion),
electron
beam
temperature
(T
T
/expansion),
e⊥
cathode
but
the
accumulation
potential
is
by
but
the
accumulation
potential
isisreduced
reduced
bybyintensive
intensive
but
potential
is
reduced
by
intensive
butthe
theaccumulation
accumulation
potential
reduced
intensive
recombination
at
the
cooler.
In
the
SIS
cooler,
direct
recombination
at
the
cooler.
In
the
SIS
cooler,
direct
recombination
atatthe
cooler.
InInthe
SIS
cooler,
direct
recombination
the
cooler.
the
SIS
cooler,
direct
experiments
were
made
to
compare
the
lifetime
of
the
experiments
were
made
to
compare
the
lifetime
of
the
experiments
were
made
to
compare
the
lifetime
of
the
experiments
were
made
to
compare
the
lifetime
of
the
Bi
beam
with
expansion
factors
of
1
and
6,
with
the
Bi
beam
with
expansion
factors
of
1
and
6,
with
the
Bi
beam
with
expansion
factors
of
1
and
6,
with
the
Bi
beam
with
expansion
factors
of
1
and
6,
with
the
same
electron
beam
densities,
and
results
are
shown
in
same
electron
beam
densities,
and
results
are
shown
in
same
electron
beam
densities,
and
results
are
shown
inin
same
electron
beam
densities,
and
results
are
shown
figure
4.
figure
4.4.
figure
figure4.
2,0
2,0
2,0
2,0
FIGURE
at an
emittance
ofof150π
mmFIGURE2.
2.The
Thecooling
coolingrate
rate
an
emittance
15071
mmFIGURE
2.2.
The
cooling
rate
an
ofof150π
mmFIGURE
The
cooling
rateatat
at
anemittance
emittance
150π
mmmrad
versus
the
electron
beam
current,
as
measured
in
SIS
mrad
versus
the
electron
beam
current,
as
measured
in
SIS
mrad
versus
the
electron
beam
current,
asasmeasured
ininSIS
mrad
versus
the
electron
beam
current,
measured
SIS
(points)
equation
(4).
(points)and
andcalculated
calculatedfrom
from
equation
(4).
(points)
and
calculated
from
(points)
and
calculated
fromequation
equation(4).
(4).
The
beam
is stopped
when
the
The accumulation
accumulation of
beam
stopped
when
the
The
accumulation
ofof
The
accumulation
of beam
beam isis
is stopped
stopped when
when the
the
losses
of
stored
beam
between
new
injections
becomes
losses
of
stored
beam
between
new
injections
becomes
losses
of
stored
beam
between
new
injections
becomes
losses of stored beam between new injections becomes
equal
The
lifetime
of
storage
equalto
tothe
theinjected
injectedincrement.
increment.
The
lifetime
of
storage
equal
toto
the
injected
increment.
The
lifetime
equal
the
injected
increment.
The
lifetimeof
ofstorage
storage
beam
by
recombination
atat the
electron
cooler
is
beam
by
recombination
the
electron
cooler
beam
beam by
by recombination
recombination atat the
the electron
electron cooler
cooler isisis
proportional
to
√(T
),
where
T
is
the
temperature
of
e⊥
e⊥
proportionaltoto
to√(T
V(Te⊥e⊥
i),
where
isisthe
the
temperature
ofof
e),
C_Lis
proportional
where
TTTe⊥
of
proportional
√(T
),the
where
thetemperature
temperature
e⊥ section.
the
cooling
In
figure
33
theelectron
electron beam
beam in
the
cooling
section.
In
figure
the
electron
beam
inin
the
cooling
section.
In
figure
3
+67
the
electron
beam
in
the
cooling
section.
In
figure
+67 in the SIS3
can
bebe seen
the
accumulation
of
Bi
+67
+67
can
seen
the
accumulation
of
Bi
in
the
SIS
can
be
seen
the
accumulation
ofof Bi
inin the
SIS
can
be
seen
the
accumulation
Bi
the
SIS
synchrotron
loss
of
ion
beam
after
end
of
synchrotron and
and the
the
loss
of
ion
beam
after
end
of
synchrotron
and
the
of
beam
after
of
synchrotron
and
the loss
loss
of ion
ion
beamformulas
after end
endfor
of
injection.
The
lines
show
fitting
injection.
The
lines
show
fitting
formulas
for
injection.
The
lines
show
fitting
formulas
for
injection.
The
lines
show
fitting
formulas
for
accumulation
(The
losses
are
dominated
by
accumulationand
andloss.
loss.
(The
losses
are
dominated
by
accumulation
and
loss.
accumulation
and
loss. (The
(Thelosses
lossesare
aredominated
dominatedby
by
ion
recombination.)
ion
recombination.)
ion
ionrecombination.)
recombination.)
beam
current
(mA)
ionion
beam
current
(mA)
ion beam current (mA)
1
1 1
0,1
0,1
0,1
SIS,
SIS,22May
May1998
1998
SIS,
2 May
1998
SIS,
2 May
1998
experiment
with
experiment
with
experiment
with
same
density
electron
experiment
with beam
0,01
same
density
electron
beam
S 0,01
same
density
electron
beam
0,01
+67
same density electron
beam
0,01 accumulation
t- accumulationand
and decay
decayBi
Bi+67
accumulation
andand
decay
Bi Bi+67
accumulation
decay
2
2
2
4
4
4
6
6
6
8
8
8
10
10
10
12
12
14
Je=133 mA exp=1
Je=133
mAmA
exp=1
Je=800
mA
exp=6
Je=133
exp=1
Je=800
mAmA
exp=6
Je=800
exp=6
16
14
16
12 (s)14
16
time
time(s)
time
(s)(s)
time
18
18
18
20
20
20
20
22
22
22
22
24
24
24
24
+
FIGURE
ion
FIGURE 4.
4. The
The accumulation
accumulation and
and loss
loss of
of Bi
Ei+67
ion beam
beam
+67
+67ion
FIGURE
4.
The
accumulation
and
loss
of
Bi
FIGURE
4.
The
accumulation
and
loss
of
Bi
ionbeam
beam
with
the
same
electron
beam
densities
but
with
different
with
the
same
electron
beam
densities
but
with
electron
beam
densities
but
with different
withthe
thesame
same
electron
beam
densities
but
different
expansion
factors
from
the
electron
gun
to with
the cooling
expansion
factors
from
the
electron
gun
expansion
expansion factors
factorsfrom
fromthe
theelectron
electrongun
guntotothe
thecooling
cooling
section.
section.
section.
section.
326
minimum
to the maximum
maximum energiesofofthe
the electron
minimum
minimum toto the
the maximum energies
energies of the electron
electron
beam.
Fig.
6
shows
results
of
an
experiment
with
beam.
beam. Fig.
Fig. 66 shows
shows results
results ofof anan experiment
experiment with
with
minimum
to
the
maximum
energies
of
the
electron
modulation
of
the
electron
energy
in
the
CELSIUS
modulation
modulation ofof the
the electron
electron energy
energy inin the
the CELSIUS
CELSIUS
beam.Modulation
Fig. 6 shows
results
of anbeam
experiment
ring.
of
the
electron
energyatatwith
at218
218
ring.
Modulation
of
the
electron
beam
energy
ring.
Modulation
of
the
electron
beam
energy
218
modulation
of the electron
energyspread
in theinCELSIUS
keV
±300V
produces
an
energy
the
proton
keV
±300V
produces
an
energy
ininthe
proton
keV
produces
anelectron
energyspread
spreadenergy
theat
proton
ring. ±300V
Modulation
of-3-33the
beam
218
beam
ofof ±1.5×10
±1.5×10
and
stabilizes
the cooling.
cooling.
beam
of
and
stabilizes
the
beam
±1.5xlO"
and
stabilizes
the
cooling.
keV ±300V produces an energy spread in the proton
-3
beam ofCELSIUS
±1.5×10
andpbeam
stabilizes
the cooling.
CELSIUS
(1999)400
400 MeV
Je=600 mA
CELSIUS(1999)
(1999) 400MeV
MeVpbeam
pbeamJe=600
Je=600mA
mA
stored ion beam current.
INSTABILITY
FOR
COOLED
INTENSE
INSTABILITY
FOR
COOLED
INSTABILITY
FOR
COOLEDINTENSE
INTENSE
ION
BEAM
INSTABILITY
FOR
COOLED
INTENSE
ION
BEAM
ION BEAM
ION
BEAM storage
Experiments
CELSIUS
ring
with
Experiments
the
CELSIUSstorage
storagering
ringwith
with
Experiments
at atat
thethe
CELSIUS
electron
cooling
show
that
injection
of
a
too
intense
electron
cooling
show
thatinjection
injectionofstorage
ofa atoo
toointense
intense
Experiments
at
the
CELSIUS
ring
with
electron
cooling
show
that
proton
beam
results
in
high
losses,
and
only
small
electron
cooling
show
that
injection
ofonly
a too
intense
proton
beam
results
in
high
losses,
and
only
small
proton
beam
results
in
high
losses,
and
aaasmall
fraction
beam
iscooled[4].
This
phenomenon
was
proton
beam
results
in highThis
losses,
and only a was
small
fraction
of
beam
is cooled[4].
cooled[4].
Thisphenomenon
phenomenon
was
fraction
of of
beam
is
called
“electron
heating”.
As
the
injection
intensities
fraction
of
beam
is
cooled[4].
This
phenomenon
called
"electron
heating".
As
the
injection
intensities
called “electron heating”. As the injection intensities was
isisis
higher
for
lighter
ions
and
residual
gas
induced
losses
called
“electron
heating”.
As
the
injection
intensities
higher
for
lighter
ions
and
residual
gas
induced
losses
higher for lighter ions and residual gas induced losses is
arehigher
not so
accumulation
of these
ions
is
forhigh,
lighterthe
ions
and residual gas
induced
losses
high,
accumulation
these
ions
are are
notnot
so so
high,
thetheaccumulation
ofofthese
ions
isis
limited,
develops
this
same
instability.
are notand
so usually
high, the
accumulation
of these
ions is
limited,
and
usually
develops
this
same
instability.
limited,
and
usually
develops
thisaccumulation
same
instability.
limited,
and
usually
develops
this
same
instability.
Figure
55 shows
experiments
with
proton
Figure
shows
experiments
with
accumulation
proton
Figure
5
shows
experiments
with
accumulation
proton
Figure
5
shows
experiments
with
accumulation
proton
beam
with
an
energy
of
180
MeV
in
the
CELSIUS
beam
with
an
energy
of
180
MeV
in
the
CELSIUS
beam
with with
an energy
of 180
MeV
in in
thethe
CELSIUS
beam
an
energy
of
180
MeV
CELSIUS
ring.
ring.
ring. ring.
CELSIUS 2 June 1997
——— CELSIUS 2 June 1997
p beam 180 MeV
CELSIUS
2180
June
1997
p beam
MeV
CELSIUS
2 June 1997
Je=1.8 A
p Je=1.8
beam 180
MeV180 MeV
pAbeam
3,5
injection with storage beam
3,5-|
injection
A storage beam
Je=1.8
AJe=1.8with
3,5
with storage
injection injection
with storage
beam beam
3,0
3,5
3,0-
p beam current (mA)
3,0
2,5
2,5
f 2,5-
p beam current (mA)
p beam current (mA)
3,0
2,5
2,0
' 2,0-
2,0
!
1,5
1,5-
!
1,0
1,0-
1,5
L
1,0
0,5
0,5-
0,5
0,0
initial stage
of accumulation
initial stage
initial
stage
afterofkick
out
accumulation
of accumulation
storage
beam
after kick out
after kick
out beam
storage
storage beam
2,0
1,5
1,0
0,5
0
50
0,0
0
0,0
0
50
100
50
100
150
200
time150
(s)
time(s)
time
150
200(s)
100
250
200
300
250
250
300
300
time (s)
FIGURE
5. Accumulation of
proton beam
at CELSIUS
FIGURE
FIGURE5. 5.Accumulation
Accumulationofofproton
proton beam
beam atat CELSIUS
CELSIUS
multiturn
injection
from
cyclotron.
multiturn
FIGURE
5. injection
Accumulation
of proton beam at CELSIUS
multiturn
injectionfrom
fromcyclotron.
cyclotron.
multiturn injection
from prescription
cyclotron. for the suppression of
The usual
The
Theusual
usualprescription
prescriptionfor
forthe
thesuppression
suppression of
of
instability
to
increase
spread
instability
is is
toto
increase
the
momentum
spread
of
the
instability
increasethe
themomentum
momentum
spreadof
ofthe
the
The isusual
prescription
for
the suppression
of
ion
beam.
Direct
of
rfrfnoise
ionion
beam.
application
ofofan
an
external
beam.
Directapplication
application
anexternal
external
noise
instability
is toDirect
increase
the momentum
spread rf
of noise
the
field
on
the
ion
beam
isisis
not
effective.
Electron
cooling
field
on
the
ion
beam
not
effective.
Electron
cooling
field
on
the
ion
beam
not
effective.
Electron
cooling
ionatbeam.
Direct
application
of
an
external
rf
noise
small
amplitudes
(in
at
small
amplitudes
(inthe
thecooled
cooledcore)
core)isisisextremely
extremely
at on
small
amplitudes
(in
the
cooled
core)
extremely
field
the
ion
beam
is
not
effective.
Electron
cooling
fast
(a
few
ms)
and
an
external
noise
applied
to
fast
(a
few
ms)
and
an
external
noise
applied
tothe
theion
ion
fast
(a
few
ms)
and
an
external
noise
applied
to
the
ion
at small
amplitudes
(in
the
cooled
core)
is
extremely
beam
can
easily
remove
the
tail
of
the
beam
without
beam
can
easily
remove
the
tail
of
the
beam
without
beam
can
easily
remove
the
tail
of
the
beam
without
fastany
(a few
ms) and an external
noise applied
to the ion
the
anyuseful
usefuleffect
effecton
the beam
beam core.
core. Energy
Energy
any
useful
effect
onon
the
beam
core.
Energy
beam
can
easily
remove
the
tail
of
the
beam
without
modulation
of
the
electron
beam
appears
to
be
a
modulation
of
the
electron
beam
appears
to
be
more
modulation
of the electron
beam
appears
to beEnergy
aamore
more
anyreasonable
useful effect
on The
the
beam
core.
solution.
ions
cool
toward
the
reasonable
solution.
The
ions
cool
toward
the
reasonable
solution.
The
ions
coolto toward
the
modulation
of
the
electron
beam
appears
be
a
more
instantaneous
electron
energy
and
if
the
modulation
instantaneous
electron
energy
and
if
the
modulation
instantaneous
electron
energy
if the
modulation
reasonable
solution.
The
ionsand
cool
the
has
aa high
frequency
(compared
to
cooling
ahigh
high
frequency
(compared
thetoward
coolingrate)
rate)
hashas
frequency
(compared
totothe
the
cooling
rate)
instantaneous
electron
energytheir
and
ifenergies
the modulation
the
ions
will
distribute
energies
from
the
ions
will
distribute
their
from
the
the ions will distribute their energies from the
the
has a high frequency (compared to the cooling rate)
the ions will distribute their energies from the
beamcurrent
current
no
modulation
beam
modulation
—x—beam
currentno
no
modulation
beamcurrent
current
300
modulation
electron
energy
beam
300
VV
electron
—i—beam
current
300
Vmodulation
modulation
electron
energy
CELSIUS
(1999)
400
MeV
pbeam
Je=600
mA energy
pbeam
r.m.s.
size
(mm)
pbeam
r.m.s.
(mm)
—x—pbeam
r.m.s.size
size
(mm)
beam current
no
modulation
pbeam
r.m.s.
size
with
300
V
modulation
pbeam
r.m.s.
with
VV
modulation
—i—pbeam
r.m.s.size
size(mm)
(mm)
with300
300
modulation
beam current
300
V(mm)
modulation
electron
energy
pbeam r.m.s. size (mm)
pbeam r.m.s. size (mm) with 300 V modulation
8
Proton
Protonbeam
beamcurrent
current (mA)
Proton beam current (mA)
These
results clearly
demonstrate that
for aa high
These
These results
results clearly
clearly demonstrate
demonstrate that
that for
for ahigh
high
expansion
factor
the
recombination
rate
increased
expansion
expansion factor
factor the
the recombination
recombination rate
rate increased
increased
These
resultsinclearly
demonstraterate.
that for
a high
without
any
increase
accumulation
without
any
increase
in
accumulation
cooling
without
any
increase
in
accumulationrate.
rate.AAAcooling
cooling
expansion
factorexpansion
the recombination
rate
increased
system
with
high
factor
is
useful
for
system
with
high
factor
for
system
with
high expansion
expansion
factor israte.
is useful
useful
for
without in
anyatomic
increase
in accumulation
Aenergy
cooling
experiments
physics
requiring
high
experiments
in
atomic
physics
requiring
high
energy
experiments
in
atomic
physics
requiring
high
energy
system but
withit high
expansion factor for
is useful
for
resolution,
systems
resolution,
but
isisat atata aadisadvantage
disadvantage
for
systems
resolution,
butinititisatomic
disadvantage
for
systems
experiments
physics
requiring
high
energy
requiring
accumulation
rate.
can
requiring
accumulation
rate. Accumulation
Accumulation
can
be
requiring
accumulation
Accumulation
canbe
be
resolution,
but
ittheisuse
atrate.
a disadvantage
for systems
further
increased
by
of
an
electron
beam
with
further
increased
by
the
use
of
an
electron
beam
with
further
increased
by the use
of anAccumulation
electron beamcan
with
requiring
accumulation
rate.
be
lower
density
at atat
thethe
center
(ne(n
(0)
<<«<n
This
lower
density
<n
e(r)>).
lower
density
the
center
(0)
<n
This
eof
e(r)>).
e(0)
e(r)>).
further
increased
bycenter
the use(n
an<<
electron
beamThis
with
cancan
give
andensity
additional
about
give
an
additional
factor
about
10-20
the
can
give
an
additional
factorof
of
about10-20
10-20inininthe
the
lower
at thefactor
center
(nof
e(0) << <n e(r)>). This
stored
ion
beam
current.
stored
ion
beam
current.
stored
ion
beam
current.
can give an additional factor of about 10-20 in the
7
6
5
4
4
3
3
8
7
6
5
4
2
2
3
1
1
2
0
01
-1
-1 00
0
-1
50
50
0
50
100
100
time
time(s)
(s)
time
(s)
100
150
150
150
time (s)
FIGURE
The
time. From
0
FIGURE6.
Theproton
protonbeam
beamcurrent
currentversus
versus
FIGURE
6.6.The
proton
beam
current
versus time.
time. From
From00
toto
30
s s the
protons
are
injected
and
accelerated,
from
30
to
FIGURE
6.
The
proton
beam
current
versus
time.
From
0
30
the
protons
are
injected
and
accelerated,
from
30
to 30 s the protons are injected and accelerated, from 30toto
170
s the
prons
are
.
to
sthethe
protons
are injected
and accelerated, from 30 to
17030
prons
arecooled
cooled.
170
s sthe
prons
are
cooled
.
170 s the prons are cooled.
NEW
NEWTOOLS
TOOLSTO
TOCONTROL
CONTROLTHE
THE
NEW
TOOLS
TO
CONTROL
THE
NEW
TOOLS
TO
CONTROL
THE
COOLING
OF
INTENSE
ION
BEAMS
COOLING
OF
INTENSE
ION
BEAMS
COOLING
OF
INTENSE
ION
BEAMS
COOLING OF INTENSE ION BEAMS
Instability
Instability problems
problems inin intense
intense ion
ion beams
beams
Instability
problems
in cooling
intense ion
ion beams
beams
Instability
problems in
stimulated
the
of
that
stimulated
the development
development
of intense
cooling systems
systems
that
stimulated
the
development
of
cooling
systems
that
stimulated
the
development
of
cooling
systems
control
idea
controlthe
thefinal
final ion-beam
ion-beamdensity.
density. The
Thesimplest
simplestthat
idea
control
the
final ion-beam
ion-beambeam
density.
The
simplest
idea
control
the
final
density.
The
simplest
idea
isis
using
a
hollow
electron
with
empty
space
near
using a hollow electron beam with empty space near
isusing
usingaawhere
hollow electron
electronofbeam
with
space
near
is
hollow
withempty
empty
space
near
thecenter
the
ion
should
thecenter
wherethe
thecore
core ofbeam
thestored
stored
ionbeam
beam
should
thecenter
where
the core
of
the
stored
ion
beam
should
thecenter
where
core
of
the
stored
ion
beam
should
be
placed
[5,6].
The
cooling
rate
is
inversely
be placed [5,6]. The cooling rate is inversely
be placed
placed [5,6].
[5,6].
The
cooling
rate
isisinversely
be
Thepower
cooling
inversely
proportional
to
ofofthe
amplitude
ofofion
proportional
tothe
thecubic
cubic
power
therate
amplitude
ion
proportional
to
the
cubic
power
of
the
amplitude
of of
ionion
oscillation.
It
is
possible
to
decrease
the
electron
proportional
to
the
cubic
power
of
the
amplitude
oscillation.
It
is
possible
to
decrease
the
electron
oscillation.
is center
possible
toto decrease
the
electron
beam
density
without
decreasing
oscillation.
ItItthe
is
possible
decrease
the
electron
beam
densityinin
in
the
centerof
ofbeam
beam
withoutdecreasing
decreasing
beam
density
the
center
of
beam
without
the
cooling
ideas
were
proposed
for
beam
densityrate.
in
the These
center
of
beam
without
decreasing
the
cooling
rate.
These
ideas
were
proposed
for
the coolinginrate.
These
ideas(IMP,
were China).
proposed Two
for
application
the
CSR
project
the
cooling in
rate.
These
ideas(IMP,
were China).
proposedTwo
for
application
the
CSR
project
application
in
thevariable
CSR project
(IMP,
China).
Two
new
coolers
with
electron
beam
profile
were
application
in
the
CSR
project
(IMP,
China).
Two
new
coolers
with
variable
electron
beam
profile
were
new coolers
with
variable
electron beam
profile
were
produced
atatwith
BINP
inin collaboration
with
IMP.
In
new
coolers
variable
electron beam
produced
BINP
collaboration
withprofile
IMP. were
produced
at BINP
in collaboration
with
IMP.
InIn
August
2002,
the
first
cooler
will
be
commissioned
atatIn
produced
at BINP
incooler
collaboration
with IMP. at
August
2002,
the first
first
cooler
willbe
becommissioned
commissioned
August 2002,
the
will
BINP.
Figure
7
shows
this
cooler
in
March
2002
.
August
2002, 7the
first this
cooler
willininbe
commissioned
at
BINP.
Figure
7 shows
shows
this
cooler
March
2002.
BINP. Figure
cooler
March
2002
.
BINP. Figure 7 shows this cooler in March 2002.
FIGURE
The new
cooler for
IMP (China)
built by
by BINP
FIGURE7.7.
FIGURE
7. The
The new
new cooler
coolerfor
forIMP
IMP(China)
(China)built
built byBINP
BINP
(Novosibirsk).
(Novosibirsk).
(Novosibirsk).
FIGURE 7. The new cooler for IMP (China) built by BINP
(Novosibirsk).
327
CONCLUSIONS
CONCLUSIONS
Figure 8 shows the measured profiles of the
Figurebeam
8 shows
thebench
measured
profiles of the
electron
at a test
for commissioning
the
electron
beam
at
a
test
bench
for
commissioning
the
electron gun and the electron collector. The electron
electron
gun and
electron
collector.the
Thevoltage
electron
beam
diameter
is the
3 cm.
By changing
on
beam
diameter
is
3
cm.
By
changing
the
voltage
on
the control electrode the electron beam is transformed
the control
the beam.
electronAnbeam
is transformed
from
a solidelectrode
to a hollow
electron
gun of this
from
a
solid
to
a
hollow
beam.
An
electron
gunelectron
of this
design can be used for optimization of the
design can
be used for optimization of the electron
cooling
process.
cooling process.
Electron cooling is very useful in the accumulation
very
useful in
accumulationof
of Electron
rare ion cooling
beams. is
For
example,
thetheaccumulation
of
rare
ion
beams.
For
example,
the
accumulation
secondary exotic nuclei prosduced at a target orofof
secondary
exotic
prosduced
a targetfoils
or of
high-charge
ions nuclei
produced
through at
stripping
can
high-charge
ions
produced
through
stripping
foils
can
be enhanced. Some new R.&.D projects in electron
be
enhanced.
Some
new R.&.D
projects
electron
cooling
for high
luminosity
colliders
have in
begun
(such
cooling
for high
begun (such
as cooling
for luminosity
RHIC). colliders
A new have
application
is the
as
cooling
new application
the
cooling
of for
highRHIC).
intensityAbeams,
where the issystem
cooling
of
high
intensity
beams,
where
the
system
really cools only the tail of the main beam to reduce
really
only
the tail
of theofmain
to reduce
losses.cools
Using
cooling
instead
onlybeam
collimating
can
losses.
Using
cooling
instead
of
only
collimating
decrease the losses and the resulting activation ofcan
the
decrease
the losses. and the resulting activation of the
vacuum chamber
vacuum chamber.
REFERENCES
REFERENCES
1. V.V. Parkhomchuk, A.N.Skrinsky, Phusics-Uspekhi 43(5)
1. V.V.
Parkhomchuk, A.N.Skrinsky, Phusics-Uspekhi 43(5)
433-452(2000)
433-452(2000)
2. V.V. Parkhomchuk, “New Insights in the Theory of
2. Electron
V.V. Parkhomchuk,
"New Insights
in the
Cooling”, Nuclear
Instruments
and Theory
Methodsofin
Electron Cooling", Nuclear Instruments and Methods in
Physics Research A 441 (2000) 9-7
Physics Research A 441 (2000) 9-7
3. M. Steck, “Beam accumulation with the SIS Electron
3. M. Steck, "Beam accumulation with the SIS Electron
Cooler”, Nuclear Instruments and Methods in Physics
Cooler", Nuclear Instruments and Methods in Physics
Research A 441 (200) 175-182.
Research A 441 (200) 175-182.
4. D. Reistad, “Measurements of Electron Cooling and
4. D. Reistad, "Measurements of Electron Cooling and
ElectronHeating
HeatingatatCELSIUS",
CELSIUS”,totoappear
appearininProceedings
Proceedings
Electron
the workshop
workshopon
onBeam
BeamCooling
Cooling2001,
2001,Bad
BadHoneff,
Honeff,
ofof the
Germany.
Germany.
FIGURE 8. The electron beam distribution for different
FIGURE 8. The electron beam distribution for different
voltages on the control electrode - 0, 100, 200, 350, 400, 600
voltages on the control electrode - 0, 100, 200, 350, 400, 600
V. The measurement was made by scanning a tungsten wire
V. The measurement was made by scanning a tungsten wire
across the electron beam.
across the electron beam.
Figure
calculated example
example of
of cooling
cooling
Figure 99 shows
shows aa calculated
with
hollow
electron
beams.
The
parameters
of the
the
with hollow electron beams. The parameters of
beam
are
SIS
injection
parameters.
The
electron
beam
beam are SIS injection parameters. The electron beam
has
an empty
empty central
central hole
hole with
with aa
has aa current
current of
of 0.5A
0.5A and
and an
diameter
of
1.5
cm.
From
fig.11
it
is
easily
seen
that
diameter of 1.5 cm. From fig. 11 it is easily seen that
the
formed aa very
very specific
specific ion
ion beam
beam
the electron
electron cooling
cooling formed
profile.
of the
the beam
beam shows
shows aa Gaussian
Gaussian
profile. The
The center
center of
profile
but
with
the
tail
cut
off
at
1.5
cm
diameter.
All
profile but with the tail cut off at 1.5 cm diameter. All
ions
in
the
initial
tail
are
cooled
into
the
central
ions in the initial tail are cooled into the central
density
density region.
region.
E.I. Antohin.
Antohin. V.N.Bocharov,
V.N.Bocharov,"Conceptual
“ConceptualProject
Projectofofanan
5.5. E.I.
Electron
Cooling
System
at
an
Energy
of
Electronsofof
Electron Cooling System at an Energy of Electrons
350keV",
keV”,Nuclear
NuclearInstruments
Instrumentsand
andMethods
MethodsininPhysics
Physics
350
Research
A
441
(2000)
87-91.
Research A 441 (2000) 87-91.
6.
Ivanov
A.V.,Parkhomchuk
ParkhomchukV.V.,
V.V.,Sukhina
SukhinaB.N.,
B.N.,Tiunov
Tiunov
6. Ivanov A.V.,
M.A, "The
“The Hollow
Hollow Electron
Electron Beam
Beam Opportunities
Opportunitiesinin
M.A,
Electron Cooling"
Cooling” toto appear
appear inin Proceedings
Proceedings ofof the
the
Electron
Workshop
on
Beam
Cooling
2001,
Bad
Honeff,
Workshop on Beam Cooling 2001, Bad Honeff,
Germany.
Germany.
0s
——— Os
0.2
0.4
——— 0.4
0.8
——— 0.8
1.0
———1.0
profile (arb. units)
100
1.2
.............. 11.4
4
i 1010,
1.6
I
1
I
1.8
——— 1.8
2.0
electron
beam
profile
beam profile
1
0,1
-3
-2
-1
0
1
2
3
X (cm)
X(cm)
FIGURE
the profile
profile of
of aa Bi
Bi ion
ion beam
beam
FIGURE 9. The development of the
with
electron beam.
beam. Profiles
Profiles at
at t=0,
t=0, 0.2,
0.2,
with cooling
cooling by a hollow electron
0.4, …,
..., 2.0s are shown.
0.4,
328