Loss analysis for -beam operation in existing CERN synchrotrons

1

Loss analysis for

-
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

M. Kirk,
C. Omet
,

P. Spiller
, J.
Stadlmann



Introduction


It
is

t
he
aim

of the Beta
-
beam
task group, which forms part of the EURISOL design study, to
prove the feasibility of producing high

flux neutrino beams
. The baseline study assumes a
scenario

at CERN using part of the existing infrastructure. The neutrinos are emitted during
beta decay processes of isotopes, which are produced by a primary proton beam impinging on
a target within the E
URISOL facility, and subsequently drift into an ECR for stripping. Post
acceleration is done by a LINAC and a Rapid Cycling Synchrotron, which both need to be
designed.
It is not decided yet if the LINAC, which is used for the other EURISOL
experiments or
a dedicated "beta
-
beam
-
linac" will be used.
Thereafter the isotopes are
accelerated to high


along the existing PS and SPS synchrotrons. Finally, the remaining
particles are injected into a planned decay storage ring in which the narrow high flux cones of

neutrinos
emanate

from its long straight sections, available

to the experimental community.

We present here the beam loss and pressure rise analysis. At present there is no dedicated
collimation system in
the accelerator chain
. It is important that in a w
ell collimated
accelerator the products of the beta
-
decay should avoid as much as possible collisions with
the beam pipe in order to avoid pressure rise and radiation damage in the magnets mainly
from neutron activation.

Collimation provides not only the a
bility to protect the magnets from
activation due to the decay ions but also allows pumps to be places close to the front surface
of the collimator, thereby greatly increasing the overall pumping speed.



Simulation


Starti
ng with the baseline scenario [
1
]

and considering a lattice
with

beam conditions at
injection, the
Strah
l
Sim

code was used simulate the distribution of losses of the decay
products Li and F along the circumference for both the PS and SPS. Strah
l
Sim is an ion optics
tracking program with t
he addition
al functionality

for describing

beam
-
vacuum interactions,
desorption and radioactive decay. The lattice magnets can also be ramped with the energy of
the beam.
The parameters of the vacuum used to determine the loss distribution alo
ng the ring
a
re listed in the appendix
.


Desorption of gases from the walls are induced by
three

processes. The main process is from
collisions of the
beta decay daughter products
Li or

F ions with the walls, that is

against the
beam pipe or a collimator
described

by
a
n angular average

desorption yield. The
second

less
dominant process is the
desorption of

rest gas molecule
s which are ionized
in collisions with
the circulating He or Ne ions.
These ionized molecules are accelerated by the electric field of
the beam to
en
ergies as high as a few hundred
eV

and impinge the wall with a perpendicular
angle of incidence
.

This desorption yield has been
estimated
for an assumed KV distribution
to be

~1

in the worst case
.

The third process is single coulom
b scattering of He or Ne

ions
off

rest gas molecules and the
ensuing

desorption

which is described
in the same manner as
the first process
.
Probabilities for the desorption of the various adsorbates are also entered into
the model accordin
g to their relative abundances.


All deso
rbed gases

can in turn
interact with

the beam. T
hus the growth
of
so called “dynamic

vacuum instabilities
”

can

be modelled.

The pumping is assumed to be uniform along the ring

2

and
therefore only the

total
pumping
speed
is required
.

All other possible loss
mechanisms
were

ignored.

Both rings have the same fractions of rest gases and the base pressures
are also
approximately the same.



Loss Distribution


The distribution of impact positions
of the beta decay daughter ions
along the PS, the so
called loss dis
tribution, is according to figure 1 relatively flat.
The vertical axis has been
scaled to represent the lost beam power per unit circumference deposited at the walls and
averaged over the machine cycle time.
Only a few of the maxima coincide with a drift s
pace
where collimators could be placed.
A low collimation efficiency is therefore to be anticipated.
The loss

pattern is sensitive to the charge
-
to
-
mass of the decay

ions and
to
the distribution of
bending and focussing fields.
An alternate gradient focuss
ing structure consisting of
combined function magnets is used in the PS where
as in the SPS the FODO layout is
employed. Neither structure lends itself to the implementation of a high efficiency collimati
o
n
scheme. Also shown in figure 1

is
the SPS loss dis
tribution
. This

distribution
is more peaked
than that in the PS due to the focussing elements providing a means of
“
channelling
”

the
decay ions which are then deflected to the walls by the dipoles.

However the fraction of losses
in the straights
is

rather
low
, as
is
also
the case in

the PS.
L
engths of the drift sections

present
additional problems concerning collimator thickness, especially in the SPS
.

PS
0.1
1
10
100
0
10
20
30
Distance along circumference [m]
Beam Losses [Wm
-1
]
He
Ne
SPS
0.1
1
10
0
20
40
60
Distance along circumference [m]
Beam Losses [Wm
-1
]
He
Ne

Figure 1
. Loss distributions at injection in the
PS and SPS
. The lattice elements have been superimposed. The F
-

and D
-
combined function magnets
each 2.4m in length
are
represented by
rectangles in
two different shades of
grey (or colours)
,

respectively. The white regions are drift spaces.

For additional

information, the dispersion for
an arbitrary longitudinal momentum offset
in the PS
has also been plotted together with the
(KV) beam edges
.


As
previously
mentioned, activation determines the operational life time of components

essential to the running o
f the accelerator
. The life time of a material
is determined by a
maximum radiation
dose

beyond which the component
is considered
ineffective
, and the dose
rate;
the power absorbed per unit mass
.

Considering that
loss distributions are

to a sufficient
exte
nt

uniform along the machine, one may take the average power per unit circumference

as
a guideline. V
iz.

[2
]
,


machine
cycle
loss
loss
nce
circumfere
t
cycle
E
l
P
*









(
1
)


where,


cycle
t
cycle
loss
dt
t
T
dt
dN
E
)
(
/
,

and


3

)
(
)
(
)
2
ln(
)
(
2
1
t
N
t
t
t
N
dt
d



,


T

is the kinetic energy of the decay ions

and
t
cycle

is the cycle time of the beta beam complex
.

Equation 1 only considers decay ions

where
as

powers per unit length have been calculated
from all known losses

for proton operation
in the PS and SPS
.

Given that the intended
operational period per year is
approximately the same for protons as for beta beams
, and the
total energy deposition of an ion with mass number A is similar to that
of A single protons
above ~
100MeV/u
, it is r
easonable to compare the average power
per unit circumference

between differen
t beams
.

I
t was found
from simulation
that the power per unit circumference
for both synchrotrons
,

with either of the two beta beams,
did not exceed the worst case
for

protons in the PS.

The PS produces an average loss of 3 Watts per meter of protons which

is
the higher than in the SPS due to its lon
g accumulation time at low

.



Pressure Rise


In both machines the dominant loss is
that caused by

beta
-
decay. Coulomb scattering has
in
comparison

a much lower probability which
even

reduces with
beam momentum
.

Gas
desorption, which can lead to considerable pressure rise and an increase in coulomb
scattering, has proven
not to be of concern since pressure reaches in the worst case a value of
~
3∙
10
-
8

mbar as shown in figure 2
.

C
ollimation
of beta beams
is theref
ore

emphasized

at
merely
shielding radiation sensitive components, particularly magnets.

O
ne could

imagine
a
geometry

closer to a block

than that of a wedge
; the

advantage

being
a
larger
shielding
thickness
.

Enhanced

vacuum
pumping speeds will improve the
situation

after all
.

It was found
that a factor of 3 higher than usual would be required in the pumping speed to keep the
pressure to within the nominal threshold of 10
-
8

mbar for continuous operation.

PS
1E-09
1E-08
1E-07
0
1
2
3
Time [s]
Pressure [mbar]
He
He, pumping*3
Ne
Ne, pumping*3
SPS
1E-09
1E-08
0
1
2
3
4
5
Time [sec]
Pressure [mbar]
He
Ne

Fig
ure 2
. Pressure
variation during the machine cycles of the PS and SPS.

The worst case estimate for the
desorption yield

for residual gas ionization

was taken, viz.

=1.

In the PS we accumulate beam for 1.9 seconds
and the beam is extracted after abou
t 2.7 seconds. For the SPS the accumulation time is
virtually

zero and
extraction takes place after approximately 1.4 seconds and 2.5 seconds with Ne and He operation, respectively.
Both beams reach a final

=100.



Intensities


The ultimate goal of course

is to maximize the final intensity in the decay ring. Table 1
therefore shows the intensities at the start and end of the machine cycles of the PS and SPS.
The initial simulation conditions were iter
at
ed until the final intensity at the end of the SPS
cyc
le matched that calculated
in [2
]

at the end of the SPS cycle
,

that is,

“top down” intensities

4

were calculated.

The required injected RCS intensities were
also
as expected
,

for reasons
already given,
very
close to those previously calculated pu
rely on the
basis of beta decay.


PS

He

Ne

P
articles

injected
1

1.80

㄰
13

5.39

㄰
1
2

P
articles

survived

9.53

㄰
12

4.32

㄰
1
2

SPS



P
articles

injected

9.53

㄰
12

4.32

㄰
1
2

P
articles

survived

9.00

㄰
12

4
.
26

㄰
1
2

Table 1. Intensity
degradation at start an
d

end of
the P
S and
SPS machine cycles.



Conclusions


The collimation efficiencies of both the PS and SPS appear to be low for beta beam operation.
The l
ifetimes of individual components should be calculated with
attention paid
not only
to
the physics in the cascade pr
ofiles

but also the geometry and layout of the collimators and
magnets
.

For such calculations a variety of
transport
codes

exist
.

The losses due to space
charge should also be included in future calculations in order to arrive at more accurate final
neutri
no production rates as well as doses to magnets and other components vital to the
operation of these machines.

On a final note
, it should be mentioned

that a new design to
replace the PS has been formulated, which is similar to the SIS100 and has
considera
bly

higher collimation efficiency, at least at injection energy, together with a faster ramp rate of 4

T/s.



References

[1]

Benedikt M., Fabich A., S. Hancock, M. Lindroos, The EURISOL Beta
-
beam Facility. Parameter and
Intensity Values, Version 2. EURISOL

DS/TASK12/TN
-
05
-
03, 14 July 2005

[2]

Fabich A., Benedikt M., Decay losses along the accelerator chain of the EURISOL Beta
-
beam
baseline design, CERN
-
AB
-
2006
-
xxx, EURISOL DS task12/12
-
05
-
05



Appendix

Table of UHV parameters.

UHV System Parameter

PS

SPS

Beam tube volume [m
3
]

6

50

Pumping speed [l/s]

37650

2280

R
esidual gas
base
pressure [mbar]

10
-
9

10
-
9

Vacuum composition

H
2

(35%), N
2

(7%),

H
2
O (50%)

H
2

(35%), N
2

(7%),

H
2
O (50%)

Desorption coefficient for beam particles


[ion
-
1
]

2.8x10
4

2.2x10
4

Des
orption coefficient for ionized gas
molecules


[mol
-
1
]

1

1

Desorption probability of CO

95%

95%

Desorption probability of H
2

5%

5%





1

This is 20 times the bunch
intensity

at the instant each of these bunches are injected into the PS.