Calculations Of Damage To Rotating Targets Under Intense
Beams For Super-Heavy Element Production
John P. Greene, Rachel Gabor† and Andreas Heinz
Physics Division, Argonne National Laboratory, 9700 S. Cass Avenue,
Argonne, IL 60439 USA
Abstract. In the production of the heaviest elements, the cross-sections for evaporation residues are very small, which,
in turn, requires the usage of intense beams. Hence, the targets used tend to exhibit shortened lifetimes as beam currents
are raised. Tightly focused beams on stationary targets of modest melting point and/or high sputtering yield material will
eventually melt or destroy the target. Defocused or “wobbled” beams enhance target survival only to a modest degree.
Rotating the target on a wheel can overcome target melting, and using, in addition, a low sputtering rate material as a
covering layer can address this issue and allow for higher beam currents to be used for experiments. The purpose of the
calculations done for this work is to attempt to predict the safe range of beam currents allowable, i.e. currents which
produce heat loads below the melting point of the target. Materials with favorable sputtering rates and thermal properties
are also examined. Calculations of the heating and sputtering these targets can withstand will show the safe limits to
which they may be exposed and still survive.
point. Defocusing the beam may be used to enhance
target survival, but places limitations on the collection
efficiency of the recoils. A further method employed
to increase target lifetime involves beam “wobbling”
i.e. deflection of the beam in the vertical dimension
using magnetic steerers upstream from the target
position. Rotating the target using a large diameter
wheel has been shown to overcome target melting and
allows the higher beam currents necessary for the
success of the experiments. The calculations employed
in this work try to predict the safe range of beam
currents which produce heat loads below the melting
point of the target material. A thorough description of
these temperature calculations of heat loads in rotating
targets exposed to high beam currents has been
presented earlier [1].
INTRODUCTION
In order to predict lifetimes of various target wheel
systems under intense heavy-ion bombardment due to
melting and sputtering of the target material,
calculations have been performed of the heat loads
occurring within the target as well as of sputtering
yields from the target surface. In the research being
carried out at the Argonne Tandem Linear Accelerator
System (ATLAS) involving the synthesis of the
heaviest elements, the target wheels prepared must be
able to survive for extended periods of time at beam
currents of several hundred pnA. Calculations of the
beam heating within these targets will determine the
current limits to which they may be exposed without
melting. Sputter yield calculations will provide an
estimate of the erosion rate of target material due to
sputtering from the target surface.
Energy Loss Calculations
The target temperature calculation needs to take into
account how much heat the beam produces in the
target, and how that heat is dissipated as the target
rotates. Heat is created in the target by the energy the
beam loses while passing through the foil and is
proportional to the beam current. This is known as the
energy loss. The energy loss is dependent on the beam
energy and the elemental composition of the target
Description Of The Heat Load
Calculations
In heavy-ion experiments, increasing the current of
a focused beam will eventually melt or destroy a
stationary target of material with a modest melting
†
Harvey Mudd College, Claremont, California 91711
CP680, Application of Accelerators in Research and Industry: 17th Int'l. Conference, edited by J. L. Duggan and I. L. Morgan
© 2003 American Institute of Physics 0-7354-0149-7/03/$20.00
775
TABLE 1. Thermal Properties for the Various Targets Used in the Calculations
Target
Emissivity
Specific Heat
Density
(J/g K)
(g/cm3)
Pb
0.63
0.1288672
11.35
Bi
0.048
0.1221728
9.74
0.2050760
9.53
PbO
0.28†
PbS
0.3 (est.)
0.2068396
7.50
†Radiant Properties of Materials, Aleksander Sala, PWN
Thermal Conductivity
(W/m K)
34.4
7.22
2.77
2.30
FIGURE 1. Calculated energy loss distributions of a
465 MeV 86Kr beam for 500 µg/cm2 Pb targets, Pb
targets on 40 µg/cm2 carbon backings and C/Pb/C
layered targets (with 10 µg/cm2 C covering) for
comparison.
layers. It may be calculated using any of several
programs available.
For the target systems under consideration, the
energy loss of the 465 MeV 86Kr beam used in the
experiments carried out so far was determined using
the Stopping and Range of Ions in Matter (SRIM) code
[2]. In this work, we assumed only a lead target layer
for the temperature calculations. This is not a realistic
approach as thin, self-supporting lead targets are
difficult to prepare. By necessity, carbon backings
were employed for the lead target wheels and, in some
instances, thin carbon coverings were also used. For
comparison, SRIM calculations were performed to
determine the energy loss of the krypton beam in 500
µg/cm2 Pb targets, 500 µg/cm2 Pb targets on 40
µg/cm2 carbon backings and C/Pb/C layered targets
consisting of 500 µg/cm2 Pb targets on 40 µg/cm2
carbon backings with 10 µg/cm2 C covering. Figure 1
gives the energy loss distributions for these three
target systems along with a gaussian fit. As there is
interest in other targets to be used for heavy element
synthesis, Figure 2 shows a comparison of energy loss
for the various target materials under consideration.
2500
Pb layer
Intensity (arb. units)
2000
Binned data from SRIM
Gaussian Fit
Centroid Fit = Energy Loss
= 8.4393 MeV
1500
1000
500
0
7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0
MeV
2500
Pb-C layers
Binned data from SRIM
Gaussian Fit
Centroid Fit = Energy Loss
= 10.269 MeV
Intensity (arb. units)
2000
Thermal Properties of the Target
Materials
1500
1000
500
0
7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0
In addition to the target thickness, the thermal
properties of the target materials under consideration
are also required for the calculation of the temperature
(T) reached in the target. The basic equation, given by
energy conservation, is:
MeV
2500
C-Pb-C Layers
Binned data from SRIM
Gaussan Fit
Centroid Fit = Energy Loss
= 10.701 MeV
2000
Intensity (arb. units)
WI=mCv dT/dt + (T-T0)λD/ρ + 2εσS(T4-T04)
The heat in the target produced by the beam
decreases over time by conduction away from the
beam spot through the foil, and it is also dissipated by
radiation. The left side of the equation represents the
heat brought into the target, with W being the energy
loss and I the beam intensity. The right side of the
equation gives the heat capacity of the target, Cv (with
m being the mass), as well as the cooling due to
conduction and radiation. For heat conduction away
1500
1000
500
0
7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0
MeV
776
from the beam spot, λ is the thermal conductivity, D
the target thickness and ρ is the density. For radiative
cooling, σ is the Stephan-Boltzman constant, ε is the
emissivity of the material and S is the surface area
irradiated by the gaussian shaped beam spot (T0 being
ambient temperature). The factor 2 takes into account
the fact that energy is radiated from both sides of the
foil. A FORTRAN program [3] was developed to
calculate the temperature distribution in the target
material periodically irradiated by the beam
(equivalent to a rotating wheel). The resulting timedependent partial differential equation for temperature
was solved using the finite difference method [4].
For our purposes, when calculating the target
heating, the heat capacity and thermal conductivity of
the carbon backing was ignored, as the majority of the
mass of the target is contained within the 208Pb layer.
An examination was, therefore, made of the
temperature effect due to the differences in emissivity
of the lead vs. carbon surfaces with equivalent beam
heating. For a beam of 100 pnA, 465 MeV 86Kr, the
maximum target temperature with radiative heat loss
from lead surfaces (ε = 0.63) was found to be 279.5°
C. For a C/208Pb/C target with only carbon surfaces (ε=
0.81), a maximum target temperature of 275.5° C was
determined, e.g. only slightly less.
Although in this work we have only calculated
target temperatures for Pb targets, Table 1 lists the
thermal input parameters for several target systems
being investigated for use in our heavy element
experiments. The values were obtained from the
Handbook of Chemistry and Physics [5]. The value for
the hemispherical total emissivity of PbS was
estimated to be 0.3, based on the spectral emissivity in
the normal direction [6] and from similar values for
PbO.
FIGURE 2. Calculated energy loss distributions of a
465 MeV 86Kr beam for 500 µg/cm2 PbO and PbS
targets on 40 µg/cm2 carbon backings and C/Bi/C
layered target (with 10 µg/cm2 C covering for Bi).
2500
PbO-C layers
Binned data from SRIM
Gaussian Fit
Centroid Fit = Energy Loss
= 11.159 MeV
Intensity (arb. units)
2000
1500
1000
500
0
7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0
MeV
2500
C-Bi-C Layers
Binned data from SRIM
Gaussian Fit
Centroid Fit = energy Loss
= 10.794 MeV
Intensity (arb. units)
2000
1500
1000
500
0
7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0
MeV
2500
Beam Parameters
PbS-C Layers
Binned data from SRIM
Gaussian fit
Centroid fit = Energy Loss
= 11.429 MeV
Intensity (arb. units)
2000
For the calculation of target heating, the constituent
beam, its energy, current and gaussian spot size are
needed as input. The heat deposited in the target was
determined using the energy loss and the beam current.
As the energy loss and target thickness are given per
unit area, the temperature rise in the target is highly
dependent on the size and shape of the beam spot. We
will assume a beam spot circular in shape. For a tightly
focused beam (estimated gaussian beam profile of
standard deviation 0.17 mm), the heat produced would
soon vaporize the target material. For the case where
the beam spot was intentionally de-focused, a standard
deviation of 0.5 mm for the beam profile was used in
the calculation. Increasing the size of the beam spot
distributes the energy (heat) deposited in the target
1500
1000
500
0
7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0
MeV
777
FIGURE 3. Plot of Temperature vs. Rotation Speed for a
465 MeV 86Kr beam with a focused and defocused beam
spot on a 500 µg/cm2 208Pb target wheel of 155 mm radius.
over a larger area.
The method of “wobbling” involves steering the
beam in the vertical direction, so as not to alter the
dispersion of the recoils through the mass separator
downstream of the target. This is accomplished at the
ATLAS facility by using a triangular waveform at
approximately 5 Hz and it greatly increases the target
area illuminated by the beam. Due to the non-coupled
motions of rotation and “wobbling,” the distance, (or
elapsed time) it takes for the beam to return to the
same point on the wheel will depend on the radius. For
our wheel, with r=155 mm, and a vertical deflection
amplitude of 5 mm, this takes an estimated 3.33
rotations. In the calculation, we can approximate the
effect of the “wobbling” by assuming a larger diameter
wheel for the increased path length and a slightly
higher rotation to compensate for the velocity.
Target Temperature as a Function of Rotation Rate
86
208
465 MeV Kr Beam on Pb 155 mm Target Wheel
2000
1800
1600
300 pnA defocused beam
300 pnA focused beam
200 pnA focused beam
100 pnA focused beam
o
Temperature ( C)
1400
1200
1000
800
600
400
o
Melting Point of Lead (327.5 C)
200
0
200
400
600
800
1000
1200
1400
Rotation Rate (rpms)
Results Of The Target Heating
Calculations
FIGURE 4. Plot of Temperature vs. Beam Current for a
465 MeV 86Kr beam with a focused, defocused, and
“wobbled” beam spot on a 500 µg/cm2 208Pb target wheel
(r=155 mm) rotating at 1000 RPM.
For our proposed, larger target wheel (r=155 mm),
calculations were carried out which explored the
effects of rotation speed on target heating. Faster
rotation should allow for higher beam currents to be
used before the onset of target melting. Ultimately, we
are constrained by the maximum speed of the motor
drive system employed. Figure 3 gives a plot of target
temperature vs. rotational speed for our rotating target
wheel system. As can be seen, by a simple defocusing
of the beam, a higher beam current of 300 pnA can be
applied to the lead target wheel, while still maintaining
a target temperature below the melting point.
1200
Target Temperature as a Function of Beam Current
86
208
465 MeV Kr Beam on 155 mm Pb target at 1000 rpm
defocused beam
focused beam
wobbled beam
800
o
Temperature ( C)
1000
The results of the target heating calculations are
presented in Figure 4, where the effects of the beam
size and shape are shown in a plot of temperature vs.
beam current. For the 208Pb target/86Kr beam system
under consideration, with a focused beam and using a
wheel of 155 mm radius rotating at 1000 RPM, the
calculations show target melting to occur at a beam
current of approximately 150 pnA. Under similar
conditions for a defocused beam, the maximum
allowable current determined was greater than 400
pnA. By employing beam “wobbling,” a beam current
approaching 500 pnA was reached before exceeding
the Pb target melting point. Included for reference is
the melting point for a lead target (m.p. 327.5 °C).
600
400
o
Melting Point of Lead (327.5 C)
200
0
1
10
100
Beam Current (pnA)
Sputtering, Multiple Scattering, And
Knockout Reactions
Another consideration of target damage is material
loss due to surface sputtering by the incoming ion
beam. This effect can be a major factor in predicting
target lifetimes. Historically, the application of a
carbon covering layer to target wheels used in heavy
element production has been empirically shown to
778
approximately 3.64 µg/hr, for an incident beam of 100
pnA intensity. Empirical evidence from several
experimental runs has revealed a modest count rate in
the FMA focal plane detectors identified as 208Pb. An
analysis of Rutherford backscattering, taking into
account the acceptance for detection at the focal plane,
predicts rates of hundreds of counts per second for
moderately high beam currents.
reduce sputtering of the target material [7]. The
sputtering yields for the various target materials under
consideration were calculated using SRIM and are
listed in Table 2. Using an incoming ion beam of 465
MeV 86Kr normal to the surface of the 208Pb target, a
sputtering yield of 0.119 atoms/ion was determined.
As shown by Maier [8], for a beam current of 100
pnA, this gives an erosion rate due to surface
sputtering of 14.79 µg/hr for a lead target. By
mounting the targets with the 40 µg/cm2 C backing
upstream to the beam, a situation also more
energetically favorable for the recoils, the erosion rate
is reduced substantially to 0.087 µg/hr for the same
beam current. This is due to the low sputtering yield of
0.012 atoms/ion calculated for carbon. In Figure 5, a
plot is given of the erosion rate vs. beam current for
each of the various target elements employed in our
experiments.
Conclusion
In conclusion, the calculations performed showed
that the anticipated target heating for our experiments
using the new target wheel system will remain below
the melting point for 208Pb (327.5 C) using a beam
current of 150 pnA for a focused beam, up to 400 pnA
for a defocused beam and possibly as high as 500 pnA
for a focused beam employing beam wobbling. The
calculation showed that a carbon covering layer,
although having minimal influence on target cooling,
nevertheless increases target lifetime by substantially
reducing the loss of material due to sputtering. The
calculations were supported by preliminary
experimental results with 76Ge targets using previous
wheel designs at modest beam currents [9] and large
target wheels of 208Pb/C at high currents. Higher
currents yet are expected in the proposed heavy
element experiments where these calculations will
provide valuable information on predicting target
damage under actual experimental conditions.
TABLE 2. Calculated Sputter Yields for
the Various Target Materials Used
Target
Sputter Yield
(atoms/ion)
Bi
0.0909
C
0.0122
Pb
0.1191
PbO
Pb
0.0422
O
0.0294
PbS
Pb
0.0402
S
0.0322
FIGURE 5. Plot of Erosion Rate vs. Beam
Current for each of the various target materials
employed in our experiments.
Sputtering rate for
C, Pb, Bi, PbO, PbS
30
Errosion Rate (µg/hr)
25
ACKNOWLEDGMENTS
Bismuth
Lead
Lead Sulfide
Lead Oxide
Carbon
20
The authors would like to acknowledge the
previous research of Dr. Birger Back and James P.
Done, a summer student working for him, upon which
the present work is based. Dr. Kim Lister gratefully
undertook the Rutherford scattering analysis. We
would also like to thank Dr. Donald Geesaman, the
Physics Division Director, and Dr. Irshad Ahmad, the
Target Facility Group Leader, for their continuing
encouragement and support of these efforts. This work
is supported by the U.S. Department of Energy,
Nuclear Physics Division, under Contract No.W-31109-Eng-38.
15
10
5
0
0
50
100
150
200
250
300
Beam Current (pnA)
Lead atoms may also leave the rear surface of the
target due to “knockout” collisions with backscattered
beam particles. Simulations performed using SRIM
and analyzed for lead atoms leaving the back of the
target give a “knockout” rate of 0.029 atoms/ion. This
migration out of the target layer was calculated to be
779
5. Handbook of Chemistry and Physics, D.R. Lide (ed.),
CRC Press, Inc. (1990)
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