A new and simple calibration independent
Applied Radiation and Isotopes 69 (2011) 247–253
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Applied Radiation and Isotopes
journal homepage: www.elsevier.com/locate/apradiso
A new and simple calibration-independent method for measuring the beam
energy of a cyclotron
Katherine Gagnon a,n, Mikael Jensen b, Helge Thisgaard b,1, Julia Publicover c,2, Suzanne Lapi c,3,
Steve A. McQuarrie a, Thomas J. Ruth c
a
Cross Cancer Institute, Edmonton PET Centre, University of Alberta, Edmonton, AB, Canada T6G 1Z2
Hevesy Laboratory, Risoe-DTU, Technical University of Denmark, Frederiksborgvej 399, DK-4000 Roskilde, Denmark
c
TRIUMF, 4004 Wesbrook Mall, Vancouver, BC, Canada V6T 2A3
b
a r t i c l e in fo
abstract
Article history:
Received 10 January 2010
Received in revised form
30 July 2010
Accepted 17 September 2010
This work recommends a new and simple-to-perform method for measuring the beam energy of an
accelerator. The proposed method requires the irradiation of two monitor foils interspaced by an energy
degrader. The primary advantage of the proposed method, which makes this method unique from
previous energy evaluation strategies that employ the use of monitor foils, is that this method is
independent of the detector efficiency calibration. This method was evaluated by performing proton
activation of natCu foils using both a cyclotron and a tandem Van de Graaff accelerator. The monitor foil
activities were read using a dose calibrator set to an arbitrary calibration setting. Excellent agreement
was noted between the nominal and measured proton energies.
& 2010 Elsevier Ltd. All rights reserved.
Keywords:
Cyclotron
Monitor reactions
Energy determination
Ionization chamber
1. Introduction
When used for medical radionuclide production, both new and
old cyclotrons need to have their beam energy checked periodically. This is not only part of good manufacturing practice and
quality assurance but is also necessary for optimising target yields
and minimising the radiation dose overhead of radionuclide
production. An example where such a validation is of particular
importance is when undesired by-products result from competing
energy-dependent reactions (e.g. production of 123I via the (p,2n)
reaction when producing 124I from 124Te). Although it is often
claimed by cyclotron operators that the energy of their machines
‘‘never change’’, were ‘‘locked at the factory’’ or were ‘‘carefully
determined at acceptance testing’’, from our experience, this is
not valid for the majority of present day negative ion cyclotrons.
The extraction of negative ion beams by a stripper foil can give
useful beam on targets even with substantial orbit centre offsets.
Changes in magnet shim or in distribution of the RF field along the
dees can cause the orbital centre to drift. Furthermore, the loss of
position calibration or damage to extractors and stripper foils can
also substantially affect the beam energy. While cyclotrons in
nuclear physics institutions often have analysing magnets with
well characterized energy definition, this diagnostic tool is not
feasible for most medical cyclotron configurations as the production targets sit more or less straight on the beam port with little or
no further collimation. As such, an off-line approach for evaluating the beam energy of a medical cyclotron is required.
For most applications the simple method of beam range
determination will not be accurate enough due to straggling. Long
stacks increase straggling, and it can be difficult by conventional
‘‘burn’’ methods to discriminate the Bragg peak end from thermal
damage. For this reason, we investigated a new, simple-toperform method for evaluating the cyclotron beam energy. By
using the universally available dose calibrator (a re-entrant ion
chamber used in every nuclear medicine facility), the proposed
method is sufficiently sensitive to achieve the necessary precision
of a few tenths of an MeV. Furthermore, the proposed method
requires neither energy nor efficiency calibration of the detector
system being used. The method works for an arbitrary dose
calibrator setting. The proposed method was extensively evaluated and tabulated for protons in the 11–19 MeV energy range,
but it should be straightforward to extend the general principle to
protons, deuterons and alphas of other energies.
n
Corresponding author. Tel.: + 1 780 432 8776; fax: + 1 780 432 8615.
E-mail address: [email protected] (K. Gagnon).
1
Present address: PET- and Cyclotron Unit, Nuclear Medicine Department,
Odense University Hospital, DK-5000 Odense, Denmark
2
Present address: University Health Network, Toronto, Canada
3
Present address: Mallinckrodt Institute of Radiology, Washington University,
St. Louis, MO, USA
0969-8043/$ - see front matter & 2010 Elsevier Ltd. All rights reserved.
doi:10.1016/j.apradiso.2010.09.012
2. Theory
Although beam monitor reactions have been extensively
published, evaluated and used for many years (see for example,
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K. Gagnon et al. / Applied Radiation and Isotopes 69 (2011) 247–253
http://www-nds.iaea.org/medportal/ ‘‘monitor reactions’’), the
reliable use of these methods, at present, requires access to and
knowledge of a well calibrated detector system (typically an HPGe
gamma spectroscopy setup). When irradiating a single, thin foil,
the production of a radionuclide is given by
A ¼ nIsð1eltb Þ,
ð1Þ
where A is the activity of the nuclide at the end of bombardment
(EOB), n is the number of target nuclei per unit area, I is the proton
current (protons/second), s is the energy dependent crosssection, l is the decay constant for the nuclide and tb is the
bombardment time. Given that the cross-sections for the reaction
of interest are well characterized, then the beam energy may be
determined by measuring A and having an accurate knowledge
of the n, I, l and tb terms. Due to variations in the foil thickness
and/or beam current, an examination of the activity ratio of two
isotopes produced simultaneously via competing reactions
(i.e. (p,n) and (p,2n)) within a single foil can be beneficial
(Blessing et al., 1995; Scholten et al., 1994):
Aj
sj ð1elj tb Þ
¼
Ak
sk ð1elk tb Þ
ð2Þ
The primary drawback in evaluating the beam energy using (1)
or (2) is that both require absolute quantification of the produced
radioisotope activity. Incorrect or offset efficiency calibration for
the gamma detector in question can therefore seriously compromise the results.
As opposed to irradiating a single monitor foil, it has been
proposed earlier to use a stack of copper foils and then analyse
every single foil by high resolution gamma spectroscopy for the
isotopes 62Zn and 65Zn (Kim et al., 2006; Blessing et al., 1995;
Scholten et al., 1994). To overcome the need for gamma spectroscopy and high quality efficiency calibrations, this study suggests
the irradiation of two monitor foils of the same material
interspaced by an energy degrader (Fig. 1). By carefully choosing
both the monitor foil material and degrader thickness, the
differential activation of the two monitor foils may be used to
determine the beam energy. This effect is illustrated in Fig. 2a and
b for proton energies of 15.0 and 15.5 MeV incident on two 25 mm
copper foils which sandwich an 875 mm aluminum degrader. The
major advantage of examining the ratio of two identical isotopes
produced in the two foils (i.e. 63Zn/63Zn), as opposed to, for
example, the 63Zn/62Zn ratio resulting from proton irradiation of a
single copper monitor foil, is that all detector efficiency calibration requirements are eliminated. Furthermore, the exponential
factors in (2) will also cancel as lj ¼ lk for the proposed method:
Aj Foil1
sj Foil1
¼
Aj Foil2
sj Foil2
ð3Þ
Through careful selection of the energy degrader thickness,
this method can be used efficiently and with high precision.
Fig. 2. A comparison of the 63Zn activation for two 25 mm copper foils and an
875 mm aluminum degrader given incident proton energies of (a) 15.0 MeV and (b)
15.5 MeV. As noted, a small change in the incident energy can yield a measurable
change in the 63Zn activity ratio. Figures were produced using the IAEA
recommended cross-section data (IAEA, 2009) and the SRIM software package
(Ziegler et al., 2009).
Since this activity ratio may be predicted using well known
published recommended cross-section data and the SRIM software package (Ziegler et al., 2009), we have developed and
included a simple lookup table (Table 1) which may be used
universally for monitoring the proton energy given experimental
evaluation of the activity ratio.
3. Materials and methods
To evaluate the proposed method, this study measured the
Zn activity ratio produced during the proton irradiation of two
copper foils interspaced by an aluminum energy degrader. Initial
measurements were performed at the Edmonton PET Centre (EPC)
using a TR 19/9 negative ion variable energy cyclotron (Advanced
Cyclotron Systems Inc., Richmond, BC). A set of six additional
measurements were also performed using the tandem Van de
Graaff at Brookhaven National Lab (BNL) in New York. As the
incident proton energy is known with greater accuracy when
63
Fig. 1. The configuration of the two copper foils and aluminum energy degrader
irradiated in this experiment. When discussing the entrance and exit energies of
the copper foils, this refers to locations A and B, respectively, for foil #1 and C and
D, respectively, for foil #2. The above figure is not to scale—the copper foil
thicknesses have been exaggerated for the purpose of illustration.
249
K. Gagnon et al. / Applied Radiation and Isotopes 69 (2011) 247–253
Table 1
The recommended aluminum degrader thicknesses and second order curve fitting terms.
Aluminum thickness (lm)
Energy range (MeV)
Second order term A
First order term B
Constant term C
Expected activity ratio range
350
500
625
750
875
1000
1125
1250
1375
10.8–11.8
12.0–12.8
13.0–13.8
14.0–14.8
15.0–15.6
15.8–16.4
16.6–17.2
17.4–18.0
18.2–18.8
1.3811
0.7058
0.5352
0.5223
0.5254
0.7218
1.1060
2.1607
4.5682
6.8958
4.0449
3.1150
2.7947
2.5192
2.8021
3.3724
4.7938
7.3352
19.408
17.795
17.527
17.696
17.837
18.380
19.029
19.934
21.028
1.55–2.50
1.65–2.85
1.50–2.85
1.30–2.40
1.05–1.80
0.80–1.50
0.60–1.20
0.45–0.85
0.35–0.65
E (MeV) ¼ Ar2 + Br +C, where r is the 63Zn activity ratio between front and back copper foil.
The straggling and the energy loss of a nominal 25 mm aluminum vacuum window are included in the calculations. The energy calculated is the energy incident on this
vacuum foil.
using an electrostatic accelerator, as compared to a cyclotron, the
measurements at BNL were performed to serve as a further
validation of the proposed method.
3.1. Monitor foils
Copper foils were the preferred choice for evaluating the
proton energy for this study as the natCu(p,x)63Zn excitation
function is well characterized (IAEA, 2009), and copper foils of
sufficient quality and purity (Z99.99%) can be purchased from
many commercial suppliers (i.e. Alfa Aesar&, Goodfellows&, etc.).
As long as the monitor foils are kept relatively thin (i.e. r25 mm),
so as to minimize the finite energy loss through the foil, the actual
thickness of the foils is not of great importance as it may be
measured and corrected for. It should be noted however that all
recommended values given in this manuscript are based on the
use of 25 mm copper monitor foils. To minimize the foil-to-foil
variations in purity and thickness, and ensure that the two foils
are of equal thickness, it is essential that the two foils are cut from
the same manufactured sheet or roll. For improved accuracy over
a screw micrometer, the foil thicknesses in this study (both of
aluminum and copper) were found by weight determination
using a 10.0 cm 10.0 cm square of foil. Although the thickness
variations across the foils were not measured, we have investigated the impact of small variations in the average thickness by
utilizing both the measured and nominal foil thicknesses to
determine the proton energy.
3.2. Degrader thickness
As noted in Fig. 3, as the degrader thickness is increased, an
increased range in the 63Zn expected activity ratio is observed
(therefore increasing the sensitivity of the technique). Striving to
achieve a reasonably thick aluminum degrader, it is immediately
noted that one thickness will not be suitable for the entire
11–19 MeV energy range of interest. For example, if we consider a
degrader which is sufficiently thick to drop 10 MeV given
Ep ¼17 MeV, such a degrader would certainly be too thick to allow
for activation of the second copper foil given an incident energy of
11 MeV. As such, we have proposed a set of recommended
thicknesses (Table 1) broken into nine energy windows between
the range of 11 and 19 MeV. Consequently, to use the recommended data of Table 1, it is assumed that there is a rough idea
(within approximately 1 MeV) of the proton energy in question.
In developing the set of recommended degrader thicknesses of
Table 1, the goal was to utilize (as noted above) a reasonably thick
degrader for increased sensitivity. What makes a thickness
‘‘reasonable’’? If the degrader is too thick, there will be a large
difference in the proton energy between the entrance and exit
Fig. 3. The expected 63Zn activity ratio calculated from (3) as a function of proton
energy for aluminum degraders ranging in thickness from 650–850 mm.
surface of the second copper foil. Due to large non-linearities in
the proton stopping power at low energies, a large difference in
energy across the foil is undesired as the technique becomes
increasingly susceptible to both thickness non-uniformities and
errors in the thickness measurements. For this reason, the
recommended degrader thicknesses were selected, so that the
average proton exit energy of the second copper foil was expected
to be no less than 5.2 MeV (determined using simulations in SRIM
(Ziegler et al., 2009)). This value of 5.2 MeV was selected for two
reasons. Firstly, this value is 1.0 MeV above the 63Cu(p,n)63Zn
reaction threshold (NNDC, 2009). Thus, despite any energy
straggling, all protons should have sufficient energy, so that the
possibility exists for them to undergo a reaction within the foil.
Next, for a 25 mm copper foil, this minimum exit energy ensures
an average energy drop of no greater than 1 MeV between the
entrance and exit surface of the second copper foil. We considered
this 1 MeV energy drop acceptable, as the IAEA recommended
cross-sections (reported in steps of 0.1 MeV) for the natCu(p,x)63Zn
reaction are highly linear (R2 40.98) over any floating 1 MeV
interval in the energy range of interest for the second copper foil.
3.3. Expected activity ratio
To evaluate the proton energy from the measured activity
ratio, a plot of proton energy as a function of the expected activity
250
K. Gagnon et al. / Applied Radiation and Isotopes 69 (2011) 247–253
Table 2
The nominal proton irradiation energies and nominal/measured foil thicknesses.
Nominal incident energy Thickness of aluminum vacuum window and
degrader (lm)
a,b
10.9
11.1a,b
11.3a,b
11.6a,b
11.8a,b
13.8b
14.6b
15.4b
16.2b
17.0b
17.8b
18.6b
11.00c
13.50c
16.00c
18.00c
Blind (12.0-12.8)c
Blind (14.0-14.8)c
a
b
c
Thickness of each copper monitor foil Thickness of aluminum energy
(lm)
degrader (lm)
Nominal
Measured
Nominal
Measured
Nominal
Measured
400
400
400
400
400
25
25
25
25
25
25
25
25
25
25
25
25
25
403.3
403.3
403.3
403.3
403.3
25.5
25.5
25.5
25.5
25.5
25.5
25.5
25.5
25.5
25.5
25.5
25.5
25.5
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
23.7
23.7
23.7
23.7
23.7
23.7
23.7
23.7
23.7
23.7
23.7
23.7
25.6
25.6
25.6
25.6
25.6
25.6
350
350
350
350
350
625
750
875
1000
1125
1250
1375
350
625
1000
1250
500
750
352.2
352.2
352.2
352.2
352.2
628.0
750.6
878.2
1000.8
1128.4
1251.0
1378.6
352.2
628.0
1000.8
1251.0
500.4
750.6
Energy achieved using additional aluminum degrader as minimum extractable energy in TR-19/9 is approximately 13.7 MeV.
Cyclotron.
Tandem.
ratio is required. In calculating the expected activity ratio, it is
first necessary to determine the effective energy within the two
copper monitor foils for a given incident energy. This was
achieved by simulating 1000 ions in the TRIM module of the
SRIM software package (Ziegler et al., 2009). As the copper foils
were of finite thickness, the effective energy within the foil was
taken as the average between the entrance and exit foil energy.
These effective energies were then employed to evaluate the
corresponding effective cross-sections within the two monitor
foils. This was achieved using polynomial interpolation of the
IAEA recommended cross-section data for the natCu(p,x)63Zn
reaction (IAEA, 2009). Finally, the activity ratio was then
calculated from Eq. (3) using the effective 63Zn cross-sections
of the two copper foils. It should be noted that error in the
magnitude of the IAEA cross-section data will not impact the
results as it is the shape of the excitation function which dictates
the cross-section ratio.
For purpose of comparison, the expected activity ratios were
determined by simulating the proton energy both using (i) the
nominal foil thicknesses reported by the manufacturer, and
(ii) the measured foil thicknesses. It is important to note that in
addition to the Cu/Al/Cu foil sandwich, a 25 mm aluminum
vacuum window is employed as part of the TR 19/9 cyclotron
target system. As this vacuum foil was included in all energy
simulations, the energy calculated using the data from Table 1
represents the energy incident on this vacuum foil.
measured energy (determined via HPGe spectroscopy methods)
had been noted previously for a thorough study of the extractor
foil in question (Avila-Rodriguez et al., 2009), the proton energies
evaluated in this experiment were compared directly with the
nominal cyclotron energy.
A total of six proton irradiations were performed using the
tandem at BNL. Of these, two of the irradiations energies were
energy-blinded. Since the choice of the aluminum energy
degrader thickness requires some idea as to the irradiation
energy, it was decided prior to irradiation that one of the blind
studies would be performed in the 12.0–12.8 MeV energy range
while the other would be performed in the 14.0–14.8 MeV energy
range. For all BNL irradiations (300 s), the foils were mounted
normal to the incident beam with the current ( 400 nA)
measured just prior to irradiation using a Faraday cup. In contrast
to the cyclotron configuration at the EPC, the BNL target station
did not require the use of an aluminum vacuum window.
Nevertheless, to eliminate the need for applying corrections to
the data in Table 1, an additional 25 mm aluminum foil was
installed prior to the Cu/Al/Cu sandwich so as to mimic the
presence of a vacuum window for the BNL irradiations. The
nominal proton energies along with the nominal and measured
aluminum and copper thicknesses employed for both the EPC and
BNL irradiations are reported in Table 2.
3.5. Foil measurements
3.4. Irradiation parameters
A total of twelve irradiations were performed on the TR 19/9
cyclotron. All foils were positioned normal to the incident beam
and electrically isolated from the target nose-piece. Foils were
irradiated for 300 s with approximately 1 mA of proton beam
current. In order to validate the proposed method in the 11 MeV
range, an aluminum degrader (375 mm nominal thickness) was
installed adjacent to the vacuum window as the TR 19/9 cyclotron
has a minimum proton extraction energy of 13.7 MeV. As good
agreement between the nominal cyclotron energy and the
When irradiating natural copper foils up to 19 MeV, three
radionuclide products require examination: 62Zn (t1/2 ¼9.186 h),
63
Zn (t1/2 ¼38.47 min), and 63Cu (t1/2 ¼9.67 min). Although 65Zn
(t1/2 ¼243.66 days) is also produced during the irradiation of
copper foil, given the irradiation conditions and assuming activity
assays are performed within 3 h post-EOB, the activity of 65Zn
will be negligible (o 1%) with respect to the large 63Zn activity
produced. Discrimination of the three isotopes only by their halflives is possible, but somewhat time consuming. An examination
of the published cross-sections for these reactions (Ghoshal, 1950;
IAEA, 2009) suggests that if we allow the 9.7 min half life 62Cu
K. Gagnon et al. / Applied Radiation and Isotopes 69 (2011) 247–253
contribution to decay, the 63Zn will dominate the dose calibrator
readings for proton energies up to approximately 16 MeV. For this
reason, we investigated the possibility of using a combination
method whereby for lower proton energies the ratio of the dose
calibrator readings at a single time point could be used, while for
higher proton energies, half-life discrimination of the measured
readings would be necessary.
All foil radioactivities were read out using CapintecTM CRC15PET and CRC-15W dose calibrators at the EPC and BNL,
respectively. As the proposed method is independent of the
calibration setting, an arbitrary setting of 100 was employed. All
irradiated foils in this study were individually measured in the
dose calibrator at approximately 20, 30, 40, 50, 60, 80, 100, 120,
150 and 180 min post-EOB, with the measurement times recorded
to the nearest second.
251
residuals were eliminated (Fig. 4). Using this fitting method,
the ratio of the C1 coefficients obtained using (6) and (4)
was taken as the ratio of 63Zn activity between first and second
copper foils.
3.6. Calculating the measured activity ratio
Although the single time point evaluation of the 63Zn activity
ratio was expected to be applicable only for the lower energy
irradiations, the 63Zn activity ratio was calculated for all
irradiations by directly using the dose calibrator readings
obtained at the 1 and 2 h time points. These time points were
investigated, as opposed to the initial 20 min measurements, in
order to allow for 62Cu decay. As the foil readings for a given
irradiation were typically measured 1–2 min apart, a corresponding 1–2 min 63Zn decay correction was applied, so that the
readings coincided with a single time point. It is not necessary to
decay correct the readings back to EOB as this factor will be the
same for both foils, and therefore will cancel when examining the
activity ratio.
To discriminate the three isotopes by their half-lives and
acquire the isotope-corrected 63Zn activity ratio, the ten serial
time point readings underwent the following described fitting
procedure.
Since the proton energy within the second foil was always
expected to be below the threshold for production of 62Cu
(11.0 MeV) and 62Zn (13.5 MeV) (NNDC, 2009), the ten dose
calibrator readings R for this foil were fit using the Curve Fitting
Toolbox in MATLAB& and the following fitting function:
l63 Z n t
RðtÞ ¼ C1 e
þB
Fig. 4. A plot of the residuals for the decay curve fitting of the ten dose-calibrator
readings for the first copper foil for the 18.6 MeV cyclotron irradiation. Plot A was
obtained using the fitting function described in (5), while B was obtained from the
fitting function of (6).
ð4Þ
where t represents the time elapsed since EOB and l63 Zn
represents the decay constant for 63Zn. The C1 coefficient was
taken to represent the 63Zn contribution at EOB, while B was
taken to represent any background activity. An original attempt at
fitting the dose calibrator readings for the first foil was performed
using the following double exponential:
l63 Z n t
RðtÞ ¼ C1 e
l62 C u t
þ C2 e
þB
ð5Þ
where C1 and C2 were fit parameters. These coefficients were
taken to represent the EOB 63Zn and 62Cu contributions,
respectively. Since the background term was not expected to
vary greatly between the two foils, the B term in (5) was not a
fitting parameter, but instead set to the value obtained for the
second foil described by (4). As this fitting procedure led to
undesired systematic trends in the residuals, the data for the first
foil were instead described by
l63 Z n t
RðtÞ ¼ C1 e
l62 C u t
þ C2 e
l62 Z n t
þC3 e
þB
ð6Þ
63
where C1, C2 and C3 were fit parameters used to describe the Zn,
62
Cu and 62Zn contribution at EOB, respectively. As before,
the background B term was taken as the value obtained by
fitting the activity readings of the second foil. By adopting this
latter fitting procedure, the systematic trends observed in the
Fig. 5. A sample plot of the proton energy, E, as a function of the expected 63Zn
ratio, r. The plot is made with the coefficients from Table 1, and assumes a nominal
350 mm aluminum foil and two nominal 25 mm copper monitor foils. The
straggling and energy loss of a nominal 25 mm aluminum vacuum window are
included in the calculations.
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K. Gagnon et al. / Applied Radiation and Isotopes 69 (2011) 247–253
Table 3
The proton energies evaluated in this experiment using the
Nominal incident energy
10.9a
11.1a
11.3a
11.6a
11.8a
13.8a
14.6a
15.4a
16.2a
17.0a
17.8a
18.6a
11.00b
13.50b
16.00b
18.00b
Blind (12.0–12.8) 12.3b
Blind (14.0–14.8) 14.4b
a
b
63
Zn activity ratio.
Curve-fit energy measurement
1 h energy measurement
2 h energy measurement
Nominal thickness
Measured thickness
Nominal thickness
Measured thickness
Nominal thickness
Measured thickness
10.9
11.2
11.4
11.7
11.9
13.9
14.6
15.5
16.4
17.2
17.9
18.5
10.96
13.45
16.10
18.17
12.32
14.42
10.9
11.2
11.4
11.6
11.9
13.8
14.6
15.5
16.4
17.2
17.9
18.5
11.00
13.48
16.12
18.18
12.36
14.43
10.9
11.2
11.4
11.6
11.9
13.8
14.5
15.4
16.2
16.9
17.5
18.1
10.93
13.47
15.92
17.56
12.32
14.36
10.9
11.2
11.4
11.6
11.9
13.8
14.5
15.4
16.2
16.9
17.4
18.1
10.98
13.51
15.94
17.59
12.36
14.37
10.9
11.2
11.5
11.7
12.0
14.0
14.6
15.5
16.2
17.0
17.5
18.1
10.97
13.49
16.00
17.69
12.36
14.42
10.9
11.2
11.4
11.7
12.0
13.9
14.6
15.5
16.2
16.9
17.5
18.1
11.01
13.53
16.02
17.71
12.40
14.44
Cyclotron.
Tandem.
4. Results and discussion
A sample plot of the proton energy as a function of the
expected 63Zn ratio (calculated from (3)) is given in Fig. 5 for a
nominal 25 mm aluminum vacuum window, a nominal 350 mm
aluminum energy degrader and two nominal 25 mm copper
monitor foils. This data was fit using a second order polynomial.
The 350 mm aluminum degrader is the thickness recommended in
this study for evaluation of proton energies in the 10.8–11.8 MeV
range. Assuming 25 mm copper monitor foils, and the presence of
a 25 mm aluminum vacuum foil, a list of suggested aluminum
proton degrader thicknesses for a wide range of energies is
presented in Table 1. Since the plots of the expected 63Zn ratios for
the other recommended aluminum foil thicknesses are similar in
appearance to Fig. 5, we have omitted the respective figures in
this publication. The coefficients to the second order polynomial
fits for each of these have however been included in Table 1. Since
a second order polynomial will always have two activity ratios
which give rise to a given energy—only one of which is physically
meaningful, it should be noted that Table 1 also includes the
corresponding range of activity ratios which are expected for the
energy range of interest.
Table 3 summarizes the energies evaluated using (i) the half-life
discriminated curve-fit based 63Zn ratio, (ii) the single 1 h time point
63
Zn ratio and (iii) the single 2 h time point 63Zn ratio. Table 3 also
includes both the energies evaluated assuming the nominal foil
thicknesses (i.e. the second order polynomial data from Table 1), as
well as the energies evaluated using the measured foil thicknesses.
When examining the blinded experiments (12.3 and 14.4 MeV) all
measurements agreed within 0.1 MeV of the nominal values.
Excellent agreement between the measured and nominal energies
was also noted regardless of the strategy employed for determining
the 63Zn ratio for proton energies up to 17.0 MeV. For this reason, we
conclude that the half-life discrimination using the 63Zn curvefitting method is only essential when the proton energy is greater
than 17.0 MeV. We also note that the minor variations from the
nominal foil thicknesses used in this study resulted in only minor
variations (r0.1 MeV) in the evaluated energy. This suggests that
small thickness variations across a foil should similarly have a minor
impact on the evaluated energy. It should be noted that caution
must be exercised when using the values from Table 1 if the
measured foil thicknesses vary by an amount greater than those
employed for this work.
5. Conclusions
In this work, we have recommended and evaluated a new and
simple-to-perform method for measuring the beam energy of a
cyclotron. This method was developed with the cyclotron
production of medical isotopes in mind, where the ability to
easily verify the beam energy to an accuracy of a few tenths of a
MeV is of great importance. The proposed method has been found
to provide an accurate determination of proton energies in the
11–19 MeV range without the use of complex analysis methods or
sophisticated equipment. To facilitate the adoption of this
technique into routine evaluation of the cyclotron beam energy,
we have included a list of recommended nominal aluminum
degrader thicknesses as well as a list of the corresponding curve
fit data for evaluation of the proton energy using the measured
63
Zn activity ratio. Application of the proposed method to the
monitoring of deuteron energies is a topic we plan to explore
further in the near future.
Acknowledgements
The authors wish to thank the following individuals for their
assistance in the irradiations: Drs. Chuck Carlson, Michael
Schueller and David Schlyer for helpful discussions and organizing
the experiments at BNL. This work was supported through Grants
from The Canadian Natural Sciences and Engineering Research
Council (TJR, KG, JP, SL).
References
Avila-Rodriguez, M.A., Rajander, J., Lill, J.-O., Gagnon, K., Schlesinger, J., Wilson, J.S.,
McQuarrie, S.A., Solin, O., 2009. Proton energy determination using activated
yttrium foils and ionization chambers for activity assay. Nucl. Instrum.
Methods B 267, 1867–1872.
Blessing, G., Brautigam, W., Boge, H.G., Gad, N., Scholten, B., Qaim, S.M., 1995.
Internal irradiation system for excitation function measurement via the
stacked-foil technique. Appl. Radiat. Isot. 46, 955–960.
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Ghoshal, S.N., 1950. An experimental verification of the theory of compound
nucleus. Phys. Rev. 80, 939–942.
IAEA, 2009. Charged-particle cross section database for medical radioisotope
production, Monitor reactions. /http://www-nds.iaea.org/medical/monitor_
reactions.htmlS.
Kim, J.H., Park, H., Kim, S., Lee, J.S., Chun, K.S., 2006. Proton beam energy
measurement with the stacked Cu foil technique for medical radioisotope
production. J. Korean Phys. Soc. 48, 755–758.
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National Nuclear Decay Center, 2009. Nuclear reaction and decay Q-values (QCalc).
/http://www.nndc.bnl.gov/qcalc/S.
¨
Scholten, B., Qaim, S.M., Stocklin,
G., 1994. Radiochemical studies of proton
induced 7Be-emission reactions in the energy range of 40–100 MeV. Radiochim. Acta 65, 81–86.
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matter (SRIM code, version 2008.03). /http://www.srim.org/S.
Contents lists available at ScienceDirect
Applied Radiation and Isotopes
journal homepage: www.elsevier.com/locate/apradiso
A new and simple calibration-independent method for measuring the beam
energy of a cyclotron
Katherine Gagnon a,n, Mikael Jensen b, Helge Thisgaard b,1, Julia Publicover c,2, Suzanne Lapi c,3,
Steve A. McQuarrie a, Thomas J. Ruth c
a
Cross Cancer Institute, Edmonton PET Centre, University of Alberta, Edmonton, AB, Canada T6G 1Z2
Hevesy Laboratory, Risoe-DTU, Technical University of Denmark, Frederiksborgvej 399, DK-4000 Roskilde, Denmark
c
TRIUMF, 4004 Wesbrook Mall, Vancouver, BC, Canada V6T 2A3
b
a r t i c l e in fo
abstract
Article history:
Received 10 January 2010
Received in revised form
30 July 2010
Accepted 17 September 2010
This work recommends a new and simple-to-perform method for measuring the beam energy of an
accelerator. The proposed method requires the irradiation of two monitor foils interspaced by an energy
degrader. The primary advantage of the proposed method, which makes this method unique from
previous energy evaluation strategies that employ the use of monitor foils, is that this method is
independent of the detector efficiency calibration. This method was evaluated by performing proton
activation of natCu foils using both a cyclotron and a tandem Van de Graaff accelerator. The monitor foil
activities were read using a dose calibrator set to an arbitrary calibration setting. Excellent agreement
was noted between the nominal and measured proton energies.
& 2010 Elsevier Ltd. All rights reserved.
Keywords:
Cyclotron
Monitor reactions
Energy determination
Ionization chamber
1. Introduction
When used for medical radionuclide production, both new and
old cyclotrons need to have their beam energy checked periodically. This is not only part of good manufacturing practice and
quality assurance but is also necessary for optimising target yields
and minimising the radiation dose overhead of radionuclide
production. An example where such a validation is of particular
importance is when undesired by-products result from competing
energy-dependent reactions (e.g. production of 123I via the (p,2n)
reaction when producing 124I from 124Te). Although it is often
claimed by cyclotron operators that the energy of their machines
‘‘never change’’, were ‘‘locked at the factory’’ or were ‘‘carefully
determined at acceptance testing’’, from our experience, this is
not valid for the majority of present day negative ion cyclotrons.
The extraction of negative ion beams by a stripper foil can give
useful beam on targets even with substantial orbit centre offsets.
Changes in magnet shim or in distribution of the RF field along the
dees can cause the orbital centre to drift. Furthermore, the loss of
position calibration or damage to extractors and stripper foils can
also substantially affect the beam energy. While cyclotrons in
nuclear physics institutions often have analysing magnets with
well characterized energy definition, this diagnostic tool is not
feasible for most medical cyclotron configurations as the production targets sit more or less straight on the beam port with little or
no further collimation. As such, an off-line approach for evaluating the beam energy of a medical cyclotron is required.
For most applications the simple method of beam range
determination will not be accurate enough due to straggling. Long
stacks increase straggling, and it can be difficult by conventional
‘‘burn’’ methods to discriminate the Bragg peak end from thermal
damage. For this reason, we investigated a new, simple-toperform method for evaluating the cyclotron beam energy. By
using the universally available dose calibrator (a re-entrant ion
chamber used in every nuclear medicine facility), the proposed
method is sufficiently sensitive to achieve the necessary precision
of a few tenths of an MeV. Furthermore, the proposed method
requires neither energy nor efficiency calibration of the detector
system being used. The method works for an arbitrary dose
calibrator setting. The proposed method was extensively evaluated and tabulated for protons in the 11–19 MeV energy range,
but it should be straightforward to extend the general principle to
protons, deuterons and alphas of other energies.
n
Corresponding author. Tel.: + 1 780 432 8776; fax: + 1 780 432 8615.
E-mail address: [email protected] (K. Gagnon).
1
Present address: PET- and Cyclotron Unit, Nuclear Medicine Department,
Odense University Hospital, DK-5000 Odense, Denmark
2
Present address: University Health Network, Toronto, Canada
3
Present address: Mallinckrodt Institute of Radiology, Washington University,
St. Louis, MO, USA
0969-8043/$ - see front matter & 2010 Elsevier Ltd. All rights reserved.
doi:10.1016/j.apradiso.2010.09.012
2. Theory
Although beam monitor reactions have been extensively
published, evaluated and used for many years (see for example,
248
K. Gagnon et al. / Applied Radiation and Isotopes 69 (2011) 247–253
http://www-nds.iaea.org/medportal/ ‘‘monitor reactions’’), the
reliable use of these methods, at present, requires access to and
knowledge of a well calibrated detector system (typically an HPGe
gamma spectroscopy setup). When irradiating a single, thin foil,
the production of a radionuclide is given by
A ¼ nIsð1eltb Þ,
ð1Þ
where A is the activity of the nuclide at the end of bombardment
(EOB), n is the number of target nuclei per unit area, I is the proton
current (protons/second), s is the energy dependent crosssection, l is the decay constant for the nuclide and tb is the
bombardment time. Given that the cross-sections for the reaction
of interest are well characterized, then the beam energy may be
determined by measuring A and having an accurate knowledge
of the n, I, l and tb terms. Due to variations in the foil thickness
and/or beam current, an examination of the activity ratio of two
isotopes produced simultaneously via competing reactions
(i.e. (p,n) and (p,2n)) within a single foil can be beneficial
(Blessing et al., 1995; Scholten et al., 1994):
Aj
sj ð1elj tb Þ
¼
Ak
sk ð1elk tb Þ
ð2Þ
The primary drawback in evaluating the beam energy using (1)
or (2) is that both require absolute quantification of the produced
radioisotope activity. Incorrect or offset efficiency calibration for
the gamma detector in question can therefore seriously compromise the results.
As opposed to irradiating a single monitor foil, it has been
proposed earlier to use a stack of copper foils and then analyse
every single foil by high resolution gamma spectroscopy for the
isotopes 62Zn and 65Zn (Kim et al., 2006; Blessing et al., 1995;
Scholten et al., 1994). To overcome the need for gamma spectroscopy and high quality efficiency calibrations, this study suggests
the irradiation of two monitor foils of the same material
interspaced by an energy degrader (Fig. 1). By carefully choosing
both the monitor foil material and degrader thickness, the
differential activation of the two monitor foils may be used to
determine the beam energy. This effect is illustrated in Fig. 2a and
b for proton energies of 15.0 and 15.5 MeV incident on two 25 mm
copper foils which sandwich an 875 mm aluminum degrader. The
major advantage of examining the ratio of two identical isotopes
produced in the two foils (i.e. 63Zn/63Zn), as opposed to, for
example, the 63Zn/62Zn ratio resulting from proton irradiation of a
single copper monitor foil, is that all detector efficiency calibration requirements are eliminated. Furthermore, the exponential
factors in (2) will also cancel as lj ¼ lk for the proposed method:
Aj Foil1
sj Foil1
¼
Aj Foil2
sj Foil2
ð3Þ
Through careful selection of the energy degrader thickness,
this method can be used efficiently and with high precision.
Fig. 2. A comparison of the 63Zn activation for two 25 mm copper foils and an
875 mm aluminum degrader given incident proton energies of (a) 15.0 MeV and (b)
15.5 MeV. As noted, a small change in the incident energy can yield a measurable
change in the 63Zn activity ratio. Figures were produced using the IAEA
recommended cross-section data (IAEA, 2009) and the SRIM software package
(Ziegler et al., 2009).
Since this activity ratio may be predicted using well known
published recommended cross-section data and the SRIM software package (Ziegler et al., 2009), we have developed and
included a simple lookup table (Table 1) which may be used
universally for monitoring the proton energy given experimental
evaluation of the activity ratio.
3. Materials and methods
To evaluate the proposed method, this study measured the
Zn activity ratio produced during the proton irradiation of two
copper foils interspaced by an aluminum energy degrader. Initial
measurements were performed at the Edmonton PET Centre (EPC)
using a TR 19/9 negative ion variable energy cyclotron (Advanced
Cyclotron Systems Inc., Richmond, BC). A set of six additional
measurements were also performed using the tandem Van de
Graaff at Brookhaven National Lab (BNL) in New York. As the
incident proton energy is known with greater accuracy when
63
Fig. 1. The configuration of the two copper foils and aluminum energy degrader
irradiated in this experiment. When discussing the entrance and exit energies of
the copper foils, this refers to locations A and B, respectively, for foil #1 and C and
D, respectively, for foil #2. The above figure is not to scale—the copper foil
thicknesses have been exaggerated for the purpose of illustration.
249
K. Gagnon et al. / Applied Radiation and Isotopes 69 (2011) 247–253
Table 1
The recommended aluminum degrader thicknesses and second order curve fitting terms.
Aluminum thickness (lm)
Energy range (MeV)
Second order term A
First order term B
Constant term C
Expected activity ratio range
350
500
625
750
875
1000
1125
1250
1375
10.8–11.8
12.0–12.8
13.0–13.8
14.0–14.8
15.0–15.6
15.8–16.4
16.6–17.2
17.4–18.0
18.2–18.8
1.3811
0.7058
0.5352
0.5223
0.5254
0.7218
1.1060
2.1607
4.5682
6.8958
4.0449
3.1150
2.7947
2.5192
2.8021
3.3724
4.7938
7.3352
19.408
17.795
17.527
17.696
17.837
18.380
19.029
19.934
21.028
1.55–2.50
1.65–2.85
1.50–2.85
1.30–2.40
1.05–1.80
0.80–1.50
0.60–1.20
0.45–0.85
0.35–0.65
E (MeV) ¼ Ar2 + Br +C, where r is the 63Zn activity ratio between front and back copper foil.
The straggling and the energy loss of a nominal 25 mm aluminum vacuum window are included in the calculations. The energy calculated is the energy incident on this
vacuum foil.
using an electrostatic accelerator, as compared to a cyclotron, the
measurements at BNL were performed to serve as a further
validation of the proposed method.
3.1. Monitor foils
Copper foils were the preferred choice for evaluating the
proton energy for this study as the natCu(p,x)63Zn excitation
function is well characterized (IAEA, 2009), and copper foils of
sufficient quality and purity (Z99.99%) can be purchased from
many commercial suppliers (i.e. Alfa Aesar&, Goodfellows&, etc.).
As long as the monitor foils are kept relatively thin (i.e. r25 mm),
so as to minimize the finite energy loss through the foil, the actual
thickness of the foils is not of great importance as it may be
measured and corrected for. It should be noted however that all
recommended values given in this manuscript are based on the
use of 25 mm copper monitor foils. To minimize the foil-to-foil
variations in purity and thickness, and ensure that the two foils
are of equal thickness, it is essential that the two foils are cut from
the same manufactured sheet or roll. For improved accuracy over
a screw micrometer, the foil thicknesses in this study (both of
aluminum and copper) were found by weight determination
using a 10.0 cm 10.0 cm square of foil. Although the thickness
variations across the foils were not measured, we have investigated the impact of small variations in the average thickness by
utilizing both the measured and nominal foil thicknesses to
determine the proton energy.
3.2. Degrader thickness
As noted in Fig. 3, as the degrader thickness is increased, an
increased range in the 63Zn expected activity ratio is observed
(therefore increasing the sensitivity of the technique). Striving to
achieve a reasonably thick aluminum degrader, it is immediately
noted that one thickness will not be suitable for the entire
11–19 MeV energy range of interest. For example, if we consider a
degrader which is sufficiently thick to drop 10 MeV given
Ep ¼17 MeV, such a degrader would certainly be too thick to allow
for activation of the second copper foil given an incident energy of
11 MeV. As such, we have proposed a set of recommended
thicknesses (Table 1) broken into nine energy windows between
the range of 11 and 19 MeV. Consequently, to use the recommended data of Table 1, it is assumed that there is a rough idea
(within approximately 1 MeV) of the proton energy in question.
In developing the set of recommended degrader thicknesses of
Table 1, the goal was to utilize (as noted above) a reasonably thick
degrader for increased sensitivity. What makes a thickness
‘‘reasonable’’? If the degrader is too thick, there will be a large
difference in the proton energy between the entrance and exit
Fig. 3. The expected 63Zn activity ratio calculated from (3) as a function of proton
energy for aluminum degraders ranging in thickness from 650–850 mm.
surface of the second copper foil. Due to large non-linearities in
the proton stopping power at low energies, a large difference in
energy across the foil is undesired as the technique becomes
increasingly susceptible to both thickness non-uniformities and
errors in the thickness measurements. For this reason, the
recommended degrader thicknesses were selected, so that the
average proton exit energy of the second copper foil was expected
to be no less than 5.2 MeV (determined using simulations in SRIM
(Ziegler et al., 2009)). This value of 5.2 MeV was selected for two
reasons. Firstly, this value is 1.0 MeV above the 63Cu(p,n)63Zn
reaction threshold (NNDC, 2009). Thus, despite any energy
straggling, all protons should have sufficient energy, so that the
possibility exists for them to undergo a reaction within the foil.
Next, for a 25 mm copper foil, this minimum exit energy ensures
an average energy drop of no greater than 1 MeV between the
entrance and exit surface of the second copper foil. We considered
this 1 MeV energy drop acceptable, as the IAEA recommended
cross-sections (reported in steps of 0.1 MeV) for the natCu(p,x)63Zn
reaction are highly linear (R2 40.98) over any floating 1 MeV
interval in the energy range of interest for the second copper foil.
3.3. Expected activity ratio
To evaluate the proton energy from the measured activity
ratio, a plot of proton energy as a function of the expected activity
250
K. Gagnon et al. / Applied Radiation and Isotopes 69 (2011) 247–253
Table 2
The nominal proton irradiation energies and nominal/measured foil thicknesses.
Nominal incident energy Thickness of aluminum vacuum window and
degrader (lm)
a,b
10.9
11.1a,b
11.3a,b
11.6a,b
11.8a,b
13.8b
14.6b
15.4b
16.2b
17.0b
17.8b
18.6b
11.00c
13.50c
16.00c
18.00c
Blind (12.0-12.8)c
Blind (14.0-14.8)c
a
b
c
Thickness of each copper monitor foil Thickness of aluminum energy
(lm)
degrader (lm)
Nominal
Measured
Nominal
Measured
Nominal
Measured
400
400
400
400
400
25
25
25
25
25
25
25
25
25
25
25
25
25
403.3
403.3
403.3
403.3
403.3
25.5
25.5
25.5
25.5
25.5
25.5
25.5
25.5
25.5
25.5
25.5
25.5
25.5
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
23.7
23.7
23.7
23.7
23.7
23.7
23.7
23.7
23.7
23.7
23.7
23.7
25.6
25.6
25.6
25.6
25.6
25.6
350
350
350
350
350
625
750
875
1000
1125
1250
1375
350
625
1000
1250
500
750
352.2
352.2
352.2
352.2
352.2
628.0
750.6
878.2
1000.8
1128.4
1251.0
1378.6
352.2
628.0
1000.8
1251.0
500.4
750.6
Energy achieved using additional aluminum degrader as minimum extractable energy in TR-19/9 is approximately 13.7 MeV.
Cyclotron.
Tandem.
ratio is required. In calculating the expected activity ratio, it is
first necessary to determine the effective energy within the two
copper monitor foils for a given incident energy. This was
achieved by simulating 1000 ions in the TRIM module of the
SRIM software package (Ziegler et al., 2009). As the copper foils
were of finite thickness, the effective energy within the foil was
taken as the average between the entrance and exit foil energy.
These effective energies were then employed to evaluate the
corresponding effective cross-sections within the two monitor
foils. This was achieved using polynomial interpolation of the
IAEA recommended cross-section data for the natCu(p,x)63Zn
reaction (IAEA, 2009). Finally, the activity ratio was then
calculated from Eq. (3) using the effective 63Zn cross-sections
of the two copper foils. It should be noted that error in the
magnitude of the IAEA cross-section data will not impact the
results as it is the shape of the excitation function which dictates
the cross-section ratio.
For purpose of comparison, the expected activity ratios were
determined by simulating the proton energy both using (i) the
nominal foil thicknesses reported by the manufacturer, and
(ii) the measured foil thicknesses. It is important to note that in
addition to the Cu/Al/Cu foil sandwich, a 25 mm aluminum
vacuum window is employed as part of the TR 19/9 cyclotron
target system. As this vacuum foil was included in all energy
simulations, the energy calculated using the data from Table 1
represents the energy incident on this vacuum foil.
measured energy (determined via HPGe spectroscopy methods)
had been noted previously for a thorough study of the extractor
foil in question (Avila-Rodriguez et al., 2009), the proton energies
evaluated in this experiment were compared directly with the
nominal cyclotron energy.
A total of six proton irradiations were performed using the
tandem at BNL. Of these, two of the irradiations energies were
energy-blinded. Since the choice of the aluminum energy
degrader thickness requires some idea as to the irradiation
energy, it was decided prior to irradiation that one of the blind
studies would be performed in the 12.0–12.8 MeV energy range
while the other would be performed in the 14.0–14.8 MeV energy
range. For all BNL irradiations (300 s), the foils were mounted
normal to the incident beam with the current ( 400 nA)
measured just prior to irradiation using a Faraday cup. In contrast
to the cyclotron configuration at the EPC, the BNL target station
did not require the use of an aluminum vacuum window.
Nevertheless, to eliminate the need for applying corrections to
the data in Table 1, an additional 25 mm aluminum foil was
installed prior to the Cu/Al/Cu sandwich so as to mimic the
presence of a vacuum window for the BNL irradiations. The
nominal proton energies along with the nominal and measured
aluminum and copper thicknesses employed for both the EPC and
BNL irradiations are reported in Table 2.
3.5. Foil measurements
3.4. Irradiation parameters
A total of twelve irradiations were performed on the TR 19/9
cyclotron. All foils were positioned normal to the incident beam
and electrically isolated from the target nose-piece. Foils were
irradiated for 300 s with approximately 1 mA of proton beam
current. In order to validate the proposed method in the 11 MeV
range, an aluminum degrader (375 mm nominal thickness) was
installed adjacent to the vacuum window as the TR 19/9 cyclotron
has a minimum proton extraction energy of 13.7 MeV. As good
agreement between the nominal cyclotron energy and the
When irradiating natural copper foils up to 19 MeV, three
radionuclide products require examination: 62Zn (t1/2 ¼9.186 h),
63
Zn (t1/2 ¼38.47 min), and 63Cu (t1/2 ¼9.67 min). Although 65Zn
(t1/2 ¼243.66 days) is also produced during the irradiation of
copper foil, given the irradiation conditions and assuming activity
assays are performed within 3 h post-EOB, the activity of 65Zn
will be negligible (o 1%) with respect to the large 63Zn activity
produced. Discrimination of the three isotopes only by their halflives is possible, but somewhat time consuming. An examination
of the published cross-sections for these reactions (Ghoshal, 1950;
IAEA, 2009) suggests that if we allow the 9.7 min half life 62Cu
K. Gagnon et al. / Applied Radiation and Isotopes 69 (2011) 247–253
contribution to decay, the 63Zn will dominate the dose calibrator
readings for proton energies up to approximately 16 MeV. For this
reason, we investigated the possibility of using a combination
method whereby for lower proton energies the ratio of the dose
calibrator readings at a single time point could be used, while for
higher proton energies, half-life discrimination of the measured
readings would be necessary.
All foil radioactivities were read out using CapintecTM CRC15PET and CRC-15W dose calibrators at the EPC and BNL,
respectively. As the proposed method is independent of the
calibration setting, an arbitrary setting of 100 was employed. All
irradiated foils in this study were individually measured in the
dose calibrator at approximately 20, 30, 40, 50, 60, 80, 100, 120,
150 and 180 min post-EOB, with the measurement times recorded
to the nearest second.
251
residuals were eliminated (Fig. 4). Using this fitting method,
the ratio of the C1 coefficients obtained using (6) and (4)
was taken as the ratio of 63Zn activity between first and second
copper foils.
3.6. Calculating the measured activity ratio
Although the single time point evaluation of the 63Zn activity
ratio was expected to be applicable only for the lower energy
irradiations, the 63Zn activity ratio was calculated for all
irradiations by directly using the dose calibrator readings
obtained at the 1 and 2 h time points. These time points were
investigated, as opposed to the initial 20 min measurements, in
order to allow for 62Cu decay. As the foil readings for a given
irradiation were typically measured 1–2 min apart, a corresponding 1–2 min 63Zn decay correction was applied, so that the
readings coincided with a single time point. It is not necessary to
decay correct the readings back to EOB as this factor will be the
same for both foils, and therefore will cancel when examining the
activity ratio.
To discriminate the three isotopes by their half-lives and
acquire the isotope-corrected 63Zn activity ratio, the ten serial
time point readings underwent the following described fitting
procedure.
Since the proton energy within the second foil was always
expected to be below the threshold for production of 62Cu
(11.0 MeV) and 62Zn (13.5 MeV) (NNDC, 2009), the ten dose
calibrator readings R for this foil were fit using the Curve Fitting
Toolbox in MATLAB& and the following fitting function:
l63 Z n t
RðtÞ ¼ C1 e
þB
Fig. 4. A plot of the residuals for the decay curve fitting of the ten dose-calibrator
readings for the first copper foil for the 18.6 MeV cyclotron irradiation. Plot A was
obtained using the fitting function described in (5), while B was obtained from the
fitting function of (6).
ð4Þ
where t represents the time elapsed since EOB and l63 Zn
represents the decay constant for 63Zn. The C1 coefficient was
taken to represent the 63Zn contribution at EOB, while B was
taken to represent any background activity. An original attempt at
fitting the dose calibrator readings for the first foil was performed
using the following double exponential:
l63 Z n t
RðtÞ ¼ C1 e
l62 C u t
þ C2 e
þB
ð5Þ
where C1 and C2 were fit parameters. These coefficients were
taken to represent the EOB 63Zn and 62Cu contributions,
respectively. Since the background term was not expected to
vary greatly between the two foils, the B term in (5) was not a
fitting parameter, but instead set to the value obtained for the
second foil described by (4). As this fitting procedure led to
undesired systematic trends in the residuals, the data for the first
foil were instead described by
l63 Z n t
RðtÞ ¼ C1 e
l62 C u t
þ C2 e
l62 Z n t
þC3 e
þB
ð6Þ
63
where C1, C2 and C3 were fit parameters used to describe the Zn,
62
Cu and 62Zn contribution at EOB, respectively. As before,
the background B term was taken as the value obtained by
fitting the activity readings of the second foil. By adopting this
latter fitting procedure, the systematic trends observed in the
Fig. 5. A sample plot of the proton energy, E, as a function of the expected 63Zn
ratio, r. The plot is made with the coefficients from Table 1, and assumes a nominal
350 mm aluminum foil and two nominal 25 mm copper monitor foils. The
straggling and energy loss of a nominal 25 mm aluminum vacuum window are
included in the calculations.
252
K. Gagnon et al. / Applied Radiation and Isotopes 69 (2011) 247–253
Table 3
The proton energies evaluated in this experiment using the
Nominal incident energy
10.9a
11.1a
11.3a
11.6a
11.8a
13.8a
14.6a
15.4a
16.2a
17.0a
17.8a
18.6a
11.00b
13.50b
16.00b
18.00b
Blind (12.0–12.8) 12.3b
Blind (14.0–14.8) 14.4b
a
b
63
Zn activity ratio.
Curve-fit energy measurement
1 h energy measurement
2 h energy measurement
Nominal thickness
Measured thickness
Nominal thickness
Measured thickness
Nominal thickness
Measured thickness
10.9
11.2
11.4
11.7
11.9
13.9
14.6
15.5
16.4
17.2
17.9
18.5
10.96
13.45
16.10
18.17
12.32
14.42
10.9
11.2
11.4
11.6
11.9
13.8
14.6
15.5
16.4
17.2
17.9
18.5
11.00
13.48
16.12
18.18
12.36
14.43
10.9
11.2
11.4
11.6
11.9
13.8
14.5
15.4
16.2
16.9
17.5
18.1
10.93
13.47
15.92
17.56
12.32
14.36
10.9
11.2
11.4
11.6
11.9
13.8
14.5
15.4
16.2
16.9
17.4
18.1
10.98
13.51
15.94
17.59
12.36
14.37
10.9
11.2
11.5
11.7
12.0
14.0
14.6
15.5
16.2
17.0
17.5
18.1
10.97
13.49
16.00
17.69
12.36
14.42
10.9
11.2
11.4
11.7
12.0
13.9
14.6
15.5
16.2
16.9
17.5
18.1
11.01
13.53
16.02
17.71
12.40
14.44
Cyclotron.
Tandem.
4. Results and discussion
A sample plot of the proton energy as a function of the
expected 63Zn ratio (calculated from (3)) is given in Fig. 5 for a
nominal 25 mm aluminum vacuum window, a nominal 350 mm
aluminum energy degrader and two nominal 25 mm copper
monitor foils. This data was fit using a second order polynomial.
The 350 mm aluminum degrader is the thickness recommended in
this study for evaluation of proton energies in the 10.8–11.8 MeV
range. Assuming 25 mm copper monitor foils, and the presence of
a 25 mm aluminum vacuum foil, a list of suggested aluminum
proton degrader thicknesses for a wide range of energies is
presented in Table 1. Since the plots of the expected 63Zn ratios for
the other recommended aluminum foil thicknesses are similar in
appearance to Fig. 5, we have omitted the respective figures in
this publication. The coefficients to the second order polynomial
fits for each of these have however been included in Table 1. Since
a second order polynomial will always have two activity ratios
which give rise to a given energy—only one of which is physically
meaningful, it should be noted that Table 1 also includes the
corresponding range of activity ratios which are expected for the
energy range of interest.
Table 3 summarizes the energies evaluated using (i) the half-life
discriminated curve-fit based 63Zn ratio, (ii) the single 1 h time point
63
Zn ratio and (iii) the single 2 h time point 63Zn ratio. Table 3 also
includes both the energies evaluated assuming the nominal foil
thicknesses (i.e. the second order polynomial data from Table 1), as
well as the energies evaluated using the measured foil thicknesses.
When examining the blinded experiments (12.3 and 14.4 MeV) all
measurements agreed within 0.1 MeV of the nominal values.
Excellent agreement between the measured and nominal energies
was also noted regardless of the strategy employed for determining
the 63Zn ratio for proton energies up to 17.0 MeV. For this reason, we
conclude that the half-life discrimination using the 63Zn curvefitting method is only essential when the proton energy is greater
than 17.0 MeV. We also note that the minor variations from the
nominal foil thicknesses used in this study resulted in only minor
variations (r0.1 MeV) in the evaluated energy. This suggests that
small thickness variations across a foil should similarly have a minor
impact on the evaluated energy. It should be noted that caution
must be exercised when using the values from Table 1 if the
measured foil thicknesses vary by an amount greater than those
employed for this work.
5. Conclusions
In this work, we have recommended and evaluated a new and
simple-to-perform method for measuring the beam energy of a
cyclotron. This method was developed with the cyclotron
production of medical isotopes in mind, where the ability to
easily verify the beam energy to an accuracy of a few tenths of a
MeV is of great importance. The proposed method has been found
to provide an accurate determination of proton energies in the
11–19 MeV range without the use of complex analysis methods or
sophisticated equipment. To facilitate the adoption of this
technique into routine evaluation of the cyclotron beam energy,
we have included a list of recommended nominal aluminum
degrader thicknesses as well as a list of the corresponding curve
fit data for evaluation of the proton energy using the measured
63
Zn activity ratio. Application of the proposed method to the
monitoring of deuteron energies is a topic we plan to explore
further in the near future.
Acknowledgements
The authors wish to thank the following individuals for their
assistance in the irradiations: Drs. Chuck Carlson, Michael
Schueller and David Schlyer for helpful discussions and organizing
the experiments at BNL. This work was supported through Grants
from The Canadian Natural Sciences and Engineering Research
Council (TJR, KG, JP, SL).
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