- Email: [email protected]
Emittance measurements from the LLUMC proton accelerator
Nuclear Instruments and Methods in Physics Research B 241 (2005) 702–707 www.elsevier.com/locate/nimb
Emittance measurements from the LLUMC proton accelerator G. Coutrakon a, G.H. Gillespie b, J. Hubbard a, E. Sanders a
a,*
Loma Linda University Medical Center, 11234 Anderson St., Rm. B121, Loma Linda, CA 92354, United States b G. H. Gillespie Associates, Inc., P.O. Box 2961, Del Mar, CA 92014, United States Available online 24 August 2005
Abstract A new method of calculating beam emittances at the extraction point of a particle accelerator is presented. The technique uses the optimization programs NPSOL and MINOS developed at Stanford University in order to determine the initial values of beam size, divergence and correlation parameters (i.e. beam sigma matrix, rij) that best fit measured beam parameters. These rij elements are then used to compute the Twiss parameters a, b, and the phase space area, e, of the beam at the extraction point. Beam size measurements in X and Y throughout the transport line were input to the optimizer along with the magnetic elements of bends, quads, and drifts. The rij parameters were optimized at the acceleratorÕs extraction point by finding the best agreement between these measured beam sizes and those predicted by TRANSPORT. This expands upon a previous study in which a ‘‘trial and error’’ technique was used instead of the optimizer software, and which yielded similar results. The Particle Beam Optics Laboratory (PBO LabTM) program used for this paper integrates particle beam optics and other codes into a single intuitive graphically-based computing environment. This new software provides a seamless interface between the NPSOL and MINOS optimizer and TRANSPORT calculations. The results of these emittance searches are presented here for the eight clinical energies between 70 and 250 MeV currently being used at LLUMC. Ó 2005 Elsevier B.V. All rights reserved. PACS: 83.10.Rs; 29.27.Fh; 29.27.Bd; 41.85.Qg; 41.85.Ew; 41.85.Lc; 29.27.Eg; 41.85.Ja; 29.27.Ac; 41.85.Ar; 87.56. v Keywords: Proton therapy; Beam optics; TRANSPORT; PBO LabTM optimizer; NPSOL; MINOS
1. Introduction
*
Corresponding author. Tel.: +1 909 558 4217; fax: +1 909 558 4083. E-mail address: [email protected] (E. Sanders).
A layout of the LLUMC proton therapy facility is shown in Fig. 1. The beam transport line, called the switchyard, is shown with dipole and quadrupole magnets located between the accelerator and treatment rooms. The goal of this paper is
0168-583X/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2005.07.119
G. Coutrakon et al. / Nucl. Instr. and Meth. in Phys. Res. B 241 (2005) 702–707
703
Fig. 1. The layout of the LLUMC proton therapy facility.
to determine the horizontal and vertical emittances exiting the accelerator at the extraction septum for each of the clinical energies being used. This is required to model the beam properties correctly in the switchyard and at the patientÕs target area. In a previous publication [1], we adjusted the emittance parameters by ‘‘trial and error’’ using TRANSPORT [2] until a good visual agreement with measured beam sizes was obtained. This was quite laborious and not as precise as the use of an objective function to minimize the difference between measured beam sizes and TRANSPORT calculations. The PBO Lab implementation of the NPSOL [3] and MINOS [4] optimizers can rapidly change the initial beam properties, and recalculate the beam size at selected points and then compare them to the measured values. (PBO LabTM is available from AccelSoft Inc. of San Diego, California, www.ghga.com/accelsoft.) Based on the resulting value of the objective function, the optimizer can change the initial beam parameters in a prescribed way, and then re-run TRANSPORT and recalculate the objective function until a minimum value is found. The technique has been addressed in a separate paper [5]. It allows one to find optimum emittances for a large number of energies very quickly once the beam size measurements in the switchyard are acquired. After this problem is solved, the problem of varying quadrupole strengths in the beam line to meet beam size constraints at the patientÕs position and achromatic conditions to increase beam position stability due to magnetic dipole power supply fluctuations can be met.
2. Method and materials Beam size measurements were obtained using multi-wire proportional chambers and parallel plate ion chambers with strip segmentation. Both types of detectors have 2 mm spacing between wire or strip readout and have separate readout for X and Y. The beam sizes have an approximately Gaussian shape and so the r.m.s. width of the beam can be calculated as FWHM/2.36. The r.m.s. beam sizes were entered into the optimizer as well as their locations in the beam line. Optimization of initial beam parameters was performed separately for the horizontal and vertical at each beam energy. The objective function was defined as OF = R(XC(i) XM(i))2, where XC(i) is the r.m.s. beam size calculated from TRANSPORT, XM(i) is the r.m.s. beam size measurement, and the summation is over all beam size measurements at all detector locations, i = 1, N. The optimizer software seeks to minimize the objective function by varying the initial sigma matrix elements (equivalent to the initial Twiss parameters a, b, and the emittance, e (see figure on p. 44 of [2], available at http://www.slac.stanford.edu/ cgi-wrap/getdoc/slac-r-530-zWholeThing.pdf) at the extraction septum and then using TRANSPORT to calculate beam sizes at the points of measurement. Dividing the OF by the square of the measurement errors, r2, and the number of degrees of freedom, we obtain the reduced chi-squared, v2 = OF/(r2(N m)). The error in each beam size measurement is taken to be ±1 mm based on the wire (or strip) spacing of 2 mm. Here, m = 3 and
704
G. Coutrakon et al. / Nucl. Instr. and Meth. in Phys. Res. B 241 (2005) 702–707
refers to the number of fitted parameters in the optimization. In total, the research room beam line has 12 beam profile detectors: the Gantry 1 beam line has 8, Gantry 2 has 11 and Gantry 3 has 12. For each beam energy, beam size measurements were taken for two beam lines: the research room beam line and a treatment room beam line which uses that energy for patient treatments. A novel feature of this software is that it can optimize emittance parameters using multiple beam lines simultaneously. The extracted beam emittance, for the same accelerator settings, remains the same for a particular energy regardless of the destination. This allows one to use more beam data in a single optimization to get a result applicable to all beam lines being considered. Beam size data from only two rooms was used due to the limited time available for this study. Typically, 20–25 beam size measurements were used to determine the emittances for X and Y for each energy.
Fig. 2. TRANSPORT predictions using the optimized emittance results and measured beam sizes for 100 MeV in Gantry 2 at 270° gantry angle. The dashed and solid lines show simulation results, while the squares and triangles display measurements.
3. Results Optimization results for two beam lines and two energies are shown in Fig. 2 and Fig. 3. These figures show the beam envelopes, or sizes, from the accelerator to the isocenter of two of the gantries. The accumulated beam length simply denotes the distance along the beam line from the acceleratorÕs extraction point. Note that the length of the beam line is longer for Gantry 2 than for Gantry 1 as illustrated in Fig. 1. The last 18 m contain the gantry (or rotating beam line) with two 45° bending magnets bending in one plane, and two 135° bending magnets which bend the beam in an orthogonal direction to form a ‘‘cork screw’’ shape beam line. Eight quadrupole magnets are distributed on each gantry as documented in an earlier publication [1]. The 90° bend in each figure is located approximately 25 m upstream of the gantry isocenter. Two horizontal beam size measurements near the end of the research room beam line resulted
Fig. 3. TRANSPORT predictions using the optimized emittance results and measured beam sizes for 200 MeV in Gantry 1 at 270° gantry angle. The dashed and solid lines show simulation results, while the squares and triangles display measurements.
G. Coutrakon et al. / Nucl. Instr. and Meth. in Phys. Res. B 241 (2005) 702–707
in poor fits to the data at all energies. For this reason they were excluded from the emittance determinations in this paper. (The reason for the discrepancy with these two detectors has not yet been determined.) Except for these points, the agreement between measured data and TRANSPORT calculations using optimized emittances appears quite good. The tables below summarize the results of the optimized Twiss parameters and the reduced v2. Generally, a reduced v2 of order unity or less is considered to be a good fit. Table 1 shows the results of the fits of a and b in X and Y for the nine energies studied while Fig. 4 shows the emittances versus energy for the same data set. For comparison, the values of bx and by in the ring are bx = 6 m and by = 2 m at the extraction septum for all energies. ax and ay are expected to be 0 at the extraction point. These results are comparable to the results of the previous study
705
[1] in which ‘‘trial and error’’ was used instead of the optimizer software, with data from only one room (Gantry 2). For example, the results of the previous study for 250 MeV were ex = 0.3p mmmrad and ey = 1.5p mm-mrad, whereas the emittance values obtained using the optimizer are ex = 0.2p mm-mrad and ey = 1.6p mm-mrad for 250 MeV. It is clear that the emittance data in Fig. 4 does not follow a smooth variation with beam energy as expected from theory [6], but the erratic variation in the data may be due to limitations in the accuracy of the beam data or the fact that the optimized parameters may not have a unique solution. To test this hypothesis, we constrained the emittances at some of the energies to lie on the fitted line and allowed a and b to vary in the optimization process. The results for five energies are shown in Table 2.
Table 1 Twiss parameters and reduced v2 obtained for nine energies using the optimizer software with TRANSPORT Energy (MeV)
Beam lines
70 100 126 149 155 186 200 225 250
RR RR RR RR RR RR RR RR RR
and and and and and and and and and
G2 G2 G1 G2 G1 G2 G1 G2 G2
ax 1.2 0.32 0.29 0.38 0.18 0.00 0.05 0.25 0.58
bx (m)
v2
ay
by (m)
v2
Assumed r.m.s. momentum spread (%)
5.8 6.1 11.0 6.2 9.1 10.9 8.5 7.2 12.0
1.2 0.23 0.30 0.75 0.29 0.28 0.17 0.25 0.44
0.14 0.31 0.66 0.37 0.71 0.15 0.62 0.75 0.59
2.7 2.6 2.3 2.3 1.7 1.2 2.0 1.8 2.1
1.2 0.64 1.2 1.0 1.1 1.1 0.48 0.95 0.19
0.0135 0.0115 0.0103 0.0105 0.0093 0.0086 0.0083 0.0080 0.0075
Fig. 4. Emittance values versus energy in x (left graph) and y (right graph), with best-fit lines superimposed. Emittances generally vary inversely with the beam energy [6]. The emittances were obtained from NPSOL as described in the text.
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G. Coutrakon et al. / Nucl. Instr. and Meth. in Phys. Res. B 241 (2005) 702–707
Table 2 Values of optimized Twiss parameters (a and b) and reduced v2 after emittances are constrained to the lines of Fig. 4 Energy (MeV)
Beam lines
100 126 149 186 250
RR RR RR RR RR
and and and and and
G2 G1 G2 G2 G2
ax
bx (m)
v2
ay
by (m)
v2
0.30 0.49
2.5 1.7
1.2 1.3
0.10
1.2
1.2
0.17
7.0
0.43
0.70
5.2
0.81
0.82
19.7
0.88
For the cases in which the v2 in Table 1 was greater than 0.65, there was very little change (<10%) in the v2 when the emittance was constrained to the lines in Fig. 4. This indicates that the emittance can change as much as 30–40% with only a small increase in the objective function. When looking at the graphs of the beam envelopes, the two cases are indistinguishable and the predicted beam size at the target varies less than 15%. In other cases, when the original fit had a v2 < 0.65, the v2 generally doubled when the emittances were constrained to the lines in Fig. 4.
However, even then, the beam envelope is quite similar to what is found from the original optimization when viewed on a graph and the beam sizes at the target (isocenter of gantry) are very similar. Fig. 5 shows an example for the 100 MeV data when the emittances are constrained to the lines of Fig. 4. In this case, the v2 in both X and Y has doubled when the emittances were constrained, but the resulting beam envelopes are very similar to the original optimization.
4. Conclusions
Fig. 5. TRANSPORT predictions using the emittance given by the best-fit line of Fig. 4 and the optimized a and b of Table 2. The measured beam sizes are for 100 MeV in Gantry 2 at 270° gantry angle. The dashed and solid lines show simulation results, while the squares and triangles display measurements.
The emittance optimizer of the PBO Lab software has shown great value in saving many days and even months in finding the best emittances for beam studies at the LLUMC proton accelerator facility. The agreement between TRANSPORT calculations of beam sizes using optimized emittance parameters and measurements is quite good. The derived emittances carry some uncertainties due to the fact that there are three fitting parameters and one of them, the emittance, can be constrained while letting the other two vary to find an optimized solution. In general, emittances should decrease as the particle energies increase. The optimizer found this trend when the data was fitted to a straight line, but the individual data points show a lot of variation from the lines. We have attempted to explain these emittance variations as a result of measurement errors coupled with an objective function which is not very sensitive to 30 or 40% changes in emittances. The result is that the beam size at the target is not extremely sensitive to this parameter and can be compensated by an alternative choice in the other two parameters.
G. Coutrakon et al. / Nucl. Instr. and Meth. in Phys. Res. B 241 (2005) 702–707
References [1] G. Coutrakon, J. Hubbard, P. Koss, E. Sanders, M. Panchal, AIP Conference Proceedings No. 680, 2003, p. 1116. [2] D.C. Carey, K.L. Brown, F. Rothacker, SLAC-R-530 (1998) 316. [3] P.E. Gill, W. Murray, M.A. Saunders, M.H. Wright, Stanford University Department of Operations Research, Report. SOL 86-2R, 1988, p. 44.
707
[4] B.A. Murtagh, M.A. Saunders, Stanford University Department of Operations Research, Report. SOL 83-20R, 1998, p. 145. [5] G.H. Gillespie, O.V. Voronkova, G.B. Coutrakon, J.E. Hubbard, E. Sanders, in: Proceedings of the 2004 European Particle Accelerator Conference, Lucerne, Switzerland, 2004, p. 2188. [6] D.A. Edwards, M.J. Syphers, An Introduction to the Physics of High Energy Accelerators, John Wiley and Sons, 1993, p. 85.
Emittance measurements from the LLUMC proton accelerator G. Coutrakon a, G.H. Gillespie b, J. Hubbard a, E. Sanders a
a,*
Loma Linda University Medical Center, 11234 Anderson St., Rm. B121, Loma Linda, CA 92354, United States b G. H. Gillespie Associates, Inc., P.O. Box 2961, Del Mar, CA 92014, United States Available online 24 August 2005
Abstract A new method of calculating beam emittances at the extraction point of a particle accelerator is presented. The technique uses the optimization programs NPSOL and MINOS developed at Stanford University in order to determine the initial values of beam size, divergence and correlation parameters (i.e. beam sigma matrix, rij) that best fit measured beam parameters. These rij elements are then used to compute the Twiss parameters a, b, and the phase space area, e, of the beam at the extraction point. Beam size measurements in X and Y throughout the transport line were input to the optimizer along with the magnetic elements of bends, quads, and drifts. The rij parameters were optimized at the acceleratorÕs extraction point by finding the best agreement between these measured beam sizes and those predicted by TRANSPORT. This expands upon a previous study in which a ‘‘trial and error’’ technique was used instead of the optimizer software, and which yielded similar results. The Particle Beam Optics Laboratory (PBO LabTM) program used for this paper integrates particle beam optics and other codes into a single intuitive graphically-based computing environment. This new software provides a seamless interface between the NPSOL and MINOS optimizer and TRANSPORT calculations. The results of these emittance searches are presented here for the eight clinical energies between 70 and 250 MeV currently being used at LLUMC. Ó 2005 Elsevier B.V. All rights reserved. PACS: 83.10.Rs; 29.27.Fh; 29.27.Bd; 41.85.Qg; 41.85.Ew; 41.85.Lc; 29.27.Eg; 41.85.Ja; 29.27.Ac; 41.85.Ar; 87.56. v Keywords: Proton therapy; Beam optics; TRANSPORT; PBO LabTM optimizer; NPSOL; MINOS
1. Introduction
*
Corresponding author. Tel.: +1 909 558 4217; fax: +1 909 558 4083. E-mail address: [email protected] (E. Sanders).
A layout of the LLUMC proton therapy facility is shown in Fig. 1. The beam transport line, called the switchyard, is shown with dipole and quadrupole magnets located between the accelerator and treatment rooms. The goal of this paper is
0168-583X/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2005.07.119
G. Coutrakon et al. / Nucl. Instr. and Meth. in Phys. Res. B 241 (2005) 702–707
703
Fig. 1. The layout of the LLUMC proton therapy facility.
to determine the horizontal and vertical emittances exiting the accelerator at the extraction septum for each of the clinical energies being used. This is required to model the beam properties correctly in the switchyard and at the patientÕs target area. In a previous publication [1], we adjusted the emittance parameters by ‘‘trial and error’’ using TRANSPORT [2] until a good visual agreement with measured beam sizes was obtained. This was quite laborious and not as precise as the use of an objective function to minimize the difference between measured beam sizes and TRANSPORT calculations. The PBO Lab implementation of the NPSOL [3] and MINOS [4] optimizers can rapidly change the initial beam properties, and recalculate the beam size at selected points and then compare them to the measured values. (PBO LabTM is available from AccelSoft Inc. of San Diego, California, www.ghga.com/accelsoft.) Based on the resulting value of the objective function, the optimizer can change the initial beam parameters in a prescribed way, and then re-run TRANSPORT and recalculate the objective function until a minimum value is found. The technique has been addressed in a separate paper [5]. It allows one to find optimum emittances for a large number of energies very quickly once the beam size measurements in the switchyard are acquired. After this problem is solved, the problem of varying quadrupole strengths in the beam line to meet beam size constraints at the patientÕs position and achromatic conditions to increase beam position stability due to magnetic dipole power supply fluctuations can be met.
2. Method and materials Beam size measurements were obtained using multi-wire proportional chambers and parallel plate ion chambers with strip segmentation. Both types of detectors have 2 mm spacing between wire or strip readout and have separate readout for X and Y. The beam sizes have an approximately Gaussian shape and so the r.m.s. width of the beam can be calculated as FWHM/2.36. The r.m.s. beam sizes were entered into the optimizer as well as their locations in the beam line. Optimization of initial beam parameters was performed separately for the horizontal and vertical at each beam energy. The objective function was defined as OF = R(XC(i) XM(i))2, where XC(i) is the r.m.s. beam size calculated from TRANSPORT, XM(i) is the r.m.s. beam size measurement, and the summation is over all beam size measurements at all detector locations, i = 1, N. The optimizer software seeks to minimize the objective function by varying the initial sigma matrix elements (equivalent to the initial Twiss parameters a, b, and the emittance, e (see figure on p. 44 of [2], available at http://www.slac.stanford.edu/ cgi-wrap/getdoc/slac-r-530-zWholeThing.pdf) at the extraction septum and then using TRANSPORT to calculate beam sizes at the points of measurement. Dividing the OF by the square of the measurement errors, r2, and the number of degrees of freedom, we obtain the reduced chi-squared, v2 = OF/(r2(N m)). The error in each beam size measurement is taken to be ±1 mm based on the wire (or strip) spacing of 2 mm. Here, m = 3 and
704
G. Coutrakon et al. / Nucl. Instr. and Meth. in Phys. Res. B 241 (2005) 702–707
refers to the number of fitted parameters in the optimization. In total, the research room beam line has 12 beam profile detectors: the Gantry 1 beam line has 8, Gantry 2 has 11 and Gantry 3 has 12. For each beam energy, beam size measurements were taken for two beam lines: the research room beam line and a treatment room beam line which uses that energy for patient treatments. A novel feature of this software is that it can optimize emittance parameters using multiple beam lines simultaneously. The extracted beam emittance, for the same accelerator settings, remains the same for a particular energy regardless of the destination. This allows one to use more beam data in a single optimization to get a result applicable to all beam lines being considered. Beam size data from only two rooms was used due to the limited time available for this study. Typically, 20–25 beam size measurements were used to determine the emittances for X and Y for each energy.
Fig. 2. TRANSPORT predictions using the optimized emittance results and measured beam sizes for 100 MeV in Gantry 2 at 270° gantry angle. The dashed and solid lines show simulation results, while the squares and triangles display measurements.
3. Results Optimization results for two beam lines and two energies are shown in Fig. 2 and Fig. 3. These figures show the beam envelopes, or sizes, from the accelerator to the isocenter of two of the gantries. The accumulated beam length simply denotes the distance along the beam line from the acceleratorÕs extraction point. Note that the length of the beam line is longer for Gantry 2 than for Gantry 1 as illustrated in Fig. 1. The last 18 m contain the gantry (or rotating beam line) with two 45° bending magnets bending in one plane, and two 135° bending magnets which bend the beam in an orthogonal direction to form a ‘‘cork screw’’ shape beam line. Eight quadrupole magnets are distributed on each gantry as documented in an earlier publication [1]. The 90° bend in each figure is located approximately 25 m upstream of the gantry isocenter. Two horizontal beam size measurements near the end of the research room beam line resulted
Fig. 3. TRANSPORT predictions using the optimized emittance results and measured beam sizes for 200 MeV in Gantry 1 at 270° gantry angle. The dashed and solid lines show simulation results, while the squares and triangles display measurements.
G. Coutrakon et al. / Nucl. Instr. and Meth. in Phys. Res. B 241 (2005) 702–707
in poor fits to the data at all energies. For this reason they were excluded from the emittance determinations in this paper. (The reason for the discrepancy with these two detectors has not yet been determined.) Except for these points, the agreement between measured data and TRANSPORT calculations using optimized emittances appears quite good. The tables below summarize the results of the optimized Twiss parameters and the reduced v2. Generally, a reduced v2 of order unity or less is considered to be a good fit. Table 1 shows the results of the fits of a and b in X and Y for the nine energies studied while Fig. 4 shows the emittances versus energy for the same data set. For comparison, the values of bx and by in the ring are bx = 6 m and by = 2 m at the extraction septum for all energies. ax and ay are expected to be 0 at the extraction point. These results are comparable to the results of the previous study
705
[1] in which ‘‘trial and error’’ was used instead of the optimizer software, with data from only one room (Gantry 2). For example, the results of the previous study for 250 MeV were ex = 0.3p mmmrad and ey = 1.5p mm-mrad, whereas the emittance values obtained using the optimizer are ex = 0.2p mm-mrad and ey = 1.6p mm-mrad for 250 MeV. It is clear that the emittance data in Fig. 4 does not follow a smooth variation with beam energy as expected from theory [6], but the erratic variation in the data may be due to limitations in the accuracy of the beam data or the fact that the optimized parameters may not have a unique solution. To test this hypothesis, we constrained the emittances at some of the energies to lie on the fitted line and allowed a and b to vary in the optimization process. The results for five energies are shown in Table 2.
Table 1 Twiss parameters and reduced v2 obtained for nine energies using the optimizer software with TRANSPORT Energy (MeV)
Beam lines
70 100 126 149 155 186 200 225 250
RR RR RR RR RR RR RR RR RR
and and and and and and and and and
G2 G2 G1 G2 G1 G2 G1 G2 G2
ax 1.2 0.32 0.29 0.38 0.18 0.00 0.05 0.25 0.58
bx (m)
v2
ay
by (m)
v2
Assumed r.m.s. momentum spread (%)
5.8 6.1 11.0 6.2 9.1 10.9 8.5 7.2 12.0
1.2 0.23 0.30 0.75 0.29 0.28 0.17 0.25 0.44
0.14 0.31 0.66 0.37 0.71 0.15 0.62 0.75 0.59
2.7 2.6 2.3 2.3 1.7 1.2 2.0 1.8 2.1
1.2 0.64 1.2 1.0 1.1 1.1 0.48 0.95 0.19
0.0135 0.0115 0.0103 0.0105 0.0093 0.0086 0.0083 0.0080 0.0075
Fig. 4. Emittance values versus energy in x (left graph) and y (right graph), with best-fit lines superimposed. Emittances generally vary inversely with the beam energy [6]. The emittances were obtained from NPSOL as described in the text.
706
G. Coutrakon et al. / Nucl. Instr. and Meth. in Phys. Res. B 241 (2005) 702–707
Table 2 Values of optimized Twiss parameters (a and b) and reduced v2 after emittances are constrained to the lines of Fig. 4 Energy (MeV)
Beam lines
100 126 149 186 250
RR RR RR RR RR
and and and and and
G2 G1 G2 G2 G2
ax
bx (m)
v2
ay
by (m)
v2
0.30 0.49
2.5 1.7
1.2 1.3
0.10
1.2
1.2
0.17
7.0
0.43
0.70
5.2
0.81
0.82
19.7
0.88
For the cases in which the v2 in Table 1 was greater than 0.65, there was very little change (<10%) in the v2 when the emittance was constrained to the lines in Fig. 4. This indicates that the emittance can change as much as 30–40% with only a small increase in the objective function. When looking at the graphs of the beam envelopes, the two cases are indistinguishable and the predicted beam size at the target varies less than 15%. In other cases, when the original fit had a v2 < 0.65, the v2 generally doubled when the emittances were constrained to the lines in Fig. 4.
However, even then, the beam envelope is quite similar to what is found from the original optimization when viewed on a graph and the beam sizes at the target (isocenter of gantry) are very similar. Fig. 5 shows an example for the 100 MeV data when the emittances are constrained to the lines of Fig. 4. In this case, the v2 in both X and Y has doubled when the emittances were constrained, but the resulting beam envelopes are very similar to the original optimization.
4. Conclusions
Fig. 5. TRANSPORT predictions using the emittance given by the best-fit line of Fig. 4 and the optimized a and b of Table 2. The measured beam sizes are for 100 MeV in Gantry 2 at 270° gantry angle. The dashed and solid lines show simulation results, while the squares and triangles display measurements.
The emittance optimizer of the PBO Lab software has shown great value in saving many days and even months in finding the best emittances for beam studies at the LLUMC proton accelerator facility. The agreement between TRANSPORT calculations of beam sizes using optimized emittance parameters and measurements is quite good. The derived emittances carry some uncertainties due to the fact that there are three fitting parameters and one of them, the emittance, can be constrained while letting the other two vary to find an optimized solution. In general, emittances should decrease as the particle energies increase. The optimizer found this trend when the data was fitted to a straight line, but the individual data points show a lot of variation from the lines. We have attempted to explain these emittance variations as a result of measurement errors coupled with an objective function which is not very sensitive to 30 or 40% changes in emittances. The result is that the beam size at the target is not extremely sensitive to this parameter and can be compensated by an alternative choice in the other two parameters.
G. Coutrakon et al. / Nucl. Instr. and Meth. in Phys. Res. B 241 (2005) 702–707
References [1] G. Coutrakon, J. Hubbard, P. Koss, E. Sanders, M. Panchal, AIP Conference Proceedings No. 680, 2003, p. 1116. [2] D.C. Carey, K.L. Brown, F. Rothacker, SLAC-R-530 (1998) 316. [3] P.E. Gill, W. Murray, M.A. Saunders, M.H. Wright, Stanford University Department of Operations Research, Report. SOL 86-2R, 1988, p. 44.
707
[4] B.A. Murtagh, M.A. Saunders, Stanford University Department of Operations Research, Report. SOL 83-20R, 1998, p. 145. [5] G.H. Gillespie, O.V. Voronkova, G.B. Coutrakon, J.E. Hubbard, E. Sanders, in: Proceedings of the 2004 European Particle Accelerator Conference, Lucerne, Switzerland, 2004, p. 2188. [6] D.A. Edwards, M.J. Syphers, An Introduction to the Physics of High Energy Accelerators, John Wiley and Sons, 1993, p. 85.