- Email: [email protected]
Ionization beam-profile monitor at HIMAC
Nuclear Instruments and Methods in Physics Research A 459 (2001) 390}397
Ionization beam-pro"le monitor at HIMAC T. Honma *, H.Y. Ogawa, Y. Sano, K. Noda , E. Takada , S. Yamada National Institute of Radiological Sciences, 4-9-1 Anagawa, Inage-ku, Chiba 263-8555, Japan Accelerator Engineering Corporation, 2-13-1 Konakadai, Inage-ku, Chiba 263-0043, Japan Received 10 July 2000; received in revised form 30 August 2000; accepted 30 August 2000
Abstract A prototype non-destructive beam-pro"le monitor employing tandem-type MCPs has been designed and tested at HIMAC. The monitor can measure the vertical beam pro"le of a circulating ion beam in the synchrotron. In a series of tests, however, it was found that the monitor had a defect in the accuracy of the measured pro"les. It was caused by an electric "eld distortion in the work area. The electric "eld was improved so as to create a uniform equipotential distribution with the aid of a 3D-"eld simulation code. The "eld-shaping electrodes were replaced to longer ones, and the applied voltages of each electrode were changed to the optimum values. The monitor has been successfully used for studies of electron cooling as well as monitoring the beam under normal-mode operation in the HIMAC synchrotron. 2001 Elsevier Science B.V. All rights reserved. PACS: 29.27.Fh; 87.56 Keywords: Beam-pro"le monitor; Non-destructive; Residual-gas; Electric "eld; MCP
1. Introduction HIMAC [1], as a heavy-ion medical accelerator, has been used for clinical trials of cancer therapy since June, 1994. More than 775 patients have been treated with carbon beams in the energy range from 290 to 400 MeV/u by February 2000. As a part of the development programs at HIMAC, an electron cooler [2] has been constructed and installed in the synchrotron for basic studies of heavy-ion therapy. In connection with the
* Corresponding author. Tel.: #81-43-251-2111-6851; fax: #81-43-251-1840.. E-mail address: honma}[email protected] (T. Honma).
construction of the electron cooler, a non-destructive beam monitor has been required to observe the circulating beam pro"le accurately during the cooling process, and to study the transverse cooling mechanisms. A useful technique for non-destructive beam diagnostics is to utilize the ionization in the residual gas by the circulating beam. The ions created by collisions are moved toward a micro-channel plate (MCP) by an external electric "eld perpendicular to the beam direction. This type of monitor has been successfully used at many accelerator facilities for a heavy-ion synchrotron, storage ring and beam-transport line [3}5]. In order to study a residual gas ionization beam pro"le monitor (RGPM), a prototype monitor was designed and has been tested at the HIMAC synchrotron. It can measure the vertical beam pro"le
0168-9002/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 0 0 ) 0 1 0 2 5 - 1
T. Honma et al. / Nuclear Instruments and Methods in Physics Research A 459 (2001) 390}397
391
Fig. 1. Cross-section of the RGPM and a block diagram of the read-out circuit; (1) tandem MCPs, (2) base-plate (BP), (3) top-plate (TP), (4) "eld-shaping electrodes (FB1}FB5) in the order of increasing voltage by PSa divided by resistors. The drift "eld is parallel to the y-axis.
of the circulating beam in the synchrotron. In tests of the RGPM, however, some unexpected behaviors were obtained concerning the measured pro"les. It was presumed to arise from the e!ect of an electric "eld distortion in the work area. Some investigations of the electric "eld property were conducted and a few improvements were made to correct it with aid of a three-dimensional (3D) "eld-simulation code [6]. This paper describes the work concerning those improvements as well as some test results of the RGPM.
2. Prototype monitor A front view of the RGPM used to measure the vertical beam pro"le is illustrated in Fig. 1 together with a block diagram of the read-out circuits. An electric "eld is applied perpendicular to the beam axis, which accelerate the positive residual gas ions created by the beam toward the tandem-type MCPs (50 mm;8 mm). In the present design, the maximum work area of the monitor is 180 mm;75 mm, which is su$ciently large for the maximum aperture of the HIMAC beam to be 120 cm;50 cm at injection for the horizontal and vertical direction, respectively. A "eld of about 50 V/mm is produced by two parallel electrodes placed on both sides of the beam pass, and a set of
2-arrays of equally spaced 5-stair electrodes. The length of the electrodes is 70 mm, measured along with the beam direction. A position-sensitive anode consists of 28 strips, having a width of 1.6 mm and a spacing of 0.2 mm etched on a printed-circuit board, which is mounted just behind the MCPs. All of those components are equipped in a cylindrical stainless-steel vacuum chamber having an inner diameter of 200 mm. Each anode strip is connected to a charge-integration circuit [7] having three -mode assembled switches and a capacitor of 1000 pF. The integration time can be changed by controlling the switching time during remote operation, while the output-signal level form the circuits is obviously proportional to the integration time, as can be seen in Fig. 2. One of the advantages of this signal read-out system is the ability to calibrate the gain balance for the each read-out circuit by the irradiation of ultra-violet light onto the surface of the MCP through a quartz window of the vacuum chamber. An additional set of electrodes was also equipped about 50 cm downstream from the RGPM to compensate for small de#ections of the circulating beam caused by the "eld of the RGPM. To estimate the number of ions produced by collisions, the energy-loss rate for a single particle passing through a material was calculated by using the Bethe}Bloch formula [8]. For a carbon particle, an energy of 290 MeV/u and a vacuum
392
T. Honma et al. / Nuclear Instruments and Methods in Physics Research A 459 (2001) 390}397
Fig. 2. Calibration curve for the charge integration time vs. output signal level for the read-out circuit.
pressure of 1;10\ Torr composed of H in the residual gas are assumed. Because the maximum energy transfer in a single collision (W ) is cal culated to be 0.73 MeV, the energy-loss rate (dE/dx) is calculated as 1.8;10\ MeV/cm with a mean excitation potential of I"19 eV. When 1;10 pps incident particles are circulating in the synchrotron, the total number of ion-pairs is estimated to be 4;10 pps. In this case, the mean energy of 35 eV to create an ion-pair for the H and the e!ective length of 8 mm for the detection length of the MCPs are take into account. If a set of the tandem-type MCPs is operated with a gain of 5;10, the total anode current should expected to be 28 nA.
3. Reliability of RGPM Because the monitor is operated by an indirect measurement, it requires great care for the reliability of the observation pro"les. The measurement errors are mainly caused by (a) the electric "eld produced by the circulating beam, (b) the thermal motion of the residual gas molecules, (c) the resolution of the detector (MCP) itself and (d) the readout electronics circuit, as reported by Ref. [3}5]. In the following, the item (a) and (b) as well as an additional source of error caused by the electric "eld distortion are described for discussions. In the case of a high-density beam, the error caused by (a) should be considered because the force due to the radial electric "eld a!ects the
trajectories of the ions. For a beam intensity of 1;10 pps with a Gaussian density-distribution circulating in the ring, the radial electric "eld strength [4] created by the beam is approximately 0.1 V/mm for a beam size of "1 mm, where is the rms beam width. It would be worth seriously conditioning such a small beam-size, though it is negligibly small for the beam under normal-mode operation in the HIMAC, because the beam size is typically more than 10 mm, even for an intensity of 3;10 pps. Due to utilization of the ionization of residual gas in this type of monitor, the error caused by (b) cannot be eliminated, principally. At room temperature, the kinetic energy of = is calculated to be approximately 13 meV, where the mean transitionally Brownian and isotropic motion of the residual gas molecule were taken into consideration. To investigate the error due to thermal motion as well as by the electric "eld, the trajectories of the ions were calculated numerically using simple equations described in Appendix A with 2-D transverse coordinates (x, y) to the beam direction, as is indicated in Fig. 1. In an ideal case in which the electric "eld components E (x, y)"0 for the lateral direction V and E (x, y)"E for the parallel direction to the W W ion drift are satis"ed in the work area, the maximum lateral displacement x due to the thermal motion at the initial ejection angle of 903 is represented from the Eqs. (A.1) and (A.2) in Appendix A as
x "
4= y . q E W
(1)
Assuming an E of 50 V/mm and a drift length (y) W of 80 mm in the RGPM, the rms value () of the lateral displacement is calculated to be about 0.2 mm in Gaussian distribution. Another source of error caused by an inhomogeneity of the electric "eld, however, cannot be ignored under certain circumstances. For example, at the beginning of tests for the RGPM in the synchrotron ring, some unexpected behavior has been observed concerning the measured pro"les: the measured pro"les changed their widths, and underwent a peak shift depending on varying the collection-"eld strength. In order to examine its
T. Honma et al. / Nuclear Instruments and Methods in Physics Research A 459 (2001) 390}397
Fig. 3. Comparison between the measured beam size by the RGPM and the real beam size.
questionable behavior, the RGPM was set in the high-energy beam transport line, and the measured of pro"les were compared with the pro"les by another monitor, which was a type of Multi Wire Proportional Chamber (MWPC) [7] pro"le monitor having an accuracy of 0.5 mm, though destructive. Those tests were performed to change the vertical beam size by varying the "eld strength of the quadrupole magnets located 5 m upstream from the RGPM. As results of the test, di!erent beam sizes were detected on the two monitors, and the beam sizes by the RGPM were relatively small compared with the other ones, as can be seen in Fig. 3. In order to investigate such an error of the RGPM, the 3D-"eld simulator was used to analyze the electric "eld properties, although it was a uniform equipotential distribution simulated by a 2Done. As a result, curved equipotential distributions, like convex surfaces, were obtained in the work area, which means that the "eld potentials were relatively low in the middle of the work area. Hence, the large lateral "eld component acts strongly on the drifting ions by a focusing force in the collecting "eld.
4. Field property In general, perfectly #at equipotentials distributed in the region of interest are obtained in the
393
Fig. 4. Ratio of the "eld distortion; (E /E ) as a function of LF V W for various lateral displacements of x"6, 10 and 14 mm at y"0 for "xed LS of 50 mm.
case of symmetrically arranged electrodes, like in the method of image-charges, and by a continuous voltage divider forming two sides in in"nite space. However, it is considerably di$cult to make such a uniform "eld in practical applications due to the limited space and non-symmetrical applied voltages to the electrodes. Therefore, the following assumption is set to design the electric "eld that, the lateral displacement; x caused by the "eld distor# tion E (x, y) should be less than the maximum V displacement by the thermal motion: (x ) with the relation E 4((x ) /y)E in the region of V W interest. A simple model similar to the RGPM with equally divided voltages applied to the electrodes was used to study the electric "eld properties by the aid of the 3D-simulator. The following geometrical quantities would be extracted for the discussions: (a) length of "eld-shaping electrodes, LF; (b) space between the electrodes and chamber wall, LS; and (c) shape of the chamber wall. Firstly, (a) and (b) strongly a!ect the potential distributions in the work area as is well understood from the result of "eld simulations. Fig. 4 shows the results of calculations of the relation between various LF and the ratio of the "eld inhomogeneity: (E /E ) at three di!erent lateral positions for a "xed V W LS of 50 mm, where E and E are the "eld compoV W nents at y"0 and the mid-plane (z"0) of the
394
T. Honma et al. / Nuclear Instruments and Methods in Physics Research A 459 (2001) 390}397
Fig. 5. Ratio of the "eld distortion; (E /E ) as a function of the V W LS for various lateral displacements of x"6, 10 and 14 mm at y"0 for "xed LF of 100 mm.
beam direction in the work area. In Fig. 5 the relation between the various LS and the ratio of the "eld inhomogenities is also shown at a "xed LF of 100 mm. They are closely related to the leakage #ux of the electric "eld between the electrodes and the chamber wall having the usual earth potential. Secondly, the e!ect by (c) is also closely connected with the LS because the leakage #uxes take a more complicate form. As a result, a longer LF and a larger LS are better, to create more uniform equipotential in the work area. In addition, it would be necessary to adjust the divided voltages applied to the electrodes in order to compensate for any unsymmetrical leakage #uxes.
5. Improvement of RGPM Based on the electric "eld studies mentioned above, the RGPM was improved to create more uniform equipotential distributions in the work area. Since the "eld distortions in the work area depend on the length of the "eld-shaping electrodes, the electrodes were extended from 70 to 100 mm in length. However, it was not su$cient for the required uniformity of the electric "eld. Because the maximum length of the electrodes were restricted by the space of the chamber wall along the beam direction, and because there is an unsymmetrical leakage #ux near to the highest positive electrode, which is close to the chamber wall. In order
Fig. 6. Adjusted voltage distributing the electrodes. The voltages of the uppermost two electrodes, FB5 and TP, were required to be higher than equally divided voltages.
to compensate for this problem, the applied voltage distributed on the electrodes was also adjusted based on the calculated result with the simulation code. It turns out that the applied voltages for the uppermost two electrodes were required to be higher than the equally divided voltages, as is shown in Fig. 6. The equipotential distribution in the "nal result of the "eld simulation for the RGPM is shown in Fig. 7. The electric "eld strength parallel to the ion drift of E (x, y) and the lateral "eld W components of E (x, y) were about 50 V/mm and V less than 0.5 V/mm in the work area, respectively. The trajectories for the ions, which have an initial kinetic energy W of 13 meV with variable ejection angles, were numerically calculated on those "eld distributions using the equations (see in Appendix A). The measurement errors using the terms of FWHM were estimated to be less than 0.6 and 1.1 mm in the case of beam sizes of 10 and 15 mm, respectively.
6. Performance of RGPM After these improvements, the RGPM was installed again in the ring, and has been tested. Fig. 8
T. Honma et al. / Nuclear Instruments and Methods in Physics Research A 459 (2001) 390}397
395
Fig. 7. Equipotential distribution in x}y plane perpendicular to the beam direction at z"0 after improvement of the RGPM.
shows an example of the measured beam pro"les during electron cooling for a 6 MeV/u carbon beam with an intensity of 3;10 ppp. Those pro"les were obtained under the condition of a 500 ms interval and an integration time of 50 ms with an ampli"cation of 4;10 for the tandem-type MCPs. The results of the measurement show that a reduction of the transverse emittance for the circulating beam has been clearly observed due to the electron cooling. In this case, the vertical emittance ( ) was 4 reduced to about one-order, i.e. from 28 to 2.7 mm mrad calculated by a simple relation of "x / , where a betatron amplitude ( ) at the 4 4 4 4 position of interest is estimated at 11 m by the lattice design, and x is the measured beam size for 4 the vertical direction, respectively. The consecutive variations of the pro"les for the carbon beam from injection to before extraction were also observed under normal-mode operation of the ring, where the carbon beam is accelerated from 6 to 230 MeV/u, respectively. The typical measured pro"les are shown in Fig. 9, with the repetition cycle
Fig. 8. Measured beam pro"les in a cooling test: (a) electron o!, (b) at 500 ms after electron on, with carbon beam of 6 MeV/u.
Fig. 9. Measured beam pro"les through normal-mode operation in the synchrotron. Pro"les (a) during injection, (b) during acceleration and (c) before extraction for a carbon beam of 6}230 MeV/u.
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T. Honma et al. / Nuclear Instruments and Methods in Physics Research A 459 (2001) 390}397
for the data-taking being 10 Hz, an integration time of 50 ms and an intensity of 6;10 ppp. It was observed that the beam width was decreasing with increasing its energy, due to adiabatic damping. In the measurements, the ampli"cation for the tandem-type MCPs was 5;10, and the signal conversion factor was 50 nA}0.25 V at 50 ms of the integration time. The noise level of the measurement system was less than 20 mV. The vacuum pressure adjacent to the monitor was about 1;10\ Torr. It is comprised mainly 40% H , 20% H O, 10% CO#N , and a few percent of CO and CH measured by a Q-mass "lter in the ring.
7. Conclusion A prototype non-destructive beam pro"le monitor employing MCPs has been tested at HIMAC. In a series of the tests some unexpected pro"les were observed. This was caused by an inhomogeneous electric-"eld distribution in the work area. To improve the RGPM, the length of the "eld-shaping electrodes was reformed to longer ones, and the divided voltages applied to the electrodes were optimized, together with the aid of a 3-D "eld simulator. As a result, more uniform potential distributions were obtained. In order to estimate the measurement accuracy of the RGPM, the ion trajectories were calculated numerically by using calculated potentials. As a result, it was calculated to be less than 0.6 and 1.1 mm within beam pro"les of 10 and 15 mm at FWHM, respectively. The RGPM has been successfully used to measure the pro"les in the electron-cooling tests and the usually used therapy beam. A new monitor with higher resolution has recently been designed to accurately measure the cooled circulating beam. The monitor will measure the beam pro"les in the both transverse plans for the horizontal and vertical directions.
discussions. The authors are also grateful to the sta! of Accelerator Engineering Corporation (AEC) for their helpful cooperation. This work was performed as a part of Research Project with Heavy-ion at NIRS-HIMAC.
Appendix A. Equation of motion for ion in electric 5eld The trajectory of ion created by ionization in the transverse x}y coordinate system is derived in non-relativistic motion as follows: q dx " E (x, y) dt M V
(A.1)
dy q " E (x, y) dt M W
(A.2)
where q and M are charge and mass of the ion, E (x, y) and E (x, y) are the electric "eld compoV W nents for the lateral and the parallel to the ion drift, respectively. These two equations can be solved by numerically using calculated electric "eld of E (x, y) and V E (x, y) on the suitable grid points with the time W t as the independent variable. In a simple case, if the uniform electric "elds E (x, y)"E and E (x, y)"E satisfy the region V V W W and initial conditions are given, the Eqs. (A.1) and (A.2) are represented by:
q 2= sin t x,(x!x )" E t# V 2M M
(A.3)
q 2= cos t y,(y!y )" E t# W 2M M
(A.4)
where x and y are the displacements at time t respect to the initial position x and y of the ion, W and are its initial kinetic energy and ejection angle.
Acknowledgements The authors would like to express their thanks to Dr. F. Soga and members of the Division of Accelerator Physics and Engineering at NIRS for helpful
References [1] S. Yamada, Proceedings of the 1995 Particle Accelerator Conference, USA, p. 9.
T. Honma et al. / Nuclear Instruments and Methods in Physics Research A 459 (2001) 390}397 [2] K. Noda, T. Murakami, E. Takada, M. kanazawa, T. Honma, S. yamada, T. Nagafuchi, I. Watanabe, H. Kozu, S. Shibuya, K. Ohtomo, S. Sasaki, Nucl. Instr. and Meth. A 441 (1999) 159}166. [3] B. Hochadel, F. albrecht, M. Grieser, D. Schwaim, E. Szmola, A. Wolf, Nucl. Instr. and Meth. A 343 (1994) 401}414. [4] W.S. Graves, Nucl. Instr. and Meth. A 364 (1995) 19}26.
397
[5] R. Anne, Y. Georget, R. Hue, C. Tribouillard, J.L. Vignet, Nucl. Instr. and Meth. A 329 (1993) 21}28. [6] `MAXWELL 3Da Field simulator, version 4.1, Ansoft corporation. [7] M. Torikoshi, K. Noda, E. Takada, T. Kanai, S. Yamada, H. Ogawa, K. Okumura, K. Narita, K. Ueda, M. Mizobata, Nucl. Instr. and Meth. A 435 (1999) 326}338. [8] W.R. Leo, Techniques for Nuclear and particle Physics Experiments, Springer, Berlin, 1987, p. 24.
Ionization beam-pro"le monitor at HIMAC T. Honma *, H.Y. Ogawa, Y. Sano, K. Noda , E. Takada , S. Yamada National Institute of Radiological Sciences, 4-9-1 Anagawa, Inage-ku, Chiba 263-8555, Japan Accelerator Engineering Corporation, 2-13-1 Konakadai, Inage-ku, Chiba 263-0043, Japan Received 10 July 2000; received in revised form 30 August 2000; accepted 30 August 2000
Abstract A prototype non-destructive beam-pro"le monitor employing tandem-type MCPs has been designed and tested at HIMAC. The monitor can measure the vertical beam pro"le of a circulating ion beam in the synchrotron. In a series of tests, however, it was found that the monitor had a defect in the accuracy of the measured pro"les. It was caused by an electric "eld distortion in the work area. The electric "eld was improved so as to create a uniform equipotential distribution with the aid of a 3D-"eld simulation code. The "eld-shaping electrodes were replaced to longer ones, and the applied voltages of each electrode were changed to the optimum values. The monitor has been successfully used for studies of electron cooling as well as monitoring the beam under normal-mode operation in the HIMAC synchrotron. 2001 Elsevier Science B.V. All rights reserved. PACS: 29.27.Fh; 87.56 Keywords: Beam-pro"le monitor; Non-destructive; Residual-gas; Electric "eld; MCP
1. Introduction HIMAC [1], as a heavy-ion medical accelerator, has been used for clinical trials of cancer therapy since June, 1994. More than 775 patients have been treated with carbon beams in the energy range from 290 to 400 MeV/u by February 2000. As a part of the development programs at HIMAC, an electron cooler [2] has been constructed and installed in the synchrotron for basic studies of heavy-ion therapy. In connection with the
* Corresponding author. Tel.: #81-43-251-2111-6851; fax: #81-43-251-1840.. E-mail address: honma}[email protected] (T. Honma).
construction of the electron cooler, a non-destructive beam monitor has been required to observe the circulating beam pro"le accurately during the cooling process, and to study the transverse cooling mechanisms. A useful technique for non-destructive beam diagnostics is to utilize the ionization in the residual gas by the circulating beam. The ions created by collisions are moved toward a micro-channel plate (MCP) by an external electric "eld perpendicular to the beam direction. This type of monitor has been successfully used at many accelerator facilities for a heavy-ion synchrotron, storage ring and beam-transport line [3}5]. In order to study a residual gas ionization beam pro"le monitor (RGPM), a prototype monitor was designed and has been tested at the HIMAC synchrotron. It can measure the vertical beam pro"le
0168-9002/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 0 0 ) 0 1 0 2 5 - 1
T. Honma et al. / Nuclear Instruments and Methods in Physics Research A 459 (2001) 390}397
391
Fig. 1. Cross-section of the RGPM and a block diagram of the read-out circuit; (1) tandem MCPs, (2) base-plate (BP), (3) top-plate (TP), (4) "eld-shaping electrodes (FB1}FB5) in the order of increasing voltage by PSa divided by resistors. The drift "eld is parallel to the y-axis.
of the circulating beam in the synchrotron. In tests of the RGPM, however, some unexpected behaviors were obtained concerning the measured pro"les. It was presumed to arise from the e!ect of an electric "eld distortion in the work area. Some investigations of the electric "eld property were conducted and a few improvements were made to correct it with aid of a three-dimensional (3D) "eld-simulation code [6]. This paper describes the work concerning those improvements as well as some test results of the RGPM.
2. Prototype monitor A front view of the RGPM used to measure the vertical beam pro"le is illustrated in Fig. 1 together with a block diagram of the read-out circuits. An electric "eld is applied perpendicular to the beam axis, which accelerate the positive residual gas ions created by the beam toward the tandem-type MCPs (50 mm;8 mm). In the present design, the maximum work area of the monitor is 180 mm;75 mm, which is su$ciently large for the maximum aperture of the HIMAC beam to be 120 cm;50 cm at injection for the horizontal and vertical direction, respectively. A "eld of about 50 V/mm is produced by two parallel electrodes placed on both sides of the beam pass, and a set of
2-arrays of equally spaced 5-stair electrodes. The length of the electrodes is 70 mm, measured along with the beam direction. A position-sensitive anode consists of 28 strips, having a width of 1.6 mm and a spacing of 0.2 mm etched on a printed-circuit board, which is mounted just behind the MCPs. All of those components are equipped in a cylindrical stainless-steel vacuum chamber having an inner diameter of 200 mm. Each anode strip is connected to a charge-integration circuit [7] having three -mode assembled switches and a capacitor of 1000 pF. The integration time can be changed by controlling the switching time during remote operation, while the output-signal level form the circuits is obviously proportional to the integration time, as can be seen in Fig. 2. One of the advantages of this signal read-out system is the ability to calibrate the gain balance for the each read-out circuit by the irradiation of ultra-violet light onto the surface of the MCP through a quartz window of the vacuum chamber. An additional set of electrodes was also equipped about 50 cm downstream from the RGPM to compensate for small de#ections of the circulating beam caused by the "eld of the RGPM. To estimate the number of ions produced by collisions, the energy-loss rate for a single particle passing through a material was calculated by using the Bethe}Bloch formula [8]. For a carbon particle, an energy of 290 MeV/u and a vacuum
392
T. Honma et al. / Nuclear Instruments and Methods in Physics Research A 459 (2001) 390}397
Fig. 2. Calibration curve for the charge integration time vs. output signal level for the read-out circuit.
pressure of 1;10\ Torr composed of H in the residual gas are assumed. Because the maximum energy transfer in a single collision (W ) is cal culated to be 0.73 MeV, the energy-loss rate (dE/dx) is calculated as 1.8;10\ MeV/cm with a mean excitation potential of I"19 eV. When 1;10 pps incident particles are circulating in the synchrotron, the total number of ion-pairs is estimated to be 4;10 pps. In this case, the mean energy of 35 eV to create an ion-pair for the H and the e!ective length of 8 mm for the detection length of the MCPs are take into account. If a set of the tandem-type MCPs is operated with a gain of 5;10, the total anode current should expected to be 28 nA.
3. Reliability of RGPM Because the monitor is operated by an indirect measurement, it requires great care for the reliability of the observation pro"les. The measurement errors are mainly caused by (a) the electric "eld produced by the circulating beam, (b) the thermal motion of the residual gas molecules, (c) the resolution of the detector (MCP) itself and (d) the readout electronics circuit, as reported by Ref. [3}5]. In the following, the item (a) and (b) as well as an additional source of error caused by the electric "eld distortion are described for discussions. In the case of a high-density beam, the error caused by (a) should be considered because the force due to the radial electric "eld a!ects the
trajectories of the ions. For a beam intensity of 1;10 pps with a Gaussian density-distribution circulating in the ring, the radial electric "eld strength [4] created by the beam is approximately 0.1 V/mm for a beam size of "1 mm, where is the rms beam width. It would be worth seriously conditioning such a small beam-size, though it is negligibly small for the beam under normal-mode operation in the HIMAC, because the beam size is typically more than 10 mm, even for an intensity of 3;10 pps. Due to utilization of the ionization of residual gas in this type of monitor, the error caused by (b) cannot be eliminated, principally. At room temperature, the kinetic energy of = is calculated to be approximately 13 meV, where the mean transitionally Brownian and isotropic motion of the residual gas molecule were taken into consideration. To investigate the error due to thermal motion as well as by the electric "eld, the trajectories of the ions were calculated numerically using simple equations described in Appendix A with 2-D transverse coordinates (x, y) to the beam direction, as is indicated in Fig. 1. In an ideal case in which the electric "eld components E (x, y)"0 for the lateral direction V and E (x, y)"E for the parallel direction to the W W ion drift are satis"ed in the work area, the maximum lateral displacement x due to the thermal motion at the initial ejection angle of 903 is represented from the Eqs. (A.1) and (A.2) in Appendix A as
x "
4= y . q E W
(1)
Assuming an E of 50 V/mm and a drift length (y) W of 80 mm in the RGPM, the rms value () of the lateral displacement is calculated to be about 0.2 mm in Gaussian distribution. Another source of error caused by an inhomogeneity of the electric "eld, however, cannot be ignored under certain circumstances. For example, at the beginning of tests for the RGPM in the synchrotron ring, some unexpected behavior has been observed concerning the measured pro"les: the measured pro"les changed their widths, and underwent a peak shift depending on varying the collection-"eld strength. In order to examine its
T. Honma et al. / Nuclear Instruments and Methods in Physics Research A 459 (2001) 390}397
Fig. 3. Comparison between the measured beam size by the RGPM and the real beam size.
questionable behavior, the RGPM was set in the high-energy beam transport line, and the measured of pro"les were compared with the pro"les by another monitor, which was a type of Multi Wire Proportional Chamber (MWPC) [7] pro"le monitor having an accuracy of 0.5 mm, though destructive. Those tests were performed to change the vertical beam size by varying the "eld strength of the quadrupole magnets located 5 m upstream from the RGPM. As results of the test, di!erent beam sizes were detected on the two monitors, and the beam sizes by the RGPM were relatively small compared with the other ones, as can be seen in Fig. 3. In order to investigate such an error of the RGPM, the 3D-"eld simulator was used to analyze the electric "eld properties, although it was a uniform equipotential distribution simulated by a 2Done. As a result, curved equipotential distributions, like convex surfaces, were obtained in the work area, which means that the "eld potentials were relatively low in the middle of the work area. Hence, the large lateral "eld component acts strongly on the drifting ions by a focusing force in the collecting "eld.
4. Field property In general, perfectly #at equipotentials distributed in the region of interest are obtained in the
393
Fig. 4. Ratio of the "eld distortion; (E /E ) as a function of LF V W for various lateral displacements of x"6, 10 and 14 mm at y"0 for "xed LS of 50 mm.
case of symmetrically arranged electrodes, like in the method of image-charges, and by a continuous voltage divider forming two sides in in"nite space. However, it is considerably di$cult to make such a uniform "eld in practical applications due to the limited space and non-symmetrical applied voltages to the electrodes. Therefore, the following assumption is set to design the electric "eld that, the lateral displacement; x caused by the "eld distor# tion E (x, y) should be less than the maximum V displacement by the thermal motion: (x ) with the relation E 4((x ) /y)E in the region of V W interest. A simple model similar to the RGPM with equally divided voltages applied to the electrodes was used to study the electric "eld properties by the aid of the 3D-simulator. The following geometrical quantities would be extracted for the discussions: (a) length of "eld-shaping electrodes, LF; (b) space between the electrodes and chamber wall, LS; and (c) shape of the chamber wall. Firstly, (a) and (b) strongly a!ect the potential distributions in the work area as is well understood from the result of "eld simulations. Fig. 4 shows the results of calculations of the relation between various LF and the ratio of the "eld inhomogeneity: (E /E ) at three di!erent lateral positions for a "xed V W LS of 50 mm, where E and E are the "eld compoV W nents at y"0 and the mid-plane (z"0) of the
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Fig. 5. Ratio of the "eld distortion; (E /E ) as a function of the V W LS for various lateral displacements of x"6, 10 and 14 mm at y"0 for "xed LF of 100 mm.
beam direction in the work area. In Fig. 5 the relation between the various LS and the ratio of the "eld inhomogenities is also shown at a "xed LF of 100 mm. They are closely related to the leakage #ux of the electric "eld between the electrodes and the chamber wall having the usual earth potential. Secondly, the e!ect by (c) is also closely connected with the LS because the leakage #uxes take a more complicate form. As a result, a longer LF and a larger LS are better, to create more uniform equipotential in the work area. In addition, it would be necessary to adjust the divided voltages applied to the electrodes in order to compensate for any unsymmetrical leakage #uxes.
5. Improvement of RGPM Based on the electric "eld studies mentioned above, the RGPM was improved to create more uniform equipotential distributions in the work area. Since the "eld distortions in the work area depend on the length of the "eld-shaping electrodes, the electrodes were extended from 70 to 100 mm in length. However, it was not su$cient for the required uniformity of the electric "eld. Because the maximum length of the electrodes were restricted by the space of the chamber wall along the beam direction, and because there is an unsymmetrical leakage #ux near to the highest positive electrode, which is close to the chamber wall. In order
Fig. 6. Adjusted voltage distributing the electrodes. The voltages of the uppermost two electrodes, FB5 and TP, were required to be higher than equally divided voltages.
to compensate for this problem, the applied voltage distributed on the electrodes was also adjusted based on the calculated result with the simulation code. It turns out that the applied voltages for the uppermost two electrodes were required to be higher than the equally divided voltages, as is shown in Fig. 6. The equipotential distribution in the "nal result of the "eld simulation for the RGPM is shown in Fig. 7. The electric "eld strength parallel to the ion drift of E (x, y) and the lateral "eld W components of E (x, y) were about 50 V/mm and V less than 0.5 V/mm in the work area, respectively. The trajectories for the ions, which have an initial kinetic energy W of 13 meV with variable ejection angles, were numerically calculated on those "eld distributions using the equations (see in Appendix A). The measurement errors using the terms of FWHM were estimated to be less than 0.6 and 1.1 mm in the case of beam sizes of 10 and 15 mm, respectively.
6. Performance of RGPM After these improvements, the RGPM was installed again in the ring, and has been tested. Fig. 8
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Fig. 7. Equipotential distribution in x}y plane perpendicular to the beam direction at z"0 after improvement of the RGPM.
shows an example of the measured beam pro"les during electron cooling for a 6 MeV/u carbon beam with an intensity of 3;10 ppp. Those pro"les were obtained under the condition of a 500 ms interval and an integration time of 50 ms with an ampli"cation of 4;10 for the tandem-type MCPs. The results of the measurement show that a reduction of the transverse emittance for the circulating beam has been clearly observed due to the electron cooling. In this case, the vertical emittance ( ) was 4 reduced to about one-order, i.e. from 28 to 2.7 mm mrad calculated by a simple relation of "x / , where a betatron amplitude ( ) at the 4 4 4 4 position of interest is estimated at 11 m by the lattice design, and x is the measured beam size for 4 the vertical direction, respectively. The consecutive variations of the pro"les for the carbon beam from injection to before extraction were also observed under normal-mode operation of the ring, where the carbon beam is accelerated from 6 to 230 MeV/u, respectively. The typical measured pro"les are shown in Fig. 9, with the repetition cycle
Fig. 8. Measured beam pro"les in a cooling test: (a) electron o!, (b) at 500 ms after electron on, with carbon beam of 6 MeV/u.
Fig. 9. Measured beam pro"les through normal-mode operation in the synchrotron. Pro"les (a) during injection, (b) during acceleration and (c) before extraction for a carbon beam of 6}230 MeV/u.
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for the data-taking being 10 Hz, an integration time of 50 ms and an intensity of 6;10 ppp. It was observed that the beam width was decreasing with increasing its energy, due to adiabatic damping. In the measurements, the ampli"cation for the tandem-type MCPs was 5;10, and the signal conversion factor was 50 nA}0.25 V at 50 ms of the integration time. The noise level of the measurement system was less than 20 mV. The vacuum pressure adjacent to the monitor was about 1;10\ Torr. It is comprised mainly 40% H , 20% H O, 10% CO#N , and a few percent of CO and CH measured by a Q-mass "lter in the ring.
7. Conclusion A prototype non-destructive beam pro"le monitor employing MCPs has been tested at HIMAC. In a series of the tests some unexpected pro"les were observed. This was caused by an inhomogeneous electric-"eld distribution in the work area. To improve the RGPM, the length of the "eld-shaping electrodes was reformed to longer ones, and the divided voltages applied to the electrodes were optimized, together with the aid of a 3-D "eld simulator. As a result, more uniform potential distributions were obtained. In order to estimate the measurement accuracy of the RGPM, the ion trajectories were calculated numerically by using calculated potentials. As a result, it was calculated to be less than 0.6 and 1.1 mm within beam pro"les of 10 and 15 mm at FWHM, respectively. The RGPM has been successfully used to measure the pro"les in the electron-cooling tests and the usually used therapy beam. A new monitor with higher resolution has recently been designed to accurately measure the cooled circulating beam. The monitor will measure the beam pro"les in the both transverse plans for the horizontal and vertical directions.
discussions. The authors are also grateful to the sta! of Accelerator Engineering Corporation (AEC) for their helpful cooperation. This work was performed as a part of Research Project with Heavy-ion at NIRS-HIMAC.
Appendix A. Equation of motion for ion in electric 5eld The trajectory of ion created by ionization in the transverse x}y coordinate system is derived in non-relativistic motion as follows: q dx " E (x, y) dt M V
(A.1)
dy q " E (x, y) dt M W
(A.2)
where q and M are charge and mass of the ion, E (x, y) and E (x, y) are the electric "eld compoV W nents for the lateral and the parallel to the ion drift, respectively. These two equations can be solved by numerically using calculated electric "eld of E (x, y) and V E (x, y) on the suitable grid points with the time W t as the independent variable. In a simple case, if the uniform electric "elds E (x, y)"E and E (x, y)"E satisfy the region V V W W and initial conditions are given, the Eqs. (A.1) and (A.2) are represented by:
q 2= sin t x,(x!x )" E t# V 2M M
(A.3)
q 2= cos t y,(y!y )" E t# W 2M M
(A.4)
where x and y are the displacements at time t respect to the initial position x and y of the ion, W and are its initial kinetic energy and ejection angle.
Acknowledgements The authors would like to express their thanks to Dr. F. Soga and members of the Division of Accelerator Physics and Engineering at NIRS for helpful
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