- Email: [email protected]
A converter for an RF-knockout system
Nuclear Instruments and Methods in Physics Research A 769 (2015) 16–19
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Generation of a multi-band spectrum using a D/A converter for an RF-knockout system Akio Shinkai, Soichiro Ishikawa, Tetsuya Nakanishi n College of Industrial Technology, Nihon University, 1-2-1 Izumicho, Narashino, Chiba 275-8575, Japan
art ic l e i nf o
a b s t r a c t
Article history: Received 25 February 2014 Received in revised form 18 August 2014 Accepted 26 September 2014 Available online 7 October 2014
A method of generating a multi-band spectrum is proposed using a digital-to-analog (D/A) converter. The multi-band spectrum is useful for the slow-beam-extraction from a synchrotron using the method of radio frequency (RF)-knockout. Data for the spectrum are calculated in advance to be saved in the memory of a D/A converter, and are output synchronized with external clocks. An experiment showed that a multi-band spectrum of 10 bands could be generated with a total bandwidth of about 16.4 MHz and each bandwidth less than 45 kHz. Beam simulation with this method showed that an RF signal from a D/A converter could be effectively used for the control of uniform spill structure. & 2014 Elsevier B.V. All rights reserved.
Keywords: Slow-beam-extraction Synchrotron RF-knockout Digital filter D/A converter
1. Introduction When the slow-beam-extraction from a synchrotron is performed based on the transverse beam heating (radio frequency (RF)-knockout method), a key technology is to diffuse a circulating beam uniformly to obtain a uniform spill structure. A simulation study, using a lattice of the HIMAC (Heavy Ion Medical Accelerator in Chiba) synchrotron, indicated that an RF signal for the RF-knockout should have a wider frequency band than that corresponding to the tune spread of a circulating beam [1]. The wider frequency band can give a more uniform spill, and the level of non-uniformity decreases with the increase of frequency range up to 10th harmonics of third order resonances. The wider frequency band, however, requires a higher power for the RF amplifier. Then a multi-band spectrum composed of narrow bands including third order resonances has been proposed to reduce the RF power [1]. The RF power could be reduced to about 10% of that for the continuous spectrum operation. The multi-band spectrum could be generated using three analog band pass filters, a sum circuit, and a white noise source [2]. However, in the experiment it was found to be difficult to generate a narrow band at high frequency. The required bandwidth had to be a few tens kHz and the maximum frequency was about 16.4 MHz for a compact carbon synchrotron designed at the National Institute of Radiological Sciences (NIRS) [2,3]. Its maximum frequency was n
Corresponding author. Tel.: þ 81 47 474 2375; fax: þ 81 47 474 2399. E-mail address: [email protected] (T. Nakanishi).
http://dx.doi.org/10.1016/j.nima.2014.09.072 0168-9002/& 2014 Elsevier B.V. All rights reserved.
calculated from a revolution frequency of the synchrotron, 3.483 MHz, and a normalized frequency 4.7 larger than the frequency of 10th harmonics 423 of third order resonances, where the normalized frequency was the value divided by the revolution frequency. To overcome this difficulty the authors propose in the present paper the use of another method using a digital-to-analog (D/A) converter. It involves following three processes: (1) calculation of the digital RF signal of the multi-band spectrum, (2) save the calculated values in the memory of D/A converter, and (3) output from the converter synchronized with external clocks as converted voltages. An experiment using a high speed D/A converter shows that the required multi-band spectrum can be obtained. Since the memory capacity is limited to 1 GB, all the numerical data during long spill time cannot be saved in the memory. The data of the memory of 1 GB, for example, are used up to the RF-knockout operation of 3 s (107 turns for particle revolution). Therefore, the data are used “repeatedly” for longer spill time than 3 s. The effect of repeated data on the spill structure is studied with beam simulation for the extraction methods of RF-knockout and QAR method. The QAR is an abbreviation for slow extraction method using a fast Quadruple magnet Assisted by RF-knockout, proposed by the authors for application in the spot scanning irradiation for cancer therapy [4]. The simulation results show that the repeated data has no bad effect on the spill uniformity. A method of generating a multi-band spectrum using a D/A converter and the performance of the system are described in the present paper, as well as the detailed results of beam simulation with this method.
A. Shinkai et al. / Nuclear Instruments and Methods in Physics Research A 769 (2015) 16–19
2. Method 2.1. Outline Beam simulation using a lattice of the HIMAC synchrotron showed that an RF-knockout signal to diffuse a circulating beam uniformly should have a normalized frequency range up to 10th harmonics of third order resonances which is about 0.3 less than 1st harmonics (1/3) to 4.7, respectively [1]. Another simulation using a compact carbon synchrotron designed at NIRS also showed a similar result. The beam simulation in the present paper is performed using a lattice of this compact synchrotron. The normalized frequency of 4.7 corresponds to 16.4 MHz for the compact synchrotron since the revolution frequency is 3.483 MHz. Each band of a multi-band spectrum should include the harmonics of third order resonance frequency because frequency bands not including the harmonics of resonant frequency hardly contribute for the diffusion of a circulating beam [1]. Hence it could be possible to use a series of the narrow bands which includes only the required harmonics of resonant frequencies. The resultant narrow bands could reduce RF power of a post-stage amplifier. Such an RF signal may be called a colored noise. Typical bandwidth of each narrow band is about 45 kHz for the QAR method and about 300 kHz for the RF-knockout method. The generation of the multi-band spectrum was first tried using three analog band pass filters, a sum circuit, and a white noise source [2]. However, it was difficult to generate the narrow band at higher frequency since the inductance required for the filter was too small. On the other hand, when we used an active filter method it induced a parasitic oscillation problem. As an alternative way we proposed the method of using a high speed D/A converter (DAC), of whose system is outlined in Fig. 1. As described briefly in the introduction, this method involves three processes. First, the digital RF signal of the multi-band spectrum is calculated as described in Section 2.3. Second, the digital data calculated are saved in the memory of the DAC as described in Section 2.2. Finally, the data are output synchronized with external clocks as voltages proportional to the values. The output RF signal is amplified and finally fed into the kicker electrode for RF-knockout through an impedance transformer and all pass network system. The RF signal from the DAC could be passed through an analog low pass filter for smoothing the waveform. 2.2. D/A converter The DAC was an APX-500/DAM-516 (AVAL DATA Corp.) which consisted of a baseboard APX-500 with a digital function and a DAM-516 with an analog function. It was mounted on the mother board of a workstation (HP Z420) through a slot of PCI Express 8
17
which gives fast data transfer. The output sampling frequency of the DAC can be adjusted from 250 MHz to 500 MHz, while it is limited to a specific value even within this range due to the specification of DAC. The memory capacity of the DAC is 1 GB, and each datum is saved in the memory with 2 bytes; therefore 512 million data at the maximum can be saved in the memory. The data in the memory are output synchronized with external clocks as converted voltages. After the final datum in the memory is output, the DAC outputs the first datum again and it is repeated while external clocks are input. 2.3. Calculation of data for the multi-band spectrum and clock frequency Data for the RF signal of the multi-band spectrum were calculated with a digital filter method [5] using the workstation. This method calculates the data for an RF signal in a frequency band using digital white noise, filter coefficients, and lower and higher cutoff frequencies. The data up to 10 bands were calculated each with lower and higher cutoff frequencies, and then they were summed to produce the multi-band spectrum. The cutoff frequencies required for the QAR method were (fL and fH)¼ (nþ0.315 and nþ0.328) and (nþ 0.672, nþ0.685) (n¼0, 1, 2, 3, and 4) normalized by revolution frequency of the synchrotron, 3.483 MHz. A horizontal bare tune of betatron oscillations for the compact synchrotron was 1.68. The width between the lower and higher cutoff frequencies was about 45 kHz. The frequencies of third order resonances were not included in the QAR method to increase the extracted particles as described in Section 4.2. Normalized maximum frequency of the RF signal was set to 4.7 as the maximal cutoff frequency is 4.685 (n¼4 case). A sampling frequency in the calculation with the digital filter method was selected as 10 times the maximal frequency, 47, to reconstruct the waveform of the RF signal accurately. Therefore, the data in the DAC must be output with a clock frequency of 47 3.483¼163.7 MHz. The required clock frequency of 163.7 MHz, however, is lower than the minimal clock frequency accepted for the DAC, 250 MHz. Hence in the present system the data were calculated with 0.655 (163.7/250) times the cutoff frequencies. This method would be also useful for a clock frequency larger than 250 MHz since a specific clock frequency cannot be selected for the present DAC system. The number of filter coefficients in the calculation was selected as 14,000 to obtain the same frequency spectrum of the previous calculation [1] because the ratio of the number of coefficients to sampling frequency determines the shape of frequency spectrum, where they were 6000 and 20 in previous calculation, respectively. The data for about 107 turns can be saved in the memory at the maximum since 512 million data can be saved in the memory of 1 GB and the normalized sampling frequency is 47. However data for 100,000 turns, 4,700,000 data, were calculated for the experiment so that the study of beam simulation for the DAC method could be tried in a shorter time. Fourier analysis of the calculated data is performed and it is found that the derived spectrum (Fig. 2) is exactly the same as expected from the digital filter method. A magnified spectrum of the first band in Fig. 2 is shown in Fig. 3. The lower and upper cutoff frequencies used for the calculation of this band were 0.2063 and 0.2148,respectively. It is found that the signal intensities at the cutoff frequencies are lower than 3 dB to the peak value.
3. Experimental result Fig. 1. Generating system of multi-band spectrum with the DAC method. DAC was mounted on the mother board of workstation through a slot of PCI Express. Digital RF signal saved in the memory of DAC is output synchronized with external clocks.
Data for 100,000 turns were saved in the memory of the DAC as described in the previous section. The data were output as converted voltages from the DAC synchronized with external
18
A. Shinkai et al. / Nuclear Instruments and Methods in Physics Research A 769 (2015) 16–19
Fig. 2. Fourier spectrum of the calculated data.
Fig. 5. Magnified spectra of the first band in Fig. 4. Frequency range is 1.08– 1.16 MHz and RBW is 1 kHz.
and the bandwidth is also nearly equal to the equivalent bandwidth of the calculated one, i.e., narrow band spectrum as required. Peak intensities of 10 spectra were nearly the same.
4. Beam simulation using the DAC method
Fig. 3. Magnified spectrum of the first band in Fig. 2.
Fig. 4. Output signal from the DAC observed with a spectrum analyzer. Frequency range is 0–16.6 MHz and RBW is 100 kHz.
clocks of 250 MHz. The signal from the DAC was observed with a spectrum analyzer. The result is given in Fig. 4 with a frequency range from 0.0 to 16.6 MHz and RBE (Resolution BandWidth) of 100 kHz. We use a digital averaging routine of the analyzer that averages the trace points in a number of successive sweeps. It is found that 10 signals can be observed in the frequency bands required for the actual operation. The frequency bandwidth of each signal at the base is wider than that of the calculated result, which is due to the RBW of 100 kHz. The magnified spectrum of the first band is given in Fig. 5 with a frequency range of 1.08–1.16 MHz and RBW of 1 kHz. The observed spectrum is similar to the expected one from the calculation (Fig. 3)
4.1. Simulation with a continuous operation of RF-knockout The process of slow-beam-extraction from the synchrotron was simulated to check what effects the repeated data (kick angles of RF-knockout) would have on the spill structure. The simulation method was described in Ref. [5]. The data for 100,000 turns were calculated with the parameters described in Section 2.3, while the cutoff frequencies were selected as (fL and fH)¼(n þ0.28 and nþ 0.37) and (n þ0.63 and n þ0.72). The width between the lower and higher cutoff frequencies was about 300 kHz. A total revolution of the simulation process was 530,000 turns, including the first 30,000 turns during the rising period of sextuple magnets of the separatrix exciter. The RF-knockout was continuously operated after the first 30,000 turns. The kick angle data for 100,000 turns were used repeatedly during 500,000 turns after the first 30,000 turns. It means that the RF-knockout signal with a colored noise is a periodical waveform repeated every 100,000 turns. Fig. 6(a) plots a simulated spill structure. A result using the kick angles calculated for 500,000 turns is also provided in Fig. 6(b). A total of 1,000,000 particles were simulated, and the number of particles extracted every 100 turns was plotted. Particles extracted during 500,000 turns were about 320,000. Their spill structures are similar, and there is no periodicity in the spill in Fig. 6(a). The spill uniformity defined as the ratio of the standard deviation to the average of the extracted particles number [1] between 330,000 and 430,000 turns is 0.34 for the repeated data (Fig. 6(a)) and 0.36 for the others (Fig. 6(b)). These values are nearly the same, and it is concluded that there is no significant differences of spill structures between the “repeated use” of data and full calculated data. 4.2. Simulation with the QAR method The QAR method involves four steps: (1) particles are diffused by RF-knockout just to the boundary of the transverse separatrix under a resonant condition, (2) the separatrix size is reduced with the excitation of a fast Q magnet (FQ) to a certain size, and the particles outside the separatrix are extracted, (3) the FQ is turned off, and (4) the above process is repeated until the entire circulating beam is extracted [4]. This method would control the beam extraction
A. Shinkai et al. / Nuclear Instruments and Methods in Physics Research A 769 (2015) 16–19
19
Table 1 Simulation conditions. Operation period [turns]
Shrinking rate of the separatrix [%] Simulated particles
FQ risetime FQ falltime RF-knockout Sum
10,000 200 2300 12,500 20 106
Fig. 6. Spill structures with (a) the same data with DAC method and (b) data calculated for all turns.
process with a fast response since the extraction could be done only with the quadruple field. The kick angles and operation time of RF-knockout are set to values that particles are not extracted during its operation. The number of particles extracted for each process could be controlled by the shrink rate of the separatrix with the FQ. However, a larger shrink rate for increasing the extracted particles results in the larger divergence of extracted particles and the deviation of beam position at an irradiation point which is not acceptable for the synchrotron operation. The extracted particles could be increased by adjusting the frequency bandwidth of the multi-band spectrum. The fractional parts of lower and higher cutoff frequencies are selected usually near those of third order resonance and a bare tune, respectively. When we select the fractional part of the cutoff frequency near third order resonance to that near the bare tune and strengthen the power of RF-knockout signal the particle density just inside the separatrix could be increased during the operation of RF-knockout, and finally we can increase the number of extracted particles [2]. The FQ field was linearly increased during 10,000 turns after the first 30,000 turns for the separatrix excitation and then decreased to zero during 200 turns. The separatrix was shrunk to 80% at a peak value of FQ field. After that, RF-knockout was operated during 2300 turns. The sequence of operations of the FQ and RF-knockout was repeated. The simulation conditions are summarized in Table 1. The simulation was performed up to 530,000 turns. The data for the kick angles for 100,000 turns were calculated with the parameters described in Section 2.3, and the data of operation period of RF-knockout were used for every 100,000 turns only after the first 30,000 turns. The cutoff frequencies were slightly different: (fL and fH)¼ (n þ0.315 and nþ0.326) and (nþ 0.674 and nþ0.685). The amplitude coefficient of the kick angles of RF-knockout was adjusted so that 0.5–1% of simulated particles were extracted during one excitation of FQ. Examples of the spill structures with the QAR method are plotted in Fig. 7(a) for the repeated data and Fig. 7(b) for the data calculated for all turns. We found that the repeated data did not have any peculiar effects on the spill structure. The variations of the number of particles extracted during one excitation of FQ were nearly the same for both cases.
Fig. 7. Spill structures with the QAR method: (a) with the same data with DAC method and (b) with data calculated for all turns.
5. Conclusions A method of generating a multi-band spectrum using a DAC was presented. The experiments demonstrated that the method could generate a multi-band spectrum with a total bandwidth of about 16.4 MHz and the individual bandwidth of less than about 45 kHz. Beam simulation showed that an RF signal output from a DAC could be effectively used for the control of extracted beam spill structure with RF-knockout and QAR methods.
Acknowledgments The authors would like to thank Dr. Takeshi Katayama for his useful discussions.
References [1] Tetsuya Nakanishi, Nuclear Instruments and Methods A 621 (2010) 62. [2] M. Tashiro, T. Nakanishi, Proceedings of IPAC 2011, San Sebastian, Spain, pp. 3508–3510. [3] T. Furukawa, et al., Proceedings of APAC 2004, Gyeongju, Korea, pp. 420–422. [4] T. Nakanishi, T. Furukawa, K. Yoshida, K. Noda, Nuclear Instruments and Methods A 553 (2005) 400. [5] T. Nakanishi, K. Tsuruha, Nuclear Instruments and Methods A 608 (2009) 37.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Generation of a multi-band spectrum using a D/A converter for an RF-knockout system Akio Shinkai, Soichiro Ishikawa, Tetsuya Nakanishi n College of Industrial Technology, Nihon University, 1-2-1 Izumicho, Narashino, Chiba 275-8575, Japan
art ic l e i nf o
a b s t r a c t
Article history: Received 25 February 2014 Received in revised form 18 August 2014 Accepted 26 September 2014 Available online 7 October 2014
A method of generating a multi-band spectrum is proposed using a digital-to-analog (D/A) converter. The multi-band spectrum is useful for the slow-beam-extraction from a synchrotron using the method of radio frequency (RF)-knockout. Data for the spectrum are calculated in advance to be saved in the memory of a D/A converter, and are output synchronized with external clocks. An experiment showed that a multi-band spectrum of 10 bands could be generated with a total bandwidth of about 16.4 MHz and each bandwidth less than 45 kHz. Beam simulation with this method showed that an RF signal from a D/A converter could be effectively used for the control of uniform spill structure. & 2014 Elsevier B.V. All rights reserved.
Keywords: Slow-beam-extraction Synchrotron RF-knockout Digital filter D/A converter
1. Introduction When the slow-beam-extraction from a synchrotron is performed based on the transverse beam heating (radio frequency (RF)-knockout method), a key technology is to diffuse a circulating beam uniformly to obtain a uniform spill structure. A simulation study, using a lattice of the HIMAC (Heavy Ion Medical Accelerator in Chiba) synchrotron, indicated that an RF signal for the RF-knockout should have a wider frequency band than that corresponding to the tune spread of a circulating beam [1]. The wider frequency band can give a more uniform spill, and the level of non-uniformity decreases with the increase of frequency range up to 10th harmonics of third order resonances. The wider frequency band, however, requires a higher power for the RF amplifier. Then a multi-band spectrum composed of narrow bands including third order resonances has been proposed to reduce the RF power [1]. The RF power could be reduced to about 10% of that for the continuous spectrum operation. The multi-band spectrum could be generated using three analog band pass filters, a sum circuit, and a white noise source [2]. However, in the experiment it was found to be difficult to generate a narrow band at high frequency. The required bandwidth had to be a few tens kHz and the maximum frequency was about 16.4 MHz for a compact carbon synchrotron designed at the National Institute of Radiological Sciences (NIRS) [2,3]. Its maximum frequency was n
Corresponding author. Tel.: þ 81 47 474 2375; fax: þ 81 47 474 2399. E-mail address: [email protected] (T. Nakanishi).
http://dx.doi.org/10.1016/j.nima.2014.09.072 0168-9002/& 2014 Elsevier B.V. All rights reserved.
calculated from a revolution frequency of the synchrotron, 3.483 MHz, and a normalized frequency 4.7 larger than the frequency of 10th harmonics 423 of third order resonances, where the normalized frequency was the value divided by the revolution frequency. To overcome this difficulty the authors propose in the present paper the use of another method using a digital-to-analog (D/A) converter. It involves following three processes: (1) calculation of the digital RF signal of the multi-band spectrum, (2) save the calculated values in the memory of D/A converter, and (3) output from the converter synchronized with external clocks as converted voltages. An experiment using a high speed D/A converter shows that the required multi-band spectrum can be obtained. Since the memory capacity is limited to 1 GB, all the numerical data during long spill time cannot be saved in the memory. The data of the memory of 1 GB, for example, are used up to the RF-knockout operation of 3 s (107 turns for particle revolution). Therefore, the data are used “repeatedly” for longer spill time than 3 s. The effect of repeated data on the spill structure is studied with beam simulation for the extraction methods of RF-knockout and QAR method. The QAR is an abbreviation for slow extraction method using a fast Quadruple magnet Assisted by RF-knockout, proposed by the authors for application in the spot scanning irradiation for cancer therapy [4]. The simulation results show that the repeated data has no bad effect on the spill uniformity. A method of generating a multi-band spectrum using a D/A converter and the performance of the system are described in the present paper, as well as the detailed results of beam simulation with this method.
A. Shinkai et al. / Nuclear Instruments and Methods in Physics Research A 769 (2015) 16–19
2. Method 2.1. Outline Beam simulation using a lattice of the HIMAC synchrotron showed that an RF-knockout signal to diffuse a circulating beam uniformly should have a normalized frequency range up to 10th harmonics of third order resonances which is about 0.3 less than 1st harmonics (1/3) to 4.7, respectively [1]. Another simulation using a compact carbon synchrotron designed at NIRS also showed a similar result. The beam simulation in the present paper is performed using a lattice of this compact synchrotron. The normalized frequency of 4.7 corresponds to 16.4 MHz for the compact synchrotron since the revolution frequency is 3.483 MHz. Each band of a multi-band spectrum should include the harmonics of third order resonance frequency because frequency bands not including the harmonics of resonant frequency hardly contribute for the diffusion of a circulating beam [1]. Hence it could be possible to use a series of the narrow bands which includes only the required harmonics of resonant frequencies. The resultant narrow bands could reduce RF power of a post-stage amplifier. Such an RF signal may be called a colored noise. Typical bandwidth of each narrow band is about 45 kHz for the QAR method and about 300 kHz for the RF-knockout method. The generation of the multi-band spectrum was first tried using three analog band pass filters, a sum circuit, and a white noise source [2]. However, it was difficult to generate the narrow band at higher frequency since the inductance required for the filter was too small. On the other hand, when we used an active filter method it induced a parasitic oscillation problem. As an alternative way we proposed the method of using a high speed D/A converter (DAC), of whose system is outlined in Fig. 1. As described briefly in the introduction, this method involves three processes. First, the digital RF signal of the multi-band spectrum is calculated as described in Section 2.3. Second, the digital data calculated are saved in the memory of the DAC as described in Section 2.2. Finally, the data are output synchronized with external clocks as voltages proportional to the values. The output RF signal is amplified and finally fed into the kicker electrode for RF-knockout through an impedance transformer and all pass network system. The RF signal from the DAC could be passed through an analog low pass filter for smoothing the waveform. 2.2. D/A converter The DAC was an APX-500/DAM-516 (AVAL DATA Corp.) which consisted of a baseboard APX-500 with a digital function and a DAM-516 with an analog function. It was mounted on the mother board of a workstation (HP Z420) through a slot of PCI Express 8
17
which gives fast data transfer. The output sampling frequency of the DAC can be adjusted from 250 MHz to 500 MHz, while it is limited to a specific value even within this range due to the specification of DAC. The memory capacity of the DAC is 1 GB, and each datum is saved in the memory with 2 bytes; therefore 512 million data at the maximum can be saved in the memory. The data in the memory are output synchronized with external clocks as converted voltages. After the final datum in the memory is output, the DAC outputs the first datum again and it is repeated while external clocks are input. 2.3. Calculation of data for the multi-band spectrum and clock frequency Data for the RF signal of the multi-band spectrum were calculated with a digital filter method [5] using the workstation. This method calculates the data for an RF signal in a frequency band using digital white noise, filter coefficients, and lower and higher cutoff frequencies. The data up to 10 bands were calculated each with lower and higher cutoff frequencies, and then they were summed to produce the multi-band spectrum. The cutoff frequencies required for the QAR method were (fL and fH)¼ (nþ0.315 and nþ0.328) and (nþ 0.672, nþ0.685) (n¼0, 1, 2, 3, and 4) normalized by revolution frequency of the synchrotron, 3.483 MHz. A horizontal bare tune of betatron oscillations for the compact synchrotron was 1.68. The width between the lower and higher cutoff frequencies was about 45 kHz. The frequencies of third order resonances were not included in the QAR method to increase the extracted particles as described in Section 4.2. Normalized maximum frequency of the RF signal was set to 4.7 as the maximal cutoff frequency is 4.685 (n¼4 case). A sampling frequency in the calculation with the digital filter method was selected as 10 times the maximal frequency, 47, to reconstruct the waveform of the RF signal accurately. Therefore, the data in the DAC must be output with a clock frequency of 47 3.483¼163.7 MHz. The required clock frequency of 163.7 MHz, however, is lower than the minimal clock frequency accepted for the DAC, 250 MHz. Hence in the present system the data were calculated with 0.655 (163.7/250) times the cutoff frequencies. This method would be also useful for a clock frequency larger than 250 MHz since a specific clock frequency cannot be selected for the present DAC system. The number of filter coefficients in the calculation was selected as 14,000 to obtain the same frequency spectrum of the previous calculation [1] because the ratio of the number of coefficients to sampling frequency determines the shape of frequency spectrum, where they were 6000 and 20 in previous calculation, respectively. The data for about 107 turns can be saved in the memory at the maximum since 512 million data can be saved in the memory of 1 GB and the normalized sampling frequency is 47. However data for 100,000 turns, 4,700,000 data, were calculated for the experiment so that the study of beam simulation for the DAC method could be tried in a shorter time. Fourier analysis of the calculated data is performed and it is found that the derived spectrum (Fig. 2) is exactly the same as expected from the digital filter method. A magnified spectrum of the first band in Fig. 2 is shown in Fig. 3. The lower and upper cutoff frequencies used for the calculation of this band were 0.2063 and 0.2148,respectively. It is found that the signal intensities at the cutoff frequencies are lower than 3 dB to the peak value.
3. Experimental result Fig. 1. Generating system of multi-band spectrum with the DAC method. DAC was mounted on the mother board of workstation through a slot of PCI Express. Digital RF signal saved in the memory of DAC is output synchronized with external clocks.
Data for 100,000 turns were saved in the memory of the DAC as described in the previous section. The data were output as converted voltages from the DAC synchronized with external
18
A. Shinkai et al. / Nuclear Instruments and Methods in Physics Research A 769 (2015) 16–19
Fig. 2. Fourier spectrum of the calculated data.
Fig. 5. Magnified spectra of the first band in Fig. 4. Frequency range is 1.08– 1.16 MHz and RBW is 1 kHz.
and the bandwidth is also nearly equal to the equivalent bandwidth of the calculated one, i.e., narrow band spectrum as required. Peak intensities of 10 spectra were nearly the same.
4. Beam simulation using the DAC method
Fig. 3. Magnified spectrum of the first band in Fig. 2.
Fig. 4. Output signal from the DAC observed with a spectrum analyzer. Frequency range is 0–16.6 MHz and RBW is 100 kHz.
clocks of 250 MHz. The signal from the DAC was observed with a spectrum analyzer. The result is given in Fig. 4 with a frequency range from 0.0 to 16.6 MHz and RBE (Resolution BandWidth) of 100 kHz. We use a digital averaging routine of the analyzer that averages the trace points in a number of successive sweeps. It is found that 10 signals can be observed in the frequency bands required for the actual operation. The frequency bandwidth of each signal at the base is wider than that of the calculated result, which is due to the RBW of 100 kHz. The magnified spectrum of the first band is given in Fig. 5 with a frequency range of 1.08–1.16 MHz and RBW of 1 kHz. The observed spectrum is similar to the expected one from the calculation (Fig. 3)
4.1. Simulation with a continuous operation of RF-knockout The process of slow-beam-extraction from the synchrotron was simulated to check what effects the repeated data (kick angles of RF-knockout) would have on the spill structure. The simulation method was described in Ref. [5]. The data for 100,000 turns were calculated with the parameters described in Section 2.3, while the cutoff frequencies were selected as (fL and fH)¼(n þ0.28 and nþ 0.37) and (n þ0.63 and n þ0.72). The width between the lower and higher cutoff frequencies was about 300 kHz. A total revolution of the simulation process was 530,000 turns, including the first 30,000 turns during the rising period of sextuple magnets of the separatrix exciter. The RF-knockout was continuously operated after the first 30,000 turns. The kick angle data for 100,000 turns were used repeatedly during 500,000 turns after the first 30,000 turns. It means that the RF-knockout signal with a colored noise is a periodical waveform repeated every 100,000 turns. Fig. 6(a) plots a simulated spill structure. A result using the kick angles calculated for 500,000 turns is also provided in Fig. 6(b). A total of 1,000,000 particles were simulated, and the number of particles extracted every 100 turns was plotted. Particles extracted during 500,000 turns were about 320,000. Their spill structures are similar, and there is no periodicity in the spill in Fig. 6(a). The spill uniformity defined as the ratio of the standard deviation to the average of the extracted particles number [1] between 330,000 and 430,000 turns is 0.34 for the repeated data (Fig. 6(a)) and 0.36 for the others (Fig. 6(b)). These values are nearly the same, and it is concluded that there is no significant differences of spill structures between the “repeated use” of data and full calculated data. 4.2. Simulation with the QAR method The QAR method involves four steps: (1) particles are diffused by RF-knockout just to the boundary of the transverse separatrix under a resonant condition, (2) the separatrix size is reduced with the excitation of a fast Q magnet (FQ) to a certain size, and the particles outside the separatrix are extracted, (3) the FQ is turned off, and (4) the above process is repeated until the entire circulating beam is extracted [4]. This method would control the beam extraction
A. Shinkai et al. / Nuclear Instruments and Methods in Physics Research A 769 (2015) 16–19
19
Table 1 Simulation conditions. Operation period [turns]
Shrinking rate of the separatrix [%] Simulated particles
FQ risetime FQ falltime RF-knockout Sum
10,000 200 2300 12,500 20 106
Fig. 6. Spill structures with (a) the same data with DAC method and (b) data calculated for all turns.
process with a fast response since the extraction could be done only with the quadruple field. The kick angles and operation time of RF-knockout are set to values that particles are not extracted during its operation. The number of particles extracted for each process could be controlled by the shrink rate of the separatrix with the FQ. However, a larger shrink rate for increasing the extracted particles results in the larger divergence of extracted particles and the deviation of beam position at an irradiation point which is not acceptable for the synchrotron operation. The extracted particles could be increased by adjusting the frequency bandwidth of the multi-band spectrum. The fractional parts of lower and higher cutoff frequencies are selected usually near those of third order resonance and a bare tune, respectively. When we select the fractional part of the cutoff frequency near third order resonance to that near the bare tune and strengthen the power of RF-knockout signal the particle density just inside the separatrix could be increased during the operation of RF-knockout, and finally we can increase the number of extracted particles [2]. The FQ field was linearly increased during 10,000 turns after the first 30,000 turns for the separatrix excitation and then decreased to zero during 200 turns. The separatrix was shrunk to 80% at a peak value of FQ field. After that, RF-knockout was operated during 2300 turns. The sequence of operations of the FQ and RF-knockout was repeated. The simulation conditions are summarized in Table 1. The simulation was performed up to 530,000 turns. The data for the kick angles for 100,000 turns were calculated with the parameters described in Section 2.3, and the data of operation period of RF-knockout were used for every 100,000 turns only after the first 30,000 turns. The cutoff frequencies were slightly different: (fL and fH)¼ (n þ0.315 and nþ0.326) and (nþ 0.674 and nþ0.685). The amplitude coefficient of the kick angles of RF-knockout was adjusted so that 0.5–1% of simulated particles were extracted during one excitation of FQ. Examples of the spill structures with the QAR method are plotted in Fig. 7(a) for the repeated data and Fig. 7(b) for the data calculated for all turns. We found that the repeated data did not have any peculiar effects on the spill structure. The variations of the number of particles extracted during one excitation of FQ were nearly the same for both cases.
Fig. 7. Spill structures with the QAR method: (a) with the same data with DAC method and (b) with data calculated for all turns.
5. Conclusions A method of generating a multi-band spectrum using a DAC was presented. The experiments demonstrated that the method could generate a multi-band spectrum with a total bandwidth of about 16.4 MHz and the individual bandwidth of less than about 45 kHz. Beam simulation showed that an RF signal output from a DAC could be effectively used for the control of extracted beam spill structure with RF-knockout and QAR methods.
Acknowledgments The authors would like to thank Dr. Takeshi Katayama for his useful discussions.
References [1] Tetsuya Nakanishi, Nuclear Instruments and Methods A 621 (2010) 62. [2] M. Tashiro, T. Nakanishi, Proceedings of IPAC 2011, San Sebastian, Spain, pp. 3508–3510. [3] T. Furukawa, et al., Proceedings of APAC 2004, Gyeongju, Korea, pp. 420–422. [4] T. Nakanishi, T. Furukawa, K. Yoshida, K. Noda, Nuclear Instruments and Methods A 553 (2005) 400. [5] T. Nakanishi, K. Tsuruha, Nuclear Instruments and Methods A 608 (2009) 37.