Parasitic slow extraction of extremely weak beam from a high-intensity proton rapid cycling synchrotron

Nuclear Instruments and Methods in Physics Research A 737 (2014) 56–64

Contents lists available at ScienceDirect

Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima

Parasitic slow extraction of extremely weak beam from a high-intensity proton rapid cycling synchrotron Ye Zou a,b, Jingyu Tang a,b,n, Zheng Yang b, Hantao Jing b a b

University of Science and Technology of China, Hefei, Anhui 230029, PR China Institute of High Energy Physics, CAS, Yuquan Road 19B, Beijing 100049, PR China

art ic l e i nf o

a b s t r a c t

Article history: Received 19 September 2013 Received in revised form 30 October 2013 Accepted 5 November 2013 Available online 21 November 2013

This paper proposes a novel method to extract extremely weak beam from a high-intensity proton rapid cycling synchrotron (RCS) in the parasitic mode, while maintaining the normal fast extraction. The usual slow extraction method from a synchrotron by employing third-order resonance cannot be applied in a high-intensity RCS due to a very short flat-top at the extraction energy and the strict control on beam loss. The proposed parasitic slow extraction method moves the beam to scrape a scattering foil prior to the fast beam extraction by employing either a local orbit bump or momentum deviation or their combination, so that the halo part of the beam will be scattered. A part of the scattered particles will be extracted from the RCS and guided to the experimental area. The slow extraction process can last about a few milliseconds before the beam is extracted by the fast extraction system. The method has been applied to the RCS of China Spallation Neutron Source. With 1.6 GeV in the extraction energy, 62.5 μA in the average current and 25 Hz in the repetition rate for the RCS, the proton intensity by the slow extraction method can be up to 2
104 protons per cycle or 5
105 protons per second. The extracted beam has also a good time structure of approximately uniform in a spill which is required for many applications such as detector tests. Detailed studies including the scattering effect in the foil, the local orbit bump by the bump magnets and dispersive orbit bump by modifying the RF pattern, the multi-particle simulations by ORBIT and TURTLE codes, and some technical features for the extraction magnets are presented. & 2013 Elsevier B.V. All rights reserved.

Keywords: Extremely weak beam Parasitic slow extraction Scattering foil Beam halo RF de-synchronization

1. Introduction Some proton applications such as detector tests and studies on space radiation effects, ask for very weak beam intensity. Detector tests also ask for a higher beam duty factor and good intensity uniformity. In general, proton synchrotrons use the third-order resonance extraction method to provide beams of large duty factors or even quasi-continuous wave, and then defocusing systems to spread out beams are used to reduce beam intensity to a very low level. It seems that no serious attempts have been made to provide a very weak proton beam from a high-intensity rapid cycling proton synchrotron where the single-turn fast extraction should be used to keep up with the high repetition rate and the requirement on low beam loss during the extraction is very strict. Beam extraction methods by foil scattering were used in early circular accelerators, but were discarded due to low extraction efficiency as compared to resonant extraction methods. At KEK/PS, the simultaneous slow extraction with the internal target experiment was used [1,2]. No one has tried to apply the scattering method to a high-intensity

synchrotron, though ISIS uses a wobbling thin needle to intercept the circulating beam in a high-intensity proton RCS to produce extremely low intensity muons for the MICE experiment [3]. In this paper, a novel method is proposed to extract extremely weak proton beam from a high-power rapid cycling proton synchrotron in the parasitic mode when keeping the normal fast extraction. The method is successfully applied to the rapid cycling synchrotron (RCS) of China Spallation Neutron Source (CSNS) with a more-or-less realistic design. The CSNS is a large scientific facility under construction [4], and mainly serves multidisciplinary research by using neutron scattering techniques. However, other applications such as those using very weak protons are also under consideration. At the CSNS-I phase, the RCS accelerates beam from 80 MeV to 1.6 GeV in a repetition rate of 25 Hz, and the beam power at extraction is 100 kW. The main parameters of the RCS are listed in Table 1.

2. Parasitic slow extraction method 2.1. Concept of the parasitic slow extraction method

n

Corresponding author at: University of Science and Technology of China, Hefei, Anhui 230029, PR China. Tel.: þ 86 10 882 35908; fax: þ 86 10 882 35908. E-mail address: [email protected] (J. Tang). 0168-9002/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nima.2013.11.021

As a parasitic working mode, the proposed slow extraction method should have no or very little influence on the fast

Y. Zou et al. / Nuclear Instruments and Methods in Physics Research A 737 (2014) 56–64

extraction. This means that the beam power from the RCS should not be reduced when the slow extraction method is applied. The principle of the method is as follows: a scattering foil is placed in a long straight section in a dispersive region of the RCS. During the normal acceleration it does not interfere with the circulating beam, which has a large emittance, usually with a dense core and a sparse halo. It is important to clear the whole beam from the foil to avoid beam losses during the acceleration. If a local orbit bump is created just a few milliseconds before the fast extraction moves the beam closer to the scattering foil, some halo particles will hit the foil and are scattered. A very small part of the scattered particles will enter the extraction channel and can be extracted, with the total number depending on how deep the scattering foil bites into the beam halo. Overwhelm particles hitting the foil continue to circulate in the ring and diffuse into a larger emittance, and this is very important to obtain good intensity uniformity for the extracted beam. To limit the beam power of the lost particles due to beam hitting on the scattering foil, which will increase the radiation dose rate in the RCS tunnel, the total particles hitting the foil are controlled below 10 W, which is comparable to the beam loss power associated with the fast extraction. Furthermore, as some halo particles are lost by the scattering process, the beam loss level at the fast extraction will be reduced. For a total beam power of 100 kW, this means that only 10  5 of the beam will be allowed to hit the foil.

Table 1 Main parameters of CSNS RCS. Circumference (m) Injection energy (GeV) Extraction energy (GeV) Super-period Number of dipoles Betatron tunes (h/v) RF harmonics RF frequency range (MHz) RF maximum voltage (kV) Transverse acceptance (πmm mrad) Collimation acceptance (πmm mrad)

227.92 0.08 1.6 4 24 4.82/4.80 2 1.0241–2.3723 165 540  350

57

With a rapid cycling magnetic field, the time duration for applying the slow extraction method with foil scattering is short, typically a few milliseconds before the single-turn extraction. Otherwise, the momentum deviation from the reference one is too large for the scattered particles to pass through the extraction channel. This will represent a beam duty-factor of about a few percentage points, which is acceptable for many applications. While only a small portion of the scattered particles is extracted at one passing at the foil, most scattered particles will continue to circulate many turns and are extracted gradually. This is very useful to obtain a more-or-less homogenous beam intensity during the extraction period or a spill. To obtain the desirable beam intensity of about 104 protons per cycle, the extraction efficiency that is defined as the extracted particles over those hitting the foil should be in the order of 10  5 or higher. At the energy of 1.6 GeV, the scattered particles are distributed overwhelmingly in the much forward direction. However, a relatively large scattered angle such as 4–61 is needed for the particles to be extracted by the downstream septum magnets due to very tight space in the arc region, which is contradictory to higher extraction efficiency. Simulations show that the required extraction efficiency can still be obtained. Other deflection elements producing less beam loss such as conventional electrostatic deflectors and novel bent crystals [5] are considered not suitable here. On one hand, they cannot provide large deflection angles; on the other hand, they cannot extract the halo particles approximately uniformly in thousands of turns without applying any resonant mechanism. If the lattice in a synchrotron can provide larger space for the slow extraction, much smaller scattered angle can be applied so that one can obtain higher extraction efficiency. 2.2. Physics design scheme for the parasitic slow extraction The most critical problem in realizing the parasitic slow extraction in the RCS is the tight space, because initially the RCS was not designed to incorporate the slow extraction. The slow extraction design has to be carried out with the existing lattice. In the center part of each RCS arc region, there is a long drift of 3.5 m with high dispersion. It is considered the ideal place to design a slow extraction system by foil scattering. It is preferred to place all

Fig. 1. Parasitic slow extraction system is applied to one of the RCS arc regions as marked by the red circle. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

58

Y. Zou et al. / Nuclear Instruments and Methods in Physics Research A 737 (2014) 56–64

Fig. 2. Schematic for the parasitic slow extraction system (blue: RCS main dipole magnets, green: bump magnets, brown: septum magnet, purple: extraction bending magnet, red: scattering foil). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Table 2 Main parameters for the local orbit bump and scattering foil. Beta-X at the foil (m) εx at 80 MeV (πmm mrad) εx at 1.6 GeV (πmm mrad) X-envelope at the foil at 80 MeV with X-envelope at the foil at 1.6 GeV with

δ ¼ 7 1% (mm) δ ¼ 7 0.2% (mm)

4 350 150 71.5 31.2

Initial bump at 80 MeV (mm) End bump at 1.6 GeV (mm) Foil position (mm) Dispersion at the foil (m) Bump by 0.8% momentum deviation

 23.2  3.8 48.3 3.38 23.8

Fig. 3. Depiction of the orbit bumps used for the parasitic slow extraction with fixed-field bump magnets (yellow line: orbit at 80 MeV, brown line: orbit at 1.6 GeV, purple line: orbit at 1.6 GeV with momentum deviation). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

the relevant extraction elements in the long drift to minimize the influence to the whole ring, though other orbit correction magnets can also be employed to enhance the orbit bump at the foil. The schematic of the slow extraction system is depicted in Figs. 1 and 2. Major elements used in the slow extraction system are the scattering foil, four bump magnets which are symmetrically arranged and produce a purely local orbit bump, one septum magnet and one bending magnet. Although the scattering foil can be designed to move in mechanically to synchronize with the beam cycle, it is preferred to have a design of fixed foil for robustness. In this case, the key limitation comes from the requirement on the bump magnets, which must be strong and perhaps fast ramping. Two solutions for the local orbit bump have been studied: one uses fast ramping magnets which produce an outward orbit bump in the last few milliseconds of the cycle; the other uses fixed-field bump magnets which produce an inward orbit bump decaying with beam rigidity. Certainly, the outward bump by fast ramping bump magnets is more straightforward, but it asks for very powerful magnets. The inward orbit bump method [6] is much easier to realize technically, but the orbit bump is weaker. The scheme with an inward orbit bump is adopted here. A design scheme is as follows: without applying the local orbit bump, it is wished to maintain the original physical acceptance of 540 πmm mrad at the foil at 80 MeV and about 350 πmm mrad at

1.6 GeV which is the collimation acceptance [7]. With an inward bump decaying from the initial 23.2 mm at 80 MeV to 3.8 mm at 1.6 GeV, and the supposed beam halo emittance shrinking from 350 πmm mrad to 150 πmm mrad also due to acceleration, and the additional orbit bump by 0.8% momentum deviation at maximum and high dispersion, one can reduce the acceptance at the foil further down to 115.6 πmm mrad. Dependent on the halo particle population, a smaller momentum deviation can be applied for a larger halo emittance. By doing so, one can move the beam halo to scrape the foil. The key parameters are listed in Table 2, and the orbit bumps are also shown in Figs. 3 and 4. The bump magnets are aligned according to the shifted orbit to save apertures. The maximum momentum deviation for the reference particle from the nominal one is limited to 0.8% for the reason to keep the maximum momentum deviation including the momentum spread of 70.2% still within 71% which is set by the original lattice design. 2.3. Additional orbit bump by momentum deviation As mentioned above, if one modifies the RF frequency pattern to create a momentum deviation from the nominal one for the reference particle, one can produce an additional orbit bump at the scattering foil which is located in a high dispersion region. This mechanism is explained in more details here.

Y. Zou et al. / Nuclear Instruments and Methods in Physics Research A 737 (2014) 56–64

59

Fig. 4. Orbit positions and beam sizes from the injection to the extraction for the parasitic slow extraction (yellow: at 80 MeV, brown: at 1.6 GeV, purple: at 1.6 GeV with momentum deviation). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

x10-5

1610 2.5

1605

E(MeV)

Scattering Probability

2.0

1.5

1600

1.0 1595 0.5 1590 0

0.0 C

Al

Cu

Ta

50

100

150

200

250

300

350

400

nParticles

Pt

Materials Fig. 5. Scattering probability for different foil materials with the same equivalent thickness calculated by FLUKA. The beam energy is 1.6 GeV and the equivalent thickness is 0.225 g/cm2.

Fig. 6. Energy distribution of the halo particles after 2500 turns, simulated by using ORBIT.

the foil. The orbit bump by the average momentum deviation is As we know, the relationship between RF frequency and momentum deviation is

Δf f

Δp 0

¼ η

p0

¼  ηδ0

ð1Þ

where f, p0, η, δ0 denote the RF frequency, reference momentum, phase-slip factor, and relative momentum deviation, respectively. δ0 is used for the average momentum deviation to differ from the momentum spread δ. In the normal operation mode, the RF frequency changes in synchronization with the ramping magnetic field during acceleration. In the RCS, the ramping magnetic field is a biased sinusoidal waveform. When the beam approaches to the extraction energy, the changing rates in the ramping magnetic field and beam momentum become very small. In real machines, the synchronization is assured by readjusting the frequency curve with the measured close-orbit errors in different dispersive locations. Here, one can intentionally create a small desynchronization to obtain momentum deviation that produces the required orbit bump at

Δx ¼ D x δ 0 ;

ð2Þ

For producing an outward orbit bump, one should increase the RF frequency slightly. For example, with the RCS design: Dx ¼3.38 m, η ¼  0.0948, for an orbit bump Δx¼10 mm, one needs the relative momentum deviation of 0.3% and the RF frequency shift by 0.028% or 69 kHz. The small change in the transverse tunes due to the natural chromaticity is also acceptable with the momentum deviation.

3. Beam-material introduction at the scattering foil The scattering foil is the key component for this new extraction method. There are several effects in the beam-foil interaction: first, it produces a very small portion of particles with a large scattering angle for extraction; second, most particles continue to circulate in the ring with a little energy loss and a divergent spread; third, a small portion of particles get lost due to large nuclear scattering or nuclear reaction. It is also important to choose the proper foil material and the effective thickness. There are two main concerns in selecting the foil: one is the portion of large-angle

60

Y. Zou et al. / Nuclear Instruments and Methods in Physics Research A 737 (2014) 56–64

Fig. 7. Hollow beam distribution with anti-correlation (Left: in the horizontal plane, the emittance ring is from 0.9ε to ε, ε is the emittance of the beam halo; Right: in the vertical plane).

Fig. 8. Beam distributions in the transverse phase planes at the foil location after different turns (106 particles, anti-correlated hollow beam).

scattered particles which is critical for the extraction efficiency, the other is the energy loss per foil transversal that is important to obtain good intensity uniformity during a large-number turns or an extraction spill. The energy loss in material due to ionization for a given equivalent thickness which means the product of the thickness and density of a material is proportional to the target atomic number, as defined by the Bethe–Bloch formula. This means that

lower-Z materials are favored to reduce the beam energy loss when multiple crossing of the circulating beam in the foil is considered. On the other hand, one wishes to have a larger portion for the particles with a large scattered angle for the extraction. Those particles are from nuclear scattering, either elastic or inelastic. For the elastic nuclear scattering, which is defined by the crosssection sel nucl , the angular distribution by this mechanism is given

Y. Zou et al. / Nuclear Instruments and Methods in Physics Research A 737 (2014) 56–64

by an empirical formula [8], dsel nucl ¼ ae  bðAÞt ; dt

ð3Þ

15

10

Y (mm)

5

0

-5

-10

-15 40

45

50

55

60

65

X (mm) Fig. 9. Beam distribution at the entrance of the septum magnet.

70

61

where t is the momentum transfer t¼(pθ)2, which is a Lorentz invariant, p is the momentum of the particles with unit of GeV/c, θ is the scattering angle, a is a coefficient and b(A) is a factor depending on the atomic mass of the target nucleus A, as b(A)¼14.1A0.65. One can see that the scattering cross-section decreases quickly with increasing momentum, atomic number and deflection angle. It also has dependence on the foil thickness. As shown in Fig. 5, the simulations by FLUKA [9] also show that with the same equivalent thickness the scattering probability at a large angle, e.g. 61, decreases when the atomic number increases. Here the scattering probability is defined as the ratio of the number of particles falling into the septum's good field region represented by a blackbody to the total particles hitting the foil. Therefore, a carbon foil has been selected here. Fig. 6 shows the energy distribution after 2500 turns by using ORBIT with synchrotron motion included. One can conclude that the energy loss has little influence onto the extraction. For the inelastic nuclear scattering, as the energy of the scattered protons from the interaction is much lower than the primary beam energy and covers a very large range, thus it is difficult to extract them for applications. Therefore, the inelastic nuclear scattering is not considered here. The multiple-scattering effect in the scattering foil will result in emittance growth for the halo particles. However, this process helps extract the halo particles more homogenously in a spill.

Fig. 10. Beam distributions in the transverse phase planes at the entrance and exit of the extraction channel (Upper: at the entrance of the septum magnet; lower: at the exit of the bending magnet).

62

Y. Zou et al. / Nuclear Instruments and Methods in Physics Research A 737 (2014) 56–64

x106 20

x10-5 20

18 16

Scattering Probability

14

nHits

12 10 8 6

15

10

5

4 2

0

0 0.5

1.0

1.5

2.0

2.5

0.5

3.0

1.0

1.5

h (mm)

2.0

2.5

3.0

h (mm)

1000

40

800 30

nHits

nExtraction

600

400

20

10 200

0

0 0.5

1.0

1.5

2.0

2.5

3.0

0.5

1.0

h (mm)

1.5

2.0

2.5

3.0

h (mm)

Fig. 11. Relationship between the extracted particles and the foil thickness (Upper left: the relationship between the particles that hit the foil and the thickness; Upper right: the relationship between the scattering probability of the remaining particles and the thickness; Lower left: the relationship between the number of particles at the entrance of the septum magnet and the thickness; Lower right: the relationship between the number of extracted particles and the thickness).

120

Another advantage using a carbon foil is that it produces low prompt and residual radiation dose rates, compared with high-Z materials.

100

4. Simulations of parasitic slow extraction

80

The parasitic slow extraction is designed to work in time duration of about 2 ms prior to the fast extraction. The RF system is programmed to produce a short flat-top at the energy of 1.6 GeV, so the beam circulates at the same energy throughout the whole parasitic slow extraction period. As the beam distribution at the extraction is usually irregular, it is not easy to predict at the design stage. In order to study the whole process of the parasitic slow extraction, an artificial beam distribution is assumed [10]: the distribution has a beam core with the emittance of 60 πmm mrad, and a sparse beam halo with the emittance of 150–250 πmm mrad. Both the beam core and beam halo distributions are Gaussian distributions truncated to 73s, and they superimpose. As the beam core is not touched by the foil, so only the halo distribution which is assumed to be 3% of the total beam is used here. In addition, only a relatively small number of particles in the halo distribution that have large Courant–Snyder invariants can hit the scattering foil. To simplify the simulation process, only the outer part of the distribution which looks like an

nHits

4.1. Simulation conditions and method 60

40

20

0 0

500

1000

1500

2000

2500

Turns Fig. 12. Number of hits per turn on the scattering foil with respect to turn number.

emittance ring and contains 1/300 of the particles in the halo distribution or 1/10000 of the total particles. A self-made FORTRAN program (‘HOLLOW BEAM’) is used to generate this kind of hollow beam distribution, see Fig. 7. The beam correlation in the transverse planes coming from the injection painting has an important impact on the slow extraction method. At CSNS, the

Y. Zou et al. / Nuclear Instruments and Methods in Physics Research A 737 (2014) 56–64

Table 3 Basic and cooling parameters of the magnets. Parameters

Bump magnets

Septum magnets

Bending magnet

Field (T) Good field regions (mm) NI (AT) Field quality (%) Current density (A/ mm2) Power loss (kW) Temperature rise (1C)

0.382 180 (H)
120 (V) 36860 0.13 20.2

1.19 30 (H)
20 (V) 23686 0.2 56.3/26

1.9 80 (H)
60 (V) 90764 0.7 25.1/10.8

12.4 14.7

12.7 19.5

94.8 14.9

Note: The two values for current density are for normal coils and thickened coils.

Fig. 13. Magnetic field distribution of the bump magnets.

63

the entrance of the extraction septum magnet, which has the same dimensions as the good field region of the septum. The blackbody records the positions and momenta of the particles hitting it. Then the extraction through the extraction channel is studied by using TURTLE. 4.2. Simulation results The beam distributions after different turns since the beam hits the foil are shown in Fig. 8. As the beam circulation proceeds, the halo particles which hit the scattering foil become almost uniformly distributed in a ribbon-shape in the horizontal plane and in the center in the vertical plane. The beam distribution at the blackbody is shown in Fig. 9, which shows evident density decrease from inner to outer due to the angular distribution of the scattering effect. The particle distributions in the two transverse phase planes at the entrance and exit of the extraction channel are shown in Fig. 10. Because we have chosen a large scattering angle of 61, the collection efficiency at the blackbody is very low. For 106 particles used for simulations, about 300 particles hit the blackbody and only about a dozen can be extracted. Many particles lost in the extraction channel have very low momenta and are from the inelastic nuclear scattering. The small transverse acceptance of the channel is another reason for the low transmission efficiency. The efficiencies with different foil thicknesses are compared in Fig. 11, and it can be found that there is no significant correlation between the efficiency and the foil thickness. A carbon foil with a thickness of about 1 mm is a good choice. Therefore, for a total protons of 1.56
1013, we can extract about 2.3
104 protons in 2500 turns or about 10 particles per turn or about 6
105 protons per second, which is considered to meet the requirement for extremely-weak proton beam applications. The intensity uniformity for the extracted beam which can be represented by the hits on the scattering foil with respect to turns as shown in Fig. 12, and it looks to be satisfactory.

5. Magnet parameters and field distributions

Fig. 14. Magnetic field distribution of the septum magnet.

anti-correlation painting method is adopted, which means that a particle with a large horizontal Courant–Snyder invariant will have a small vertical Courant–Snyder invariant. For simplicity, the beam distribution in the longitudinal phase plane is assumed a uniformly filled ellipse with a momentum spread of 70.2%. In total 106 particles are used for simulations. Both TURTLE [11] and ORBIT [12] codes have been used to study the details. The initial hollow beam generated by “HOLLOW BEAM” is tracked by ORBIT. A blackbody is set at the position of

This part will show that the magnets used for the parasitic slow extraction are technically feasible. We are not intending to give the engineering magnets design but just basic 2-D field and water cooling calculations. The SUPERFISH code [13] is used to calculate the magnetic fields. The basic and cooling parameters for the magnets are summarized in Table 3. The bump magnets are used to produce a dynamic local orbit to control the spacing between the circulating beam and the scattering foil. For the extracted particles to clear from them, the magnets are designed to be asymmetric window-frame type, with the outer iron yoke thinner than that the inner one. The magnetic field distribution is showed in Fig. 13. The septum magnet is to produce the first kicking to the entering particles in the extraction channel and prepare sufficient orbit separation from the circulating beam for the downstream bending magnet. To reduce the power consumption in the coils which poses cooling problem, the back-leg side of the coils has a doubled thickness (see Fig. 14), while the septum is only 20 mm for the designed field of 1.19 T. The bending magnet makes the major bending to the extracted particles. As the main dipole magnets of the RCS are very wide, the extraction bending magnet has to produce a very large angle of 221 to clear off the nearby ring magnet. This dictates a strong field design of 1.9 T with an effective length of 1.6 m. The magnet is also designed to be asymmetric window-frame type just as the bump magnets due to the space limitation. The inner side is overlapped

64

Y. Zou et al. / Nuclear Instruments and Methods in Physics Research A 737 (2014) 56–64

Although the studies have been carried out with the CSNS parameters [14], the method should be applicable to other highintensity proton synchrotrons with available space in large dispersion regions. A different approach also based on the halo particle scattering was studied in parallel [15], which shares use of the fast extraction channel. Acknowledgements This work was supported by the National Natural Science Foundation of China (10975150, 10775153) and the CSNS project. The authors would like to thank CSNS colleagues for discussions, and Yifang Wang for stimulating the need on extracting extremely weak protons from the RCS.

Fig. 15. Magnetic field distribution of the bending magnet.

with one of the bump magnets in the longitudinal direction, thus it has a thinner yoke. The calculated field distribution is showed in Fig. 15.

6. Conclusions The conceptual study and simulations show that the parasitic slow extraction method by scattering halo particles is an effective one in combined with the single-turn extraction method in highintensity proton RCSs. Even in relatively compact RCSs such as CSNS/RCS where the arc regions have very tight space, it is also applicable. Different measures such as decaying orbit bump by DC magnets, slight de-synchronization of the RF frequency and the magnetic field, and properly chosen foil together makes the method adaptable for different beam halo settings. Although the extraction magnets for the parasite slow extraction have quite high requirements, the preliminary magnet designs show that they are still feasible with usual techniques.

References [1] Kuninori Endo, Yoshitaka Kimura, IEEE Trans. Nucl. Sci. NS26 (3) (1979) 3170. [2] M.J. Shirakata, K. Marutsuka, H. Sato, Proc. of PAC1995, Vancouver, BC, (1997) p. 267. [3] M. Bogomilov, et al., (MICE collaboration), J. Instrum. 7 (2012) P05009. [4] S.X. Fang, S.N. Fu, Q. Qin, J.Y. Tang, S. Wang, J. Wei, C. Zhang, J. Korean Phys. 48 (4) (2006) 697. [5] A.A. Asseev, M. Yu. Gorin, in: Proceedings of PAC1995, Dallas, Texas, (1995) p. 1955. [6] J.Y. Tang, Nucl. Instrum. Methods Phys. Res., Sect. A 575 (2007) 328. [7] J.Y. Tang, J.F. Chen, Y. Zou, PRST-AB 14 (2011) 050103. [8] N. Catalan-Lasheras, Transverse and Longitudinal Beam Collimation in a HighEnergy Proton Collider (LHC), CERN- THESIS-2000-019, p. 25. [9] A. Ferrari, P.R. Sala, et al., FLUKA: A Multi-particle Transport Code, Version 2011, CERN, Geneva. [10] J.Y. Tang, G.H. Wei, C. Zhang, NIM-A 582 (2007) 326. [11] D.C. Carey, TURTLE (Trace Unlimited Rays Through Lumped Elements): A Computer Program for Simulating Charged Particle Beam Transport Systems, January 1971. [12] J.D. Galambos et al., ORBIT User Manual Version 1.10, July 1999. [13] M.T. Menzel, H.K. Stokes, User's Guide for the POISSON/SUPERFISH Group of Codes, January 1987. [14] J.Y. Tang, S.N. Fu, L. Ma, High intensity aspects of the CSNS accelerators, in: Proceedings of HB2010, Morschach, Switzerland, (2010) p. 38. [15] N. Wang, M.Y. Huang, N. Huang, S. Wang, feasibility studies of the foil scattering extraction in CSNS/RCS, in: Proceedings of IPAC2011, San Sebastián, Spain, (2011) p. 3517.