- Email: [email protected]
Interaction of Super Proton Synchrotron beam with solid copper target: Simulations of future experiments at HiRadMat facility at CERN
ARTICLE IN PRESS Nuclear Instruments and Methods in Physics Research A 606 (2009) 186–192
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Interaction of Super Proton Synchrotron beam with solid copper target: Simulations of future experiments at HiRadMat facility at CERN N.A. Tahir a,, R. Schmidt b, M. Brugger b, R. Assmann b, A. Shutov c, I.V. Lomonosov c, V.E. Fortov c, A.R. Piriz d, C. Deutsch e, D.H.H. Hoffmann f a
¨ r Schwerionenforschung, Planckstrasse 1, 64291 Darmstadt, Germany Gesellschaft fu CERN–AB, 1211 Geneva 23, Switzerland c Institute of Problems of Chemical Physics, 142432 Chernogolovka, Russia d ETSI Industriales and Instituto de Investigaciones Energe´ticas, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain e LPGP, Universite Paris-Sud, 91405 Orsay, France f ¨t Darmstadt, 64289 Darmstadt, Germany ¨ r Kernephysik, Technische Universita Institut fu b
a r t i c l e in f o
a b s t r a c t
Available online 5 April 2009
In this paper we present numerical simulations of interaction of 450 GeV/c proton beam that is generated by Super Proton Synchrotron (SPS) at CERN, with a solid copper target. These simulations have been carried out using a two-dimensional hydrodynamic computer code, BIG2. This study has been done to assess the damage caused by these highly relativistic protons to equipment including collimators, absorbers and others in case of an uncontrolled accidental release of the beam. In fact a dedicated experimental facility named HiRadMat is under construction at CERN that will allow one to study these problems experimentally. The simulations presented in this paper will be very useful in designing these experiments and later to interpret the experimental results. & 2009 Elsevier B.V. All rights reserved.
Keywords: Large Hadron Collider Super Proton Synchrotron High Enegry Density physics Strongly coupled plasmas
1. Introduction Completion of the Large Hadron Collide (LHC) at CERN is the culmination of decades of hard work by thousands of scientists around the world. By far, it is the most powerful particle accelerator that has ever been built over this planet. This impressive facility will allow collisions between two counter rotating proton beams that will be accelerated to energy of 7 TeV/c over a circumference of 26.7 km. Each LHC beam will comprise 2808 proton bunches with each bunch containing 1:15 1011 protons. This corresponds to a total energy of 350 MJ in each beam which is sufficient to melt 500 kg of copper. Safety of the equipment and the personnel while working with such extremely powerful beams is an issue of utmost importance and must be addressed meticulously well before the commissioning phase of the facility. One of the important steps in this direction was our previous study [1,2] that was done with the help of a two-dimensional (2D) hydrodynamic code, BIG2 [3], to assess the damage caused by full impact of an LHC beam with a solid copper target. Although the likelihood of such a worst case scenario is extremely remote, nevertheless from the safety point of view, it is necessary to have sufficient knowledge about the
Corresponding author.
E-mail address: [email protected] (N.A. Tahir). 0168-9002/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2009.03.086
consequences of such an accident, if it ever happens. Our simulations showed that the 7 TeV/c LHC protons can penetrate up to 30–40 m in solid copper which implies that in such an accident, two to three superconducting magnets will be damaged. It is to be noted that the Super Proton Synchrotron (SPS) is used as injector to the LHC as well as it accelerates protons for neutrino production (CNGS Project). For LHC injection, the proton bunches are accelerated to a momentum of 450 GeV/c and are transferred to LHC via two beam lines. Several SPS cycles will be required to fill the LHC while in one cycle, a batch of 288 bunches can be accelerated. Such batches are extracted from the SPS by a fast kicker magnet and transferred via a 3 km long beam line into the LHC injection point. A second fast kicker magnet deflects the beam into the LHC. Although the energy stored in the batch is less than 1% of the LHC beam energy at 7 TeV/c, it still is sufficient to cause considerable damage in case of a failure. To assess the damage level caused by such an accident, limited experiments on target irradiation by the SPS beam have been done in a beam transfer line between the SPS and the LHC/CNGS target [4,5]. This will not be possible in the years to come, whereas such studies will be required on regular basis. For this reason, a facility for tests with extreme thermo-mechanical shocks, named HiRadMat, is being constructed as part of the phased implementation for LHC collimators [6]. It will allow sending of several MJ energy beam in ms pulses to a dedicated target station that will be constructed. The main use of this facility will be to test the consequences of
ARTICLE IN PRESS N.A. Tahir et al. / Nuclear Instruments and Methods in Physics Research A 606 (2009) 186–192
2. Super Proton Synchrotron at CERN The Super Proton Synchrotron, SPS is used as LHC injector, but also to accelerate and extract protons and ions for fixed target experiments and for producing neutrinos (CNGS). In particular the risks during the fast extraction of LHC and CNGS beams must be considered since any failure during this process can lead to serious equipment damage. The SPS accelerator is 6.9 km long (circumference) and accelerates protons from 14 or 26 GeV/c to a momentum of up to 450 GeV/c. It is a cycling machine with cycles having a length of about 10 s. The transverse beam size is largest at injection and decreases with the square root of the beam energy during acceleration. For the operation as a synchrotron, the beam size is typically of the order of 1 mm. When the SPS operates as LHC injector, up to 288 bunches are accelerated, each bunch with about 1:1 1011 protons. The bunch length is 0.5 ns and two neighboring bunches are separated by 25 ns so that the duration of the entire beam is about 7 ms. The normalized emittance is 3:75 106 m. Assuming a beta function of 100 m, the beam size (s of the Gaussian intensity distribution) is 0.88 mm. When the SPS was used as proton–antiproton collider, the luminosity was maximized by minimizing the beta function to 0.5 m. Assuming this value the beam size would be about 0.06 mm. We have carried out simulations using three different beam sizes, namely, s ¼ 0:088, 0.28 and 0.88 mm, respectively.
3. Energy deposition by SPS protons in solid copper High-energy protons impinging on the studied material samples produce particle cascades depositing their energy in matter that leads to an increase in temperature. The required energy deposited by the 450 GeV/c SPS beam as a function of material and geometry has been calculated using the FLUKA code [15,16]. This is a fully integrated particle physics and multipurpose Monte Carlo simulation package capable of simulating all components of the particle cascades in matter up to TeV energies. Further details can be found elsewhere [15,16]. The target is assumed to be a solid copper cylinder with a length ¼ 1 m and radius ¼ 5 cm that is facially irradiated by the SPS beam. Specific energy deposition is plotted in Fig. 1 in longitudinal direction along the beam axis (r ¼ 0:0), by a single bunch that consists of 1:1 1011 protons assuming three different values of s of the Gaussian transverse intensity distribution, namely, 0.088, 0.28 and 0.88 mm, respectively. Fig. 2 shows the corresponding profiles in radial direction at L ¼ 10 cm (point of maximum
450 GeV protons on solid copper 150
Specific Energy (J/g)
125 sigma = 0.088 mm sigma = 0.280 mm sigma = 0.880 mm
100 75 50 25 0 0
20
60 40 Cylinder Length (cm)
80
100
Fig. 1. Cylindrical copper target, length ¼ 2 m, radius ¼ 5 cm, FLUKA simulations, specific energy deposited by a single proton bunch using three different values of beam focal spot, along longitudinal direction at r ¼ 0:0.
450 GeV protons on solid copper 150 125 Specific Energy (J/g)
beam impact on beam absorbers, collimators and other objects, which is mandatory for the design of such devices to be installed in LHC and other future accelerator facilities like FAIR, at Darmstadt [7]. These experiments therefore will be very useful to validate our previous simulations [1,2] that have been done for the LHC beam. In addition to that, other areas of research including material sciences and High Energy Density (HED) states in matter [2,8–14,18–20] will also benefit from these experiments. In this paper we present numerical simulations of hydrodynamic and thermodynamic response of a solid copper target that has been irradiated with full SPS beam. The results show that the target will be destroyed by the beam, thereby generating large samples of HED matter. In Section 2 are presented the SPS beam parameters while the problem of energy deposition by protons in copper is treated in Section 3. Hydrodynamic simulation results are given in Section 4 whereas conclusions drawn from this work are noted in Section 5.
187
sigma = 0.088 mm sigma = 0.280 mm sigma = 0.880 mm
100 75 50 25 0 0
0.1
0.2
0.3
0.4
0.5
Cylinder Radius (cm) Fig. 2. Cylindrical copper target, length ¼ 2 m, radius ¼ 5 cm, FLUKA simulations, specific energy deposited by a single proton bunch using three different values of beam focal spot, along radial direction at L ¼ 10 cm.
deposition). The focal spot sizes corresponding to these values are within the typical operational limits of the SPS proton antiproton collider. To obtain the smallest beam sizes in HiRadMat, additional quadrupole magnets need to be installed. The bunch length is 0.5 ns while two neighboring bunches are separated by 25 ns so that the total pulse length is about 7 ms.
4. Simulation results on target heating by the beam The energy deposition data generated by the FLUKA code (described in the previous section) are used as input to the BIG2 code to study the target heating by the protons and the results are presented in this section. It is to be noted that in previous studies [17],we considered the target cross-section at L ¼ 10 cm (which is the point of maximum energy deposition along the beam direction) and simulated heating and hydrodynamic expansion of the cylinder along radial direction at this fixed point. This implies that the position of the point of maximum energy deposition remains fixed during the
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target irradiation. This assumption is good enough to provide a qualitative estimate of level of target heating by the beam. However, in practice, as the target is heated by few tens of proton bunches, high pressure is generated in the beam heated region that launches a strong outgoing radial shock wave which leads to a substantial reduction in the target density. As a consequence, the protons that are delivered in subsequent bunches penetrate further into the target which leads to a significant increase in the range of the protons compared to the static model that we used previously [17]. In the work presented in this paper, the specific energy deposition is normalized according to the line density of the cylindrical target along the axis which allows one to simulate longer penetration of the protons into the target due to density reduction. In these simulations we consider a copper cylinder with a length ¼ 2 m and a radius ¼ 5 cm that is facially irradiated by the SPS beam. The beam consists of 288 proton bunches while each bunch comprises 1:1 1011 protons. The bunch length is 0.5 ns and two neighboring bunches are separated by 25 ns so that the duration of the entire beam is about 7 ms. The energy deposition data provided by the FLUKA code presented in Section 3 are used as input to the BIG2 [3] code. In the following we present target simulation results using a beam spot size with a s ¼ 0:088 mm.
distributed over a much larger volume of the target and therefore we have lower average specific energy deposition of 5 kJ/g. This naturally leads to lower temperatures, nevertheless the target is still destroyed by the beam as discussed in the following subsections. 4.2. Temperature evolution In this subsection we present evolution of the target temperature as a result of beam heating. In Fig. 4 we plot target temperature on a length–radius plane at t ¼ 500 ns when about 20 out of 288 bunches have been delivered. It is to be noted that the temperature variation is mostly limited to the beam heated region, we therefore only show region that lies within inner 1 cm radius of the cylinder. This figure corresponds to the case with a maximum specific energy deposition of 1.5 kJ/g shown in Fig. 3. The target temperature is plotted in Fig. 5 at t ¼ 2500 ns which is after 100 bunches have deposited their energy. It is seen that a maximum temperature of 7400 K is generated in the heated part of the target. Moreover, it is seen that the temperature is fairly
4.1. Specific energy deposition In Fig. 3, we plot specific energy deposition along target axis at four different times during irradiation. It is seen from the curve labeled with 500 ns that after delivery of about 20 bunches, the peak specific energy deposition along the axis is 1.5 kJ/g while the position of this peak is still at L ¼ 10 cm. At t ¼ 2500 ns when about 100 bunches have been delivered, a maximum of 4.5 kJ/g specific energy has been deposited while the position of the peak has moved to a new position at L ¼ 20 cm. This is due to increase in penetration depth of protons as a result of density reduction. It is further seen that the maximum energy deposition at t ¼ 7200 ns (end of the beam), is of the order of 5 kJ/g and the position of the peak is at L ¼ 80 cm. This is due to strong reduction in the target density along the axis as discussed above. It is also to be noted that in previous study of this problem [17] where we used a static model (peak of deposition fixed), a maximum specific energy deposition of about 40 kJ/g was achieved whereas in the present calculations the energy is
Fig. 4. Beam incident from left-to-right: temperature on length–radius plane at t ¼ 500 ns, solid copper cylindrical target facially irradiated by 450 GeV/c SPS proton bunches, target length ¼ 200 cm, target radius ¼ 5 cm, Gaussian intensity distribution in transverse direction with s ¼ 0:088 mm, 288 bunches with each bunch composed of 1:1 1011 protons, bunch length ¼ 0:5 ns, bunch separation ¼ 25 ns (any significant temperature variation is localized to beam heated region so only the inner 1 cm radius is shown in these figures).
6 t = 500 ns t = 2500 ns t = 5000 ns t = 7200 ns
Specific Energy (kJ/g)
5 4 3 2 1 0 0
25
50
75 100 125 Target Length (cm)
150
175
200
Fig. 3. Specific energy deposition along the target axis at four different times during target irradiation.
Fig. 5. Same as in Fig. 4, but at t ¼ 2500 ns.
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uniform in axial direction in the beam heated region. This is because of shifting of the peak of energy deposition along the axis due to density reduction. Fig. 6 is plotted at t ¼ 5000 ns. By this time about 200 bunches have been delivered to the target. It is seen that the maximum temperature has increased to about 8000 K which is not a substantial increase compared to that in Fig. 4. This is due to the fact that the beam energy is being deposited in a larger volume of the target. Fig. 7 is plotted at t ¼ 7200 ns which is at the end of the pulse. It is seen that a maximum temperature of about 8100 K is achieved in most of the beam heated region. It is to be noted that there is no significant change in the target temperature compared to Fig. 6. It is also to be noted that the maximum temperature along the target axis in the present case is about a factor of 4 lower than that predicted in our previous study [17]. This is due to the fact that in the calculations presented in Ref. [17], we did not consider the effect of density variation on energy deposition and the range was fixed that. As a consequence the peak of energy deposition was always at the same point (L ¼ 10 cm). This led to a higher energy deposition at this point. In the present calculations, on the other hand, the specific energy deposition is normalized according to the line density along the target axis, that allows to simulate the range lengthening of the protons.
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Fig. 8 is plotted at t ¼ 9500 ns that shows that the temperature has been reduced to 6600 K due to expansion of the material. In Fig. 9 we plot the temperature along the target axis at different times corresponding to Figs. 4–8. It is seen that the temperature within 100 cm target length is between 6000 and 8000 K. It is interesting to note that on the right of the maxima of every curve, there is a small region of constant temperature. This represents the melting of the target and it is also to be noted that this region moves rightwards as the proton range lengthens. It is also to be noted that the material in the beam heated region in the inner part of the target is in state of a strongly coupled plasma. Similar results have also been obtained using heavy ion beams [12].
4.3. Pressure evolution Target pressure at t ¼ 500 ns (corresponding to Fig. 4) is plotted in Fig. 10. It is seen that a maximum pressure of about 4.5 GPa has been generated in the region of maximum energy deposition. This pressure generates a strong shock wave in radial direction as seen in Fig. 11 which is plotted at t ¼ 2500 ns. It is seen that the pressure has increased up to 1 cm in radial direction due to the spread of the shock wave and up to about 80 cm due to the longer penetration of the protons into the target.
Fig. 6. Same as in Fig. 4, but at t ¼ 5000 ns.
Fig. 8. Same as in Fig. 4, but at t ¼ 9500 ns.
t = 500 ns t = 2500 ns t = 5000 ns t = 7200 ns t = 9500 ns
Temperature (K)
8000
6000
4000
2000
0 0
25
50
75
100
125
150
175
Target Length (cm) Fig. 7. Same as in Fig. 4, but at t ¼ 7200 ns.
Fig. 9. Temperature along target axis at different times.
200
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Figs. 12 and 13 are plotted at t ¼ 5000 and 7200 ns, respectively, that show further spreading of the high pressure region in the radial as well as longitudinal direction. Moreover, development of negative pressure in the target is also seen.
Fig. 10. Beam incident from left-to-right: pressure on length–radius plane at t ¼ 500 ns, solid copper cylindrical target facially irradiated by 450 GeV/c SPS proton bunches, target length ¼ 50 cm, target radius ¼ 5 cm, Gaussian intensity distribution in transverse direction with s ¼ 0:088 mm, 288 bunches with each bunch composed of 1:1 1011 protons, bunch length ¼ 0:5 ns, bunch separation ¼ 25 ns. Fig. 13. Same as in Fig. 9, but at t ¼ 7200 ns.
Fig. 11. Same as in Fig. 9, but at t ¼ 2500 ns. (Propagation of shock wave generated by thermal pressure is clearly seen.)
Fig. 14. Same as in Fig. 9, but at t ¼ 9500 ns.
5 t = 500 ns t = 2500 ns t = 5000 ns t = 7200 ns t = 9500 ns
Pressure (GPa)
4
3
2
1
0 0
Fig. 12. Same as in Fig. 9, but at t ¼ 5000 ns.
50
100 Target Length (cm)
150
Fig. 15. Pressure along target axis at different times.
200
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Since the beam is over at t ¼ 7200 ns, it is seen in Fig. 14 (at t ¼ 9500 ns) that the pressure does not increase in longitudinal direction, but the shock wave continues to propagate in the radial direction. In Fig. 15, we plot pressure along the target axis at different times that again shows movement of the pressure peak rightwards along the beam axis due to the reasons discussed above. It is also seen that although the temperature is fairly uniform within first 100 cm of the target length (Fig. 9), the pressure is quite low on the left side of every pressure peak. This again is due to the reduction in density generated by the radial shock wave.
191
t ¼ 2500 ns, the target density in this region has been reduce to 3:6 g=cm3 due to the radial shock wave. Figs. 18–20 show further substantial reduction in the density in the beam heated region.
4.4. Density evolution In the following we discuss the density evolution of the target. In Fig. 16 is plotted the density on a length–radius plane at t ¼ 500 ns. It is seen that a slight reduction in the target density has already occurred in a small region where the peak energy deposition takes place (around L ¼ 10 cm). Fig. 17 shows that at Fig. 18. Same as in Fig. 16, but at t ¼ 5000 ns.
Fig. 16. Beam incident from left-to-right: density on length–radius plane corresponding to Fig. 4; t ¼ 500 ns (any significant density variation is localized to beam heated region so only the inner 1 cm radius is shown in these figures).
Fig. 19. Same as in Fig. 16, but at t ¼ 7200 ns.
Fig. 17. Same as in Fig. 16, but at t ¼ 2500 ns.
Fig. 20. Same as in Fig. 16, but at t ¼ 9500 ns.
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Density (g/cc)
8 t = 500 ns t = 2500 ns t = 5000 ns t = 7200 ns t = 9500 ns
6
4
2
0 0
25
50
75 100 125 Target Length (cm)
150
175
200
Fig. 21. Density along target axis at different times.
In Fig. 21 we plot the target density along the target axis at different times. It is seen that at t ¼ 7200 ns (end of the pulse) the protons have penetrated up to 125 cm whereas from Fig. 1 it is seen that using a static model the beam deposition will occur up to 50 cm. It is therefore very important to take into account these dynamic effects when estimating thickness of, for example, a sacrificial beam stopper. It is also seen from this figure that at t ¼ 9500 ns, there is no further density reduction in longitudinal direction whereas the density continues to decrease in the radial direction due to the shock wave. It is also to be noted that according to our simulations, the target is severely damaged even in case of the largest focal spot size with s ¼ 0:88 mm. In this case a specific energy of 3.77 kJ/g is deposited at the target center whereas the maximum temperature is of the order of 6500 K that sufficient to generate a strongly coupled copper plasma. The minimum density at the end of the pulse in the target center is 4:5 g=cm3 while the penetration depth of the protons is about 85 cm. This of course is shorter compared to 125 cm in case of s ¼ 0:088 mm discussed above.
cylindrical target irradiated by a proton beam that is generated by the SPS at CERN. The target length is 200 cm and radius is 5 cm. The proton energy is 450 GeV/c and the beam comprises 288 bunches with each bunch consisting of 1:1 1011 protons. Bunch length is 0.5 ns and two neighboring bunches are separated by 25 ns so that the total length of the beam is 7:2 ms. Transverse intensity distribution in the focal spot is Gaussian and three focal spot sizes corresponding to s ¼ 0:088, 0.28 and 0.88 mm are considered. Proton energy deposition in the target is calculated by the FLUKA code and these data are used as input to a 2D hydrodynamic computer code BIG2. In this study, the effect of penetration of the protons deeper into the target as a result of density reduction caused by the radial shock wave is modeled by normalizing the specific energy deposition with the line density of the target along the axis. These simulations have shown that the target will be severely damaged by the SPS beam and the protons will penetrate much longer distance in the target compared to the static model used previously. These simulations can be very helpful in designing the future experiments at the HiRadMat facility at CERN to study such problems. An additional outcome of this work is that one may also carry out experiments at this facility to study HED physics problems. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]
5. Conclusions In this paper we have reported numerical simulations of the hydrodynamic and thermodynamic response of a solid copper
[17] [18] [19] [20]
N.A. Tahir, et al., J. Appl. Phys. 97 (2005) 083532. N.A. Tahir, et al., Phys. Rev. Lett. 94 (2005) 135004. V.E. Fortov, et al., Nucl. Sci. Eng. 123 (1996) 169. V. Kain, et al., CERN-LHC-Project-Report 822, Geneva, CERN, 2005. R. Assmann et al., LHC collimators: design and results from prototyping and beam tests, CERN-LHC-Project Report-850, 2005. R. Assmann, private communication. W.F. Henning, Nucl. Instr. and Meth. A 214 (2004) 211. N.A. Tahir, et al., Phys. Rev. E 60 (1999) 4715. N.A. Tahir, et al., Phys. Rev. E 61 (2000) 1975. N.A. Tahir, et al., Phys. Rev. E 62 (2000) 1224. N.A. Tahir, et al., Phys. Rev. Spec. Topics Beams Accel. 6 (2003) 020101. N.A. Tahir, et al., Phys. Rev. Lett. 95 (2005) 035001. N.A. Tahir, et al., Phys. Rev. E 63 (2001) 016402. N.A. Tahir, et al., Phys. Rev. B 67 (2003) 18410. A. Fasso et al., FLUKA: a multi-particle transport code, CERN-2005-10, INFN/ TC-05/11, SLAC-R-773, 2005. A. Fasso et al., The physics models of FLUKA: status and recent developments, in: Conference on Computing in High Energy and Nuclear Physics, La Jolla, USA, March 24–28, 2003, arXiv:hep-ph/0306267. N.A. Tahir, et al., Laser Part. Beams 26 (2007) 639. A.R. Piriz, et al., Phys. Rev. E 66 (2002) 056403. A.R. Piriz, et al., Phys. Rev. E 67 (2003) 017501. A.R. Piriz, et al., Plasma Phys. Controlled Fusion (2003) 1733.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Interaction of Super Proton Synchrotron beam with solid copper target: Simulations of future experiments at HiRadMat facility at CERN N.A. Tahir a,, R. Schmidt b, M. Brugger b, R. Assmann b, A. Shutov c, I.V. Lomonosov c, V.E. Fortov c, A.R. Piriz d, C. Deutsch e, D.H.H. Hoffmann f a
¨ r Schwerionenforschung, Planckstrasse 1, 64291 Darmstadt, Germany Gesellschaft fu CERN–AB, 1211 Geneva 23, Switzerland c Institute of Problems of Chemical Physics, 142432 Chernogolovka, Russia d ETSI Industriales and Instituto de Investigaciones Energe´ticas, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain e LPGP, Universite Paris-Sud, 91405 Orsay, France f ¨t Darmstadt, 64289 Darmstadt, Germany ¨ r Kernephysik, Technische Universita Institut fu b
a r t i c l e in f o
a b s t r a c t
Available online 5 April 2009
In this paper we present numerical simulations of interaction of 450 GeV/c proton beam that is generated by Super Proton Synchrotron (SPS) at CERN, with a solid copper target. These simulations have been carried out using a two-dimensional hydrodynamic computer code, BIG2. This study has been done to assess the damage caused by these highly relativistic protons to equipment including collimators, absorbers and others in case of an uncontrolled accidental release of the beam. In fact a dedicated experimental facility named HiRadMat is under construction at CERN that will allow one to study these problems experimentally. The simulations presented in this paper will be very useful in designing these experiments and later to interpret the experimental results. & 2009 Elsevier B.V. All rights reserved.
Keywords: Large Hadron Collider Super Proton Synchrotron High Enegry Density physics Strongly coupled plasmas
1. Introduction Completion of the Large Hadron Collide (LHC) at CERN is the culmination of decades of hard work by thousands of scientists around the world. By far, it is the most powerful particle accelerator that has ever been built over this planet. This impressive facility will allow collisions between two counter rotating proton beams that will be accelerated to energy of 7 TeV/c over a circumference of 26.7 km. Each LHC beam will comprise 2808 proton bunches with each bunch containing 1:15 1011 protons. This corresponds to a total energy of 350 MJ in each beam which is sufficient to melt 500 kg of copper. Safety of the equipment and the personnel while working with such extremely powerful beams is an issue of utmost importance and must be addressed meticulously well before the commissioning phase of the facility. One of the important steps in this direction was our previous study [1,2] that was done with the help of a two-dimensional (2D) hydrodynamic code, BIG2 [3], to assess the damage caused by full impact of an LHC beam with a solid copper target. Although the likelihood of such a worst case scenario is extremely remote, nevertheless from the safety point of view, it is necessary to have sufficient knowledge about the
Corresponding author.
E-mail address: [email protected] (N.A. Tahir). 0168-9002/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2009.03.086
consequences of such an accident, if it ever happens. Our simulations showed that the 7 TeV/c LHC protons can penetrate up to 30–40 m in solid copper which implies that in such an accident, two to three superconducting magnets will be damaged. It is to be noted that the Super Proton Synchrotron (SPS) is used as injector to the LHC as well as it accelerates protons for neutrino production (CNGS Project). For LHC injection, the proton bunches are accelerated to a momentum of 450 GeV/c and are transferred to LHC via two beam lines. Several SPS cycles will be required to fill the LHC while in one cycle, a batch of 288 bunches can be accelerated. Such batches are extracted from the SPS by a fast kicker magnet and transferred via a 3 km long beam line into the LHC injection point. A second fast kicker magnet deflects the beam into the LHC. Although the energy stored in the batch is less than 1% of the LHC beam energy at 7 TeV/c, it still is sufficient to cause considerable damage in case of a failure. To assess the damage level caused by such an accident, limited experiments on target irradiation by the SPS beam have been done in a beam transfer line between the SPS and the LHC/CNGS target [4,5]. This will not be possible in the years to come, whereas such studies will be required on regular basis. For this reason, a facility for tests with extreme thermo-mechanical shocks, named HiRadMat, is being constructed as part of the phased implementation for LHC collimators [6]. It will allow sending of several MJ energy beam in ms pulses to a dedicated target station that will be constructed. The main use of this facility will be to test the consequences of
ARTICLE IN PRESS N.A. Tahir et al. / Nuclear Instruments and Methods in Physics Research A 606 (2009) 186–192
2. Super Proton Synchrotron at CERN The Super Proton Synchrotron, SPS is used as LHC injector, but also to accelerate and extract protons and ions for fixed target experiments and for producing neutrinos (CNGS). In particular the risks during the fast extraction of LHC and CNGS beams must be considered since any failure during this process can lead to serious equipment damage. The SPS accelerator is 6.9 km long (circumference) and accelerates protons from 14 or 26 GeV/c to a momentum of up to 450 GeV/c. It is a cycling machine with cycles having a length of about 10 s. The transverse beam size is largest at injection and decreases with the square root of the beam energy during acceleration. For the operation as a synchrotron, the beam size is typically of the order of 1 mm. When the SPS operates as LHC injector, up to 288 bunches are accelerated, each bunch with about 1:1 1011 protons. The bunch length is 0.5 ns and two neighboring bunches are separated by 25 ns so that the duration of the entire beam is about 7 ms. The normalized emittance is 3:75 106 m. Assuming a beta function of 100 m, the beam size (s of the Gaussian intensity distribution) is 0.88 mm. When the SPS was used as proton–antiproton collider, the luminosity was maximized by minimizing the beta function to 0.5 m. Assuming this value the beam size would be about 0.06 mm. We have carried out simulations using three different beam sizes, namely, s ¼ 0:088, 0.28 and 0.88 mm, respectively.
3. Energy deposition by SPS protons in solid copper High-energy protons impinging on the studied material samples produce particle cascades depositing their energy in matter that leads to an increase in temperature. The required energy deposited by the 450 GeV/c SPS beam as a function of material and geometry has been calculated using the FLUKA code [15,16]. This is a fully integrated particle physics and multipurpose Monte Carlo simulation package capable of simulating all components of the particle cascades in matter up to TeV energies. Further details can be found elsewhere [15,16]. The target is assumed to be a solid copper cylinder with a length ¼ 1 m and radius ¼ 5 cm that is facially irradiated by the SPS beam. Specific energy deposition is plotted in Fig. 1 in longitudinal direction along the beam axis (r ¼ 0:0), by a single bunch that consists of 1:1 1011 protons assuming three different values of s of the Gaussian transverse intensity distribution, namely, 0.088, 0.28 and 0.88 mm, respectively. Fig. 2 shows the corresponding profiles in radial direction at L ¼ 10 cm (point of maximum
450 GeV protons on solid copper 150
Specific Energy (J/g)
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100 75 50 25 0 0
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60 40 Cylinder Length (cm)
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Fig. 1. Cylindrical copper target, length ¼ 2 m, radius ¼ 5 cm, FLUKA simulations, specific energy deposited by a single proton bunch using three different values of beam focal spot, along longitudinal direction at r ¼ 0:0.
450 GeV protons on solid copper 150 125 Specific Energy (J/g)
beam impact on beam absorbers, collimators and other objects, which is mandatory for the design of such devices to be installed in LHC and other future accelerator facilities like FAIR, at Darmstadt [7]. These experiments therefore will be very useful to validate our previous simulations [1,2] that have been done for the LHC beam. In addition to that, other areas of research including material sciences and High Energy Density (HED) states in matter [2,8–14,18–20] will also benefit from these experiments. In this paper we present numerical simulations of hydrodynamic and thermodynamic response of a solid copper target that has been irradiated with full SPS beam. The results show that the target will be destroyed by the beam, thereby generating large samples of HED matter. In Section 2 are presented the SPS beam parameters while the problem of energy deposition by protons in copper is treated in Section 3. Hydrodynamic simulation results are given in Section 4 whereas conclusions drawn from this work are noted in Section 5.
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sigma = 0.088 mm sigma = 0.280 mm sigma = 0.880 mm
100 75 50 25 0 0
0.1
0.2
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Cylinder Radius (cm) Fig. 2. Cylindrical copper target, length ¼ 2 m, radius ¼ 5 cm, FLUKA simulations, specific energy deposited by a single proton bunch using three different values of beam focal spot, along radial direction at L ¼ 10 cm.
deposition). The focal spot sizes corresponding to these values are within the typical operational limits of the SPS proton antiproton collider. To obtain the smallest beam sizes in HiRadMat, additional quadrupole magnets need to be installed. The bunch length is 0.5 ns while two neighboring bunches are separated by 25 ns so that the total pulse length is about 7 ms.
4. Simulation results on target heating by the beam The energy deposition data generated by the FLUKA code (described in the previous section) are used as input to the BIG2 code to study the target heating by the protons and the results are presented in this section. It is to be noted that in previous studies [17],we considered the target cross-section at L ¼ 10 cm (which is the point of maximum energy deposition along the beam direction) and simulated heating and hydrodynamic expansion of the cylinder along radial direction at this fixed point. This implies that the position of the point of maximum energy deposition remains fixed during the
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target irradiation. This assumption is good enough to provide a qualitative estimate of level of target heating by the beam. However, in practice, as the target is heated by few tens of proton bunches, high pressure is generated in the beam heated region that launches a strong outgoing radial shock wave which leads to a substantial reduction in the target density. As a consequence, the protons that are delivered in subsequent bunches penetrate further into the target which leads to a significant increase in the range of the protons compared to the static model that we used previously [17]. In the work presented in this paper, the specific energy deposition is normalized according to the line density of the cylindrical target along the axis which allows one to simulate longer penetration of the protons into the target due to density reduction. In these simulations we consider a copper cylinder with a length ¼ 2 m and a radius ¼ 5 cm that is facially irradiated by the SPS beam. The beam consists of 288 proton bunches while each bunch comprises 1:1 1011 protons. The bunch length is 0.5 ns and two neighboring bunches are separated by 25 ns so that the duration of the entire beam is about 7 ms. The energy deposition data provided by the FLUKA code presented in Section 3 are used as input to the BIG2 [3] code. In the following we present target simulation results using a beam spot size with a s ¼ 0:088 mm.
distributed over a much larger volume of the target and therefore we have lower average specific energy deposition of 5 kJ/g. This naturally leads to lower temperatures, nevertheless the target is still destroyed by the beam as discussed in the following subsections. 4.2. Temperature evolution In this subsection we present evolution of the target temperature as a result of beam heating. In Fig. 4 we plot target temperature on a length–radius plane at t ¼ 500 ns when about 20 out of 288 bunches have been delivered. It is to be noted that the temperature variation is mostly limited to the beam heated region, we therefore only show region that lies within inner 1 cm radius of the cylinder. This figure corresponds to the case with a maximum specific energy deposition of 1.5 kJ/g shown in Fig. 3. The target temperature is plotted in Fig. 5 at t ¼ 2500 ns which is after 100 bunches have deposited their energy. It is seen that a maximum temperature of 7400 K is generated in the heated part of the target. Moreover, it is seen that the temperature is fairly
4.1. Specific energy deposition In Fig. 3, we plot specific energy deposition along target axis at four different times during irradiation. It is seen from the curve labeled with 500 ns that after delivery of about 20 bunches, the peak specific energy deposition along the axis is 1.5 kJ/g while the position of this peak is still at L ¼ 10 cm. At t ¼ 2500 ns when about 100 bunches have been delivered, a maximum of 4.5 kJ/g specific energy has been deposited while the position of the peak has moved to a new position at L ¼ 20 cm. This is due to increase in penetration depth of protons as a result of density reduction. It is further seen that the maximum energy deposition at t ¼ 7200 ns (end of the beam), is of the order of 5 kJ/g and the position of the peak is at L ¼ 80 cm. This is due to strong reduction in the target density along the axis as discussed above. It is also to be noted that in previous study of this problem [17] where we used a static model (peak of deposition fixed), a maximum specific energy deposition of about 40 kJ/g was achieved whereas in the present calculations the energy is
Fig. 4. Beam incident from left-to-right: temperature on length–radius plane at t ¼ 500 ns, solid copper cylindrical target facially irradiated by 450 GeV/c SPS proton bunches, target length ¼ 200 cm, target radius ¼ 5 cm, Gaussian intensity distribution in transverse direction with s ¼ 0:088 mm, 288 bunches with each bunch composed of 1:1 1011 protons, bunch length ¼ 0:5 ns, bunch separation ¼ 25 ns (any significant temperature variation is localized to beam heated region so only the inner 1 cm radius is shown in these figures).
6 t = 500 ns t = 2500 ns t = 5000 ns t = 7200 ns
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5 4 3 2 1 0 0
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Fig. 3. Specific energy deposition along the target axis at four different times during target irradiation.
Fig. 5. Same as in Fig. 4, but at t ¼ 2500 ns.
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uniform in axial direction in the beam heated region. This is because of shifting of the peak of energy deposition along the axis due to density reduction. Fig. 6 is plotted at t ¼ 5000 ns. By this time about 200 bunches have been delivered to the target. It is seen that the maximum temperature has increased to about 8000 K which is not a substantial increase compared to that in Fig. 4. This is due to the fact that the beam energy is being deposited in a larger volume of the target. Fig. 7 is plotted at t ¼ 7200 ns which is at the end of the pulse. It is seen that a maximum temperature of about 8100 K is achieved in most of the beam heated region. It is to be noted that there is no significant change in the target temperature compared to Fig. 6. It is also to be noted that the maximum temperature along the target axis in the present case is about a factor of 4 lower than that predicted in our previous study [17]. This is due to the fact that in the calculations presented in Ref. [17], we did not consider the effect of density variation on energy deposition and the range was fixed that. As a consequence the peak of energy deposition was always at the same point (L ¼ 10 cm). This led to a higher energy deposition at this point. In the present calculations, on the other hand, the specific energy deposition is normalized according to the line density along the target axis, that allows to simulate the range lengthening of the protons.
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Fig. 8 is plotted at t ¼ 9500 ns that shows that the temperature has been reduced to 6600 K due to expansion of the material. In Fig. 9 we plot the temperature along the target axis at different times corresponding to Figs. 4–8. It is seen that the temperature within 100 cm target length is between 6000 and 8000 K. It is interesting to note that on the right of the maxima of every curve, there is a small region of constant temperature. This represents the melting of the target and it is also to be noted that this region moves rightwards as the proton range lengthens. It is also to be noted that the material in the beam heated region in the inner part of the target is in state of a strongly coupled plasma. Similar results have also been obtained using heavy ion beams [12].
4.3. Pressure evolution Target pressure at t ¼ 500 ns (corresponding to Fig. 4) is plotted in Fig. 10. It is seen that a maximum pressure of about 4.5 GPa has been generated in the region of maximum energy deposition. This pressure generates a strong shock wave in radial direction as seen in Fig. 11 which is plotted at t ¼ 2500 ns. It is seen that the pressure has increased up to 1 cm in radial direction due to the spread of the shock wave and up to about 80 cm due to the longer penetration of the protons into the target.
Fig. 6. Same as in Fig. 4, but at t ¼ 5000 ns.
Fig. 8. Same as in Fig. 4, but at t ¼ 9500 ns.
t = 500 ns t = 2500 ns t = 5000 ns t = 7200 ns t = 9500 ns
Temperature (K)
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Target Length (cm) Fig. 7. Same as in Fig. 4, but at t ¼ 7200 ns.
Fig. 9. Temperature along target axis at different times.
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Figs. 12 and 13 are plotted at t ¼ 5000 and 7200 ns, respectively, that show further spreading of the high pressure region in the radial as well as longitudinal direction. Moreover, development of negative pressure in the target is also seen.
Fig. 10. Beam incident from left-to-right: pressure on length–radius plane at t ¼ 500 ns, solid copper cylindrical target facially irradiated by 450 GeV/c SPS proton bunches, target length ¼ 50 cm, target radius ¼ 5 cm, Gaussian intensity distribution in transverse direction with s ¼ 0:088 mm, 288 bunches with each bunch composed of 1:1 1011 protons, bunch length ¼ 0:5 ns, bunch separation ¼ 25 ns. Fig. 13. Same as in Fig. 9, but at t ¼ 7200 ns.
Fig. 11. Same as in Fig. 9, but at t ¼ 2500 ns. (Propagation of shock wave generated by thermal pressure is clearly seen.)
Fig. 14. Same as in Fig. 9, but at t ¼ 9500 ns.
5 t = 500 ns t = 2500 ns t = 5000 ns t = 7200 ns t = 9500 ns
Pressure (GPa)
4
3
2
1
0 0
Fig. 12. Same as in Fig. 9, but at t ¼ 5000 ns.
50
100 Target Length (cm)
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Fig. 15. Pressure along target axis at different times.
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Since the beam is over at t ¼ 7200 ns, it is seen in Fig. 14 (at t ¼ 9500 ns) that the pressure does not increase in longitudinal direction, but the shock wave continues to propagate in the radial direction. In Fig. 15, we plot pressure along the target axis at different times that again shows movement of the pressure peak rightwards along the beam axis due to the reasons discussed above. It is also seen that although the temperature is fairly uniform within first 100 cm of the target length (Fig. 9), the pressure is quite low on the left side of every pressure peak. This again is due to the reduction in density generated by the radial shock wave.
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t ¼ 2500 ns, the target density in this region has been reduce to 3:6 g=cm3 due to the radial shock wave. Figs. 18–20 show further substantial reduction in the density in the beam heated region.
4.4. Density evolution In the following we discuss the density evolution of the target. In Fig. 16 is plotted the density on a length–radius plane at t ¼ 500 ns. It is seen that a slight reduction in the target density has already occurred in a small region where the peak energy deposition takes place (around L ¼ 10 cm). Fig. 17 shows that at Fig. 18. Same as in Fig. 16, but at t ¼ 5000 ns.
Fig. 16. Beam incident from left-to-right: density on length–radius plane corresponding to Fig. 4; t ¼ 500 ns (any significant density variation is localized to beam heated region so only the inner 1 cm radius is shown in these figures).
Fig. 19. Same as in Fig. 16, but at t ¼ 7200 ns.
Fig. 17. Same as in Fig. 16, but at t ¼ 2500 ns.
Fig. 20. Same as in Fig. 16, but at t ¼ 9500 ns.
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Density (g/cc)
8 t = 500 ns t = 2500 ns t = 5000 ns t = 7200 ns t = 9500 ns
6
4
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Fig. 21. Density along target axis at different times.
In Fig. 21 we plot the target density along the target axis at different times. It is seen that at t ¼ 7200 ns (end of the pulse) the protons have penetrated up to 125 cm whereas from Fig. 1 it is seen that using a static model the beam deposition will occur up to 50 cm. It is therefore very important to take into account these dynamic effects when estimating thickness of, for example, a sacrificial beam stopper. It is also seen from this figure that at t ¼ 9500 ns, there is no further density reduction in longitudinal direction whereas the density continues to decrease in the radial direction due to the shock wave. It is also to be noted that according to our simulations, the target is severely damaged even in case of the largest focal spot size with s ¼ 0:88 mm. In this case a specific energy of 3.77 kJ/g is deposited at the target center whereas the maximum temperature is of the order of 6500 K that sufficient to generate a strongly coupled copper plasma. The minimum density at the end of the pulse in the target center is 4:5 g=cm3 while the penetration depth of the protons is about 85 cm. This of course is shorter compared to 125 cm in case of s ¼ 0:088 mm discussed above.
cylindrical target irradiated by a proton beam that is generated by the SPS at CERN. The target length is 200 cm and radius is 5 cm. The proton energy is 450 GeV/c and the beam comprises 288 bunches with each bunch consisting of 1:1 1011 protons. Bunch length is 0.5 ns and two neighboring bunches are separated by 25 ns so that the total length of the beam is 7:2 ms. Transverse intensity distribution in the focal spot is Gaussian and three focal spot sizes corresponding to s ¼ 0:088, 0.28 and 0.88 mm are considered. Proton energy deposition in the target is calculated by the FLUKA code and these data are used as input to a 2D hydrodynamic computer code BIG2. In this study, the effect of penetration of the protons deeper into the target as a result of density reduction caused by the radial shock wave is modeled by normalizing the specific energy deposition with the line density of the target along the axis. These simulations have shown that the target will be severely damaged by the SPS beam and the protons will penetrate much longer distance in the target compared to the static model used previously. These simulations can be very helpful in designing the future experiments at the HiRadMat facility at CERN to study such problems. An additional outcome of this work is that one may also carry out experiments at this facility to study HED physics problems. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]
5. Conclusions In this paper we have reported numerical simulations of the hydrodynamic and thermodynamic response of a solid copper
[17] [18] [19] [20]
N.A. Tahir, et al., J. Appl. Phys. 97 (2005) 083532. N.A. Tahir, et al., Phys. Rev. Lett. 94 (2005) 135004. V.E. Fortov, et al., Nucl. Sci. Eng. 123 (1996) 169. V. Kain, et al., CERN-LHC-Project-Report 822, Geneva, CERN, 2005. R. Assmann et al., LHC collimators: design and results from prototyping and beam tests, CERN-LHC-Project Report-850, 2005. R. Assmann, private communication. W.F. Henning, Nucl. Instr. and Meth. A 214 (2004) 211. N.A. Tahir, et al., Phys. Rev. E 60 (1999) 4715. N.A. Tahir, et al., Phys. Rev. E 61 (2000) 1975. N.A. Tahir, et al., Phys. Rev. E 62 (2000) 1224. N.A. Tahir, et al., Phys. Rev. Spec. Topics Beams Accel. 6 (2003) 020101. N.A. Tahir, et al., Phys. Rev. Lett. 95 (2005) 035001. N.A. Tahir, et al., Phys. Rev. E 63 (2001) 016402. N.A. Tahir, et al., Phys. Rev. B 67 (2003) 18410. A. Fasso et al., FLUKA: a multi-particle transport code, CERN-2005-10, INFN/ TC-05/11, SLAC-R-773, 2005. A. Fasso et al., The physics models of FLUKA: status and recent developments, in: Conference on Computing in High Energy and Nuclear Physics, La Jolla, USA, March 24–28, 2003, arXiv:hep-ph/0306267. N.A. Tahir, et al., Laser Part. Beams 26 (2007) 639. A.R. Piriz, et al., Phys. Rev. E 66 (2002) 056403. A.R. Piriz, et al., Phys. Rev. E 67 (2003) 017501. A.R. Piriz, et al., Plasma Phys. Controlled Fusion (2003) 1733.