Impact of the new CLIC beam parameters on the design of the post-collision line and its exit window

Transcription

1 CERN - EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH CLIC Note 739 EUROTeV-Report Impact of the new CLIC beam parameters on the design of the post-collision line and its exit window A. Ferrari Uppsala University, Sweden CERN-OPEN /6/28 Following the recent modification of the CLIC beam parameters, we present an updated design of the post-collision line. As a result of the increase of the beamstrahlung photon cone size, the separation of the outgoing beams by the vertical magnetic chicane is more difficult, but still possible. The main changes in the post-collision line design include the implementation of a common dump for the wrong-sign charged particles of the coherent pairs and for the low-energy tails of the disrupted beam, as well as a significant reduction of the overall lattice length (allowing removal of the large refocusing quadrupoles). The thermal and mechanical stresses in the new exit window, 15 m downstream of the interaction point, were computed. We conclude that, despite the recent changes of the CLIC beam parameters and the necessary modifications of the post-collision line and its exit window, their performance is not significantly affected. Geneva, Switzerland June 4, 28

2 1 Introduction The Compact Linear Collider (CLIC) aims at multi-tev e + e collisions using the twobeam acceleration technology [1]. In this concept, the RF power needed to accelerate the main (colliding) beams is extracted from a drive-beam running parallel to the main linac. At the interaction point, the incoming beams must be focused to very small spot sizes in order to achieve high charge densities and thereby reach the desired luminosity. As a result, the colliding beams experience strong electromagnetic fields. The subsequent bending of their trajectories leads to the emission of beamstrahlung photons, which can then turn into e + e coherent pairs. A careful design of the post-collision line must be performed to transport all outgoing beams from the interaction point to the dump, with as small losses as possible. In addition, the thin window that separates the beam dump from the accelerator vacuum at the end of the post-collision line must withstand a huge power, not only when e + e collisions occur (in which case the charged beams are widened at the interaction point), but also in the case of non-colliding beams, for which the local energy deposition is much larger. A conceptual design of the CLIC post-collision extraction line was presented in [2]. It separates the various components of the outgoing beam thanks to a vertical magnetic chicane, before transporting them to their respective dump. As for the vacuum window at the end of the post-collision line, a thick (1.5 cm) layer of carbon-carbon composite with a thin (.2 mm) Aluminium leak-tight foil was proposed [3]. However, these two design studies were performed using the CLIC beam parameters of [4] as a reference, which are now obsolete. In particular, the RF frequency and the accelerating gradient were lowered, respectively from 3 to 12 GHz and from 15 to 1 MV/m. As a result, the beam properties at the interaction point had to be reviewed [5]. Obviously, these changes may also have an impact on the lattice downstream, i.e. the post-collision line and its exit window. In Section 2, we discuss the modifications brought to the CLIC beam parameters at the interaction point and we show how the distributions of the outgoing beams are affected. Then, in Sections 3 and 4, we discuss the impact of the new CLIC beam parameters on the performance of the post-collision line and its exit window, respectively. Finally, a summary is given in Section 5. 2 Main characteristics of the incoming and outgoing beams at the interaction point Table 1 shows a comparison between the main CLIC incoming beam parameters at the interaction point used as a reference until 27 [4] and presently [5]. The modification of the RF frequency and of the accelerating gradient result from an optimization of the machine performance as well as its cost. 2

3 Parameter Symbol Old value New value Unit Centre-of-mass energy E cm 3 3 TeV Acceleration frequency f RF 3 12 GHz Acceleration gradient g ACC 15 1 MV/m Particles per bunch N b Bunches per RF pulse n Bunch-bunch spacing Δt b ns Repetition frequency f 15 5 Hz Primary beam power P b MW Proposed site length L tot km Beam crossing angle θ c 2 2 mrad Horizontal normalized emittance (βγ)ɛ x nm.rad Vertical normalized emittance (βγ)ɛ y 1 2 nm.rad Horizontal rms beam size σx 6 4 nm Vertical rms beam size σy.7 1. nm Full-width energy spread σ E /E 1 1 % Rms bunch length σ z μm Peak luminosity L cm 2 s 1 Table 1: Old [4] and new [5] incoming beam parameters of the CLIC machine. The outgoing beam distributions were derived from GUINEA-PIG simulations [6], with 1 5 macro-particles. The transverse distributions and the energy spectrum of the (old and new) CLIC disrupted beams are shown in Figures 1 and 2, respectively. The long low-energy tails result from the emission of beamstrahlung photons during the bunch crossing. With the new beam parameters, in average, the energy loss of each incoming beam δ B is 29% and 2.2 beamstrahlung photons are emitted per incoming electron or positron. These parameters were respectively 16% and 1.1 in the previous design of the CLIC machine. In addition, as illustrated in Figure 3, the beamstrahlung photon cone becomes larger in the new CLIC design, especially along the horizontal direction. Finally, as a result of the beam parameter changes, the luminosity within 1% of the nominal energy decreases from 3.3 to cm 2 s 1. In the presence of a strong electromagnetic field, beamstrahlung photons can turn into e + e coherent pairs, with a probability that mostly depends on the parameter Υ [7]: Υ= 5 γre 2N b 6 ασ z σ y (1 + σ x /σ y ), (1) where α =1/137 and r e = m are respectively the fine-structure constant and the classical electron radius. In the new CLIC design, Υ 5.4 and the expected number of e + e coherent pairs is per bunch crossing, which is about an order of magnitude larger than with the old beam parameters. The electrons and positrons of the coherent pairs carry typically about 1% of the primary beam energy. 3

4 Amount of particles Amount of particles x (nm) Amount of particles Amount of particles y (nm) x (μrad) y (μrad) Figure 1: Transverse distributions of the disrupted beam at the interaction point, as obtained with the new (full line) and old (dashed line) beam parameters. Amount of particles δp/p = (E-E )/E Figure 2: Energy spectrum of the disrupted beam at the interaction point, as obtained with the new (full line) and old (dashed line) beam parameters. 4

5 Amount of particles Amount of particles x (μrad) y (μrad) Figure 3: Angular distributions of the beamstrahlung photons at the interaction point, as obtained with the new (full line) and old (dashed line) beam parameters. For simplicity, the plots are normalized to roughly the same number of photons. We now consider the non-colliding beams. At a distance s from the interaction point, if there are no magnetic elements on the path of the undisrupted beam, the betatron functions are given by: ( ) 2 s β(s) =β(ip) 1+. (2) β(ip) Here, β x (IP)=4mmandβ y (IP)=.9 mm. Figure 4 shows how the rms transverse sizes of the non-colliding beam depend on the distance to the interaction point, when all magnetic elements along the beam path are switched-off. In the conceptual design of the CLIC post-collision line performed in [2], the exit window is placed 247 m downstream of the interaction point and the smallest beam spot size there is 2.1 mm 1.9 mm. With the new CLIC parameters, it becomes 2.5 mm 2.8 mm. Rms beam size (mm) Horizontal Vertical s (m) Figure 4: Transverse sizes of the undisrupted beam as a function of the distance s to the interaction point if all magnets are switched-off along the beam path. 5

6 3 Impact of the new CLIC beam parameters on the post-collision line A detailed design of the CLIC post-collision line was performed in [2]. A schematic layout of this beam line is shown in Figure 5. In a first step, 16 m downstream of the interaction point, it separates the various components of the outgoing beam in four extraction magnets, which provide a total bending angle of 3.2 mrad at 1.5 TeV. Following their physical separation from the other beam components, the particles of the coherent pairs with the wrong-sign charge are immediately brought to their dump. The energy spectrum of the coherent pairs is derived from the vertical distribution of the wrong-sign charged beam. As for the disrupted beam and the beamstrahlung photons, they are transported in the same vacuum pipe to a common dump. The bend provided bytheextractionmagnetsisfollowedbyabend in the opposite direction, using four C-type magnets, in order to eventually have D y =. All beamstrahlung photons and charged particles with more than 15% of the nominal beam energy pass through the vertical chicane and reach the dump (the lost particles are absorbed in collimators). At the exit of the chicane, the low-energy particles of the disrupted beam, which still have y <, receive a positive kick when passing through 16 vertically focusing quadrupoles (meanwhile, the high-energy core of the beam remains unaffected). This allows some flexibility in the design of the last section of the post-collision line, because the vertical rms size of the disrupted beam after the refocusing region decreases with the distance from the interaction point to the dump. An accurate analysis of the final transverse beam profiles allows to derive relevant information on the e + e collisions. In particular, small vertical offsets in position and/or angle between the incoming beams, which affect the disruption process, can be identified by measuring the displacement and/or the distorsion of the outgoing beams. Note that these offsets may lead to additional losses along the post-collision line, however these mostly occur in the collimators. Four extraction magnets with collimators Coherent pairs dump Separation Four C type region Collimators magnets Refocusing region Beamstrahlung photons Charged particles 1111 Dump for the disrupted beam and the photons Figure 5: Schematic layout (not on scale) of the CLIC post-collision extraction line of [2], where the arrows show the path of the beamstrahlung photons and of the charged particles (disrupted beam and coherent pairs). In this section, we review all parts of the post-collision line, from the interaction point to the main dump, and we check how their geometry and their performance are affected by the modification of the CLIC beam parameters. For this purpose, having generated all outgoing beams with GUINEA-PIG, particle trackings are performed with DIMAD [8]. 6

7 3.1 Extraction and separation of the outgoing beams The first magnetic elements of the CLIC post-collision line are four extraction dipoles, which are spaced by 1 m, with a field strength of 1 T and a length of 4 m each. The distance from the interaction point to the entrance of the first magnet is L IP =16m. All these parameters were chosen in order to ensure an excellent separation between the beamstrahlung photons and the high-energy peak of the disrupted beam. Indeed, with the beam parameters of [4], the vertical deviation for 1.5 TeV particles at the exit of the fourth magnet (δy =3.4 cm) is 1 times larger than the worst rms photon cone size (.28 cm), derived from the largest rms value of the vertical angular divergence of the beamstrahlung photons (Max[σ γ y ] 8 μrad with a small position offset between the colliding beams at the interaction point). With the new beam parameters, our GUINEA-PIG simulations with beam-beam offsets in position and/or angle show that Max[σ γ y ] becomes.2 mrad. It is obtained with a vertical position offset of 22 nm at the interaction point. Without any modification of the post-collision line, the vertical deviation at the exit of the fourth extraction magnet would be only 4.5 times larger than the worst rms photon cone size. In addition, due to the larger beamstrahlung losses for the main beam and, in turn, the larger number of e + e coherent pairs, more power losses would occur in the collimators between the magnets. In the horizontal direction, the beam size increases linearly with the distance to the interaction point and the most stringent constraint for the horizontal aperture of the vacuum pipe comes from the coherent pairs, which have the largest horizontal angular divergences: with the new CLIC parameters, Max[σ x ] is.3 mrad for particles with the wrong-sign charge and.45 mrad for particles with the right-sign charge (both are obtained in the case of ideal e + e collisions). These values are respectively 1.5 and 2.2 times larger than with the old parameters. However, this does not significantly affect the design of the extraction magnets, because the horizontal (rms) extension for the right-sign charged particles of the coherent pairs grows by only 1 cm for every 2 m of beam line, and therefore remains generally much smaller than the gap of the magnet. The design of the first section of the CLIC post-collision line was reviewed, and a few modifications of its layout are proposed in order to keep beam losses at a reasonable level in the magnets and to ease insertion of longer collimators, see Figure 6: The distance between the interaction point and the entrance of the first extraction magnet is increased from 16 to 2 m: this allows to gain a few cm for the horizontal dimension of the magnets and thereby for their gap. The length and the field strength of the four extraction magnets are not modified, but the vertical dimension of the vacuum pipe is increased by 5 cm in each dipole. The distance between two consecutive extraction magnets is increased from 1. to 1.5 m and, instead of using two collimators with a length of 2 cm each, we propose to install one 9 cm long collimator between two dipoles, which starts 3 cm after the exit of the magnet upstream and ends 3 cm before the entrance of the magnet downstream. 7

8 Magnet (4 m, 1 T) Drift (1.5 m) Wrong sign charged particles of the coherent pairs Beamstrahlung photons L IP = 2 m Right sign charged particles (disrupted beam, coherent pairs) Collimator (9 cm) L sep Figure 6: Schematic layout of the first section of the CLIC post-collision line, for the extraction and separation of the outgoing beams. The four magnets used for the separation of the outgoing beams are (compact) window frame dipoles. A schematic layout of their cross section is shown in Figure 7. IRON YOKE COILS (ni) B h d BEAM g Figure 7: Cross section of a window frame magnet, with the relevant parameters to be considered for its design. If ni is the number of Ampere-turns circulating in the coils, and if there is no saturation in the iron yoke, then: ni = H ds B g. (3) μ 8

9 We assume that half of the excitation coil cross section is used for cooling and we use a current density J =1A/mm 2.WithX coil = g, we find that: Y coil = 2B =15.9 cm. (4) μ J In order to avoid the (elliptical) vacuum pipe to collapse because of the air pressure on its outer side, the thickness of its wall should be larger along the horizontal axis than along the vertical axis (some external reinforcements should also be considered). In the following, the thickness T of the beam pipe wall is set to 5 mm along the vertical axis and, for the sake of simplicity, we assume that the ratio between T x and T y is the same as between the transverse apertures of the pipe. When taking into account these constraints, one obtains: h [cm] = Y pipe + Y coil +2T y = Y pipe cm, (5) g [cm] = X pipe +2T x = X pipe +1cm Y pipe. (6) X pipe Finally, one must make sure that the iron yoke is large enough in order to allow the magnetic flux to fully return through it. If the maximal field strength in the iron is B max, then one must impose: d h B. (7) 2B max The geometrical characteristics of each extraction magnet are summarized in Table 2. In order to derive the minimum horizontal dimension 2d + g, we use equation (7) with B max =1.7 T. The horizontal spacing between the post-collision line and the incoming beam line (4, 51, 62 and 73 cm at the entrance of the first, second, third and fourth dipole, respectively) is large enough to allow insertion of all magnets. Extraction X pipe Y pipe g h ni d + g/2 Magnet (cm) (cm) (cm) (cm) (ka.turns) (cm) Table 2: Main characteristics of the four extraction magnets installed at the beginning of the new CLIC post-collision line. One way to keep simultaneously the power losses and the transverse dimensions of the extraction magnets at a reasonable level is to install a 9 cm long collimator between them. Its purpose is to absorb some of the particles found in the low-energy tails, which are far away from the reference beam trajectory. 9

10 In DIMAD, as soon as an electron or positron has y y Y c inside a (rectangular) collimator, it is removed from the list of tracked particles. Here, y refers to the vertical position of the reference charged particle at 1.5 TeV. Having introduced these aperture limitations, the power losses can be estimated using: P loss = N b nf N tracks N loss i=1 E i. (8) Here, N b is the number of particles per bunch, n is the number of bunches per RF pulse, f is the repetition frequency (in Hz), E i is the energy of the lost particle i (in GeV), N tracks and N lost are respectively the number of tracked and lost particles. With these conventions, P loss is expressed in Watts. In Table 3, we summarize the values chosen for the half-aperture Y c of each collimator, as well as the expected power losses. All particles absorbed by the collimators have δ<.95. The power losses found using the new CLIC parameters are much larger than with the old ones. This results from the larger fraction of low-energy particles in the disrupted beam and the number of e + e coherent pairs, but also from the necessity to use a longer collimator in order to protect the magnets, where the beam loss density remains well below 1 W/m. Collimator Y c Beam losses (kw) number (in mm) Disrupted Cohplus Cohminus Table 3: Vertical half-apertures of the collimators between the extraction magnets, and corresponding power losses for the disrupted beam, the particles of the coherent pairs with the right-sign (Cohplus) and wrong-sign (Cohminus) charge. Downstream of the fourth magnet, the particles of the coherent pairs with the wrongsign charge are physically separated from the other components of the outgoing beam. The vertical dispersion (and thus the distance between the centre of the beamstrahlung photon cone and the 1.5 TeV reference wrong-sign charged particle of the coherent pairs) depends on the distance L sep to the exit of the fourth extraction dipole: D y [cm] = L sep [m]. (9) As for the vertical size σ y (γ) of the beamstrahlung photon cone in the separation region, it depends on the vertical angular divergence σ γ y at the interaction point as follows: σ y (γ) [cm]=.1 σ γ y [mrad] (L sep +4.5 [m]). (1) 1

11 y (cm) In the worst case scenario (i.e. with a beam-beam position offset of 22 nm), σyγ may reach.2 mrad. If one requires Dy to be 1 times larger than the worst rms photon cone size, then Lsep must be at least 4 m. One would then have to build an unrealistically large vacuum pipe in order to transport the charged beams without significant losses over such a long distance. Adding more extraction magnets is not a viable solution either, because one would need the beam pipe (and thereby the dipoles themselves) to have a large vertical aperture, which also has direct consequences on the horizontal dimension 2d + g of the magnets. Therefore, in addition to the technical challenges connected to the design of window frame magnets with a large opening, one would face some severe encumbrance problems. Hence, one must accept a somewhat worse separation between the beamstrahlung photons and the charged beams. If Lsep is set to 8.5 m, then Dy is 6 times larger than the worst rms photon cone size. Along this drift, Ypipe must increase from 1.3 to 2.5 m in order to avoid power losses between the fourth magnet and the separation region. As for the horizontal vacuum pipe aperture Xpipe, the only constraint comes from the proximity of the incoming beam line. We choose to increase Xpipe from 3 cm at the exit of the fourth magnet to 4 cm in the separation region. Figure 8 shows the transverse beam profiles, as obtained in the separation region, i.e. 49 m downstream of the interaction point x (cm) Figure 8: Transverse beam profiles obtained in the separation region, 49 m downstream of the interaction point. 11

12 The overall geometry is similar to the one presented in [2], however the beam pipe dimensions are larger. The stars show the inner wall of the common vacuum pipe, prior to the separation. It has X pipe =4cmandY pipe = 25 cm. For the beamstrahlung photons, the disrupted beam and the same-sign charged particles of the coherent pairs, the vacuum pipe just after the physical separation consists of two joined half-ellipses. The upper one has its origin at the centre of the beamstrahlung photon cone, and its two semi-axis are X up =2cmandY up = 5 cm. The lower half-ellipse is centred on the path of the 1.5 TeV reference charged particle, with X down =2cmandY down = 119 cm. 3.2 Transport of the outgoing beams to their respective dump Following their physical separation from the other beam components, the particles of the coherent pairs with the wrong-sign charge should be immediately analysed and brought to their dump. Indeed, in order to recover information on the coherent pairs, only the particles with the wrong-sign charge can be used (the other ones can not be distinguished from the low-energy tail of the disrupted beam). The energy spectrum of the coherent pairs can be derived from the analysis of the vertical distribution of the wrong-sign charged particles at their dump. As far as the main beam is concerned, one needs the exit window to the dump to be far away from the interaction point, so that the transverse sizes of the non-colliding beam become a few mm, typically. The bend provided by the four extraction magnets must be followed by a bend in the opposite direction, in order to rapidly have D y =atthe exit of the vertical chicane (and at the dump). For this purpose, four C-type dipole magnets are used and they must be placed after the dump of the wrong-sign charged particles of the coherent pairs, in order to avoid encumbrance problems. Upstream of these magnets, the vertical aperture of the vacuum pipe must gradually decrease, which inevitably leads to beam losses. In the design study of [2], five collimators are placed along the first 1 m of the transport line for the disrupted beam, after the separation region, in order to absorb the particles that would not reach the C-type magnets. A schematic layout of this part of the postcollision line is shown in Figure 9 (for the disrupted beam transport line) and Figure 1 (for the collection and analysis of the wrong-sign charged particles of the coherent pairs), as proposed in [2]. We propose a somewhat different lattice for the transport lines between the separation region and the C-type magnets, including the dump for the wrong-sign charged particles of the coherent pairs. In this new design, the vacuum pipe for the beamstrahlung photons and the right-sign charged beams passes through the dump of the coherent pairs, which therefore plays the same role as the five collimators by absorbing the low-energy particles that would not reach the C-type magnets, see Figure

13 Particles of the coherent pairs with wrong sign charge Dump Photons & disrupted beam C type magnets Collimators Dump Figure 9: Schematic layout of the second part of the vertical chicane, which bends back the disrupted beam and the particles of the coherent pairs with the same charge, ensuring that D y vanishes at the exit of the last C-type magnet. E = E = E Instrumented dump Active material Figure 1: Schematic layout of the transport line between the exit of the separation region and the dump for the particles of the coherent pairs with the wrongsign charge. 6 m Instrumented dump for the wrong sign charged particles of the coherent pairs 4 C type magnets Beamstrahlung photons Disrupted beam Figure 11: Schematic layout of the transport line between the separation region and the C-type magnets, which passes through the instrumented dump of the wrong-sign charged particles of the coherent pairs. 13

14 Since the collection and analysis of the wrong-sign charged particles of the coherent pairs was already discussed in [2], we only focus on the transport line of the disrupted beam and of the beamstrahlung photons. It first passes through the 6 m long instrumented dump, before reaching the first C-type magnet, which is installed 1 m downstream. The transverse dimensions of the vacuum pipe that goes through the dump, and in turn the beam losses occuring there, depend on the design of the C-type magnets and will therefore be discussed later. g BEAMS B COIL h IRON YOKE d Figure 12: Cross section of a C-type dipole magnet, with the relevant parameters to be considered for its design. The beamstrahlung photons travel between the upper coils, while the disrupted beam passes between the poles. In the following, we use g = 45 cm, in order to keep the same horizontal aperture for the beam pipe all the way from the separation region until the exit of the fourth C- type magnet. In that case, an excitation current of 36 ka.turns is required in order to produce a field of 1 T in the gap. This leads to a cross section of 72 cm 2 for the coils, if we assume that half of it is used for cooling and that the current density is 1 A/mm 2. The horizontal dimension of the C-type magnet is g +2(d + X coil ), where the distance d must be large enough to allow the magnetic flux to fully return through the iron yoke. If the maximal field strength inside the iron yoke is B max (chosen to be 1.7 T as in the case of the window frame magnets), then the distance d is roughly constrained by: d B B max (h +.5g). (11) In order to keep the same magnet design as in [2], we choose h = 64 cm. As a result, the smallest value of d is 51 cm. If the horizontal and vertical sizes of the excitation coils are set to respectively 2 cm and 36 cm, then the minimum horizontal dimension of the C-type magnets is 187 cm (the spacing between the post-collision line and the incoming beam line is 112 cm at the entrance of the first C-type magnet). 14

15 A schematic drawing of the vacuum pipe used for the transport of the disrupted beam and the beamstrahlung photons through the four C-type magnets is shown in Figure 13. The vertical dispersion is 8.24 cm at the entrance of the first magnet. The half-ellipse which defines the lower half-aperture of the vacuum pipe is centred on the 1.5 TeV reference particle, and it has Y down = 6 cm. The other half-ellipse, which defines the upper half-aperture of the vacuum pipe, is centred on the beamstrahlung photon cone, and it has Y up = 8 cm. This ensures that no photon is lost along the C-type magnets. Along the horizontal direction, we choose the semi-axis to be X down = X up =2cm, which leaves 2.5 cm between the inner wall of the vacuum pipe and the pole, on either side. y (cm) 2 1 X up Y up -1-2 D y X down -3 Y down x (cm) Figure 13: Schematic drawing of the vacuum pipe transporting the disrupted beam and the beamstrahlung photons, shown here inside the first C-type magnet: two half-ellipses with the same horizontal semi-axis (X down and X up ), but different vertical semi-axis (Y down and Y up ), are separated by a distance equal to the dispersion D y. The overall shape of the vacuum pipe remains the same from the separation region to the exit of the fourth C-type magnet. However, one must take into account the increasing vertical dispersion. Also, a fraction of the charged particles must be absorbed in the dump in order to protect the four magnets placed downstream. Therefore, the distance between the two half-ellipses, as well as their semi-axis, must change along the path of the disrupted beam and the beamstrahlung photons, as shown in Figure

16 The horizontal semi-axis which is common to both half-ellipses decreases from 2 to 12 cm over the first meter in the dump, stays at this value over the following 4 m, before increasing back to 2 cm over the 2 m long drift upstream of the first C-magnet (half of this drift lies inside the dump). The narrow section in the middle of the dump allows to absorb particles with x > 2.4 mrad before the disrupted beam and the beamstrahlung photons pass through the C-type magnets. The vertical semi-axis of the half-ellipse close to the beamstrahlung photons Y up increases from 5 to 8 cm over the first meter in the dump and stays at this value until the exit of the fourth C-type magnet. As for the half-ellipse on the charged beam side, the vertical semi-axis Y down decreases from 119 to 4 cm over the first meter in the dump, stays at this value over the following 4 m, before increasing up to 6 cm over the 2 m long drift upstream of the first C- magnet. This allows to efficiently protect the four C-type magnets, as all particles with δ<.84 are absorbed in the dump. The corresponding power losses are 14.8 kw for the disrupted beam and 37.9 kw for the right-sign particles of the coherent pairs. The dump must be carefully designed, not only in order to absorb, but also to measure the large power losses associated to the low-energy particles, as they are related to the beamstrahlung parameter and thus provide information on the e + e collisions. D y (cm) X up = X down (cm) Y up (cm) s (m) Y down (cm) s (m) s (m) s (m) Figure 14: Variations of the dimensions of the vacuum pipe for the disrupted beam and the beamstrahlung photons along their path, from the separation region to the exit of the fourth C-type magnet. 16

17 Energy (GeV) Energy (GeV) Each of C-type magnet is 4 m long and two consecutive magnets are spaced by 1 m. As already discussed in [2], one must set the magnetic field to.973 T in the four C-type magnets, in order to compensate for the emission of synchrotron radiation in the eight magnets of the CLIC post-collision chicane. Figure 15 shows the y and y distributions of the disrupted beam after the last C-type magnet (75 m downstream of the interaction point), as a function of the energy. The vacuum pipe has the same shape as in Figure 13, but now with Dy = 11.3 cm, Xup = Xdown = 2 cm, Yup = 8 cm and Ydown = 6 cm. The particles found in the core of the high-energy peak at y = leave the chicane parallel to the beamstrahlung photons, i.e. with y =. On the other hand, the low-energy particles still have y < y(cm) y (mrad) Figure 15: y and y distributions as a function of the energy for the disrupted beam, at the exit of the post-collision vertical chicane. In the design study of [2], the low-energy particles are refocused using 16 quadrupoles (meanwhile the core of the charged beam remains unaffected). The main argument for the implementation of this refocusing region was the following. The exit window of the CLIC post-collision line must be placed far (about 25 m) from the interaction point because, at the impact of the non-colliding beam, the density of the energy deposition (and thereby the instantaneous temperature increase, as well as the thermal stress) must remain at an acceptable level. Without further action along the 18 m long drift between the last C-type magnet and the dump, the increasing vertical extension of the disrupted beam would lead to a large exit window and, in turn, a high mechanical stress. But, in view of the results presented in [3], the situation is not so critical, because both the mechanical and thermal stresses in the exit window stay well below the levels at which failures occur. In addition, with the new CLIC parameters, despite a higher charge per bunch train, the beam power is 7% lower and the transverse sizes of the non-colliding beam grow faster. The exit window of the CLIC post-collision line can thus be moved closer to the interaction point. As a result, there is no need for a refocusing region. 17

18 Let us assume that the transverse size of the exit window is more or less the same as in [3]. Since the beam power is 7% smaller with the new CLIC parameters, then the new equilibrium temperature at the beam impact is roughly: ΔT new eq.7δt old eq σold x σx new σ old y σ new y. (12) With the old CLIC parameters, the rms beam area σ x σ y on the exit window (at 25 m from the interaction point) is 4 mm 2. In order to keep roughly the same equilibrium temperature at the impact of the non-colliding beam, we now propose to install the exit window 15 m downstream of the interaction point, where σ x σ y is 2.5 mm 2. Over the 5 m following the exit of the vertical chicane, the vacuum pipe gradually gets a race-track shape. Its straight length is 64 cm, while the semi-axis of both the upper and lower half-ellipses are respectively 2 cm and 8 cm in the horizontal and vertical directions, see the left-hand side plot of Figure 16. Along the 75 m long drift between the fourth C-type magnet and the exit window, the particles with the lowest energy move about 4 cm away from the core of the disrupted beam (they have y.55 mrad). Meanwhile, the vertical radius of the beamstrahlung photon cone increases by a factor 2, and so should the vertical semi-axis of the upper half-ellipse. The right-hand side plot of Figure 16 shows the race-track shape of the vacuum pipe at the exit window. The semi-axis of the upper and lower half-ellipses are now set to 2 cm, both horizontally and vertically, while the length of the straight line is 54 cm. Note that the upper half-ellipse has now its centre 4 cm below the axis of the beamstrahlung photon cone. If the horizontal aperture of the vacuum pipe is kept equal to 4 cm along the drift after the last C-type magnet, then a small fraction of the beamstrahlung photons are lost upstream of the exit window. In order to prevent this from occuring, particles with x > 1.25 mrad should be absorbed early in a collimator which, if placed 8 m after the interaction point, must have a width of 2 cm. Here, we assume a length of 2 m but, thanks to the space availability, this is a very flexible parameter. The power deposited in the additional collimator is 17 W, and it only comes from the beamstrahlung photons (no charged particle is lost). Figure 17 shows the horizontal and vertical apertures seen by the outgoing beams along their path from the entrance of the first window frame magnet to the exit of the first C-type magnet (note that only the disrupted beam, the particles of the coherent pairs with the same charge and the beamstrahlung photons reach that point). Figure 18 shows the distribution of the power losses along this same path. They clearly occur in the collimators and in the dump of the wrong-sign charged particles of the coherent pairs, and there are practically no loss downstream of it. 18

19 y (cm) 2 y (cm) x (cm) 1 2 x (cm) Vertical aperture (cm) Horizontal aperture (cm) Figure 16: Transverse profiles for the charged beam and the beamstrahlung photons, shown here 5 m after the vertical chicane (left) and at the exit window (right), where the vacuum pipe has a race-track shape Distance from IP (m) Distance from IP (m) Figure 17: Horizontal and vertical apertures seen by the outgoing beams between the the entrance of the first window frame magnet and the exit of the first C-type magnet. 19

20 δp/p P loss = 111. kw (disrupted) -.84 P loss = 42.3 kw (cohplus) -.86 P loss = 4.3 kw (cohminus) Distance from IP (m) Figure 18: Power loss distribution along the CLIC post-collision line. 4 Impact of the new CLIC beam parameters on the design of exit windows Having updated the design of the CLIC post-collision line, we now check the performance of the exit window for the main beam. For its fabrication, similarly to the LHC dump window [1], a thick (1.5 cm) layer of carbon-carbon composite SIGRABOND 151G and a thin (.2 mm) leak-tight Aluminium foil have been proposed. This material yields a small thermal stress and also quickly transports away the heat resulting from the beam impact. In the design study of [3], the thickness of the CLIC exit window is much smaller than one radiation length (ensuring that only ionization losses occur during the beam passage) but still large enough to withstand the pressure difference. The passage of a single bunch train with nn b particles through the CLIC exit window leads to an instantaneous temperature rise at the centre of the beam distribution. When assuming a Gaussian beam and neglecting the temperature dependence of the heat capacity C, the instantaneous local heating is [11]: ΔT inst = ( ) de nn b. (13) ρdx 2πCσbeam 2 If α is the thermal expansion coefficient and E is the elastic modulus, the (cyclic) thermal stress due to the (repetitive) temperature increase is: σ c = αeδt inst. (14) 2

21 The largest temperature increase is caused by the non-colliding beam at 1.5 TeV (with a failure of all magnets on its path), for which σ 2 beam = σ x σ y is the smallest, 2.5 mm 2 if the post-collision line is 15 m long. The corresponding energy deposition in the window was computed with FLUKA [12, 13]. The following results were reported in [3]: Along the carbon-carbon composite window, one observes a small increase of the energy deposition with the amount of material seen by the incident beam (from 1.6to1.8MeV/gcm 2 ), because some particle multiplication occurs, although a full electromagnetic shower has not developed yet. In the thin Aluminium foil, the deposited energy is 1.7 MeV/g cm 2. The instantaneous temperature increase and the corresponding cyclic thermal stress were calculated with the new CLIC beam parameters, in the carbon-carbon thick window and in the thin Aluminium leak-tight foil, see Table 4. Material E (GPa) α (K 1 ) C (J/g K) ΔT inst (K) σ c (MPa) C-C composite Aluminium Table 4: Mechanical and thermal properties of the materials used in the exit window, instantaneous temperature increase and cyclic thermal stress at the impact of the non-colliding beam. The passage of a bunch train through the window and its subsequent local heating occur at a repetition frequency of 5 Hz. The heat then diffuses towards the edge of the window, which is kept at a constant temperature T edge. For the sake of simplicity, we consider a circular symmetry, which allows to simplify the analytical calculations. In cylindrical coordinates, the equilibrium temperature distribution is derived from the heat equation with no time dependence: k r r r T = p(r). (15) r In this equation, k is the thermal conductivity (expressed in W/Km) and p(r) isthe power distribution (per unit volume). In the following, we proceed as in [11] and we assume that the power distribution is: ( ) de 2σbeam 2 p(r) =nn b f. (16) dx π(r 2 +2σbeam 2 )2 It is similar to a Gaussian distribution, and it has the advantage that equation (15) can be solved analytically. The highest temperature at the centre of the round window is: T = T edge + ( de dx ) nn b f 4πk ln ( ) 1+ R2 2σbeam 2. (17) 21

22 The CLIC exit window has a race-track shape. The radius of the upper and lower halfcircles is 2 cm and the length of the straight line is 54 cm. In the worst case scenario (with a failure of all magnets along the path of the undisrupted beam), the impact occurs 4 cm over the centre of the upper half-circle. One can thus not determine the equilibrium temperature analytically. However, it is possible to make a rough estimate assuming that the exact geometry of the window and the location of the beam impact do not have a significant influence on the equilibrium temperature. One may indeed argue that the most relevant quantity is the average distance between the beam impact point and the edge of the window, which determines how fast the heat is diffused, once the thermal conductivity k is known. In order to estimate the equilibrium temperature difference between the beam spot and the edge of the window, we use equation (17), replacing the term under the logarithm by the ratio between the surface of the window with a race-track shape (.34 m 2 ) and the rms area of the beam (2πσ x σ y =15.7 mm 2 ). Our results are summarized in Table 5. They are not significantly different from those computed in [3], and well below the melting temperatures of the materials used for the fabrication the exit window. Material ρ (g/cm 3 ) k (W/K cm) ΔT eq (K) C-C composite Aluminium Table 5: Estimated temperature increase at equilibrium, due to the repetitive passage of one bunch train with a frequency of 5 Hz. In addition to the cyclic thermal stress σ c, the exit window must withstand the pressure difference between its two faces. The corresponding static stress σ s is computed with ANSYS [14], only for the carbon-carbon composite, since the Aluminium thin leak-tight foil is fully supported by the thick window. Assuming an atmospheric pressure load of.1 MPa, uniformly distributed over the cross section of the window, as well as no degree of freedom around its circumference, our simulations yield a maximal mechanical stress of 35 MPa and a displacement of.3 mm at the centre of the window. Figures 19 and 2 show the distribution of the stress intensity over the window. The largest stress is obtained on the lateral edges of the window, where there is almost no thermal stress. In the beam impact region, σ s is about 2-3 times smaller, and it lies around 1-15 MPa. These stress levels are larger than for the exit window of [3]. This results from the increase of its cross section area, from.18 to.34 m 2. However, the tensile strength of the SIGRABOND 151G carbon-carbon composite is still much larger (35 MPa typically). Consequently, we do not expect any problem with the use of such a large exit window, the surface of which is only 2% larger than for the LHC dump window. 22

23 1 NODAL SOLUTION STEP=1 SUB =1 TIME=1 SINT (AVG) DMX =.36E-3 SMN = SMX =.35E+8 FEB :32:54 PLOT NO. 1 Y MN Z X MX E+7.8E+7.119E+8.157E+8.196E+8.234E+8.273E+8.311E+8.35E+8 Figure 19: Race-track shape of the CLIC exit window and distribution of the mechanical stress intensity over its cross section. 1 NODAL SOLUTION STEP=1 SUB =1 TIME=1 SINT (AVG) DMX =.36E-3 SMN = SMX =.35E+8 FEB :33:58 PLOT NO. 1 Y Z X MN MX E+7.8E+7.119E+8.157E+8.196E+8.234E+8.273E+8.311E+8.35E+8 Figure 2: Mechanical stress intensity and displacement, which result from the pressure difference between the two faces of the CLIC exit window. Another exit window has to be fabricated for the wrong-sign charged particles of the coherent pairs. We also propose a 1.5 cm thick layer of carbon-carbon composite and a.2 mm thin foil of Aluminium. This second exit window has an elliptical shape, with a surface of.26 m 2, therefore we expect roughly the same mechanical stress levels as in the.34 m 2 exit window of the main beam. In addition, the thermal stress is negligible because, whenever produced, the wrong-sign charged particles of the coherent pairs carry much less power than the main beam and are spread all over the window. 23

24 5 Conclusion Following the modification of the CLIC beam parameters at the interaction point, we have updated the design of the post-collision line and its exit window. The increase of the beamstrahlung photon cone transverse sizes lead to a somewhat worse separation of the outgoing beams by the four window frame extraction magnets, however it is still possible to efficiently collect and analyse the wrong-sign charged particles of the coherent pairs. Their dump is now also used to absorb the low-energy tails of the charged beams, and thereby protect the four C-type magnets placed downstream, which bend back the core of the disrupted beam. Thanks to the safe operation of the exit window, the reduction by 3% of the beam power and the increase of the non-colliding beam transverse dimensions, a significant reduction of the overall length of the CLIC postcollision line is possible, allowing removal of the large refocusing quadrupoles. A new exit window, to be placed 15 m downstream of the interaction point, was designed. The instantaneous temperature increase and the thermal stress at the (undisrupted) beam impact point become somewhat larger than in the previous design but still reasonable, while the equilibrium temperature is not significantly changed. The mechanical stress was computed and found to be 2-3 times larger than in the previous design, but still far from the tensile strength of the carbon-carbon composite used for the fabrication of the window. We conclude that, despite the recent changes of the CLIC beam parameters and a few necessary modifications of the post-collision line and its exit window, their performance is not significantly affected. Recently, ideas for post-collision diagnostics were reported in [15]. For completeness, one should also study in more details the power losses along the post-collision line, and in particular the influence of the back-scattered particles on the background at the interaction point. Acknowledgements This work is supported by the Commission of the European Communities under the 6 th Framework Programme Structuring the European Research Area, contract number RIDS References [1] I. Wilson, The compact linear collider CLIC, CLIC note 617, CERN-AB-24-1, published in Phys. Rep (24) [2] A. Ferrari, Conceptual design of a post-collision transport line for CLIC at 3 TeV, CLIC note 74, EUROTeV-Report [3] A. Ferrari and V. Ziemann, Conceptual design of a vacuum window at the exit of the CLIC post-collision line, CLIC note 732, EUROTeV-Report

25 [4] F. Tecker et al., Updated CLIC parameters 25, CLIC note 627. [5] [6] D. Schulte, TESLA-97-8 (1996). [7] P. Chen, Coherent Pair Creation from Beam-Beam Interaction, SLAC-PUB 586 (1989). [8] [9] T. Zickler, private communications. [1] R. Veness, B. Goddard, S.J. Mathot, A. Presland and L. Massidda, Design of the LHC beam dump entrance window, proceedings of EPAC6, Edinburgh, Scotland. [11] M. Seidel, An Exit Window for the TESLA Test Facility, DESY-TESLA [12] A. Fasso, A. Ferrari, J. Ranft and P.R. Sala, FLUKA: a multi-particle transport code, CERN-25-1, INFN/TC 5/11, SLAC-R-773. [13] A. Fasso, A. Ferrari, S. Roesler, P.R. Sala, G. Battistoni, F. Cerutti, E. Gadioli, M.V. Garzelli, F. Ballarini, A. Ottolenghi, A. Empl and J. Ranft, The physics models of FLUKA: status and recent developments, Computing in High Energy and Nuclear Physics 23 Conference (CHEP23), La Jolla, CA, USA, March 24-28, 23, paper MOMT5, econf C33241, hep-ph/ [14] (ANSYS v. 11. Academic Research). [15] V. Ziemann, CLIC post-collision diagnostics, CLIC note 736, EUROTeV-Report