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Synchrotron Radiation Dominated Hadron Colliders EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH European Laboratory for Particle Physics Large Hadron Collider Project LHC Project Report 102 SYNCHROTRON RADIATION DOMINATED HADRON COLLIDERS Eberhard KEIL Abstract The synchrotron radiation damping time becomes small compared to the beam lifetime when the beam energy in a circular hadron collider reaches about 100 TeV and the dipole field about 10 T. This paper discusses an approach to the design of these colliders such that the desired performance parameters, e.g. beam-beam tune shift and luminosity are achieved at the equilibrium values of the beam emittance and momentum spread. The design procedure is described, involving the design of the interaction regions, the arcs, and the RF system. The thresholds and/or growth rates of several collective effects, and the growth times for intra-beam scattering are estimated. The consequences of the synchrotron radiation are discussed in the conclusions. Presented at 1997 Particle Accelerator Conference, Vancouver, 12-16 May 1997. Administrative Secretariat LHC Division CERN CH - 1211 Geneva 23 Switzerland Geneva, 3 June 1997 SYNCHROTRON RADIATION DOMINATED HADRON COLLIDERS E. Keil, CERN, Geneva, Switzerland Abstract 2.1 Interaction Region Design The synchrotron radiation damping time becomes small For round beams with equal normalised horizontal and ver- 2 = = z compared to the beam lifetime when the beam energy in tical emittances z , equal -functions and van- z a circular hadron collider reaches about 100 TeV and the ishing dispersion at the interaction point IP, and ignoring dipole field about 10 T. This paper discusses an approach crossing angle and “hourglass” effect, luminosity L and N to the design of these colliders such that the desired per- beam-beam tune shift are with bunch population and formance parameters, e.g. beam-beam tune shift and lumi- collision frequency f : nosity are achieved at the equilibrium values of the beam 2 N f Nr emittance and momentum spread. The design procedure is p = = L (2) 4 4 y n described, involving the design of the interaction regions, x the arcs, and the RF system. The thresholds and/or growth rates of several collective effects, and the growth times for The beams cross at an angle in order to separate them at intra-beam scattering are estimated. The consequences of the parasitic collision points at multiples of half the bunch the synchrotron radiation are discussed in the conclusions. spacing near the interaction point. Solving (2) for Nf yields with the usual relativistic factor : 1 INTRODUCTION Nf = L r =( ) p x (3) As noticed in the high-field option of really large hadron = x y The choices of at the IP and of the crossing angle colliders (RLHC) [1], the damping time z of the oscilla- tions in the three degrees of freedom due to the emission are related [5]. Tab. 1 shows the assumed and resulting IP f s = c =f c of synchrotron radiation becomes about an hour at a beam parameters. The bunch spacing s fixes by ; = L N x y 100 B 12 energy E TeV and a dipole field T: is the speed of light. For given and , fol- lows from (3), and from (2). The beam-beam lifetime 16644 C = (r =c )( C= ) p tot x bb is calculated for one interac- (h)J = z z (1) 2 L C 1=E (TeV )B (T) 2 E tion region, independent of , proportional to and , and small for good performance parameters (small x and x y Here, z labels the plane ( for horizontal, for vertical be- = 120 large ); tot mb is the total cross section.The small s J tatron oscillations, for synchrotron oscillations), z is the = y RMS radii x , compared to LHC [6] or SSC [2], are damping partition number, C is the circumference and largely due to the higher energy and adiabatic damping.The 2 > R the bending radius in the arcs of the collider; C= normalised emittance n has about 1/3 of the SSC value. includes the long straight insertions for the experiments. p Scaling their length like E from the SSC [2], and assum- 2 = R + 1708 ing four interaction regions, one gets C= m. Table 1: Interaction region parameters for a 100 TeV p-p = = 0:003 = = 0:5 y x y Since the beam lifetime and the duration of a colliding collider with x [6], m, s =3:75 =60 beam run are usually many hours, the beams have the equi- m, total inelastic cross section inel mb. 9 10 librium beam parameters, given by the equilibrium of quan- Bunch population N= 9.03 tum excitation and synchrotron radiation damping, during Normalised emittance n /nm 367.4 = = y most of their lifetime. Designing an RLHC such that the RMS beam radius x m 1.313 0 0 = = beam-beam limit and the desired luminosity are achieved at RMS divergence r 2.626 x y 1 the equilibrium beam parameters has the advantage that the Luminosity L/(nbs) 30.1 n = L =f inel emittances of the injected and circulating beams are decou- Events/collision c 22.6 pled, and that the collider is insensitive to slow phenomena Beam-beam lifetime bb /h 42.4 with growth times longer than the damping time. 2 DESIGN PROCEDURE + 2.2 Arc Design The design procedure for e e colliders [3] in the DE- SIGN program [4] adjusts the arc and RF system param- The arcs should provide just enough quantum excitation to eters to achieve a specified luminosity. Adapting it to p-p achieve the emittance listed in Tab. 1. The average arc ra- m r R> p colliders implies setting the mass p , classical radius , dius includes space for the quadrupoles, sextupoles, and Compton wavelength p to their proton values. etc., and short straight sections in the arc cells. In separated = f = 400 y RF function FODO cells with x , normalised horizontal frequency MHz, unloaded shunt impedance Q L Z =60:3 T =2:4 p f emittance n , arc tune and cell length are related by: G/m and filling time s, similar to the LHC values, suffice for the design of the RF system. The 3 1 RF () R 55 x p DESIGN program finds the RF system parameters listed p = L = p n (4) 2 J Q Q 32 3 x s in Tab. 4; e and are small. However, the bunch area 4E =c s e , is comparable to those of LHC and SSC. () The correction factor for finite phase advances F [7] = ! 0 y tends towards unity for x . The insertions do not contribute to quantum excitation and momentum com- Table 4: Parameters of the RF system of a 100 TeV p-p col- 2 = (2R=C )Q paction . I assume that round beams = 228:9 lider with circumference C km, harmonic number x with y are achieved by coupling horizontal and ver- h = 305415 =24 q RF , and quantum lifetime h. tical betatron oscillations, and apply a factor 1/2 to the tra- V Voltage RF /MV 35.9 ditional form of (4). Tab. 2 shows the parameters of the 6 =10 Relative RMS energy spread e 6.53 arcs. The dipole field shown [8] is needed in order to ob- 6 Bucket height/10 22.5 tain colliders in the parameter range I wish to study. 3 Q =10 Synchrotron tune s 1.27 Bunch length s /mm 27.5 E =c Table 2: Parameters of the arcs of a 100 TeV p-p collider 4 s Bunch area e /eVs 0.754 =12 =27:78 R= =1:25 with B T, km and [6] Arc tune Q 80.62 The time needed for a particle to radiate all its energy, =2 = =2 y Phase advance x 0.25 and thus also the time needed for acceleration to the oper- L Cell length p /m 677 ating energy (when synchrotron radiation is neglected) is Maximum amplitude function x /m 1156 T one half of x . If the acceleration time is to be shorter D Maximum dispersion x /m 8.93 =2 than x , the peak RF voltage must be higher than that =(2T ) listed in Tab. 4 in the ratio x . The cold vacuum chamber acts as a cryopump. The per- forated beam screen absorbs the synchrotron radiation. Its 3 COLLECTIVE EFFECTS temperature should be much higher than that of the vacuum chamber for good Carnot efficiency. Collective effects, in The resistive wall instability, coherent synchrotron tune particular the resistive wall instability (cf. Section 3.1), and shift, longitudinal microwave instability, and transverse the forces during a magnet quench must also be considered. mode coupling instability TMCI are important [10] for the RLHC [11]. I only study the dominant contribution, and 4E =c = s 2.3 Synchrotron Radiation assume injection at 5 TeV, and a bunch area e 1 I I eVs there. Below, is the total beam current, and b Tab. 3 shows several parameters related to the synchrotron Z is the bunch current. The effective impedances e are radiation. The total synchrotron radiation power P per (! ) the weighted sums of Z and the bunch power spec- beam is three orders of magnitude higher than the 3.6 kW trum [12]. Tab. 5 lists thresholds and growth rates at the = P=2R in the LHC. The normalised power p is almost energies where they are most critical.The longitudinal mi- two orders of magnitude higher than the 0.2 W in the LHC. crowave and the transverse mode coupling instabilities are The photon flux , the number of photons per metre of arc below threshold by good factors [13], and not discussed.
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