- Email: [email protected]
A dedicated hadronic B-factory: accelerator considerations
Nuclear Instruments and Methods in Physics Research A 408 (1998) 296—307
A dedicated hadronic B-factory: accelerator considerations Gerald P. Jackson* Fermi National Accelerator Laboratory, MS 306 P.O. Box 500, Batavia IL 60510, USA
Abstract There is interest in the high-energy physics program at a dedicated hadronic B-factory. After general considerations are explored for such a facility, a potential implementation at the Fermi National Accelerator Laboratory is presented. ( 1998 Elsevier Science B.V. All rights reserved.
1. Introduction At this time the world has two e`e~B-factories under construction, one at SLAC [1] in the United States and the other at KEK [2] in Japan. Simultaneously the CESR [3] e`e~ storage ring at Cornell University is being upgraded to B-factory luminosity levels. This level of activity and monetary expenditure indicates that the study of B-meson decays is the most important question facing high-energy physicists not operating at the energy frontier. All three of these storage rings will be capable of discovering certain aspects of B-meson decays, such as CP violation. Unfortunately, the rate at which Bmesons are observed is too low for high statistics studies such as standard model tests. On the other hand, a dedicated hadronic Bfactory would have the advantage of accumulating at least two orders-of-magnitude more B-meson events per year than at an e`e~ B-factory. It is the promise of such high statistics physics that make the construction of a dedicated hadronic B-factory a priority in the not-to-distant future. Such a 3 TeV * E-mail: [email protected]
proton—proton collider is presently being discussed at Fermilab [4]. It is needed as an injector for a 100 TeV center-of-mass frame proton—proton energy frontier collider well after the LHC [5] has had adequate time to discover what lies within its energy reach. It would also be useful as a technology demonstration for the higher energy collider. In this paper the discussion is divided into two distinct parts. The first part is an overview of general considerations for an optimized, dedicated, “green-field” hadron collider beyond the LHC for B-physics. The second part is a suggestion (recruitment) to take advantage of a 3]3 TeV proton— proton collider project which is under study at Fermilab, which for the purposes of this paper is referred to as Tevatron-B. 2. Detector considerations A B-physics optimized detector in a dedicated hadron collider has specific preferred beam and accelerator conditions. In this section those accelerator and beam parameters which can be adjusted to maximize the data taking rate of the B-detector are discussed.
0168-9002/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved PII S 0 1 6 8 - 9 0 0 2 ( 9 8 ) 0 0 3 3 6 - 2
G.P. Jackson/Nucl. Instr. and Meth. in Phys. Res. A 408 (1998) 296—307
2.1. Maximum luminosity With the use of silicon tracking detectors, a maximum data acquisition frequency of approximately 30 MHz is presently the state of the art. In a dedicated proton—proton collider the optimum bunch crossing frequency f is equal to this maximum data " acquisition frequency. The maximum rate of B-meson production is limited by the average number of interactions per crossing that the detector can handle while still performing its particle identification and trajectory tracking missions. The inelastic cross-section p which determines this interaction */%rate has an approximate value of 49 mb at energies above 1 TeV. The typical limitation on the average number of interactions per crossing k is unity. The relationship between interactions per crossing and luminosity is described by the equation kf ¸" " . p */%-
(1)
The conversion factor from millibarns to square centimeters is 1]10~27 cm2/mb. Plugging in the above values, the peak luminosity which can be tolerated by present day B-detectors is approximately 6.1]1032 cm~2 s~1. The statement that k "1 is the limit for BMAX detectors comes from the assumption that crossing with no interactions and crossings with multiple interactions will not cause the trigger to perform data acquisitions. The probability that there are r interactions in a given crossing is described by the Poisson statistics density function kre~k f(r, k)" . r!
(2)
For example, at k"1 the fraction of crossings with zero interactions is 0.368, the fraction with one interaction is 0.368, and the fraction with multiple interactions is 0.264. By taking the derivative of the Poisson probability distribution with respect to k and setting the result equal to zero for r"1, the average number of interactions per crossing which maximizes the fraction of crossings with a single interaction can be calculated. The result is that k"1 is indeed the optimum. If it were possible to
297
handle more than one interaction per crossing, as discussed in Section 2.3, then the average number of interactions per crossing will be increased. 2.2. Transverse beam size In hadron colliders the transverse beam size is typically much smaller than any other physical length such as the distance to the closest silicon vertex detectors. The beam distribution at the Bdetector is predominantly Gaussian in both the horizontal and vertical directions, with a round aspect ratio. Around this Gaussian distribution is a very diffuse halo whose boundary is delimited by thick steel collimators spaced judiciously around the storage ring. The B-detector has a preference for small transverse beam sizes due to the useful trigger constraint that tracks must originate within the beam. As the beam size increases, the efficiency of this constraint is gradually reduced. For the purposes of this discussion it will be assumed that the r.m.s. horizontal (vertical) beam size p is less x(y) than 100 lm. 2.3. Bunch length If k"1 the r.m.s. bunch length p should be s infinitesimally short. For high luminosity detectors the bunch length can be as long as the value of the focusing function b* before loss of luminosity occurs. In the case of dedicated B-detectors the length of the luminous region is determined by the need to maintain a high track reconstruction efficiency. If one invests more money into the silicon components of the detector, it may be possible to spread out the region over which interactions can be efficiently reconstructed. In this case, if the longitudinal vertex reconstruction resolution is shorter than the bunch length, then crossings with more than one interaction can be reconstructed.
3. Interaction region length From an accelerator physics point of view, the magnetic lattice of a collider generates a focussing
VI. SUMMARIES
298
G.P. Jackson/Nucl. Instr. and Meth. in Phys. Res. A 408 (1998) 296—307
Fig. 1. Example of a magnetic lattice surrounding an interaction point (IP). In this case the Fermilab Tevatron Collider at the CDF and D0 detectors is shown.
envelope called the beta-function. For example, the dipoles and quadrupoles surrounding the CDF detector in the Tevatron Collider [6] are sketched in Fig. 1. In a detector straight section between the focusing “low-b” quadrupoles where the transverse shape of the beam is round (which is traditional for hadron colliders, unlike the flat beams in electron colliders), the r.m.s. size of the beam p depends x(y) on longitudinal position s according to the equation
C A BD
s 2 p2 (s)"p2 (0) 1# * , x(y) x(y) b x, y
(3)
where b* is the accelerator lattice parameter x(y) called beta-star and p (0) is the horizontal (vertix(y) cal) r.m.s. size of the beam at the interaction point. In Fig. 2 the horizontal (vertical) beta function [7] b (s) is displayed for one-half of the interacx(y) tion region. On the other side of the interaction point the horizontal and vertical beta functions reverse roles, making the interaction region lattice anti-symmetric. Fig. 3 shows the evolution of the r.m.s. transverse beam sizes p as a function of x(y) position in half of the interaction region. Note that in a drift region before the quadrupoles and for sAb* the beam size grows linearly with distance. x(y) The relationship between the r.m.s. beam size at the collision point and b* is x(y)
S
p " x(y)
eb n x(y), 6b c 3 3
(4)
where e is the 95% normalized transverse beam n emittance (in the horizontal or vertical plane,
Fig. 2. Horizontal and vertical beta function around the CDF and D0 detectors in the Fermilab Tevatron Collider. The dark lines on the horizontal axis show the locations of the Q4, Q3, and Q2 focusing “low-b” quadrupoles on either side of the interaction point. The origin of the horizontal axis is at the interaction point itself, and the beta functions are anti-symmetric about this point.
299
G.P. Jackson/Nucl. Instr. and Meth. in Phys. Res. A 408 (1998) 296—307
Fig. 3. The r.m.s. transverse beam sizes for the Tevatron Collider at 900 GeV assuming a transverse 95% emittance in both planes of 20p mm mr.
whichever is appropriate) and b and c are the 3 3 relativistic velocity and energy of the protons (antiprotons). Fig. 4 contains a sketch of this r.m.s. beam size as a function of position in one-half of the interaction region and the value of b*. The lower the value of b* the higher the maximum beta in the quadrupoles. Given that these quadrupoles have a limited aperture, there is a limit to how low b* can become for a given length of interaction region. The job of the first of three approximately equal strength quadrupoles on either side of the interaction region is to focus particle trajectories leaving the interaction region into a parallel beam. For magnets which are short compared to the length of the interaction region, this means that the focal length is equal to the interaction region length. If the length of the interaction region scales proportionally with beam momentum, the same quadrupoles can always be used. This is because for a fixed magnetic field gradient the focal length is also proportional to momentum. As the region gets longer, the beam size increases proportionally. But as beam momentum increases, the beam size is reduced by the square root of the
momentum. Therefore, the beam size at the entrance to the first quadrupole only increases as the square root of momentum. 4. Luminosity calculations The economics of proton and antiproton beam production are completely different given the fact that one gets roughly 15 antiprotons for every million protons striking the production target. Therefore, the calculation of luminosity for proton—antiproton and proton—proton operations are presented separately here. 4.1. Proton—antiproton collisions The luminosity ¸ at each HEP detector is
AB
N (N B) f (6b c ) b* ¸" P *A 0 3 3 H 2pb (e #e ) p nP nA s
1
, (5) 2a2p2(b c ) 1# * s 3 3 b (e #e ) nP nA where a is the beam crossing half-angle, N and P N are the bunch intensities, B is the number of A
S
VI. SUMMARIES
300
G.P. Jackson/Nucl. Instr. and Meth. in Phys. Res. A 408 (1998) 296—307
Fig. 4. Beam size vs. position in the detector region for b* values of 0.5, 1.0, 2.0, and 5.0 m. Note that as the value of b* increases, the smaller the maximum value of b(s) inside the quadrupoles but the larger the beam at the interaction point.
bunches per beam, f is the revolution frequency, 0 p is the r.m.s. bunch length, and H is the hour glass s factor which has the form H(x)"xJp [1!'(x)]ex2.
(6)
The ultimate limit to luminosity in hadron colliders to date has been the beam—beam interaction. This limit has been a total beam—beam linear antiproton tune shift m of approximately 0.025 generated by the proton beam current and charge, where N IP is the total number of interaction points, r "1.535]10~18 m, and 1 3r N m" 1 P N . IP 2p e n
(7)
The ratio of the proton bunch intensity to its normalized transverse emittance is limited by the total beam—beam tune shift suffered at all interaction regions. Plugging the equation for this tune shift into the equation for luminosity per interac-
tion region yields the result (N B) m f (6b c ) ¸" A * MAX 0 3 3 2, (8) N b e IP 3r 1# nA 1 e nP where the factors whose values can be modified significantly appear in the left fraction on the right-hand side of the equation. The quantity (N B) A is just the total antiproton intensity injection into the collider ring, independent of the bunch spacing. Unique to a dedicated B-physics collider is the added constraint that the number of interactions per crossing is limited to kK1. This quantity is equal to
A
B
p ¸ k" */%- . (9) fB 0 Note that f B is limited by the detector trigger rate. 0 By plugging this equation into the luminosity equation, it is found that the minimum number of bunches into which the antiprotons must be
301
G.P. Jackson/Nucl. Instr. and Meth. in Phys. Res. A 408 (1998) 296—307
Table 1 Instructive parameters to compare luminosity optimization of existing and proposed hadronic B-factories if they could be run as proton-antiproton colliders Parameter
Tev
Tev-B
LHC
VLHC
Beam energy (TeV) Beam—beam tune shift Interaction regions Interactios/crossing Inelastic cross-section (mb) Total antiprotons (]1012) Beta-star (m) Minimum d of bunches Revolution frequency (kHz) Bunch frequency (MHz) Luminosity (]1030 cm~2 s~1)
1 0.025 2 1 49 10 5 92 48 4.4 79
3 0.025 2 1 49 10 5 276 8.8 2.4 44
7 0.025 2 1 49 10 5 643 8.8 5.7 102
50 0.025 2 1 49 10 5 4595 0.5 2.3 44
distributed is
described by the equation
p (6b c ) (N B) m B " A * MAX */%- 3 3 2. MIN kN b e IP 3r 1# nA 1 e nP
N2Bf (6b c ) b* 0 3 3 H ¸" 4nb*e p n s
A
B
(10)
Note that as the energy of the ring increases, the number of bunches must increase proportionally if the number of interaction per crossing is to be controlled. If one assumes that every antiproton which is available is used, Table 1 can be generated from the above equation. Most parameters are kept artificially constant to show how the bunch spacing is affected by energy. In Table 1 a number of additional assumptions have been made. First, while the Tevatron and LHC circumference assume the existing tunnels, the Tevatron-B and VLHC numbers assume a high packing of 2 T superferric magnets. Second, the choice of 5 m for b* assumes that a $40 m long interaction region is always desired. In addition, the maximum beta-function value at the focusing quadrupoles around the interaction region is )350 m. 4.2. Proton—proton collisions Assuming identical counter-revolving proton beams, the luminosity at each HEP detector can be
AB
1
. (11) a2p2(b c ) s 3 3 1# b*e n Again, the limit to luminosity and to the proton brightness is the beam—beam interaction
S
3r N (12) m" 1 N . 2p e IP n Plugging this constraint into the luminosity equation yields the result NBf (6b c ) m 0 3 3 MAX 2. ¸" (13) 6b* rN 1 IP Note that the luminosity is proportional to proton current in the accelerator and the beam energy. There is also the added constraint of the number of interactions per crossing. Plugging this limit into the luminosity equation, one finds that the constrained quantity is the proton bunch intensity kb*r N 1 IP . (14) (b c )m */%- 3 3 MAX The number of bunches is unconstrained, so the luminosity is not limited until the crossing rate exceeds the detector trigger speed. Table 2 can be generated from this equation. Most of the parameters are kept artificially constant to show how the bunch spacing is affected by beam energy. The
N " MAX p
VI. SUMMARIES
302
G.P. Jackson/Nucl. Instr. and Meth. in Phys. Res. A 408 (1998) 296—307
Table 2 Instructive parameters to compare luminosity optimization of existing and proposed hadronic B-factories if they could be run as proton—proton colliders Parameter
Tev
Tev-B
LHC
VLHC
Beam energy (TeV) Beam—beam tune shift Interaction regions Interactios/crossing Inelastic cross-section (mb) Total antiprotons (]1012) Beta-star (m) Max. bunch intensity (]109) Max. bunch frequency (MHz) Bunches/beam Luminosity (]1030 cm~2s~1)
1 0.025 2 1 49 10 5 175 27 558 610
3 0.025 2 1 49 10 5 39 27 3023 610
7 0.025 2 1 49 10 5 16 27 3023 610
50 0.025 2 1 49 10 5 2.4 27 50379 610
choice of 5 m for the beta-star assumes that the interaction region length is $40 m. In addition, it is assumed that the maximum beta function value in the focussing quadrupoles on either side of the interaction region is 4350 m. 5. Interaction region geometry Over the years the Tevatron Collider has run with electrostatic separators to minimize the beam—beam tune disruption in the arcs which occurs with multiple bunches. The experience is that these devices are very sensitive and unreliable. In other storage rings implementing a crossing angle between the colliding beams has met with mixed success. In this section the implications of running without electrostatic separators and crossing angles are explored. 5.1. Proton—proton geometry The goal is to create head-on collisions without crossing angles at the interaction point. There are many benefits to this arrangement. First, the beam is more stable because the nonlinear dynamics of the beam—beam interaction are simpler to understand, interpret, and correct. Second, the luminosity is independent of the bunch length, which grows during a store. Third, the beam is more reliable since random sparks from electrostatic separators will not cause emittance growth in the beams.
Fig. 5. Sketch of an elegant interaction region geometry for a proton—proton collider where both beams have the same energy. Because the dipole at the center of the interaction point steers the two proton beams in different directions, it eliminates the need for expensive and unreliable electrostatic separators.
In a likely situation in which the two proton beams have roughly equal energy, the existence of the B-detector analyzing dipole magnet at the interaction point makes this geometry easy to realize. As can be seen in Fig. 5, the two proton beams bend in opposite directions horizontally. The bunch spacing is parameterized by the variable ¹ . This allows " the two proton beams to separate cleanly into their separate vacuum chambers as well as provide a simple method by which to prevent parasitic beam—beam interactions on either side of the dipole magnet. Table 3 summarizes some typical parameters which can be anticipated for such a geometry. 5.2. Proton-antiproton geometry Again, the goal is to create head-on collisions without crossing angles at the interaction point. In
303
G.P. Jackson/Nucl. Instr. and Meth. in Phys. Res. A 408 (1998) 296—307 Table 3 Typical parameters to compare beam separation at the interaction region of a dedicated proton—proton B-detector. Parameter
Tev
Beam energy (TeV) Emittance (pmm mr 95% Inv.) Beta-star (m) Beam divergence (lrad) Min. beam deflection (lrad) Min. dipole field (T m) Beam separation @ 40 m (mm) Bunch spacing (ns) Nearest secondary crossing (m)
1 3 7 15 15 15 5 5 5 22 13 8.2 220 130 8.2 1.5 2.6 3.8 18 10.4 6.6 38 38 38 5.6 5.6 5.6
Table 4 Typical parameters to compare beam separation at the interaction region of a dedicated proton-antiproton B-detector where the proton and antiprotons are at wildly different energies
Tev-B LHC VLHC 50 15 5 3.1 31 10.3 2.5 38 5.6
Fig. 6. Sketch of a proton—antiproton collision geometry in which the antiprotons have a much smaller momentum in order to get the beams separated before head-on parasitic crossings on either side of the interaction point.
the case of proton—antiproton collisions the bending magnet at the center of the B-detector bends both energy by the same amount in the same direction as long as the protons and antiprotons are at the same energy. On the other hand, if the antiproton beam has a significantly lower momentum, then it would be deflected by a much larger angle than the protons. As seen in Fig. 6 and Table 4, enough energy asymmetry makes the beams separate again at the parasitic crossing points, by the same amount as the proton—proton passages.
6. Bunch length What should be expected for the bunch length, and hence the luminous length? The answer to this question depends on the intensity per bunch needed to reach the desired luminosity. To zeroth
Parameter
Tev
Tev-B
LHC
VLHC
Beam energy (TeV) Beam divergence (lrad) Min. pbar deflection (lrad) Min. dipole field (T m) Beam separation @ 40 m (mm)
1]0.33 22]38 220 1.5 18
3]1 13]23 130 2.6 10.4
7]2.3 8.2]14 8.2 3.8 6.6
50]17 3.1]5.4 31 10.3 2.5
order, proton bunch intensities below 1]1011 do not require any special RF manipulations. With a high-energy recycling storage ring for antiprotons, RF manipulations are never necessary for large numbers of antiprotons bunches. Just as there is a normalized emittance in the transverse plane which defines an energy independent beam temperature, in the energy plane there is also an invariant bunch area. The conjugate coordinates defining this area are momentum spread and time spread. The RF system is used to mold the shape of this “phase space” in order to generate a desired bunch length. But in order to halve the bunch length, 16 times the RF gradient must be generated. This can be accomplished by turning up the RF voltage by 16] (which implies 256] times more power to halve the bunch length), increase the RF frequency by 16] (better have bunches which are already shorter than the new RF wavelength), or some combination of the two. Invariant bunch areas of 0.1—0.5 eV s are achievable for hadronic B-factories when special RF manipulations are not required. These manipulations are often used to increase the number of particles per bunch at the expense of the bunch area. For a fixed RF gradient, the bunch length scales with the square root of the bunch area. For example, in the Tevatron 1 MV of RF at 53 MHz yielded a longitudinal bunch area during Run I of 3 eV s, with a resultant r.m.s. bunch length of 45 cm. As another example, by eliminating presently standard special RF manipulations the Tevatron bunch area could be reduced by 10], which means
VI. SUMMARIES
304
G.P. Jackson/Nucl. Instr. and Meth. in Phys. Res. A 408 (1998) 296—307
that the bunch length would shrink by 3]. As this beam is accelerated beyond 1 TeV, for the same RF gradient the bunch length will shrink further by the square root of the energy increase.
7. Luminosity evolution simulations When protons (and antiprotons) are injected into a collider ring, a number of mechanisms determine the evolution of the luminosity with time. Each of these effects are taken into account in a spreadsheet program which predicts Tevatron Collider performance with very high fidelity. The dominant particle loss effect is the actual inelastic collisions between the beam particles inside the B-detector. As the luminosity is increased, the rate at which protons (and antiprotons) are consumed increases proportionally. In any scenario discussed in this paper this effect is orders of magnitude more severe than particle loss with residual molecules in the storage ring vacuum chamber. The particles within a bunch undergo Coulomb scattering with one another, an effect called intrabeam scattering. As the bunch intensity is increased, the bunch area reduced, or the transverse emittance decreased, emittance and bunch area growth rates increase dramatically. Intrabeam scattering cannot be counteracted and acts as the fundamental limit to beam brightness. Finally, power supply ripple and electronic noise cause the beam particles to undergo minuscule random walks which end up as emittance and bunch area growth. Though in principle it is possible to completely eliminate this effect, in practice there is a point of diminishing return as single offenders are corrected and hundreds of tiny sources are left. In reality every hadron storage ring ends up with a non-negligible emittance and bunch area growth rate from noise. Applying the Tevatron model [8] to a 3]3 TeV proton—proton hadronic B-physics collider, the parameters in Table 5 are used as input information. The values of these parameters are chosen to be as close to reasonable expectations as possible. The results of this simulation are shown in Figs. 7—10. Note that the luminosity decays with
Table 5 Input parameters for the luminosity performance simulation of a 3]3 TeV B-physics storage ring. Parameter
Tev-B
Beam energy (TeV) Initial emittance (pmm mr 95% Inv.) Beta-star (m) Initial bunch area (eV s) Initial bunch intensity (]109) Number of interaction regions Revolution period (kHz) Number of bunches Emittance growth rate (pmm mr/h) Bunch area growth rate (eVs/h)
3 15 3 0.5 77 2 8.8 3023 1 0.03
Fig. 7. Evolution of Tevatron-B luminosity with time assuming colliding proton beams with the parameters listed in Table 5. Note that approximately 12 h are required to reduce the luminosity by a factor of 2.
Fig. 8. Proton bunch intensity as a function of time. Note the suppressed zero on the vertical scale. Clearly, the bunch intensity does not have a very big impact on luminosity lifetime.
time, reaching half of its original value in approximately 12 h. The dominant cause of this luminosity reduction is clearly the transverse emittance growth, which is dominated by intrabeam scattering
G.P. Jackson/Nucl. Instr. and Meth. in Phys. Res. A 408 (1998) 296—307
305
in the beginning of the store and by noise-induced emittance growth after the first 8 h.
8. Luminosity leveling The problem with this luminosity reduction with time is that the interactions per crossing limit the peak luminosity, but are not a problem for the remainder of the store. It would be very advantageous if the luminosity could be continuously adjusted to be at the detector limit. The solution to this problem may be a procedure called luminosity leveling [8]. By adiabatically
Fig. 9. Evolution of the r.m.s. transverse beam size as a function of time in the colliding beam store. Since the transverse emittance has grown by 40% in 12 h, and the luminosity has dropped by almost the same amount, it is clear that transverse emittance growth is the dominant mechanism causing short luminosity lifetimes.
Fig. 10. Increase in the r.m.s. proton bunch length during a colliding beam store. Though the bunch length increases by more than a factor of 2, the impact on luminosity is small. This is because the bunch length is much shorter than the value of b*.
Fig. 11. Luminosity evolution with time when luminosity leveling is assumed to be functioning. By sacrifing luminosity at the beginning of the store, the same integrated luminosity can be delivered to the detectors by keeping the luminosity constant.
Fig. 12. Required b* curve for implementing luminosity leveling. The gentle nature of the changes implies that the control system could generate a software feedback system to maintain direct control over the luminosity.
changing the strengths of the low-b quadrupoles around the interaction point, the r.m.s. beam size is modified in order to keep luminosity constant. The simulation of this scenario also exists, where the initial value of b* is 723 m and the initial bunch intensity is 120]109 particles. The increased bunch intensity makes sure that the average luminosity remains equal to the scenario without luminosity leveling. Figs. 11 and 12 show the luminosity and b* evolutions with time. As required, the luminosity is now constant in time running at the detector interactions/crossing limit. 9. Tevatron-B Because of the '10-year time to design and approve an accelerator and the '10-year
VI. SUMMARIES
306
G.P. Jackson/Nucl. Instr. and Meth. in Phys. Res. A 408 (1998) 296—307
construction time required by limited funding profiles, it is important for the hadron labs FNAL & CERN to develop a leap-frog strategy in which one lab designs the next step while the other lab is building the present step. Therefore, people at FNAL have begun the design and R&D for the next machine after the LHC, sometimes called the VLHC (very large hadron collider). The preliminary goal is to build a proton—proton collider at FNAL with 100 TeV in the center-of-mass (50 TeV/beam). 9.1. Introduction Circular accelerators can only operate over a 20 : 1 range of beam momentum due to iron saturation and remnant fields. Because the FNAL Main Injector has an extraction energy of 150 GeV, a new accelerator which increases the beam energy from 150 GeV to 3 TeV is needed for injection into the VLHC. This allows the VLHC to reach 60 TeV/beam. The proposal is to build the 3 TeV accelerator with the same inexpensive super-ferric magnet technology envisioned for the VLHC. The cost GOAL (not estimate) for this machine is 4500 M$, about the price of an e`e~B-factory. The main reason for building this 3 TeV machine first is to demonstrate some underlying assumptions. First, that super-ferric magnet technology works. Second, that the super-ferric magnet technology is as inexpensive as expected. Third, to demonstrate the reduced costs of modern tunneling technologies. Fourth and finally, to show that it is possible in the US to build an accelerator under the surrounding suburban communities. One key for making this low project cost goal a reality is the new magnet technology proposed by Bill Foster. This magnet abandons the costly cosine-theta design, returns to 2 T iron dominated magnets, but still uses superconducting cable to carry the current. To date a 2 m prototype has already been successfully built. A 1 m prototype has already been powered and measured. This year we expect to build and test a 30 m long prototype. Because the magnets are weaker, the circumference of the accelerator is larger. For the 3 TeV
Table 6 Author’s optimistic schedule scenario for the construction of Tevatron-B Fiscal Tevatron-B tasks year
Limitations and competition
1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Ongoing main injector project Main injector project finished NUMI is funded NUMI is funded NUMI is funded NUMI project finished Tevatron33 underway Start designing VLHC VLHC R&D Write VLHC TDR Get VLHC approval Get VLHC approval Start VLHC funding
Magnet/tunnel R&D Magnet/tunnel R&D Write design report Get DOE approval Start tunneling Start magnets Tunneling complete Magnets complete Commissioning Do B-physics Do B-physics Do B-physics Do B-physics
machine the circumference is 34 km, 10] larger than the present Main Injector/Recycler construction project. Therefore, it is vital to reduce tunneling costs. People at FNAL have been actively discussing micro-tunneling options with new high-tech companies. This year it is desired to start a tunneling R&D program at nearby rock quarries who are already in the layer of rock which would house both the Tevatron-B and VLHC tunnels. 9.2. The pitch This is a green field accelerator. It has no other mission than accelerator R&D and eventually an injector for the VLHC. It would be MUCH more likely to be promptly approved if it had a physics case which was relatively inexpensive and nonchallenging. Why not B-physics? 9.3. Project goals As stated, the project goal is to come in below 500 M$. To date this cost is dominated by costing traditional tunneling technology. If micro-tunneling is found to be feasible, this cost could come down by 42] and the project cost could be as low as 300 M$.
G.P. Jackson/Nucl. Instr. and Meth. in Phys. Res. A 408 (1998) 296—307
The schedule depends on how badly the HEP community wants to do this project. Table 6 contains a personal schedule scenario which may be achieved if enough of the community gets excited about the physics potential behind Tevatron-B. The column named “limitations and competition” is meant to indicate where scarce money and manpower may be assigned, in direct competition with the needs of a Tevatron-B project. Acknowledgements I would like to thank Bill Foster, Peter Schlein, Ernie Malamud, and Shekhar Mishra for interesting and provocative discussions about the feasibility of building a dedicated hadronic B-factory.
307
References [1] PEP II Conceptual Design Report, LBL-PUB 5379, SLAC-418, CALT-68-1869, UCRL-ID-114055, UCIIRPA-93-01, June 1993. [2] Shin-ichi Kurokawa, KEKB Status and Plans, Proc. 1995 Part. Acc. Conf., Dallas 1995, p. 491. [3] David L. Rubin, CESR Status and Plans, Proc. 1995 Part. Acc. Conf., Dallas 1995, p. 481. [4] Supported by the United States Department of Energy. [5] L.R. Evans, The Large Hadron Collider, Proc. 1995 Part. Acc. Conf., Dallas 1995, p. 40. [6] V. Bharadwaj, Status and Future of the Tevatron, Proc. 1995 Part. Acc. Conf., Dallas 1995, p. 396. [7] E. Courant H. Snyder, Ann. Phys 3 (1958) 1. [8] G. Jackson (Ed.), Recycler Ring Technical Design Report, Fermi National Accelerator Report TM-1991, November 1996.
VI. SUMMARIES
A dedicated hadronic B-factory: accelerator considerations Gerald P. Jackson* Fermi National Accelerator Laboratory, MS 306 P.O. Box 500, Batavia IL 60510, USA
Abstract There is interest in the high-energy physics program at a dedicated hadronic B-factory. After general considerations are explored for such a facility, a potential implementation at the Fermi National Accelerator Laboratory is presented. ( 1998 Elsevier Science B.V. All rights reserved.
1. Introduction At this time the world has two e`e~B-factories under construction, one at SLAC [1] in the United States and the other at KEK [2] in Japan. Simultaneously the CESR [3] e`e~ storage ring at Cornell University is being upgraded to B-factory luminosity levels. This level of activity and monetary expenditure indicates that the study of B-meson decays is the most important question facing high-energy physicists not operating at the energy frontier. All three of these storage rings will be capable of discovering certain aspects of B-meson decays, such as CP violation. Unfortunately, the rate at which Bmesons are observed is too low for high statistics studies such as standard model tests. On the other hand, a dedicated hadronic Bfactory would have the advantage of accumulating at least two orders-of-magnitude more B-meson events per year than at an e`e~ B-factory. It is the promise of such high statistics physics that make the construction of a dedicated hadronic B-factory a priority in the not-to-distant future. Such a 3 TeV * E-mail: [email protected]
proton—proton collider is presently being discussed at Fermilab [4]. It is needed as an injector for a 100 TeV center-of-mass frame proton—proton energy frontier collider well after the LHC [5] has had adequate time to discover what lies within its energy reach. It would also be useful as a technology demonstration for the higher energy collider. In this paper the discussion is divided into two distinct parts. The first part is an overview of general considerations for an optimized, dedicated, “green-field” hadron collider beyond the LHC for B-physics. The second part is a suggestion (recruitment) to take advantage of a 3]3 TeV proton— proton collider project which is under study at Fermilab, which for the purposes of this paper is referred to as Tevatron-B. 2. Detector considerations A B-physics optimized detector in a dedicated hadron collider has specific preferred beam and accelerator conditions. In this section those accelerator and beam parameters which can be adjusted to maximize the data taking rate of the B-detector are discussed.
0168-9002/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved PII S 0 1 6 8 - 9 0 0 2 ( 9 8 ) 0 0 3 3 6 - 2
G.P. Jackson/Nucl. Instr. and Meth. in Phys. Res. A 408 (1998) 296—307
2.1. Maximum luminosity With the use of silicon tracking detectors, a maximum data acquisition frequency of approximately 30 MHz is presently the state of the art. In a dedicated proton—proton collider the optimum bunch crossing frequency f is equal to this maximum data " acquisition frequency. The maximum rate of B-meson production is limited by the average number of interactions per crossing that the detector can handle while still performing its particle identification and trajectory tracking missions. The inelastic cross-section p which determines this interaction */%rate has an approximate value of 49 mb at energies above 1 TeV. The typical limitation on the average number of interactions per crossing k is unity. The relationship between interactions per crossing and luminosity is described by the equation kf ¸" " . p */%-
(1)
The conversion factor from millibarns to square centimeters is 1]10~27 cm2/mb. Plugging in the above values, the peak luminosity which can be tolerated by present day B-detectors is approximately 6.1]1032 cm~2 s~1. The statement that k "1 is the limit for BMAX detectors comes from the assumption that crossing with no interactions and crossings with multiple interactions will not cause the trigger to perform data acquisitions. The probability that there are r interactions in a given crossing is described by the Poisson statistics density function kre~k f(r, k)" . r!
(2)
For example, at k"1 the fraction of crossings with zero interactions is 0.368, the fraction with one interaction is 0.368, and the fraction with multiple interactions is 0.264. By taking the derivative of the Poisson probability distribution with respect to k and setting the result equal to zero for r"1, the average number of interactions per crossing which maximizes the fraction of crossings with a single interaction can be calculated. The result is that k"1 is indeed the optimum. If it were possible to
297
handle more than one interaction per crossing, as discussed in Section 2.3, then the average number of interactions per crossing will be increased. 2.2. Transverse beam size In hadron colliders the transverse beam size is typically much smaller than any other physical length such as the distance to the closest silicon vertex detectors. The beam distribution at the Bdetector is predominantly Gaussian in both the horizontal and vertical directions, with a round aspect ratio. Around this Gaussian distribution is a very diffuse halo whose boundary is delimited by thick steel collimators spaced judiciously around the storage ring. The B-detector has a preference for small transverse beam sizes due to the useful trigger constraint that tracks must originate within the beam. As the beam size increases, the efficiency of this constraint is gradually reduced. For the purposes of this discussion it will be assumed that the r.m.s. horizontal (vertical) beam size p is less x(y) than 100 lm. 2.3. Bunch length If k"1 the r.m.s. bunch length p should be s infinitesimally short. For high luminosity detectors the bunch length can be as long as the value of the focusing function b* before loss of luminosity occurs. In the case of dedicated B-detectors the length of the luminous region is determined by the need to maintain a high track reconstruction efficiency. If one invests more money into the silicon components of the detector, it may be possible to spread out the region over which interactions can be efficiently reconstructed. In this case, if the longitudinal vertex reconstruction resolution is shorter than the bunch length, then crossings with more than one interaction can be reconstructed.
3. Interaction region length From an accelerator physics point of view, the magnetic lattice of a collider generates a focussing
VI. SUMMARIES
298
G.P. Jackson/Nucl. Instr. and Meth. in Phys. Res. A 408 (1998) 296—307
Fig. 1. Example of a magnetic lattice surrounding an interaction point (IP). In this case the Fermilab Tevatron Collider at the CDF and D0 detectors is shown.
envelope called the beta-function. For example, the dipoles and quadrupoles surrounding the CDF detector in the Tevatron Collider [6] are sketched in Fig. 1. In a detector straight section between the focusing “low-b” quadrupoles where the transverse shape of the beam is round (which is traditional for hadron colliders, unlike the flat beams in electron colliders), the r.m.s. size of the beam p depends x(y) on longitudinal position s according to the equation
C A BD
s 2 p2 (s)"p2 (0) 1# * , x(y) x(y) b x, y
(3)
where b* is the accelerator lattice parameter x(y) called beta-star and p (0) is the horizontal (vertix(y) cal) r.m.s. size of the beam at the interaction point. In Fig. 2 the horizontal (vertical) beta function [7] b (s) is displayed for one-half of the interacx(y) tion region. On the other side of the interaction point the horizontal and vertical beta functions reverse roles, making the interaction region lattice anti-symmetric. Fig. 3 shows the evolution of the r.m.s. transverse beam sizes p as a function of x(y) position in half of the interaction region. Note that in a drift region before the quadrupoles and for sAb* the beam size grows linearly with distance. x(y) The relationship between the r.m.s. beam size at the collision point and b* is x(y)
S
p " x(y)
eb n x(y), 6b c 3 3
(4)
where e is the 95% normalized transverse beam n emittance (in the horizontal or vertical plane,
Fig. 2. Horizontal and vertical beta function around the CDF and D0 detectors in the Fermilab Tevatron Collider. The dark lines on the horizontal axis show the locations of the Q4, Q3, and Q2 focusing “low-b” quadrupoles on either side of the interaction point. The origin of the horizontal axis is at the interaction point itself, and the beta functions are anti-symmetric about this point.
299
G.P. Jackson/Nucl. Instr. and Meth. in Phys. Res. A 408 (1998) 296—307
Fig. 3. The r.m.s. transverse beam sizes for the Tevatron Collider at 900 GeV assuming a transverse 95% emittance in both planes of 20p mm mr.
whichever is appropriate) and b and c are the 3 3 relativistic velocity and energy of the protons (antiprotons). Fig. 4 contains a sketch of this r.m.s. beam size as a function of position in one-half of the interaction region and the value of b*. The lower the value of b* the higher the maximum beta in the quadrupoles. Given that these quadrupoles have a limited aperture, there is a limit to how low b* can become for a given length of interaction region. The job of the first of three approximately equal strength quadrupoles on either side of the interaction region is to focus particle trajectories leaving the interaction region into a parallel beam. For magnets which are short compared to the length of the interaction region, this means that the focal length is equal to the interaction region length. If the length of the interaction region scales proportionally with beam momentum, the same quadrupoles can always be used. This is because for a fixed magnetic field gradient the focal length is also proportional to momentum. As the region gets longer, the beam size increases proportionally. But as beam momentum increases, the beam size is reduced by the square root of the
momentum. Therefore, the beam size at the entrance to the first quadrupole only increases as the square root of momentum. 4. Luminosity calculations The economics of proton and antiproton beam production are completely different given the fact that one gets roughly 15 antiprotons for every million protons striking the production target. Therefore, the calculation of luminosity for proton—antiproton and proton—proton operations are presented separately here. 4.1. Proton—antiproton collisions The luminosity ¸ at each HEP detector is
AB
N (N B) f (6b c ) b* ¸" P *A 0 3 3 H 2pb (e #e ) p nP nA s
1
, (5) 2a2p2(b c ) 1# * s 3 3 b (e #e ) nP nA where a is the beam crossing half-angle, N and P N are the bunch intensities, B is the number of A
S
VI. SUMMARIES
300
G.P. Jackson/Nucl. Instr. and Meth. in Phys. Res. A 408 (1998) 296—307
Fig. 4. Beam size vs. position in the detector region for b* values of 0.5, 1.0, 2.0, and 5.0 m. Note that as the value of b* increases, the smaller the maximum value of b(s) inside the quadrupoles but the larger the beam at the interaction point.
bunches per beam, f is the revolution frequency, 0 p is the r.m.s. bunch length, and H is the hour glass s factor which has the form H(x)"xJp [1!'(x)]ex2.
(6)
The ultimate limit to luminosity in hadron colliders to date has been the beam—beam interaction. This limit has been a total beam—beam linear antiproton tune shift m of approximately 0.025 generated by the proton beam current and charge, where N IP is the total number of interaction points, r "1.535]10~18 m, and 1 3r N m" 1 P N . IP 2p e n
(7)
The ratio of the proton bunch intensity to its normalized transverse emittance is limited by the total beam—beam tune shift suffered at all interaction regions. Plugging the equation for this tune shift into the equation for luminosity per interac-
tion region yields the result (N B) m f (6b c ) ¸" A * MAX 0 3 3 2, (8) N b e IP 3r 1# nA 1 e nP where the factors whose values can be modified significantly appear in the left fraction on the right-hand side of the equation. The quantity (N B) A is just the total antiproton intensity injection into the collider ring, independent of the bunch spacing. Unique to a dedicated B-physics collider is the added constraint that the number of interactions per crossing is limited to kK1. This quantity is equal to
A
B
p ¸ k" */%- . (9) fB 0 Note that f B is limited by the detector trigger rate. 0 By plugging this equation into the luminosity equation, it is found that the minimum number of bunches into which the antiprotons must be
301
G.P. Jackson/Nucl. Instr. and Meth. in Phys. Res. A 408 (1998) 296—307
Table 1 Instructive parameters to compare luminosity optimization of existing and proposed hadronic B-factories if they could be run as proton-antiproton colliders Parameter
Tev
Tev-B
LHC
VLHC
Beam energy (TeV) Beam—beam tune shift Interaction regions Interactios/crossing Inelastic cross-section (mb) Total antiprotons (]1012) Beta-star (m) Minimum d of bunches Revolution frequency (kHz) Bunch frequency (MHz) Luminosity (]1030 cm~2 s~1)
1 0.025 2 1 49 10 5 92 48 4.4 79
3 0.025 2 1 49 10 5 276 8.8 2.4 44
7 0.025 2 1 49 10 5 643 8.8 5.7 102
50 0.025 2 1 49 10 5 4595 0.5 2.3 44
distributed is
described by the equation
p (6b c ) (N B) m B " A * MAX */%- 3 3 2. MIN kN b e IP 3r 1# nA 1 e nP
N2Bf (6b c ) b* 0 3 3 H ¸" 4nb*e p n s
A
B
(10)
Note that as the energy of the ring increases, the number of bunches must increase proportionally if the number of interaction per crossing is to be controlled. If one assumes that every antiproton which is available is used, Table 1 can be generated from the above equation. Most parameters are kept artificially constant to show how the bunch spacing is affected by energy. In Table 1 a number of additional assumptions have been made. First, while the Tevatron and LHC circumference assume the existing tunnels, the Tevatron-B and VLHC numbers assume a high packing of 2 T superferric magnets. Second, the choice of 5 m for b* assumes that a $40 m long interaction region is always desired. In addition, the maximum beta-function value at the focusing quadrupoles around the interaction region is )350 m. 4.2. Proton—proton collisions Assuming identical counter-revolving proton beams, the luminosity at each HEP detector can be
AB
1
. (11) a2p2(b c ) s 3 3 1# b*e n Again, the limit to luminosity and to the proton brightness is the beam—beam interaction
S
3r N (12) m" 1 N . 2p e IP n Plugging this constraint into the luminosity equation yields the result NBf (6b c ) m 0 3 3 MAX 2. ¸" (13) 6b* rN 1 IP Note that the luminosity is proportional to proton current in the accelerator and the beam energy. There is also the added constraint of the number of interactions per crossing. Plugging this limit into the luminosity equation, one finds that the constrained quantity is the proton bunch intensity kb*r N 1 IP . (14) (b c )m */%- 3 3 MAX The number of bunches is unconstrained, so the luminosity is not limited until the crossing rate exceeds the detector trigger speed. Table 2 can be generated from this equation. Most of the parameters are kept artificially constant to show how the bunch spacing is affected by beam energy. The
N " MAX p
VI. SUMMARIES
302
G.P. Jackson/Nucl. Instr. and Meth. in Phys. Res. A 408 (1998) 296—307
Table 2 Instructive parameters to compare luminosity optimization of existing and proposed hadronic B-factories if they could be run as proton—proton colliders Parameter
Tev
Tev-B
LHC
VLHC
Beam energy (TeV) Beam—beam tune shift Interaction regions Interactios/crossing Inelastic cross-section (mb) Total antiprotons (]1012) Beta-star (m) Max. bunch intensity (]109) Max. bunch frequency (MHz) Bunches/beam Luminosity (]1030 cm~2s~1)
1 0.025 2 1 49 10 5 175 27 558 610
3 0.025 2 1 49 10 5 39 27 3023 610
7 0.025 2 1 49 10 5 16 27 3023 610
50 0.025 2 1 49 10 5 2.4 27 50379 610
choice of 5 m for the beta-star assumes that the interaction region length is $40 m. In addition, it is assumed that the maximum beta function value in the focussing quadrupoles on either side of the interaction region is 4350 m. 5. Interaction region geometry Over the years the Tevatron Collider has run with electrostatic separators to minimize the beam—beam tune disruption in the arcs which occurs with multiple bunches. The experience is that these devices are very sensitive and unreliable. In other storage rings implementing a crossing angle between the colliding beams has met with mixed success. In this section the implications of running without electrostatic separators and crossing angles are explored. 5.1. Proton—proton geometry The goal is to create head-on collisions without crossing angles at the interaction point. There are many benefits to this arrangement. First, the beam is more stable because the nonlinear dynamics of the beam—beam interaction are simpler to understand, interpret, and correct. Second, the luminosity is independent of the bunch length, which grows during a store. Third, the beam is more reliable since random sparks from electrostatic separators will not cause emittance growth in the beams.
Fig. 5. Sketch of an elegant interaction region geometry for a proton—proton collider where both beams have the same energy. Because the dipole at the center of the interaction point steers the two proton beams in different directions, it eliminates the need for expensive and unreliable electrostatic separators.
In a likely situation in which the two proton beams have roughly equal energy, the existence of the B-detector analyzing dipole magnet at the interaction point makes this geometry easy to realize. As can be seen in Fig. 5, the two proton beams bend in opposite directions horizontally. The bunch spacing is parameterized by the variable ¹ . This allows " the two proton beams to separate cleanly into their separate vacuum chambers as well as provide a simple method by which to prevent parasitic beam—beam interactions on either side of the dipole magnet. Table 3 summarizes some typical parameters which can be anticipated for such a geometry. 5.2. Proton-antiproton geometry Again, the goal is to create head-on collisions without crossing angles at the interaction point. In
303
G.P. Jackson/Nucl. Instr. and Meth. in Phys. Res. A 408 (1998) 296—307 Table 3 Typical parameters to compare beam separation at the interaction region of a dedicated proton—proton B-detector. Parameter
Tev
Beam energy (TeV) Emittance (pmm mr 95% Inv.) Beta-star (m) Beam divergence (lrad) Min. beam deflection (lrad) Min. dipole field (T m) Beam separation @ 40 m (mm) Bunch spacing (ns) Nearest secondary crossing (m)
1 3 7 15 15 15 5 5 5 22 13 8.2 220 130 8.2 1.5 2.6 3.8 18 10.4 6.6 38 38 38 5.6 5.6 5.6
Table 4 Typical parameters to compare beam separation at the interaction region of a dedicated proton-antiproton B-detector where the proton and antiprotons are at wildly different energies
Tev-B LHC VLHC 50 15 5 3.1 31 10.3 2.5 38 5.6
Fig. 6. Sketch of a proton—antiproton collision geometry in which the antiprotons have a much smaller momentum in order to get the beams separated before head-on parasitic crossings on either side of the interaction point.
the case of proton—antiproton collisions the bending magnet at the center of the B-detector bends both energy by the same amount in the same direction as long as the protons and antiprotons are at the same energy. On the other hand, if the antiproton beam has a significantly lower momentum, then it would be deflected by a much larger angle than the protons. As seen in Fig. 6 and Table 4, enough energy asymmetry makes the beams separate again at the parasitic crossing points, by the same amount as the proton—proton passages.
6. Bunch length What should be expected for the bunch length, and hence the luminous length? The answer to this question depends on the intensity per bunch needed to reach the desired luminosity. To zeroth
Parameter
Tev
Tev-B
LHC
VLHC
Beam energy (TeV) Beam divergence (lrad) Min. pbar deflection (lrad) Min. dipole field (T m) Beam separation @ 40 m (mm)
1]0.33 22]38 220 1.5 18
3]1 13]23 130 2.6 10.4
7]2.3 8.2]14 8.2 3.8 6.6
50]17 3.1]5.4 31 10.3 2.5
order, proton bunch intensities below 1]1011 do not require any special RF manipulations. With a high-energy recycling storage ring for antiprotons, RF manipulations are never necessary for large numbers of antiprotons bunches. Just as there is a normalized emittance in the transverse plane which defines an energy independent beam temperature, in the energy plane there is also an invariant bunch area. The conjugate coordinates defining this area are momentum spread and time spread. The RF system is used to mold the shape of this “phase space” in order to generate a desired bunch length. But in order to halve the bunch length, 16 times the RF gradient must be generated. This can be accomplished by turning up the RF voltage by 16] (which implies 256] times more power to halve the bunch length), increase the RF frequency by 16] (better have bunches which are already shorter than the new RF wavelength), or some combination of the two. Invariant bunch areas of 0.1—0.5 eV s are achievable for hadronic B-factories when special RF manipulations are not required. These manipulations are often used to increase the number of particles per bunch at the expense of the bunch area. For a fixed RF gradient, the bunch length scales with the square root of the bunch area. For example, in the Tevatron 1 MV of RF at 53 MHz yielded a longitudinal bunch area during Run I of 3 eV s, with a resultant r.m.s. bunch length of 45 cm. As another example, by eliminating presently standard special RF manipulations the Tevatron bunch area could be reduced by 10], which means
VI. SUMMARIES
304
G.P. Jackson/Nucl. Instr. and Meth. in Phys. Res. A 408 (1998) 296—307
that the bunch length would shrink by 3]. As this beam is accelerated beyond 1 TeV, for the same RF gradient the bunch length will shrink further by the square root of the energy increase.
7. Luminosity evolution simulations When protons (and antiprotons) are injected into a collider ring, a number of mechanisms determine the evolution of the luminosity with time. Each of these effects are taken into account in a spreadsheet program which predicts Tevatron Collider performance with very high fidelity. The dominant particle loss effect is the actual inelastic collisions between the beam particles inside the B-detector. As the luminosity is increased, the rate at which protons (and antiprotons) are consumed increases proportionally. In any scenario discussed in this paper this effect is orders of magnitude more severe than particle loss with residual molecules in the storage ring vacuum chamber. The particles within a bunch undergo Coulomb scattering with one another, an effect called intrabeam scattering. As the bunch intensity is increased, the bunch area reduced, or the transverse emittance decreased, emittance and bunch area growth rates increase dramatically. Intrabeam scattering cannot be counteracted and acts as the fundamental limit to beam brightness. Finally, power supply ripple and electronic noise cause the beam particles to undergo minuscule random walks which end up as emittance and bunch area growth. Though in principle it is possible to completely eliminate this effect, in practice there is a point of diminishing return as single offenders are corrected and hundreds of tiny sources are left. In reality every hadron storage ring ends up with a non-negligible emittance and bunch area growth rate from noise. Applying the Tevatron model [8] to a 3]3 TeV proton—proton hadronic B-physics collider, the parameters in Table 5 are used as input information. The values of these parameters are chosen to be as close to reasonable expectations as possible. The results of this simulation are shown in Figs. 7—10. Note that the luminosity decays with
Table 5 Input parameters for the luminosity performance simulation of a 3]3 TeV B-physics storage ring. Parameter
Tev-B
Beam energy (TeV) Initial emittance (pmm mr 95% Inv.) Beta-star (m) Initial bunch area (eV s) Initial bunch intensity (]109) Number of interaction regions Revolution period (kHz) Number of bunches Emittance growth rate (pmm mr/h) Bunch area growth rate (eVs/h)
3 15 3 0.5 77 2 8.8 3023 1 0.03
Fig. 7. Evolution of Tevatron-B luminosity with time assuming colliding proton beams with the parameters listed in Table 5. Note that approximately 12 h are required to reduce the luminosity by a factor of 2.
Fig. 8. Proton bunch intensity as a function of time. Note the suppressed zero on the vertical scale. Clearly, the bunch intensity does not have a very big impact on luminosity lifetime.
time, reaching half of its original value in approximately 12 h. The dominant cause of this luminosity reduction is clearly the transverse emittance growth, which is dominated by intrabeam scattering
G.P. Jackson/Nucl. Instr. and Meth. in Phys. Res. A 408 (1998) 296—307
305
in the beginning of the store and by noise-induced emittance growth after the first 8 h.
8. Luminosity leveling The problem with this luminosity reduction with time is that the interactions per crossing limit the peak luminosity, but are not a problem for the remainder of the store. It would be very advantageous if the luminosity could be continuously adjusted to be at the detector limit. The solution to this problem may be a procedure called luminosity leveling [8]. By adiabatically
Fig. 9. Evolution of the r.m.s. transverse beam size as a function of time in the colliding beam store. Since the transverse emittance has grown by 40% in 12 h, and the luminosity has dropped by almost the same amount, it is clear that transverse emittance growth is the dominant mechanism causing short luminosity lifetimes.
Fig. 10. Increase in the r.m.s. proton bunch length during a colliding beam store. Though the bunch length increases by more than a factor of 2, the impact on luminosity is small. This is because the bunch length is much shorter than the value of b*.
Fig. 11. Luminosity evolution with time when luminosity leveling is assumed to be functioning. By sacrifing luminosity at the beginning of the store, the same integrated luminosity can be delivered to the detectors by keeping the luminosity constant.
Fig. 12. Required b* curve for implementing luminosity leveling. The gentle nature of the changes implies that the control system could generate a software feedback system to maintain direct control over the luminosity.
changing the strengths of the low-b quadrupoles around the interaction point, the r.m.s. beam size is modified in order to keep luminosity constant. The simulation of this scenario also exists, where the initial value of b* is 723 m and the initial bunch intensity is 120]109 particles. The increased bunch intensity makes sure that the average luminosity remains equal to the scenario without luminosity leveling. Figs. 11 and 12 show the luminosity and b* evolutions with time. As required, the luminosity is now constant in time running at the detector interactions/crossing limit. 9. Tevatron-B Because of the '10-year time to design and approve an accelerator and the '10-year
VI. SUMMARIES
306
G.P. Jackson/Nucl. Instr. and Meth. in Phys. Res. A 408 (1998) 296—307
construction time required by limited funding profiles, it is important for the hadron labs FNAL & CERN to develop a leap-frog strategy in which one lab designs the next step while the other lab is building the present step. Therefore, people at FNAL have begun the design and R&D for the next machine after the LHC, sometimes called the VLHC (very large hadron collider). The preliminary goal is to build a proton—proton collider at FNAL with 100 TeV in the center-of-mass (50 TeV/beam). 9.1. Introduction Circular accelerators can only operate over a 20 : 1 range of beam momentum due to iron saturation and remnant fields. Because the FNAL Main Injector has an extraction energy of 150 GeV, a new accelerator which increases the beam energy from 150 GeV to 3 TeV is needed for injection into the VLHC. This allows the VLHC to reach 60 TeV/beam. The proposal is to build the 3 TeV accelerator with the same inexpensive super-ferric magnet technology envisioned for the VLHC. The cost GOAL (not estimate) for this machine is 4500 M$, about the price of an e`e~B-factory. The main reason for building this 3 TeV machine first is to demonstrate some underlying assumptions. First, that super-ferric magnet technology works. Second, that the super-ferric magnet technology is as inexpensive as expected. Third, to demonstrate the reduced costs of modern tunneling technologies. Fourth and finally, to show that it is possible in the US to build an accelerator under the surrounding suburban communities. One key for making this low project cost goal a reality is the new magnet technology proposed by Bill Foster. This magnet abandons the costly cosine-theta design, returns to 2 T iron dominated magnets, but still uses superconducting cable to carry the current. To date a 2 m prototype has already been successfully built. A 1 m prototype has already been powered and measured. This year we expect to build and test a 30 m long prototype. Because the magnets are weaker, the circumference of the accelerator is larger. For the 3 TeV
Table 6 Author’s optimistic schedule scenario for the construction of Tevatron-B Fiscal Tevatron-B tasks year
Limitations and competition
1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Ongoing main injector project Main injector project finished NUMI is funded NUMI is funded NUMI is funded NUMI project finished Tevatron33 underway Start designing VLHC VLHC R&D Write VLHC TDR Get VLHC approval Get VLHC approval Start VLHC funding
Magnet/tunnel R&D Magnet/tunnel R&D Write design report Get DOE approval Start tunneling Start magnets Tunneling complete Magnets complete Commissioning Do B-physics Do B-physics Do B-physics Do B-physics
machine the circumference is 34 km, 10] larger than the present Main Injector/Recycler construction project. Therefore, it is vital to reduce tunneling costs. People at FNAL have been actively discussing micro-tunneling options with new high-tech companies. This year it is desired to start a tunneling R&D program at nearby rock quarries who are already in the layer of rock which would house both the Tevatron-B and VLHC tunnels. 9.2. The pitch This is a green field accelerator. It has no other mission than accelerator R&D and eventually an injector for the VLHC. It would be MUCH more likely to be promptly approved if it had a physics case which was relatively inexpensive and nonchallenging. Why not B-physics? 9.3. Project goals As stated, the project goal is to come in below 500 M$. To date this cost is dominated by costing traditional tunneling technology. If micro-tunneling is found to be feasible, this cost could come down by 42] and the project cost could be as low as 300 M$.
G.P. Jackson/Nucl. Instr. and Meth. in Phys. Res. A 408 (1998) 296—307
The schedule depends on how badly the HEP community wants to do this project. Table 6 contains a personal schedule scenario which may be achieved if enough of the community gets excited about the physics potential behind Tevatron-B. The column named “limitations and competition” is meant to indicate where scarce money and manpower may be assigned, in direct competition with the needs of a Tevatron-B project. Acknowledgements I would like to thank Bill Foster, Peter Schlein, Ernie Malamud, and Shekhar Mishra for interesting and provocative discussions about the feasibility of building a dedicated hadronic B-factory.
307
References [1] PEP II Conceptual Design Report, LBL-PUB 5379, SLAC-418, CALT-68-1869, UCRL-ID-114055, UCIIRPA-93-01, June 1993. [2] Shin-ichi Kurokawa, KEKB Status and Plans, Proc. 1995 Part. Acc. Conf., Dallas 1995, p. 491. [3] David L. Rubin, CESR Status and Plans, Proc. 1995 Part. Acc. Conf., Dallas 1995, p. 481. [4] Supported by the United States Department of Energy. [5] L.R. Evans, The Large Hadron Collider, Proc. 1995 Part. Acc. Conf., Dallas 1995, p. 40. [6] V. Bharadwaj, Status and Future of the Tevatron, Proc. 1995 Part. Acc. Conf., Dallas 1995, p. 396. [7] E. Courant H. Snyder, Ann. Phys 3 (1958) 1. [8] G. Jackson (Ed.), Recycler Ring Technical Design Report, Fermi National Accelerator Report TM-1991, November 1996.
VI. SUMMARIES