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Kaons for TRIUMF Craddock, M. K.; Betz, M.; Ng, J. N.; Richardson, J. R.; Rosenthal, A. S.; Thomas, A. W. May 31, 1981

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T R I U MFKAONS FOR TRIUMFM.K. Craddock Department of Physics, University of British ColumbiaM. Betz, J.N. Ng, J.R. Richardson,* A.S. Rosenthal and A.W. ThomasTRIUMF*on leave from UCLAMESON FACILITY OF: UNIVERSITY OF ALBERTASIMON FRASER UNIVERSITY UNIVERSITY OF VICTORIA  UNIVERSITY OF BRITISH COLUMBIA TRI-81-2ERRATUM TRI-81-2The reference to the second sentence on page 12 was inadvertently omitted and should read:C. Dover, Nukleonika, vol. 25, p. 521, 1980TRI-81-2TRIUMFKAONS FOR TRIUMFM.K. Craddock Department of Physics, University of British ColumbiaM. Betz, J.N. Ng, J.R. Richardson,* A.S. Rosenthal and A.W. ThomasTRIUMF*on leave from University of California, Los AngelesPostal address:TRIUMF4004 Wesbrook Mall Vancouver, B.C.Canada V6T2A3 May 1981C O N T E N T SPage1. Introduct ion 12. 'Kaons' or 'Chaos' —  Eiectroweak Interaction Possibilities 2(J.N. Ng)2.1 CP violation 32.2 Rare decay modes of kaons 52.3 Neutrino physics 62.4 Conclusion 73. Strong Interactions and Nuclear Physics 8(A.S. Rosenthal and A.W. Thomas)3.1 Kaon-nucleon interactions 83.2 Charm 93-3 Hypernuclei 103.4 K+-nuclear interactions 124. Antiproton Physics 13(M. Betz)4.1 Low-energy nucleon-antinucleon scattering 134.2 Nucleon-antinucleon annihilation 134.3 Baryonium 144.4 Interactions of low-energy antinucleons with nuclei 164.5 Conclusion 165. The Proper Energy for Kaon and/or Antiproton Production 17(J.R. Richardson)5.1 The role of TRIUMF in a K/p” factory 196. Synchrotrons 20(J.R. Richardson)6.1 Injection 206.2 Single 20 GeV synchrotron 206.3 Two synchrotrons in series 217. 'CANUCK' High-Energy Cyclotrons 23(M.K. Craddock)7.1 Betatron oscillations and fringing field effects 247.2 Magnet and RF design 25APPENDICESA. Summary of some physics possibilities at a kaon factory 28B. Kaon factory feasibility studies 30INTRODUCTIONKaon and antiproton experiments have a history of remarkable productivity, but further progress is being hindered by the low intensities and purities of K and p beams. The TRIUMF 0.5 GeV cyclotron could be used as the injector to a 'kaon factory1 to provide beams 100-1000 times more intense than those at present available, enabling advances in kaon and antiproton physics comparable to those made possible in pion and muon physics by construction of the existing meson factories. Intense beams of other particles would also be available— protons, neutrons (both fast and thermal), pions, muons and both muon- and electron-neutrinos. Significant new experiments would become possible on weak decay processes, symmetry violations, baryonic resonance spectra, kaon-nucleus interactions, hypernuclei, exotic atoms, antiproton interactions and neutrino behaviour (see Secs. 2-4 and Appendix A).Preliminary studies are therefore being made of accelerator designs which would boost an intense beam of protons, extracted from the TRIUMF cyclotron, to at least 8 GeV for kaon and 20 GeV for antiproton production. Two alternative accelerator schemes are being considered and are described in Secs. 5_7- One, 'CANUCK1, con­sists of 3 GeV and 8.5 GeV superconducting ring cyclotrons, each capable of accelerat­ing 400 pA. The other involves a one- or two-stage 20 GeV synchrotron accelerating 100-200 pA currents.During the summer of 1979 a Kaon Factory Workshop was sponsored by TRIUMF to consider both the physics potential and practical design of an accelerator. Informal studies in both areas have continued since then, and a design study will be undertaken as a minor project during 1981/82 to further investigate the project's feasibility and prepare a formal proposal. The scope of this feasibility study is outlined in Appendix B.- 2 -2. 'KAONS' OR 'CHAOS' -  ELECTROWEAK INTERACTION POSSIBILITIESOne of the central tasks of particle physics is the identification of the basic constituents of matter in the universe and the determination of the 'forces' by which they interact. In the pursuit of the above objectives physicists have always been guided by the idea of using a few simple fundamental concepts to construct elegant frameworks in which to describe the interactions of these particles.In the last decade the following picture has emerged. The basic constituents of matter are the quarks and leptons. They are arranged in three generations as fo11ows:where L and R denote left- and right-handedness. The t-quark has yet to be discovered.The framework that describes the electromagnetic and weak interactions, or electroweak in short, is the gauge theory of Weinberg-Sa1 am based upon the gauge group SUl(2) x U(l). A set of four gauge particles W4 , Z° and y are employed as the medi­ator of the electroweak force. The interaction that binds the quarks can also be fitted into the above framework. The gauge group is SU(3) and the mediators are the eight colour gluons.This leads to a third quest, namely the unification of the above electroweak and colour interactions currently known as grand unified theories. The aim is to describe the electroweak and colour forces as components of a single 'force' which carries just one basic charge. This will entail finding a grand unified group G which contains the current SU(2) x U(1) x SU(3) as a subgroup.the above is proven. More importantly, are there new pieces to be added to the above? Can some parts of that be altered? Below we list a number of important problems.stituents such as preons or subquarks?2) Are the gauge bosons themselves composite objects?3) Why is the E R missing? Are neutrinos really massless, thereby signifying a chiralinvariance for the neutral lepton which is broken for the charged fermions?A) Is there a new interaction, such as a horizontal gauge force, that connects thegenerations?5) Is the SU(2) x U (1) electroweak theory going to be modified at energies in or above the TeV range and how?6) What is the physics of spontaneous symmetry breaking (SSB) that is employed to give masses to the W-bosons and the charged fermions in the SU(2) x U (1) theory?Although the above is the consensus picture or general framework, there are many fundamental unsolved problems. From the experimental point of view not every piece of1) Why do the generations repeat themselves? Does that signal more fundamental con-- 3 -7) Where are the fundamental Higgs bosons which result from SSB?8) Is there a grand unification? If so, what is the group G?9) Is there a left-right symmetry extension of the SU(2) x U(l) theory in the TeVregion before grand unification?10) Establish the proper weak transitions among the six quarks. In other words, we need to determine and achieve a theoretical understanding of the three mixing angles between the d-, s- and b-quark and the CP violating phase. This under­standing is currently lacking and not possible in the SU(2) x U(l) theory.11) Further tests are needed to confirm quantum chromodynamics as the true theory of strong interactions. In particular an approximate scheme that can account for the observed hadrons will require new experimental input.12) The verification of the W* and Z° at high energy machines such as pp collidersand e+e” machines will be instrumental in establishing the SU(2) x U(l) theoryas being correct.13) The experimental verification of radiative corrections of SU(2) x U(l) theory is required. These experiments will play the same role that g-2 of the muon and electron and the Lamb shift of the hydrogen atom did for QED.The above list is certainly not exhaustive but indicative of the experimental task that is facing us. A consolidation of our current understanding is urgently needed so that we can reach the next level of understanding.The construction of a kaon factory with high intensity kaon beams, together with the expected new detector technology, will undoubtedly shed light on the above fundamental questions. The study of kaons has indisputably been very fruitful in formulating our current understanding. We will mention CP violation and the suppres­sion of strangeness changing neutral currents via the G1ashow-I 11iopolous-Maiani mechanism as two vivid examples.2 .1 CP violationThe kaon system is still the only one to date that gives a positive signal in CP violation. The origin of the CP non-invariance is still an open question. In the context of gauge theories there exist several mechanisms. The first one is a phenonem- ological parametrization due to the existence of more than four quarks. This follows from the assumption that the quarks that constitute the hadrons have non-degenerate masses. They form an eigenbasis for the mass matrix of the charge -1/3 quarks. In general this basis does not diagonalize the weak interaction Hamiltonian. However, one can obtain the weak eigenstates from the mass eigenstates by a unitary transforma­tion. For n-doublets the unitary transformation is an nxn matrix. In particular for three doublets we have a 3X3 matrix. An nxn unitary matrix is parametrized by n ^  ^  real rotation angles plus complex phases. For two-quark doubletsonly we have one angle which is the usual Cabibbo rotation that mixes the s- and d- quarks and no complex phase. For the three quark doublets we have three mixing angles (6j, 02, 83) plus one phase which is the CP-violating phase 6. This is the Kobayashi- Maskawa parametrization. In this approach CP violation is placed on the same footing as the Cabibbo-like mixing angles.-  k -A more dynamical model for CP violation within the framework of gauge theories was proposed by T.D. Lee and S. Weinberg. It entails including two or more Higgs doublets in the standard model. In this case there exists physical charged Higgs bosons in addition to the one neutral Higgs boson of the standard model. The exchange of virtual Higgs bosons then induces CP violation. Obviously this has to be considered as an additional contribution to CP violation due to the KM phase. We emphasize that the above Lee-Weinberg extension is the simplest, and many other alternatives are poss ibl e .We mentioned previously that one fundamental problem in particle physics is the understanding of parity-violation in weak interactions. Is it a low energy phenomenon due to the spontaneous breaking of parity at current energies? If so we expect res­toration of parity being a good quantum number at higher energies in the TeV range.The SU|_(2) x SUr(2) A  U(l) models are the simplest examples with a rich phenomenology.In addition to the three right-handed intermediate vector bosons W^ and Z^, this class of models contains CP violation in terms of an effective milliweak interaction.It has long been recognized that the SSB mechanism to give masses to the inter­mediate bosons is rather ad hoc. The number of elementary scalars or Higgs bosons required in the minimal 6-quark six leptons SU(2) x U(l) theory is small; namely, one Higgs doublet with four elementary fields. The number of couplings to different fer­mions is large, arbitrary and incalculable within the theory. Recently, intensive efforts have been spent in developing a theory replacing the elementary scalar fieldsby bound states of new fermions. This idea of dynamical symmetry-breaking was firstintroduced by Anderson in superconductivity. It necessitates introducing a new strong interaction called technicolour or hypercolour. In other words, the colour gauge group is extended from SU(3) to SU(A) for the simplest case. Mew families of hyper­colour quarks are needed, together with the hypercolour gauge bosons. Effective 'elementary' scalar particles are formed as the bound states of these heavy hypercolour quarks under the new strong hypercolour gauge interactions. The hyperfermions are necessarily heavy so as not to disturb the currently successful phenomenology of light quarks. However, to give masses to the light quarks one has to introduce sideways gauge interactions (Gsw) that bridge the light quarks with the hyperfermions. Ob­viously, this will induce reactions that connect the three families above. Thus, p+ e+y, p+ -»■ e+e“e+ and P+e“ is predicted by this class of theory as a resultof sideways gauge interactions. A CP-violating phase from Gsw is also present.In Table I we present the various estimates of the CP-violating parameters based on the above four classes of theories as compared with the present experimental status. The parameters are defined by the amplitudes of the K£ and Kg decays, namely_ A(KL -x tt0 7t ° )n°° A(KS ->■ ir°Tt0)andA(K[_ -*■ n+ A(Ks -* Tr°TT°)- 5 -Table I13] _ 7100 n+- OnSuperweak 0 <10-29KM 0.7 - 2 x io-2 ~10"3 0Weinberg Higgs 2 x IQ-2 ~10"21tTechn i col our - ~10"21tSUL(2)xSUL (2)xU(l) 0 >10-29Exper iment <2 x 10-2 < 1 O-24|n+-| = (2.274 ± 0.022) x 10"3 |n0 0 1 = (2 -32 ± 0.09) x 1 0 - 3Dn is the neutron dipole which if non-vanishing measures violation of time reversal i nvar i ance.From an examination of the table we see that the current experiment and the plan­ned one at Fermi lab which measures 1 - to 0.01 can only distinguish the superweak model (with effective strength 10~9 Gp) from the rest of the gauge models which are milliweak (10-3 Gp). In order to distinguish between the various gauge models with far-reaching consequences, we would require an experiment at the 10~3 level. A clean kaon beam with high intensity can certainly achieve that.We have singled out the K° and K° system for discussion because they give usthe only available experimental information on CP violation. Important information can be obtained from y+ polarization measurements of K+ -> iry+v decay, or K+ -> y+vy as well as studies of the rare decays such as K£ -*■ yy and K ire+e". Currently such studies are limited by both the quality and the intensity of available kaon beams.2.2 Rare decay modes of kaonsWe have seen that the study of CP violation which is unique to the K°-K° system is very valuable for the deeper understanding of particle physics; however, it is not the only area where a dedicated kaon facility can contribute. The various rare decay modes of kaon will offer a unique way of probing physics in the multi-TeV region.Here we can divide into two main categories. The first class are those decay modes that would violate lepton numbers or more appropriately they probe transitions between the families. For example, decays such as K£ -*• y+e" or y"e+ , K+ -> TT- e+ e+ , K+ -»• ir+e+y-, etc. The second class are the more mundane decays which are allowed or expected as higher-order electroweak interactions. Examples are K£ yy, K£ -* y+y", K+ -*• ir+vv, etc. These are suppressed by virtue of the GIH mechanism.In the first category experimental limit on Kp P+e-/K£ -> all < 2 x 10"9 pro­vides the information that horizontal gauge bosons must be of the order of 10 TeV.Obviously, the observation of this decay would shed a great deal of light on hyper­colour theories where sideways interactions are introduced; on grand unified theories- 6 -where lepton number is violated by the introduction of flavour-changing Higgs; and on left-right symmetric models where Majorana neutrinos are the agents that break lepton number conservation. If quarks and leptons were indeed composite, these reactions will provide much needed information on the "effective masses" and the interactions of these substructures. Currently, u -»• ey provides the most stringent limit on the distance scale where sublepton can occur. The branching ratio of p + ey/y -*■ evv <1.9 x 10-10 gives the inverse radius A of possible subleptons to beA » 2 x 102 TeV.The anomalous magnetic moments of the muon and the electron give a less strin­gent limit. This is to be compared with the centre-of-mass energies /s" of:1) PETRA and PEP /if ^ 3 - 8  x 10"2 TeV2) LEP II /s =* 3 x 10_1 TeV3) HERA and CHEER /s ^ 0 . 2  TeV4) FNAL Tevatron /if —  4 x 1CT2 TeVClearly, the rare decay modes of kaons if pushed to the level of current sensitivity of y- •+ e- conversion would be a powerful tool for the study of physics in the hundreds of TeV region.While the lepton number or generation changing decays of kaons explores the un­known territory of particle physics, the decays of the second category serve to con­solidate our current knowledge. We have seen that the three-generation minimal SU(2) x U(l) model contains three real angles 0j, i = 1,2,3 besides the CP-violating phase. To completely determine the 0; we need very precise measurements of the kaon decays, K^-Kg mass difference, hyperon decays, charm and b-quarks decays. We are now just beginning to study the b-quark decays. The measurements of these angles will give very important information on the t-quark, which is now expected to be within the kinematic region covered by LEP I (maximum /s" = 100 GeV). The t-quark is expected to mainly decay into the b-quark which decays preferentially into the c-quark rather than the u-quark. This hierarchial decay is still unfolding and a complete study of the s-, d- and b-quark decays will be needed to determine the possible connection between masses and the mixing of the charge -1/3 quarks. Such relations have been widely speculated about especially within the context of grand unified theories (GUTS).2.3 Neutrino physicsWe have emphasized above the scope of physics that can be explored by studying the kaon decays. A dedicated kaon facility also offers opportunities for experiments using various other secondary beams. One unique possibility is the construction of intermediate energy neutrino beams. In particular we can envisage having 100 MeV ve beams which are not attainable at the moment. Present experiments suggest that neu­trinos are massive and that mixing between them may occur. It appears that such effects may be more prominent for the ve than for Vy. This has stimulated more work at both LAMPF and the higher-energy neutrino beams of FNAL and CERN. Neutrino masses and mixing parameter measurements are crucial for GUTS and cosmology.- 7 -In addition to the above, Vy beams in the GeV range of very high intensity com­pared to the Brookhaven beam now available would be very useful for a high precision measurement of sin20w in neutral current reactions. If sin20w is known to better than one per cent, it will play a role as important as proton decay in determining whether GUTS is the right avenue to explore. More importantly, it will also establish the correctness of radiative corrections or higher-order contributions in SU(2) x U(l).A cornerstone in gauge theories is renormalizabi1ity and the finiteness of higher correction. An experimental test of this is clearly of paramount importance.2.4 ConclusionIt is obvious that a kaon factory can contribute a substantial amount towards answering a lot of the basic questions in particle physics. The experiments that can be done are both exploratory and of a consolidating nature. Similarly, this is true for high energy, low intensity machines that are being planned for the later part of this decade. Besides the above physics, it also opens new areas of research in nuc­lear physics via neutrino beams, the possibility of the formation of charmed nuclei, the production of higher-lying strange baryons, etc. These will undoubtedly add new experimental input into the formulation of an approximate scheme of QCD which may help in solving the confinement problem. Thus we find that a dedicated kaon facility will be competitive with the high energy machines since it explores the unknown in its unique way of being able to perform very high precision measurements. It also has versatility in providing neutrino beams, and other secondary beams when the need arises. A wide area of physics can be covered of a scope that has never been achieved before.STRONG INTERACTIONS AND NUCLEAR PHYSICSThe great progress of the past decade in elementary particle physics has led to a new picture of the basic structure of matter. In this model the hadrons are made of quarks bound together by forces which have a very high degree of symmetry. Paradoxically, this great symmetry of the forces imposes large problems for extract­ing the mathematical features of the model, and it remains to be seen how this picture can contribute to our understanding of the low-energy properties of nucleons and other strongly interacting particles. On the other hand, we already possess a broad physical insight into many of these properties from the rich assortment of low- energy phenomenologies. Unification of these pictures, of the partially successful phenomenological models with the colour-quark models, is the most important problem facing strong interactions physics today. Solutions of the problems will require both an improved understanding of the emerging models and of the less explored areas of low-energy physics. The kind of high intensity proton accelerator described as a kaon factory can supply much of this understanding.3.1 Kaon-nucleon interactionsAmong the first experiments to be performed with this accelerator would be Kp and Kd scattering leading to improved phase-shift analyses of KN scattering ampli­tudes. These measurements are essential prerequisites for modelling other kaon- induced nuclear reactions but they have added significance. One of the most success­ful pictures of low-energy hadron physics is chiral SU(3). In this model the strong interactions are, at some stage, seen as invariant under individual left- or right- handed rotations in unitary spin space, an invariance which is spontaneously broken resulting in an octet of pseudoscalar Goldstone mesons. These are collective exci­tations whose existence is due to the spontaneous symmetry-breaking and whose masses measure the strength of symmetry-violating forces. These forces are poorly under­stood although their symmetry properties are one of the closer points of contact with QCD (or any such model). Low-energy K+N phase shifts directly measure the kaonic Goldberger-Treiman relations, and reliable KN cross sections are necessary input to dispersion calculations of off-shell amplitudes and for evaluating chiral sum rules and the KN cr-commutator. This last quantity is known only within errors of over 1001 at present. The existence of resonances in the K+N cross sections has been the subject of heated controversy. Any such resonance would be a q^q" state unaccounted for in the conventional three-quark picture of baryons but predicted by some bag models. Verification of even one such resonance would be a major event in particle phys i cs.The K"N system is the incident channel from which most of the hyperonic spec­trum has been studied. At the present time a large number of the states predicted by the [SU(6) x 0(3)]s model are missing from the observed K'N spectrum, and it is very important to clarify this situation by improved K'p and K”d measurements. For most of the observed resonances only a mass and a rough decay rate are known. Kaon beams- 9 -in excess of 106 K/sec would allow observation of a large number of decay modes and branching ratios which would, in turn, impose strict requirements on models of hadron structure. A similar spectroscopy could be studied for the excited mesonic states which would be copiously produced by such an accelerator.A proton facility operating in the 20-30 GeV range would be an ideal source of those hyperons which belong to the nucleon octet. The measured properties of these hyperons are the most basic source of information on baryon structure, and although their masses and decay rates are fairly well known, their other properties need to be more accurately measured. For example, the magnetic moment of the A particle is known to two significant figures but that of the E" to only 50%. A considerable amount of theoretical effort has been devoted to understanding these moments, and improved measurements of the 2“ and E- moments would be helpful.The nuclear force is related to the hyperon-nucieon and hyperon-hyperon forces at several levels. The Yukawa picture of meson exchanges relates these forces, but very imperfectly in existing one-boson-exchange pictures. At another level it is the dynamics of confined quarks which provides a basic for comparison. One would like to have a sufficient amount of NN, YN and YY scattering data to make these comparisons and deepen our understanding of the off-shell properties of the NN force. This will require much more data on YN scattering. The sort of high-energy kaon factory needed for this work would also be useful for studying meson-meson interactions. Experimen­tal studies of these are carried out by isolating the one-meson-exchange contribution to meson production amplitudes, as shown in Fig. 1(a). With a 20-30 GeV facility one can entertain the hope of studying the KK interaction in reactions such as those of Fig. 1(b).Fig. 1. (a) Production amplitude used to study K-n scattering;(b) Analogue of 1(a) for KK scattering.3.2 CharmA rather ambitious, but exciting, possibility raised by the availability of clean K-beams is that one make and study charmed nuclei via the (K,F) reaction anal­ogous to the (u,K) reaction which is being used to study hypernuclear physics. The advantage of a kaon beam is a momentum transfer which, though large, is reduced com­pared to other mesic or photo-induced reactions. The threshold for this reaction on a reasonably heavy nucleus is about 3-5 GeV. The discovery of a charmed nucleus- 10 -would be significant in itself, and if it proved possible to study energy levels or other properties we could expect to learn a great deal about nuclear and particle phys i cs.The confinement mechanism for a charmed quark seems to be rather different from that of the light quarks. For example, the confining boundary conditions in a bag model are quite different. Thus the study of the C-N interaction in nuclearmatter may provide new insights into the structure of Q.CD itself. We emphasize thatthe idea is highly speculative, but certainly worth a try!3-3 HypernucleiA kaon factory would open a new era in the study of hypernuclei. This study is an essential part of nuclear physics. Structure and reaction calculations for hypernuclei have more control of many-body effects than in the case where no dis­tinguished particle is present and thereby serve to test the models of conventional nuclear physics. The lack of a Pauli principle allows hypernuclear states to be formed with permutation symmetries inaccessible to ordinary nuclei. Unique collec­tive degrees of freedom are available which can couple to the well-studied nuclear collective and single particle motions. In addition, the competition between theT UMI and AN NN decay modes is a potentially powerful probe of the nuclear momen­tum d i stri but ion.The recent use of the ( K ~ , tt) reaction to study hypernuclei has revealed exciting and unexpected features which only a high flux kaon beam can explore further. A very conservative estimate is that the number of known hypernuclear states would be extended by one order of magnitude within the first year of accelerator operation. This should be compared to the fact that several years ago the resolution of a single pair of excited states in ^ 0  was sufficient to cause a rethinking of the entire theoretical foundations of the subject.In that case the questions concerned a doublet, presumably (P3/2 ) A(p3/2-1)n and (P 1/2.) A(pl/2-1)n whose splitting was found to be 6 MeV, very close to the spin- orbit splitting in non-strange 160. This could be taken as implying that the AN spin-orbit force is very weak, in contrast to meson-exchange models where the dominant AN force is expected to be mediated by two-pion exchange with a virtual 2 intermediate state and a consequent strong spin-orbit force. The absence of such an interaction could be due to some mechanism which suppresses A-I transitions in the presence of nucleons or to a deficiency in the meson-exchange calculations. The former possibil­ity deserves study if only because of its analogy with an outstanding problem in nuclear physics, the N-A transition in nuclear matter. The latter possibility would have enormous consequences for our understanding of nuclear forces and could best be studied by free hyperon scattering. It may even be that the AN spin-orbit force is not weak at all but that the observed states (and a similar doublet in 1*°Ca) have a peculiar structure which conceals this.A longstanding puzzle in hypernuclear physics is the binding energy of a A in nuclear matter. Experimental estimates often differ markedly from calculated values and binding energies of hypernuclei with A > 40 are needed. Another important question is the origin and magnitude of the large isospin-violating component of the AN force. Clarification of this problem will require the binding energies of isotriplets such as (pe, iLi*. ’He) or [JB, ^Be", ^Li)- At present no complete set of three hypernuclear isotriplet binding energies has been measured.The recent observation of the hypernucleus ^Be (and probably as well) opens the way to an exciting new spectroscopy. The important current question is why these systems are observed at all, inasmuch as the decay width r(EN ■+ AN) is expected to exceed 20 MeV on very general grounds. Several explanations have been advanced, some of which question these estimates of Tfree while others describe the quasi-stabi1ity (fexp MeV) as due to coherence effects in the hypernuclear wave function. These have an important bearing on the binding energy of E hyperons in nuclear matter. The two models referred to above predict very different lifetimes for E-hypernuclear ground states, none of which have yet been observed.A kaon factory could also address the longstanding problem of the possible stability of the E-n and E_nn systems. It appears likely that these systems are slightly unbound, although there is at least one experiment which claims to have ob­served a bound E~n state. Such a 1hyper-deuteron', if it exists, would be an invaluable system for studying general properties of the YN force.Intense kaon fluxes could also be used to produce E-hypernuclei in sufficient quantity to observe rare decay modes like EA -*■ A + ir with their peculiar spectroscopic selectivi ty.Radiative kaon capture at rest is another potential source of information on both A- and E-hypernuclei. Within the past few years radiative pion capture has become a very important tool for probing the distribution of Ml strength in nuclei, and corresponding experiments for hypernuclei would be a unique source of knowledge of this property. The kinematics are less favourable for this reaction than for radia­tive pion capture, in that the final state momentum is Py\ —  1.5 F"1 compared to ~  0.5 F-1 for i t N -+ yN, but this is certainly a feasible experiment for a kaon factory producing in excess of 106 K/sec.E-hyperons will be produced in the high energy p+ nucleus primary collisions and also in (K“ ,K+) reactions on nuclei. It is not known whether these hyperons live long enough in the presence of nucleons to form bound states with nuclei; if they do the resulting systems would add an important new dimension to our understanding of hypernuclei. The 5 has strangeness -2 and is expected to interact relatively weakly with nucleons, most likely by the same kind of two-step mechanism that has long been thought to represent the dominant component of the AN interaction:- 12 -A determination of the average H-nuclear well depth would be an important advance in understanding YN forces and the effective EN spin-orbit force would be of equal importance. The experiments needed for this are (K“ ,K+) or (K- ,K°) reactions, where the estimated cross sections for producing good hypernuclear states are in the nano­barn region.The large decay width EN -*■ AA may rule out the possibility of forming such exotic hypernuclei (although similar arguments were made about S-hypernuclei not long ago), in which case the (K",K+) reactions would serve primarily as a source of double-A hypernuclei. Almost nothing is presently known about these systems other than their mere existence. Bizarre symmetry schemes become realizable for these nuclei, such as the y^He ground state (Is)6 configuration, which would probe nuclear forces under extreme conditions. In addition, double hypernuclei are the most impor­tant source of experimental information on the YY interaction.3.4 K+-nuclear interactionsK mesons offer a particularly interesting method of probing conventional nuclear structure, a method which is complementary to leptonic and ir-mesic probes.The K+ interacts only weakly with nucleons, the mean free path in nuclear matter ex­ceeding nuclear radii for the energies at which kaon beams will operate. This particle is primarily sensitive to the one-body nuclear matter density as distinguished from the sensitivity of electrons to the nuclear charge density and of photons to the electric dipole density. The pion is also sensitive primarily to matter distribu­tions but in a strongly energy- and momentum-dependent fashion because of the A resonance. The K+ is in the unique position of being a fairly simple and direct probe of nuclear densities. Perhaps the ultimate utility of K+-nuclear elastic and inelastic scattering data will come from comparisons with similar excitation by other probes, comparisons which can help break through the ubiquitous problem of structure vs. reaction mechanism that bedevils nuclear reaction analysis.Before these experiments are carried out it will be necessary to sharpen our understanding of the K+N force. Measurements of recoil polarization or of asymmetries in K+ scattering from polarized targets would be extremely helpful, as would charge exchange angular distributions.The vast range of possibilities opened by such an accelerator include testing the conservation and invariance laws under new conditions. Double-A hypernuclei will allow tests of the spin-statistics theorem for A particles while the ratio of the asymmetries in K[ + nev and irpv will test CPT.In the above paragraphs we have tried to restrict ourselves to those aspects of strong interaction physics about which we are most informed. Much more could be added on the subjects of resonance propagation in nuclei, kaon regeneration and nuclear spectroscopy with kaon beams. The strongly partisan nature of the above remarks is an indication of a feeling that is gaining ground within the nuclear physics community: that a kaon factory is the next step forward in nuclear research.- 13 -k. ANTI PROTON PHYSICSWith the availability of primary proton beams above 15 GeV, the possibility of performing experiments with p-beams can be seriously considered. A comparison of the predictions of standard models of low-energy hadron-hadron interactions (e.g., one- boson-exchange models) with pT-nucleon scattering data would constitute an important test of these models. The study of p'-nucleon and p-nucleus interactions is expected to provide new information on some little known aspects of strong interactions and should be of crucial help in bridging the gap between low-energy phenomenologies and the most widely accepted fundamental theory of strong interactions (QCD).4.1 Low-energy nucleon-antinucleon scatteringLow-energy nucleon-nucleon interactions are successfully described by one-boson- exchange (OBE) models, which picture the NN force as arising from the exchange of mesons with masses below 1 GeV. In this model the NN interaction is related to the NN interaction by G-parity transformation. The comparison of the predictions of this model to phenomenological NN phase shifts would therefore constitute a crucial test of the OBE description of low-energy NN interactions. Because NN channels are not restricted by the Pauli principle and because large inelasticities due to annihilation are expected even at low energy, copious data on elastic scattering and charge exchange (pp •+ rTn) would be required for a phase-shift analysis to be possible. Experiments with polarized beams and targets would be highly desirable. Arguments based on the G-parity transformation also suggest that the presently widely used models for pion production in NN collisions could be tested by studying the analogous reaction in NN collisions. This might help to settle the controversial issue of the importance of p-meson rescattering in this process.A .2 Nucleon-antinuc1 eon annihilationThe most unique channel available to the pp system is, of course, annihilation. The study of this reaction is expected to be particularly rewarding for several reasons. Firstly, in understanding NN interactions at the hadron level, as discussed above, NN phase-shift analyses will be greatly facilitated by the knowledge of the coupling of individual partial waves to the annihilation channels. Secondly, at the quark level, NN annihilation is expected to proceed via short-range quark-antiquark interactions, such as gluon exchange, gluon bremsstrahlung or qq annihilation into gluons. Thus annihilation occurs when the two-quark bags constituting the hadrons overlap significantly and should be sensitive to the radius of the bags. Knowledge of this quantity is central to our understanding of many nuclear phenomena. The 'hadronization' process whereby the gluons materialize into physical hadrons should in principle be explainable by QCD. Quantitative predictions of low-energy phenomena based on that theory are difficult and usually rely on some semi-phenomenologica1 model. The determination of the branching ratios to the various possible final states will provide many useful tests of these models.- 1 4 -For the experimental investigation of annihilation, the very low-energy region is particularly attractive. For momenta below 800 MeV/c, the pion production channel is closed. Apart from charge exchange (which accounts for about 6% of the total cross section), the only inelastic channel open is annihilation. For momenta below 100 MeV/c the charge exchange channel is also suppressed. In addition, the interpretation of the data should be easiest at low energy because of the small number of partial waves involved. The study of pp annihilation for stopped p" should be of particular interest. The determination of the widths and shifts of the levels of protonium (pp atom) due to strong interactions will give information about the dependence of annihilation on the spin and angular momentum of the initial pp state. Equivalent information for individual annihilation channels can be obtained by detecting X-rays in coincidence with specific annihilation products, since this makes possible the tagging of the ini­tial atomic state from which annihilation occurs.Other facets of pp annihilation which seem particularly noteworthy are:1) The study of annihilation channels which proceed through intermediate mesonic resonances.2) The determination of UU-IIII amplitudes, which are important ingredients in the construction of the NN interaction from dispersion theory.3) The study of reactions such as pp -+ KK, which cannot proceed by simple rearrange­ment and are expected to give information about the sea quark distribution in baryons.A) The use of the reaction pp e -e” to determine the electric and magnetic formfactors of the proton in the time-like region. Because the branching ratio issmall (3 x 10-7), a high i ntens i ty p" beam is required to obtain accurate data.5) The search for exotic mesonic states which couple weakly to ordinary mesons andtherefore cannot be easily investigated by other means. The existence of suchstates (known under the generic name of baryonium) is suggested by most theoret­ical models. As this is one of the most fascinating issues in p" physics, it is discussed in some detail below.4. 3 Baryoni urnSince the intermediate range attraction in the NN interaction is mostly due to the two-pion-exchange contribution, which is unaffected by the G-parity transformation, it is natural to expect that the NN system possesses at least one bound state, analo­gous to the deuteron. In fact, because the io-exchange contribution, which provides most of the short-range repulsion in the NN interaction, becomes attractive in the NN case, the OBE model predicts a large number of NN bound states and low-energy reso­nances. Specifically, a deeply bound 1=0 band and a cluster of 1=1 states near threshold should exist. It should be stressed, however, that these predictions are based on the neglect of annihilation effects, whose theoretical estimation is difficult as they depend sensitively on the range of the relevant interactions and on the- 15 -spatial extent of the bound state wave function. Several recent calculations suggest that these effects might be so strong as to wipe out completely the structures described above. A better understanding of the annihilation mechanism is required to settle this question.The quark model also suggests the existence of bound states or resonances in the NN system. These states are characterized by an exotic quark content, different from the qq configuration of ordinary mesons. States containing only gluons (glue- balls), qq states with large gluon admixture and q2q^ states have been proposed.States of the latter type can be thought of as elongated diquark-antidiquark bags, such that the quarks within a diquark (antidiquark) are in relative S-state, while the relative angular momentum of the diquark with respect to the antidiquark is large. These states are prevented from falling apart into two ordinary qq" mesons by the large angular momentum barrier. They can be classified in two groups according to the colour structure of the diquark (antidiquark) at one end of the bag. States in the first group contain a diquark in the antisymmetric 3 representation of SU(3)-colour. Since the addition of one quark to such a diquark can give a colour singlet, these states are expected to decay mostly by excitation of a qq- pair with the quantum num­bers of the vacuum and subsequent separation into a pair of qqq and qqq colourless objects, i.e. a baryon-antibaryon pair. For this reason these states are usually called true-baryoniurn; they should appear as BB quasi-bound states or resonances with typical strong interaction widths of order 100 MeV. States in the second group (mock- baryonium) have a diquark in the symmetric 6 representation of SU(3)-colour. The addition of a quark to such a diquark cannot give a colour singlet. Decays of these states into BB are therefore inhibited. They are predicted to decay mostly by cascade (pion emission) into states of the same nature with lower diquark-antidiquark orbital angular momentum, and eventually into a BB pair through small admixture of 3"3 colour configurations. Such states are expected to be quite narrow. Their observation would be evidence for 'hidden' colour and would therefore be a particularly striking confirmation of contemporary ideas about strong interactions.Some of the experiments with antiprotons that are most likely to shed light on the question of baryonium are:1) Accurate measurements of pp total, elastic, charge exchange and annihilation cross sections as a function of incident energy. As in the case of pp scatter­ing where the evidence for dibaryon resonances comes from polarization data, experiments with polarized beams and targets would be particularly useful. Similar measurements of pd cross sections would be required to pin down the isospin of resonant states.2) Measurements of pp elastic differential cross sections. Since a large diffrac­tion peak dominates at forward angles, effects associated with resonances are expected to show up most clearly at back angles.- 16 -3) pp annihilation into specific final states. Although the decay widths of baryonium in such channels are expected to be small, two-body final states TT+ir- , Tr°TT° and KK should be of particular interest since they impose useful selection rules on the initial states and are amenable to partial wave ana 1ys i s.b) Detection of monochromatic y-rays produced by the transition from an atomic bound state to a baryonium state.5) Measurements of pion spectra from the reaction pp -*• X*’0 + ir*’0 .6) Search for structure in the spectra of protons and neutrons from the reaction pd X" + p and pd + X° + n.b .b Interactions of low-energy antinucleons with nucleiThe availability of intense low-energy p" beams will open up the presently un­explored field of p'-nucleus physics. Theoretical speculations point to many interest­ing phenomena. For example, the difference in radius between the real and imaginary part of the p'-nucleus optical potential could lead to resonances in p'-nucleus elastic scattering, due to the orbiting of the p' around the nucleus. The possibility of studying the behaviour of nuclear matter under the abnormal conditions created by the annihilation of a p inside a nucleus is particularly exciting. Although most [T1 s will be annihilated in the nuclear surface it is expected that, because of the strong p'-nucleus attraction, a significant number will penetrate deep inside the nucleus.The release of a large number of pions in nuclear matter might produce exotic modi­fications of the nuclear pion field (pion condensation). If several of the pions have energies in the A resonance region, their strong interactions with surrounding nucleons could produce a 'nuclear explosion', resulting in the emission of a large number of fragments. It is also conceivable that annihilation will lead to the formation of a spot of quark matter, which could swallow neighbouring nucleons to form an extended quark bag.b .5 Conclus ionIn conclusion, many exciting experiments could be performed with an intense low-energy p” beam. The controversial and speculative nature of present theoretical considerations regarding p" interactions, as well as the confused experimental situa­tion, point to the need for much theoretical and experimental work. Although the LEAR facility, soon to become operational at CERN, will permit great advances in this field, one may expect that many questions will remain open (and new ones will be raised) in the years ahead. A "p facility at TRIUMF can play a significant role in providing definite answers.- 17 -5. THE PROPER ENERGY FOR KAON AND/OR ANT I PROTON PRODUCTIONIn deciding on the design energy of a kaon/p factory it is essential to know the production cross section for the particles of interest as a function of the energy of the incident proton. Unfortunately this information is somewhat uncertain— even contra­dictory in some cases. For example, early data on ]) production as collated byBarashenkov and Patera1 are shown in Fig. 2. From these data one would conclude thatthe variation of p" production with energy has a continuously increasing slope in the energy range 5-30 GeV. However, Fig. 3, compiled by D. Berley2 and based on the per­formance of K and p" beam lines at various laboratories, indicates a quite different dependence on energy. It should be noted that the knees in both curves at approximately 10 GeV are primarily due to unpublished Argonne data, and the assessment of the true shape of the curves depends critically on the estimate of the error assigned to these data.Because of the uncertainty in the K and p" production cross-sections it is pro­posed to undertake measurements at CERN (Geneva) making use of their variable energy proton beam. It appears that production cross-sections in the energy range 7-20 GeV would be extremely valuable in settling on the best design energy from the point of view of the usual compromise between cost and the intensity of the beams of secondaryparticles. The optimum energy for pT production is likely to be higher than the corre­sponding energy when one is concerned primarily with K production.Other characteristics of accelerators which are important for experimental research, in addition to the intensity and energy, are the following:Duty factor:For a number of experiments the duty factor of the accelerator is not impor­tant. However, for most experiments involving coincidence-counting a duty factor of 50% or more is extremely desirable in order to minimize accidental counting. On the other extreme, neutrino experiments require very small duty factors such as 1/106 in order to discriminate against cosmic rays.Variable energy:The ability to vary the energy of the proton beam is desirable but not essential, since most of the experiments will make use of the secondary particles such as K, p", etc. However, some experiments will be investigating the proton-induced primary reac­tions, and in this case variable proton energy might be important.Beam qua 1i ty:A good beam quality in the primary proton beam is highly desirable, even though most of the experiments will make use of the secondary beams. Good beam quality and small energy spread minimize beam loss and consequent radiation problems and remote handling requirements as well as the cost of beam transport.- 18 -Fig. 2. The relative number of antiprotons produced per incident proton as a function of the energy of the incident proton. These data come from the 1963 compilation of Barashenkov and Patera. The data have been normalized to a pion production proportion­al to E p T h e  figures in parentheses give the momentum of the p beam.Fig. S. The production cross sections for 700 MeV/c K~ and 850 MeV/c p as a function of the incident proton energy for a 10 cm copper target (Berley2). The solid curve is based on kinematic reflection from higher-energy data; the broken curves are to guide the eye only. Note that the cross section for K~ production is approximately 100 times that for p. The Kf/K~ ratio is about 4.- 19 -5.1 The role of TRIUMF in a K/p factoryBecause of space charge and phase space limitations it turns out that the most difficult and expensive part of the acceleration process for intense beams of protons is that which brings the particles up to some 500 MeV of energy. In this sense some equivalent of the TRIUMF cyclotron is an essential part of a K/p factory, and it represents a considerable fraction of the total investment in the acceleration process. From the point of view of cost there is considerable incentive in using one of the present meson factories as injector for the larger facility.There are two lines of accelerator development which have been followed in a very preliminary way at TRIUMF as possible multi-GeV accelerators for K/p" factories.One line of possible development consists of two superconducting ring cyclotrons ("CANUCK" - for Canadian University Cyclotrons for Kaons). The first would accelerate protons from TRIUMF from A50 to 3000 MeV and the second from 3 GeV to 8.5 GeV.Although limited in maximum energy, these machines, because of their cw operation, would be capable of accelerating the full current from TRIUMF (100 pA, or A00 pA eventually). The other development line results in either one or two synchrotrons.In the latter case the first synchrotron of the two would accelerate TRIUMF protons to 3 GeV, followed by the second synchrotron accelerating the particles to 20 GeV. The other case envisages direct injection from TRIUMF into a single 20 GeV synchrotron, resulting in somewhat lower final intensity. The synchrotron designs offer somewhat less intensity because of their pulsed operation, but are unlimited in their potential for reaching higher energies.References1. V.S. Barashenkov and J. Patera, Fortschr. Phys. J_J_, A69 (1963) -2. 0. Berley, Brookhaven report BNL 50579 (1976), P- 257-- 20 -6. SYNCHROTRONS6.1 In ject ionThe principal problem in using TRIUMF as injector for a higher-energy synchro­tron lies in matching the continuous time structure of the cyclotron to the discontinu­ous structure of the synchrotron. This problem can be reduced by stacking some 100 turns in the cyclotron and then repeatedly injecting these "packets" into the synchro­tron over its injection period. Because the spread in the sine of the phase angle (A sina) is essentially constant in TRIUMF the spread in phase angle which might gofrom 0° to 10° at injection into TRIUMF can be made to go from 52° to 75° at a radius of7.6 m (450 MeV). Over the next radial interval of 25 mm the field can be tailored so the ions take approximately one hundred turns in going from 5 2o_90° and back to 52° and also from 75O-90° and back. The result is some hundred turns of all phases collected in a pocket 25 mm wide in radius. An axial electric field of 15 kV/cm applied over an azimuthal distance of 25 cm is sufficient to sweep all the ions in the packet onto a foil stripper, which removes the two electrons from the H“ ions and allows the protons to escape the magnetic field. This is accomplished over two ion revolutions (10 RF pulses) for a pulse length of 0.43 psec. This process is repeated every 100 TRIUMF ion revolutions (21.7 ysec). In the 100 turns at 450 MeV the total loss due to stripping (both electromagnetic and gas) is less than 2%. The energy spread in the extracted beam will be about 2.5 MeV FWHM.In tailoring the falling magnetic field to ensure a similar number of turns for all the initial phases between 52° and 75°, it is necessary to vary the departure from isochronism over the 25 mm radial region where the extraction is to take place. If t0 is the isochronous field and 7t is the departure from t 0 °  then in practice one sets 7t)t0  at about 0.0012 over the first 10 mm in order to turn back those ions at large phase angles. In order to take care of those ions with phases down to 52° it is necessary to increase 6B/B; to 0.0033. Other falling field regimes can be used; in the case of a smaller initial phase spread the problem of obtaining a similar number of turns for all phases in the 25 mm packet becomes easier.6.2 Single 20 GeV synchrotronIn some ways direct injection from TRIUMF into a single full energy synchrotron would be the most advantageous. The repetition rate appears to be conservative at 5“10 Hz, depending on the duty factor desired, but the rise time required is 26 msec.The maximum bending magnetic field is 14 kG, which is not unreasonable and corresponds to a mean radius of 78 m.Because of the time structure problem, 1 40 synchrotron turns are envisaged at injection, considerably more than have been tried in the past, but on the other hand representing only 15% of the available phase space in the synchrotron. If I is the time average current from TRIUMF the average output current at 20 GeV would be 0.54 I at 1/6 x 1o1* duty factor and 0.27 I at 50% duty factor. These estimates must be- 21 -modified according to the losses encountered at injection, acceleration and extraction from the synchrotron. Even at I = **00 yA these currents are well below the space charge limit of 2 x 101Lf protons per cycle. One result of the fairly short cycle time and the high efficiency desired is reflected in the radio-frequency system. The design calls for an energy gain per turn of 1.5 MeV and a frequency change of **6.1 to62.3 MHz. This will be expensive.Most of the parameters of this single synchrotron design appear to be within the state of the art, with the exception of the multi-turn injection. It is proposed to carry out detailed studies of the injection process in order to investigate its feasibi1i ty.6.3 Two synchrotrons in seriesAn alternative design to the single synchrotron is a fast-cycling accumulator- booster at 3 GeV followed by a slow-cycling synchrotron up to 20 GeV.The first synchrotron would have a radius of 30 m and a maximum bending field of only 8 kG. The repetition rate would be 2** Hz but the acceleration time would be 7 msec. This would require an energy gain per turn of **00 keV and a frequency swing from **6.2 to 60.5 MHz.Again multi-turn injection would be required with some 160 synchroturns filling about 221 of the available phase space. The time average current would be 0.7 I yA.The 3 GeV accumulator-booster acts as injector to a 20 GeV ring of more normal time structure. It is tempting to investigate the possibility of making the main ring superconducting in this case. With a 5 sec cycle time and maximum bending field of 30 kG the average radius would be 36 m. Again multi-turn injection would be required, about 100 turns in the main ring from the 2** Hz booster. The net time average current at 20 GeV would be 0.56lyA at a duty factor of 1/6 x 106 or 0.28lyA at 50% duty factor, ignoring possible losses during injection, acceleration and extraction. The RF accelerating system for this design of the main ring presents no problems since the energy gain per turn is only 150 keV and the frequency swing is from 60.5 to 62.3 MHz.The principal aspects of this two-synchrotron design which require major devel­opment are multi-turn injection and the use of superconducting magnets at a repetition rate of 0.2 Hz and a 500 msec rise time.In comparing the two schemes (single 20 GeV synchrotron vs. two synchrotrons) it is apparent that the time average final current is essentially the same in the two schemes. Inadequate information precludes a comparison of the total costs at this time. A reliable comparison would be one of the results of the proposed study. Ope­rationally, the major difference is the availability in the two synchrotron schemes of a variable energy (3~20 GeV) pulse of 1.7 x 1013 I protons every 5 sec. This difference might represent a major advantage for neutron work and neutrino studies. Unless the TRIUMF ion source is pulsed, 30 to **0% of the beam would continue to be available at **50 MeV and lower intensities would be available at high duty factor.- 22 -Table II. Synchrotron design parameters.Single 20 GeV synchrotronDua 13 GeV boostersynchrotron20 GeV main ringRad i us ECOI-"* 30.6 m 36 m®bend 14 kG 8.2 kG 30 kG^average 9 kG 4.1 kG 19-5 kGMinimum cycle time 11 4 msec 42 msec 4.2 secDuty factor (min) 1 1 16 x M812 4 x io4oXLAT  •Time average current 0.5b IyA 0.71 yA 0.571 yARepetition rate 8.8 Hz 24 Hz 0.24 HzFor 50% duty factor: Time average current 0.27 I yA 0.33 I yA 0.34 I yARepetition rate 4.4 Hz 12 Hz 0.12 HzRF frequency 46.1+62.3 MHz 46.1+60.5 MHz 60.5+62.3 MHzEnergy gain/turn 1.5 MeV 400 keV 150 keVNumber of turns 13,000 6,400 130,000aTime average current assumes no loss in injection, acceleration or extraction.- 23 -7. "CANUCK" HIGH-ENERGY CYCLOTRONSThe high intensities achieved by cyclotron meson factories are in large measure attributable to their cw operation. It is therefore natural to consider the possibil­ity of designing isochronous (cw) cyclotrons which could accelerate the full 500 MeV beam current at least as far as the shoulder of the cross-section for kaon production at ~9 GeV. Cyclotron designs in the few GeV range have previously been considered by a number of authors.1-4The chief problems in designing a high-energy cyclotron are, of course, the rapid rise of average field with radius (dB/dr~ By3) needed to maintain isochronism, and the consequent axial defocusing. The flutter F2 = (B/B - l)2 and spiral angle e needed to keep the axial tune v2 real therefore rise drastically with energy. For y »  1 we require ^2F2 tane £ y. To avoid excessive spiral it is therefore vital to have large flutter. In this respect the design criteria lead naturally to the choice of a ring cyclotron with separated sector magnets. In the designs described below we have chosen F2 —  2 at maximum energy, so that for example at y = 10 (8.5 GeV) a spiral tane > 5 is sufficient— a value still within the bounds of practical possibility.Separated sector machines have other important design advantages:1) Large regions between the magnets where the injection, extraction, pumping, diagnostic and acceleration systems may be located (with all the advantages of separated function design).2) These wide gaps also increase the cyclotron radius and hence the turn separation (making extraction easier) and reduce the radial derivatives of flutter, spiral and average field (making the magnets easier to construct).Of course, wider valleys and larger radii also imply higher costs in equipment and buildings. This argument was perhaps crucial until the advent of reliable super­conducting magnets over the past few years. With the factor 2 gain in hill field whichthese provide the machine radius required is halved and the costs drastically reduced--in the case of the magnet steel by about a factor 8. That the savings in capital costs and power bills more than offset the extra cost of refrigeration is, of course, the reason for the growing wave of interest in cyclotrons with superconducting magnets.The 8.5 GeV cyclotron parameters are listed in Table III. A hill field of 5 T is assumed and the orbit time and cyclotron radius (rc = 20.6 m) are chosen to be exactly twice as large as in the present machine, giving a minimum flutter value of 2.3.If a single machine were used to accelerate protons at 450 MeV (3 = 0.71) from TRIUMF to 8.5 GeV (B = 0.995) the sector magnets would still be undesirably large— the gain in radius being ~6 m. However, by designing the machine in two stages, the lower energy one with a smaller value of rc , substantial saving can be achieved, together with greater versatility in the shape of beams of intermediate energy— advantages which should outweigh the complication of additional extraction and injection systems.Choosing the same cyclotron radius (10.3 m) and frequency (4.61 MHz) as in TRIUMF the- 24 -Table III. Ring cyclotron kaon factory.For axial motion fringing field effects reduce the axial focusing strength in two ways— firstly the bend is incomplete at the point of maximum field gradient so that the effective crossing angle is reduced, and secondly there is a thick lens effect. To minimize the loss in focusing the field edge must be kept as hard as possible by using a small vertical gap between the poles (2.5 cm in the present des i gn).To explore the orbit properties in the proposed machines accurately we have tracked protons through a simulated magnet field with tanh-shaped field edges, using the equilibrium orbit code CYCLOPS. Starting from the hard edge solution the spiral profile tane(r) was adjusted iteratively until the desired value of v| (c^ 3) was obtained at all radii. For a y = ^ to 10 cyclotron with N = 30, a uniform fieldFirst stage Second stageInjection energy (MeV) 450 3000Extraction energy (MeV) 3000 8500rc = c/u)p (m) 10.3 20.6Number of sectors 15 30Primary cavities 8 at 46 MHz 15 at 69 MHzHarmon i c cav i t i es 4 at 92 MHz 6 at 207 MHzApprox. dimensions ofprimary cavities (m2) 5.9 x 3.6 4 x 2.6secondary cavities (m2) 5.9 x 1.6 4 x 1 . 5Total RF power (MW) 2.0 1 .7Peak energy gain/turn (MeV)at injection 1 .2 7-9at extraction 3-6 7-9AE/Ar (MeV/mm)at injection 0.23 1 .9at extraction 5.6 30Radius gain per turn (mm)at injection 5.3 4.2at extraction 0.64 0.26Crude estimate of magnetweight (m tons) 2000 1800Approx. number of turns 900 700lower energy orbits are halved in size. For a maximum y of 4 (B = 0.968, T ^  3 GeV), the gain in radius is only 2.4 m (similar to SIN) while the flutter factor F2 = 3-2.7.1 Betatron oscillations and fringing field effectsTo determine the optimum number of sectors (N) and the variation of spiral angle with radius, we need to know fairly accurately how the radial and axial tunes vr and vz depend on the machine parameters. For vr the ir-stop band is reached when y ~  N/3 in the cases studied, where F2 =* 2. It is therefore necessary to choose the number of sectors N > 3 max- Thus N = 15 for the first stage (y = 4) and N = 30 for the second stage (y = 10).Fig. 4. Plan view of superconducting sector magnet design for a second stage 3 to 8.5 GeV isochronous ring cyclotron.= 5.0 T and a pole gap g = 25 mm, the spiral required rises smoothly to a maximumtane = 6.5, and the resulting pole shape is shown in Fig. k. With a high energy gain per turn the betatron oscillation resonances are not expected to pose a serious problem.7.2 Magnet and RF designThe proposed arrangement of sectors and cavities for the two cyclotrons is shown in Fig. 5- In the 8.5 GeV machine the cavities are arranged in three groups ofseven in order to keep groups of three neighbouring valleys clear for injection andextraction systems.In considering the radio frequency to be used in coupled cyclotrons the conven­tional wisdom states that the frequency should be the same in the two stages. This requirement would present a serious problem in our case since TRIUMF operates at 23 MHz, and SIN-type cavities at this frequency are very large and expensive and would require large amounts of (K power. The reason for the requirement is that a phase spread of ±14° in TRIUMF would become ±28° at 46 MHz, resulting in an increase in the spread in energy gain per turn from 3% to 12% over the phase interval. However, superposition of 251 2nd harmonic (92 MHz) would reduce the spread in energy gain per turn to less than 1%— at the cost of a reduction of 25% in peak energy gain per turn. In this case we are using "f1at-topping" to make the transition from the low TRIUMF frequency to a higher frequency in the second cyclotron without increasing the spread in energy gain.It is also possible in a two-stage post-accelerator to use the first stage cyclotron as a phase compressor by arranging that the cavity voltage increase with radius. If the first stage accelerates from y = 1.5 to y = 4 with a cyclotron radius rc = c/ojp = 10.3 m, the increase in radius is 2.3 m. An RF cavity can be arranged so that its peak electric field coincides with the final orbit, and if its dimensions are 5-9 m (horizontal) by 3-6 m the accelerating voltage will increase by a factor of 3 from initial to final orbit, resulting in a phase compression by a factor of 3- TheFig. 5. Possible c of the 3 and 8.5 Ge cyclotrons fed fron 2A of the present i cyclotron.- 27 -beam can now be injected into the second stage cyclotron with a phase spread for an accelerating frequency of 69 MHz just equal to that on leaving TRIUMF at 23 MHz.Third harmonic cavities (207 MHz) can be installed in the second stage to give "flat- topping" there— at a loss of 1/9 of the peak energy gain.An important possibility in magnet design for superconducting ring cyclotrons is the use of part of the return flux along a channel or "gully" between a hill andvalley to increase the flutter. This gully would have a reverse field of 12-20 kG, beparallel to the edge of the hill and increase the flutter by some 30-50%. In making the extremely crude estimate of magnet weight shown in Table III it has been assumed that enough iron will be provided to provide a complete return flux in iron (except for the gu11ies).It therefore appears that it is not only technically feasible to accelerate a high-intensity beam of protons to many GeV in a cyclotron, but that with the help of superconducting technology it is economically feasible also. Provided pole gaps are kept small and separated sector magnets and gullies are used to obtain high flutter, axial focusing can be maintained to 8.5 GeV with not unreasonable spiral angles. The use of 2nd and 3rd harmonic cavities and phase compression can reduce the energy spread to 1% or better. The major question remaining to be tackled is that of extraction.If the full 3II mm-mrad emittance of TRIUMF were injected the incoherent radial ampli­tude of the beam would be 1.1 mm at 3 GeV and 0.7 mm at 8.5 GeV— several turns in eachcase. A 1% energy spread corresponds to 10 turns. With the help of radial resonances (vr = 6 at 3 GeV and vr = 12 at 8.5 GeV) and some reduction in energy spread and emittance, reasonably efficient extraction would seem to be within reach.References1. L.A. Sarkisyan, Proc. 2nd All-Union Conf. on Charged Particle Accelerators (Moscow, 1972) I, 33; Nucl. Instrum. Methods 1A2, 393 (1977)-2. M.M. Gordon, quoted by H. Blosser in Cyclotrons— 1972, AIP Conf. Proc. 9_, 16 (1972).3. G.H. Mackenzie, private communication.A. W. Joho, private communication.- 28 -I.II.APPENDIX A. SUMMARY OF SOME PHYSICS POSSIBILITIES AT A KAON FACTORYPARTICLE PHYSICSA. Rare Kaon Decay Modes1. CP violation parametersa. High precision measurements (1% or better) to test GUT's2. CPT violation search 3- AI / 1/2 form factorsA. Electron/muon number violation searchB. Common Decay Modes1. Form factors, branching ratiosC. Excited States of the Kaon1. Production amplitudes2. Decay rates and branching ratiosD. KN Scattering Amplitudes1. Phase-shift analyses of elastic and inelastic scattering2. Kaonic atoms3. Production amplitudes (NN K + baryons)A. 1* exoticsE. YN Scattering Amplitudes1. Direct (emulsions?, bubble chamber?, spark chamber?)2. Final states in reactions like K-3He -*■ Apn, E°pn, £”pp3. Hyperonic atoms (2T, H")A. Strange dibaryon searchF. Neutrino Physics1. v e produced in K decays2. Vy,\iy produced in high energy pion decaysa. Scattering from hadron targetsb. Mass testsc. Osci1lat ion testsG. Charmed NucleiH. Heavy Mesons (NN -* heavy + baryons)HYPERNUCLEAR PHYSICSA. A-Hypernuclei1. Excited states of light hypernucleia . L•S force 2 . Isosp in v i olat i ons3. AN -* NN form factorsA. Ground states of heavy hypernuclei- 29 -B. E-Hypernuclei1 . Spectroscopy2. Binding energies of light E-hypernuclei3. E-N potential in nuclear matterk. E-n bound state?C. E- and AA-hypernuclei 1 . B i nd i ng energi es2. Decay modesIII. NUCLEAR PHYSICSA. Elastic and Charge Exchange Reactions, especially with K+B. Inelastic Form FactorsC. Regeneration AmplitudesD. Double Strangeness Exchange- 30 -APPENDIX B. KAON FACTORY FEASIBILITY STUDIES*General DescriptionTwo alternative accelerator designs have been suggested for kaon factories with the TRIUMF 0.5 GeV cyclotron as injector. One, using a two-stage superconducting ring cyclotron, would accelerate a hOO yA proton beam to 8.5 GeV. The other, using a one- or two-stage proton synchrotron,would reach 20 GeV but with a lower proton beam current. Both designs involve novel features, and it would be the first purpose of this study to determine the feasibility of each of the designs. The second aim would be to decide which design is most suitable for a kaon factory at TRIUMF. The study would be completed by the preparation of a proposal suitable for submission to the National Research Council.Technical DetailsThe major technical objectives are to determine the feasibility of:1) Injecting and extracting beam from the 3 GeV and 8 GeV cyclotrons. Effect of resonances, beam quality and polarization.2) Extracting 100-turn packets from TRIUMF for injection into a synchrotron. Feasibility of injecting 100-150 synchrotron turns into a synchrotron.3) Non-circular and/or pulsed superconducting magnets.*t) RF cavities for 3 GeV and 8 GeV cyclotrons.5) The high power broad frequency accelerator system required for the single synchrotron.6) The suggested experiments, with estimates of the beam intensity and quality needed. Towards this goal it is proposed to hold a workshop on kaon factory physics in the summer of 1981.*Excerpt from TRIUMF Facility Development PlanBEST-PRINTER CO. LTD

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