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Beam Cooling BEAM COOLING D.Möhl CERN, Geneva, Switzerland. Abstract To date, four main methods to increase the phase-space density of + - circulating beams in storage rings are operational: cooling of e e -beams by synchrotron radiation, stochastic cooling of (anti-)protons and ions by a feedback system, cooling of protons and ions by electrons, and cooling of special ions by laser light. A fifth method, ionisation cooling of muons, is under intense development. Each of these techniques is covered in detail in previous accelerator school proceedings and other tutorial articles [1]. The present paper is the write-up of a one-hour lecture at the CERN Accelerator School as well as of an opening talk at a workshop (‘Phase- Space Cooling and Related Topics’, Bad Honnef, May 2001). The object is to introduce the different techniques in a common framework, to put them into perspective and to point to potential future developments. 1. INTRODUCTION Beam cooling aims at ‘the impossible’, namely at reducing --without loss of particles-- the (normalized) emittance of beams, thereby increasing their density also called ‘brightness’. To make this possible, one has to circumvent Liouville’s theorem [2]. For a long time this good old maxim was assumed to imply that in all beam handling operations the normalized phase space density can only decrease or at best stay constant. It took perseverance and insight, to overthrow this dogma. Beam cooling is thus a fascinating subject [3]. It attracts our curiosity as engineers and physicists for several good reasons: it was long thought to be impossible; it (still) is one of the most advanced techniques for beam handling; it has lead --and it will continue to lead-- to spectacular achievements in elementary particle research. The physics of beam cooling is very rich in itself and some of the papers are of great depth, and beauty. Take e.g. Sands’ ‘essay’ [4] on radiation cooling, Robinson’s derivation of the theorem on the sum of the decrements [5], van der Meer’s first (internal!) report on “stochastic damping of betatron oscillations” [6]. Take Budker and Skrinsky’s seminal tract on “electron cooling and new possibilities in the physics of elementary particles” [7], or Neuffer’s illuminating explanation of ionisation cooling [8]. As a rule (or almost), these ideas and papers were so much ahead of their time that an experimental verification and the development of the technology were only started some 8 to 10 years after the invention. In fact the history of beam cooling begins around 1950 with the bright idea to make good use of synchrotron radiation, which had for long been regarded as a mere nuisance, limiting the energy of circular e-machines, betatrons at that time. The new suggestion (or suspicion) [9],[5] was that it might serve for ‘radiation damping’ of electrons (and positrons). A decade later when the - pioneering e+e -‘cooling rings’ like AdA/ADONE at Frascati and VEPP1 at Novosibirsk and had just started to work, the first proposals for electron cooling [10] and stochastic cooling [6] were dreamt up. By now, some 40 years later, these three cooling methods are very widely used. They have revolutionised beam physics and indeed offered the new possibilities, which only the visionaries had dared to foresee, sometimes with doubt and hesitation. 224 The idea of laser cooling of ions in storage rings [11] came around 1980 after the very successful development of laser cooling in ion traps. After (this time) a short incubation period, first demonstrations succeeded in 1989/90 at the storage rings TSR in Heidelberg [12] and ASTRID in Aarhus [13]. Finally ionisation cooling [8] has recently (re-)started to boom. The conception took place already in the late 1960s fostered (in parallel to electron cooling) by Budker and Skrinsky [14] (Sacha Skrinsky tells me that the fathers of the idea are A. Lebedev in the USSR and independently G. O’Neil in the USA). Later on, D. Neuffer [8] at Fermilab joined the early promoters. The object for Budker, Skrinsky and Neuffer was cooling of muon beams for a muon collider. Since a few years, these ideas, and the related concept of a neutrino factory based on the decay of circulating muon beams, have received a very wide attention [15]. Muon cooling is instrumental for these projects and large collaborations in the USA [16] and in Europe [17] are discussing experiments to test ionisation cooling. In this introductory lecture, I will try to sketch the principles of the five cooling techniques, work out their common features, underline their specific characteristics, and point to possible future developments. All of the methods mentioned are treated in detail in previous proceedings of accelerator schools and in other popular articles [1]. I hope that my introduction can serve as ‘appetiser’ to those more substantial dishes. 2. RADIATION COOLING Back in 1956, A.A. Kolomenski and A.N. Lebedev [9] pointed out that the ‘synchrotron light’ emitted by an electron moving on a curved orbit can have a damping effect on the motion of the particle. This is because the radiation is sharply peaked in the forward direction. The continuous emission of synchrotron radiation leads to a friction force opposite to the direction of the motion. For a particle moving on the design orbit, the energy loss is restored and the friction force is on average compensated by the rf-system. For a real particle the residual friction force tends to damp the deviation from the design orbit (Fig. 1). This cooling force is counteracted by the ‘radiation excitation’: synchrotron light is really emitted in discrete quanta and these many small kicks tend to heat the particle. The final emittances result from the equilibrium of radiation damping and excitation. We will see that a similar interplay between a specific cooling and heating mechanism is characteristic also for the other cooling methods. Fig. 1: The principle of transverse cooling by synchrotron radiation (transverse velocities exaggerated) The theory of cooling by synchrotron radiation is in a mature state. Following up on Sands’ classical treatment on “the physics of electron storage rings”, radiation cooling has found its place in 225 text books. The immense success of modern electron–positron machines, both ‘synchrotron light facilities’ (like ESRF, ALS, APS, BESSY, SPRING8…) and colliders (like LEP, PEP II, KEKB…) would not have been possible without the full understanding of radiation effects. Virtually all these machines depend critically on radiation cooling to attain the minute emittances necessary in their application. Linear e+e- -collider schemes (like CLIC, TESLA, NLC, JLC) too, have to rely on ‘damping rings’ in their injector chain to produce the ultra-high phase-space density required. The cooling rates as well as the final beam size and momentum spread depend on the lattice functions in regions where the orbit is curved. The art is then to ‘arrange’ these functions such that the desired beam property results. The strategy for ‘low emittance lattices’ is well developed and ‘third-generation machines’ providing beams of extremely high brightness have come into operation. To enhance the cooling, wiggler magnets are used, producing a succession of left and right bends. This increases the radiation and thereby the damping rates. The heating can be kept small by placing the wiggler at locations where the focussing functions of the ring are appropriate to make the particle motion insensitive to kicks. Radiation cooling and lattice properties of the storage ring are thus intimately linked and by smart design, orders of magnitude in the equilibrium emittances have been gained. This may serve as example for other cooling techniques for which the art of ‘low emmittance lattices’ is only now emerging. 3. STOCHASTIC COOLING For (anti-)protons and heavier ions, radiation damping is almost negligible at the energies currently accessible in accelerators. One of the ‘artificial’ cooling methods devised for these heavy particles is stochastic cooling by a broadband feedback system (Fig. 2). The name ‘stochastic damping’ was coined by van der Meer to underline the statistical basis of the method. At its core is the observation, that the phase-space density can be increased by a system that acts to reduce the deviation of small sections, called samples, of the beam. By measuring and correcting the statistical fluctuations (baptised ‘Schottky noise’) of the sample averages, the spreads in the corresponding beam properties are gradually reduced. Stochastic cooling may thus be viewed as a ‘sampling procedure’ where samples are continuously taken from the beam and the average of each sample is corrected. Fig. 2: The basic set up for (horizontal) stochastic cooling 226 A somewhat different picture is based on the behaviour of a test particle. At each passage it receives its own ’coherent’ kick plus the ‘incoherent’ random kicks due to all other sample members. The sample length Ts (response-time) is given by the bandwidth of the system through Ts=1/2W and the number Ns of particles per sample is proportional to Ts. Hence large bandwidth is important to work with small samples. Present day cooling rings have a revolution time of 500- 1000 ns and a sample length of less than 1 ns , thus each sample contains only a small fraction of the beam population. Another important ingredient is ‘mixing’, i.e. the renewal of the sample population due to the spread of the particle revolution frequencies Based on the ‘sampling’ and/or the ‘test particle picture’ one derives in a few steps [18] a simplified relation for the cooling rate of emittance ( 1/τ = (1/ε)dε/dt ) or momentum deviation (1/τ = (1/∆p)d∆p/dt ): ~ 1 = W 2g(1− M −2 ) − 2 (M +U / Z 2 ) ( 1 ) τ N []g < −coherent effect − > <− incoherent effect - > The parameters appearing in (1) have the following significance: N: No.
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