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• W2470296729 abstract "The history of linear accelerators is now more than 50 years old and after a difficult start presented many remarkable successes. Theory and technology encounter difficult problems briefly presented here with the solutions so far developed on orbit stability, focusing, RF structure and beam dynamics computations. Questions still remain however about high intensity limits which, when answered, might still open a more brilliant future for these types of machine. 1 . BRIEF HISTORY OF LINACS The first accelerators built for nuclear physics were of electrostatic type; such machines were efficient but limited in voltage due to electrical breakdown. In 1924 a proposal was made by Ising to add several accelerations without having anywhere the total voltage. The method was based on the use of drift tubes and time varying fields, as sketched in Fig. 1. Fig. 1 Drift tube accelerator of Ising Along the axis of metallic tubes, charged particles can drift without being subject to any electric field except at their ends, in the gaps between two consecutive drift tubes, according to their respective voltage V. If an accelerating voltage is applied initially to all the tubes and is switched off on each of them between the time of entrance and exit of a charged particle, the particle will receive in each gap a succession of accelerations. In practice, voltage pulses are more appropriate, as used in present day induction linacs; needless to say, however, that at the time of the proposal shape and timing of high voltage pulses were not good enough to produce a useful operation. In 1928, Wideroe proposed to replace voltage pulses by an RF voltage (with a constant frequency, the drift tube lengths have to increase with the β of the particles). The method was tested on a single drift tube (input + output) and with 25 kV RF peak voltage, it was possible to observe an acceleration of 50 keV for singly-charged Na and K ions. In 1931 Sloan and Lawrence built a real linac of 30 drift tubes giving to Hg ions an energy of 1.25 MeV; lengthening it later in 1934 to 36 drift tubes and increasing their voltage they reached 2.8 MeV. the intensity was of course very low and the beam quality not specified: R.F. voltage differed from Ising pulses, having no real flat top, phase stability (see Section 2) was not yet discovered and focusing was not ensured, except maybe by ES lens effect (see Section 5). No further development occurred until the war, due to the lack of proper high power RF technology (limited then to 10 MHz) and to the discovery of the cyclotron. The length of the Sloan and Lawrence machine approached 2 m with a βmax of only a few thousandths; with the 1) More details on the subject can be found in a Los Alamos report LA 11601 MS, Proton Linear Accelerators, or in a CERN Yellow Report (in French) CERN 87-09 same RF wavelength of 30 m acceleration of protons would have led to a prohibitive length. In cyclotrons, on the contrary, the spiralling of the trajectories together with some focusing effect allowed the succession of many accelerations over a limited extent, leading to the possibility of producing 10 MeV protons. The development of radars offered, after the war, pulsed high voltage equipment in the metric and centimetric wave ranges; science and technology of electromagnetism and beam dynamics of already high level were then available. The parallel development of circular accelerators (synchrocyclotrons and synchrotrons) was also helpful with the discovery of phase stability. Ginzton, Hansen, Chodorow, Slater, Walkinshaw used 3 GHz to accelerate electrons. Alvarez and Panofsky used 200 MHz for protons. 2 . LONGITUDINAL MOTION. PHASE STABILITY. ACCELERATION BY A TRAVELLING WAVE For a given geometry of the drift tubes which corresponds to a certain rate of acceleration, particles must receive at each gap an exact energy gain and the voltage must have an exact value. The RF voltage V applied is larger and there are two phases per RF period for which the voltage has the right value Vs (see Fig. 2). When the field is rising the phase is stable since a particle arriving too early will be less accelerated and slip slightly in phase until the next gap; vice versa for a late particle. The other phase is unstable. The stable phase is called the synchronous phase φs and one has Vs = Vcosφ s with φ = 0 corresponding to the crest (proton case). Fig. 2 Phase instability In a first approach one can replace the discrete gap configuration by an equivalent continuous interaction (in Section 5 will appear a justification). One may say that the field distribution along the axis in the successive gaps presents an analogy with a standing wave pattern, sum of a forward and a backward wave. One would then consider the interaction of the forward synchronous wave with the particles. Introducing relativity symbols and letting φs , βs , γ s refer to the synchronous particle, one has γ = 1 + W m0c 2 and putting δγ = γ − γ s one can write, following the path of a particle, along the axis m0c 2 w d δγ ( ) ds = qET w cosφ − cosφs ( ) dφ ds = ω c 1 β − 1 βs     = − ω c δγ βs γ s 3 whence m0c 3 d ds βs γ s 3 ω dφ ds     = −qET cos φ − cos φs ( ) Forgetting about the change in γs one then obtains δγ 2 + 2qETβs γ s 3 ωm0c sin φ − φcos φs ( ) = C where ET is the amplitude of the synchronous wave. Such a motion derives from the Hamiltonian H = − ω c δγ 2 2βs γ s 3 − qET m0c 2 sin φ − φcos φs ( ) Neglecting the change in γs is only valid for heavy particles (protons and ions) for which it is slow enough. It corresponds to an acceleration fighting against a constant breaking force (or to a forced pendulum model as often presented for circular machines). One gets from it the usual stability bucket of Figs. 3 and 4; Fig. 5 shows the phase space plot relative to an operation with φs = 0 (fixed point as used by Sloan and Lawrence). Taking into account the change in γs opens up the bucket and gives the so-called golf club, see Fig. 6 (notice that the coordinates used are not conjugate). Fig. 3 Classical stability bucket Fig. 4 Non-accelerating bucket Fig. 5 Fixed-point operation" @default.
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• W2470296729 title "Introduction to RF linear accelerators (linacs)" @default.
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