Introduction to Accelerator Physics - Luminosity and Beam-Beam Effects. Lecture #5. February 27,1998. Dr. Bob Siemann

Transcription

1 Introduction to Accelerator Physics - Luminosity and Beam-Beam Effects Lecture #5 February 27,1998 Dr. Bob Siemann

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6 697 I I 11 5 I I I 1 1 T = IO 1.,*J I I 1 I I... I I I I I 1 = 35.-" z/oz I 1 1 U F i i & Transverse density distributions durimg the disioa of two Gaussian barns with D = 1.

7 698 -I ;[ - I 1 I I... I I I I 1 I I - 1 = 35 I I I I I I T 7 20 T = 40. I I I I I I -S

8 699 m I I * I I I I 1 I I, I.. $...:... I-.. F i ZbZ,.I & Trwrerse density distributions during the cdlision of two Gaussian LcprrritL D=S

9 I I I I I I I 0.- Gaussian Transverse Profile fb *IO DISRUPTION PARAMETER 131rAdi D

10 *u 61 VAS 1 I - - A bn \ bh X I I I I I l l l l I I 1 1 I Ill /\4

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13 (b) ELECTRIC FIE1 ELECTRON (C 1 MAGNETIC X

14 blocks of the main linac power units for these projects are shown in Fig. 2. Because of the large quantities of identical components involved, the design, engineering, mass production, cost and reliability of operation of these power units are crucial to the success of whchever linear collider ultimately gets selected and built. LlNF.AR COLLIDER HUB LABOI?ATORIES CORRESPONDING TEST FACILITIES DESIGN mm mechanical cavity detuning due to the Lorentz foolce, the absolute need to suppress field emission to avoid heat losses and captured dark current, the construction of the rf coupler, and alignment of components within the cryostats. The electron bunch train can be produced from a laserdriven gun but the positron bunch train is too intense for a conventional target to survive. Hence, the intent is to shoot the spent e- beam after the IP through an undulator to produce y.y which then produce positrons in a thin rotating target. The 32 km damping rings (often called dogbones because of their elongated shape with TESLA DESY TESLA Test Facility VLEPP CW: SBLC DESY S-Band Test Facility JLC(C) KEK RF SYSTEMS JLC(X) KEK Accelerator Test Facility NLC(X) SLAC SLC, FFTB, NLC Test Accelerator LBNL, LLNL Relativistic Two-Accelerator Test Facility VLEPP(J) BINP VLEPP Test Facility CLIC CERN CLIC Test Facility Table 11. Linear Collider World Picture C. TESLA (Group 1) This machine is in a category by itself because it is the only one that uses superconducting accelerator sections for the main linacs. The rf frequency is the lowest (1.3 GHz) and the beam aperture is the largest (2a = 7 cm). All the characteristics of TESLA result from these basic features. The advantages are that the rf pulse is long, the bunch spacing is wide (708 ns), the transverse wakefields are weakest, and corresponding alignment tolerances are loosest (by at least a factor of 5 for multibunches). As a result, emittance growth is easiest to control. Ground motion effects may be compensated by fast feedback controls and by bunch-to-bunch steering at the end of each * linac. At a repetition rate of 5 Hz, Or must be 19nm to achieve the desired luminosity. The biggest challenge for TESLA is to perfect the rf superconducting technology to the point where accelerating gradients of 25 MV/m can be attained reliably with Q o s of at least 5x1OY, and where costs can be made affordable. As this article is being prepared, the TESLA superconducting cavities are undergoing a ~hape-redesign ~ which is expected to greatly enhance their performame and lower their cost. The main linacs consist of 616 power units (see Fig. 2), each invol viwg a pulsed modblator supplying an 8 MW peak power klystron which in rurn drives 32 one-meter long superconducting structures in four long cryostats, incorporating higher-order modes couplers and quadrupoles. Related requirements are the compensation of the frep (Hz) nb Bunch Spacing (=W N(IO l), PBlbeam (MW) I JI I400 Table 111. Overall Linear ColIider Parameters Starting at a Center-of-Mass Energy of 500 GeV IO0 2 drive linac I 4

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18 -5- L( 1030cm-2~-1) t c c N W P vl c m o 0 0 P P P P

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21 - 7% - A pnlen variety par-tric oscillator is sham in Fig. 3 (courtesy of Nari ffistry). By raising d larering his center of rass. the rider alters the natural f-cy systematically thew pqiw qn the oscillation until the energy minned by w ing just curpensates the arm host by bp@. Hcn the vertical betatron coodimate is analogous to the pndulm -le, md the horizontal betatron mtion is malm tm the wmtka8 efforts of the rider. d- \I,( 11 J - ip. -,1,1 - Fig. 3 A garden variety parametric oscillator (I I, YJ ivl Features of the analyticat solution. I will just list salient features to give the general flamwr of the calculation. The equation of motion is a second-order non-linear differare equatim uhidn we haw solved exactly, accounting for a19 resonances. The ampli- tuk ym can bc expressed as a &&le brier series in tenns of ~e independent frequencies vx, and w The tme w differs frm w owing to the hem beam force. Using fast Fourier Y' Y YO trmsform., AyA can bc similarly expan&d. The series are ro-expressed in tenns of sun and difference f-ies which then permits improvement of the coefficients hy iteration. At this stage, -e dcnainators are irportant. As the bea nnarmt is increased, an "instability threshold" v is ohtained at a Y =x r e d l y well &fined value I-. tfigher hemnics proliferate rapidly for currents near Illax and the iteration fails. Inclufing rore ~ellns or more stages of iteration does not change Illax very udl. Also at similar values of I, phase plots be- very contorted and, even with wing pment, orbits do not ds, inta %he origin but settle into orbits for which the wplituk iacrases with I. v) Features of tk atmng-atxmg sinulotioa. We track many (e.g. 1M) particles in each Lar in 6D ph.ase space. (&antun excitation rd dsmping are included. Synchrotron oscillathms are also present, which is signifiont only if *here is dispersion at the crossing

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