THE SENSITIVITY OF THE PEP BEAM-TRANSPORT LINE TO PERTURBATIONS

HOTKC Ifcfc atpon aw pnpwtd m m tccwm of wort fpn*oftd by Ac U s M Sttft* CommmMt. NKther * « IMM4 h t w M I ft* IMttd Sutn Dtptntmiif of Gangy, Mr My of * * * waptoym, nor any of feetr THE SENSITIVITY OF THE PEP BEAM TRANSPORT LINE OJ K V M M M «f a*ytefonMUoa,tfytmut, product or fVMHi *UrdM4, Of rfKNMtl A H M W MUM AM PEP-208 SLAC-PUB-2269 TO PERTURBATIONS* J.M. Peterson** and K.L. Brown*** Abstract The sensitivity of a beam-transport line to vari­ ous perturbations determines the extent to which one can simplify component design and relax tolerances. For the PEP injection lines we have studied the ef­ fects of various fabrication errors, magnet misalign­ ments, and residual gas scattering. Using the TURTLE ray-tracing program ', we find that magnetic-field errors corresponding to a relative sextupole strength In the dipoles of 0.51 and/or a relative sextupole or octupole strength in the quadrupoies of 5% are per­ missible. This allows relatively loose tolerances in magnet fabrication. Transverse misalignment of a quad­ ruple by a distance x causes the beam centroid to be displaced downstream by as much as 5x. This requires a quadrupole alignment accuracy of t 0.5 mm or better. No compensation for the earth's field is necessary be­ cause an integral number of optical wavelengths and a short wavelength were used for the design. Analysis shows that beam broadening from multiple coulomb scat­ tering is Insignificant for pressures of less than 1/10 torr. Introduction The sensitivity of a beam-transport line to vari­ ous perturbations determines the extent to which one can simplify component design and relax manufacturing and operational tolerances. For the beam-transport lines of the PEP injection system we have studied the effects of magnetic errors, magnet misalignments, and residual gas scattering on the transmission and quality of the beam. From these results we have determined the corresponding manufacturing and operational criteria. The PCP Beam-Transport System The PEP injection system requires two identical beam transport lines to bring the electron and positron beams from the Stanford two-mile linear accelerator to the two Injection points in the PEP storage ring, as Illustrated in Figure 1. Each line consists basically of a regular, strong focusing F0D0 lattice with Inter­ spersed bending magnets. Optically each line 1s three wavelengths long plus one short matching section. The bend magnets are distributed so that each wavelength 1s an achromatic section. There are 24 quadrupoies and 11 principal bending magnets in each line. Each line is about 225 meters long and bends the beam by 60 degrees. The aperture of the line was designed to transmit an emittance of at least 0.6 n nrn-mr and a momentum spread of • 0.8 percent, corresponding to the maximum acceptance of the SLAC linac. The horizontal disper­ sion function has a maximum value of 30 mm/percent at quadrupoies Q2, Q4, Q12, andQ14. The limiting aper­ tures are ± 10 mm vertically (defined at the bend mag­ nets), and i 25 mm horizontally (defined at the quadru­ poies). The range of operation is from 4 to 15 GeV/c in beam momentum. Fig. 1. A general layout of the SLAC-PEP injection system. The Effects of Magnetic Errors The effects of magnetic errors was Investigated using the TURTLE ray-tracing program'). In each mag­ netic configuration 5000 rays were traced. These were distributed uniformly over a specified transverse and momentum phase space. At the end of the line, the sur­ viving particles were analyzed with respect to the beam's size, angular spread, and momentum distribution. The results for a matched incident beam cf 0.3 s nrn-mr in each plane and t 0.B percent momentum spread are shown in Figure 2 as a function of the strength of a negative sextupole error in each of the quadrupoies. A beam loss of 10 percent and widening of the sur­ viving beam of the same order of magnitude occurs when the strength of the sextupole distortion reaches approx­ imately 5 percent of the quadrupole field strength at a radius of 25 mm. Factors of 2 in beam loss and in in­ creased beam width occur when the sextupola strength is about 10 or 20 percent of the quadrupole strength. There is a small difference in the degradation with respect to the sign of the sextupole component; the transport line is slightly more tolerant of positive than of negative sextupole components. The beam loss occurs predominately at the first high-dispersion point in the line. The loss occurs only at the positive edge of the momentum spectrum up to a negative sextupole strength of 10 percent. Above 10 percent both edges of the spectrum are lost at approxi­ mately the same rate. For positive sextupole perturba tions, the situation is just reversed. •This work was supported by the Office of High Energy and Nuclear Physics Division of the U.S. Department of Energy under contract No. W-7405-ENG-48. Lawrence Berkeley Laboratory, Berkeley, CA 94720 • Stanford Linear Accelerator Center, Stanford, CA