Betatron Matching into the Linac

In high energy linear colliders, the low emittance beam from a damping ring has to be preserved all the way to the linac, in the linac and to the interaction point. In particular, the R,hg-‘bLinac (RTL) section of the SLAC Linear Collider (SLC) should provide an exact betatron and dispersion match from the damping ring to the linac. A beam with a non-zero dispersion shows up immediately as an increased emittance, while with a betatron mismatch the beam filaments in the linac. Experimental tests and tuning procedures have shown that the linearized beta matching algorithms are insufficient if the actual transport line has mrne unknown errors not included in the model. Also, adjusting quadrupole strengths steers the beam if it is offset in the quadrupole magnets. These and other effects have lead to a lengthy tuning process, which in the end improves the matching, but is not optimal. Different ideas will be discussed which should improve this matching procedure and make it a more reliable, faster and simpler process. 1 Theoretical Considerat ions A mismatch inpetatron functions of the beam (a, ,9) and the lattice (a, p) and a non-zero dispersion (9 or,v’ # 0) at the beginning of the linac enlarges the epective emittance (Q/J). A dispersion q causes different beam positions for different energies AZ = qAE/E. This effect can be es timated by the following example. For an energy spread +dEc: 1 %, a dispersion of q = 10 mm will lead to an emittance growth of roughly 10% (at a beam size of 00 = fl= 316pm): ‘c//P = u2 = I$ + ~~6~ = (0.1 + 0.01) mm’, (1) if there is a similar disturbance in the angular component with q’. Otherwise the full expression has to be recognized: Cl/j = q/l + Iv2 + (P# + aqg2] < 62 > /(c/q, (2) which corresponds to a bigger (and additionally mismatched [l]) ellipse in phase space. A betatron mismatch has no immediate effect on the emittance, but will increase the emittance by the filamentation of the phase space ellipse induced by an energy *Work ~ppotied by the Department of Energy contract DE AC03-76SFOO515. spread. This magnification due to the betatron mismatch is given by: e.g.: ff = & = 0 1.0 0.25 2.0 0.67 4.0 1.60 n > 10 w n/P Fig. 1 shows the beam in real space for /3, v-mismatch and also higher order contributions. Besides the theoretical considerations, the observed practical problems during the actual minimization process will be described.