Longitudinal Phase Space Setup for the SLC Beams

The longitudinal phase space distribution of the SLC beams is affected by many different machine parameters and constraints. By using a technique of over-compression [1] in the ring to linac transfer line, a small energy spread of 0.12 % can be achieved at the end of the linac for a bunch length of 1.2 mm (σ). In the final focus a small energy spread is desirable to reduce emittance dilution due to chromatic effects. Optimization of the bunch length is also important as a longer bunch of 1.2 mm can contribute up to 40 % luminosity enhancement due to disruption. If there is a correlated energy variation along the bunch, for example due to mistuning of the optimal rf phase with respect to the beam, the bunch will be further compressed as it passes through the SLC Arcs. The resulting bunch can be too short to produce the desired disruption enhancement, but will radiate more beam-strahlung during collisions giving a false indication of higher luminosity. This paper discusses the interplay of these issues from the damping ring to the interaction point. Presented at the 1997 Particle Accelerator Conference Vancouver, B.C., Canada 12-16 May 1997 † Work supported by the Department of Energy contract DE-AC03-76SF00515. Longitudinal Phase Space Setup for the SLC Beams F.-J. Decker, K.L.F. Bane, M.G. Minty, P. Raimondi, Stanford Linear Accelerator Center , Stanford University, Stanford, CA 94309 USA R.L. Holtzapple, LNS, Cornell University † Work supported by the Department of Energy contract DE-AC03-76SF00515. Abstract The longitudinal phase space distribution of the SLC beams is affected by many different machine parameters and constraints. By using a technique of over-compression [1] in the ring to linac transfer line, a small energy spread of 0.12 % can be achieved at the end of the linac for a bunch length of 1.2 mm (σ). In the final focus a small energy spread is desirable to reduce emittance dilution due to chromatic effects. Optimization of the bunch length is also important as a longer bunch of 1.2 mm can contribute up to 40 % luminosity enhancement due to disruption. If there is a correlated energy variation along the bunch, for example due to mistuning of the optimal rf phase with respect to the beam, the bunch will be further compressed as it passes through the SLC Arcs. The resulting bunch can be too short to produce the desired disruption enhancement, but will radiate more beam-strahlung during collisions giving a false indication of higher luminosity. This paper discusses the interplay of these issues from the damping ring to the interaction point. 1 GOALS AND PROBLEMS The longitudinal phase space is setup to give a small energy spread for the limited band-pass [2] at the interaction point (IP) and to give no reason for luminosity weighted polarization [3]. No energy spread also helps to have no compression in the arcs to get a long bunch length at the IP. This gives luminosity enhancement due to disruption, when the hour-glass effect due to a large angular divergence is not yet limiting. A long bunch in the linac experiences bigger transverse wakefield kicks, and a correlated energy spread would help stability (BNS-damping). Due to beam loading from the first bunch (positrons) to the second one (electrons), the accelerator structure should only be partially filled (off the PSK energy peak) to have the same energy for both bunches. This costs energy overhead and leads to a setup with a shorter positron bunch, which is further off the rf crest getting less energy. Short bunches give more beam-beam background at the IP, and have more low and high energy tails, which create other background along the way. 2 INITIAL CONDITIONS AND HIGHER ORDER EFFECTS The bunch length in the damping ring depends strongly on the beam current. Based on the data in [4] a 10 % in current changes the bunch length by 5 %. The dependence of the bunch length on the gap voltage is weaker at high current (fourth-root) than at low current (square root) [4]. At high current and high gap voltage a higher than expect bunch length is seen, which could be due to the microwave instability (saw-tooth) [5]. The measured energy spread varies from 0.080 % at low current to 0.092 % at 4⋅10 particles per bunch. The expected spread at low current is close to 0.071 %. There should be no dependence on gap voltage, except from the microwave instability. Increasing the gap voltage from 750 to 950 keV, the energy spread changes from 0.089 to 0.094 % at 4⋅10. The bunch length is strongly distorted by the potential well in the damping ring. The asymmetry factor is A = (σh – σt) / (σh + σt) = -0.4 at 4 ⋅10, which means that for σz = 7.5 mm, the head has a σh = 4.5 mm (40 % less) while the tail has a σt =10.5 mm. The centroid is 1.6 A σz = –4.8 mm shifted from the peak. There are several higher order effects in the RTL, which are utilized to obtain the smallest possible energy spread with no energy tails at the end of the linac. These include: 2.1 Higher Order Dispersion The T 566 term is about 1.5 R56 = –900 mm, which means that higher and lower energy particles in the RTL are bent backwards (late), which is the right direction (sharp rise). This term can not be varied easily without a lattice design change. Figure 1 shows the 1, 2, and 3 sigma contour lines of the compression and the resulting linac bunch distribution. 2.2 Non-linear rf curvature A similar effect can be achieved by decelerating the centroid of the beam in the compressor cavity using a phase offset. 2.3 Bunch Precompression in the DR With bunch pre-compression [6] a quadrupole mode oscillation without phase oscillations is induced by successive application of two changes to the gap voltage. While advantageous for increasing the beam current, the advantages of bunch over-compression for bunch shaping are somewhat reduced. Interestingly [7] pre-compression of the bunch does not flip the asymmetry in the longitudinal beam distribution in the damping ring. 2.4 Sawtooth Instability The sawtooth instability of the new damping ring [5] is visible as bursts in a 180 kHz signal and as ±3 % changes in the wings of the beam distribution at about 20 % peak