Simulation and Compensation of Multibunch Energy Variation in NLC*

The SLAC NLC design for a next-generation linear collider utilizes multibunching (acceleration of a train of bunches on each RF fill) to increase the luminosity and energy efficiency. It is necessary to control the energy spread of the beam, in order to minimize chromatic emittance dilution and be within the energy acceptance of the final focus. It is anticipated that the NLC may run with bunch trains having length equal to a substantial fraction of the filling time. Multibunch energy simulation methods and compensation schemes appropriate to this regime are presented. INTRODUCTION Utilizing multibunching in a next-generation linear collider (NLC) q re uires that the energies of the bunches be tightly controlled. To be within the acceptance of the final focus system and to control chromatic emittance ty5t$on in the linac, 6EIE needs to be less than about Bl adjusting the timing of injection of the bunch train with respect to the RF pulse, and choosing the bunch spacing appropriately, one may cancel most of the energy variation between bunches in the train. The basic idea is to have the RF structure fill with sufficient extra energy between bunch passages to make up for the energy lost in accelerating the preceding bunches in the train. However, with the simplest form of this “matchedfilling” scheme [l], there is a “sag” in energy at the middle of the bunch train, and the longer the bunch train the greater the sag. In this paper we shall focus on compensation that permits running longer bunch trains (a filling time) while maintaining an acceptable energy spread. Long trains are under consideration as a way of obtaining the maximum possible luminosity and energy efficiency. We begin by discussing the factors that affect the energy spread of the beam. A detailed simulation program has been written, the elements of which are outlined here. In this simulation, one may take account of input RF pulse shaping and timing, the dispersion of the RF pulse as it transits the structure, the longitudinal distribution of charge within the bunches, the long range wake (LRW) including both the fundamental (accelerating) mode and higher order modes (ROM’s), the short range wake (SRW), and phasing of the bunches with respect to the crests of the RF. We shall focus only on the inter-bunch energy spread in the present paper. * Work supported by Department of Energy contract DE-AC03-76SF00515. BASIS OF SIMULATION We begin by considering a single accelerating section, fed at its upstream end by an input RF waveform that travels to the other end and is absorbed in a load. At some specified time with respect to the entry of the RF pulse, a train of relativistic (u = c) bunches enters the structure, and the electrons in each bunch are accelerated by the fields (sum of RF pulse and wake fields) they encounter in the structure. The total charge in each bunch is divided into a finite number of longitudinal slices, small enough that the longitudinal position and the energy gain of the electrons in a given slice may be taken to be equal. The total voltage gained in the section by slice r of bunch n may be broken down into AK,,, = Al’-;,; + AV,,;: + AV;,Tw . (1) We denote the time of entry of this slice into the section by t,,,, and longitudinal position in the section by s, where s runs from 0 to the structure length L, and consider each of these three contributions to the total section voltage gain. The voltage AVz{ due to the RF pulse is