SLAC-PUB-15921 WAKE FIELDS IN SLAC LINAC COLLIMATORS A. Novokhatski#, F.-J. Decker, H. Smith, M. Sullivan SLAC National Accelerator Laboratory, Stanford University, Menlo Park, California, 94025, U.S.A. Abstract additional energy jitter and a change to the trajectory of When a beam travels near collimator jaws, it gets an the beam. It also leads to a degradation of the FEL energy loss and a transverse kick due to the back reaction performance at the LCLS. This is because of the special of the beam field diffracted from the jaws. The effect character of the wake fields: the response reaction becomes very important for an intense short bunch when depends on the longitudinal position of the particles in the a tight collimation of the background beam halo is bunch. The “head” of the bunch is not deflected at all, but required. In the Linac Coherent Light Source (LCLS) at the “tail” gets the maximum deflection force. This kind of SLAC a collimation system is used to protect the kick leads to the bunch being geometrically tilted. undulators from radiation due to particles in the beam Because the “tail” of the bunch may oscillate in the halo. The halo is most likely formed from gun dark lattice, the orientation of the bunch in space will oscillate current or dark current in some of the accelerating too. Effectively, the transverse projected emittance is sections. However, collimators are also responsible for increased and the FEL performance is degraded. the generation of wake fields. The wake field effect from We suggest that because of the rectangular shape of the the collimators not only brings an additional energy jitter collimator jaw, a geometrical diffraction model may be and change in the trajectory of the beam, but also rotates used to calculate the longitudinal and transverse wake the beam on the phase plane, which consequently leads to fields excited by a short bunch. This approach is a degradation of the performance of the Free Electron described in reference [7]. Because it is difficult to find Laser (FEL) at the LCLS. In this paper, we describe a this reference, we will briefly explain the model following model of the wake field radiation in the SLAC linac the description of the SLAC linac collimator below. collimators. We use the results of a numerical simulation to illustrate the model. Based on the model, we derive SLAC LINAC COLLIMATOR simple formulas for the bunch energy loss and the average Nine adjustable beam collimators are used in the LCLS kick. We also present results from experimental operation, mainly accomplished in two main sections: at measurements which confirm our model. the end of the SLAC linac and in the region from the linac to the undulators (LTU). Each collimator is composed of INTRODUCTION horizontal and vertical pairs of rectangular collimator The electron beam collimators in the LCLS must jaws. A sketch of a vertical collimator is shown in Fig. 1. remove the halo particles in the beam before they affect The geometry of a collimator assembly is very and eventually degrade the very precise fields of the complicated because each jaw is independently and permanent magnet undulators [1]. However, collimators remotely adjustable and can completely shadow the beam also cut the electromagnetic field of the electron bunch path. In the center of Fig. 1, we can see two longitudinal and produce (in this way) freely propagating fields which jaws with bellows. The beam moves in a horizontal are wake fields. The wake field effect of collimators with direction, and part of the beam (beam halo) can be small apertures on the transverse beam dynamics was dissipated in jaws. The length of a jaw is not enough to observed during the operation of the Stanford Linear fully capture the high-energy beam (4-14 GeV). Collider (SLC) [2]. Several attempts were made to estimate and to measure the effect of collimator transverse wake fields [2-6]. Special measurements have been made for longitudinally tapered collimators, designed for the applications in future linear colliders. Detailed analysis of these measurements and analytical results can be found in reference [6]. Different formulas have been suggested to describe the collimator kick, but unfortunately they do not explain the experimental results very well in many cases. The problem of wake fields excited by collimators becomes more important for linac operation and x-ray production at the LCLS. The backward reaction of the wake field from the collimators on the beam brings an This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-76SF00515. Figure 1: A sketch of a SLAC linac collimator. The dash- the diagram (T=1) and the bunch is now past the dot line can be a beam trajectory when the beam goes diaphragm (T=2). close to the upper jaw. A collimator is essentially a kind of assembly of RF When the bunch approaches the diaphragm it carries its cavities coupled to the beam. The bellows with a chamber 'own' field, which has only transverse components in the form two quarter-wave coaxial cavities. There are several ultra-relativistic case (T=0 in Fig.3). Some part of the trapped RF modes inside the collimator volume. In a 'self' field is cut off by the diaphragm and reflected back multi-bunch operation, some energy is deposited in this into the beam pipe (T=1 in Fig.3). Beyond the diaphragm, region. One jaw can be in a position that is too close to the bunch forms its “own” field, giving off a fraction of the beam path while the other jaw has been moved out. its kinetic energy to the field energy (T=2 in Fig.3). The jaws have a titanium alloy body with a slightly curved face (10-m radius) and a titanium-nitride jaw According to the law of superposition of the surface for improved conductivity and survivability electromagnetic fields we can separate the bunch “self” against beam hits [8]. Currently the gap between jaws is field from the total field. In the case of an infinitely thin kept approximately plus–minus 1.6 mm in all collimators. diaphragm, the field behind the diaphragm can be However, the spontaneous beam halo requires smaller represented as a sum of the bunch “self” field and the gaps. A photo of a vertical collimator is shown in Fig. 2. “cut-off” field, the latter being the same as to the left of We can see how the jaws together with the bellows the diaphragm but mirror-reflected. Fig. 4 illustrates this strongly disturb the smooth inner surface of the beam concept. pipe. Figure 4: Total field as a sum of wake fields and a bunch “self” field. The “cut-off” and the “mirror-reflected” fields are separated from a bunch and propagate independently. We usually call these fields “wake fields”. It can be seen in Fig. 4, that the energy of the “cut-off” field determines the backward-emitted energy. The “mirror-reflected” field is propagating in the forward direction and chasing the Figure 2: A photo of a vertical collimator. bunch. The energy of the “mirror-reflected” field is almost the same as the energy of the “cut-off” field for an GEOMETRIC OPTICS OF THE WAKE infinitely thin diaphragm. So the total energy loss will be FIELDS equal to the double energy of the “cut-off” field. In the calculation of the energy of the “cut-off” field we need to As an introduction let us consider the dynamics of the also include the energy of the magnetic component of the radiation fields when a bunch travels through a hole in a bunch field metal diaphragm placed in a pipe. Fig. 3 illustrates the picture of the force lines of an electric field of a bunch at 22 W dz00 Ebb H ds (1) various moments: the bunch before the diaphragm, S passing the diaphragm and beyond the diaphragm. Fortunately, this is easy to do because in the ultra- relativistic case the energy of the electric component is the same as the energy of the magnetic component of the bunch field. The averaged potential for a bunch with a total charge Q will be W E (2) Q With this concept of the radiation process one can obtain estimates for the energy loss of a bunch in some Figure 3: Plot of electric force lines for three time steps: a simple cases. For example, the energy, emitted by a point- bunch approaches the diaphragm (T=0), the bunch passes like charged particle passing through a hole in an infinite #[email protected] metal screen will be proportional to the energy of a disk with a hole is installed in a cylindrical tube. This particle and inversely proportional to the radius of the Green’s function is: hole in a diaphragm cZ0 bs1 Q G s s ln F0 E ~ (3) a a a 2 a 0 22 arcsin for x 2 (6) Q is the total bunch charge, is a relativistic factor, 0 is xx Fx0 a dielectric constant of free space, a is a radius of the hole for x 2 in a diaphragm. It is necessary to emphasize that the radiation energy increase is linear with the particle energy x of the bunch. Formula (3), derived in this very simple The main part of the Green’s function is a delta function way is in good agreement with the results of more which means that an energy loss inside the bunch is complicated analytical calculations, which were carried proportional to the bunch charge density.