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Research is underway at SLAC to, develop accelerator structures for a next generation linear collider. A fullscale prototype X-band structure has been built in which the dipole mode frequencies were detuned to suppress the long-range transverse wakefield by about two orders of magnitude. To verify that the detuning works as expected, a facility to measure the long-range wakefield, called the Accelerator Structure SETup. or ASSET, was constructed in the SLAC Linear Collider (SLC). This paper presents the results from the measurement of the prototype X-band structure with this facility.The designs being considered at SLAC for the Next Linear Collider (NLC) employ multi-bunch operation in a high acceleration gradient X-band linac [l]. One problem that has to be addressed in such an approach is the blowup of the transverse motion of the bunch train due to wakefield forces. That is, the long-range transverse wakefield generated by the bunch train in the X-band accelerator structures resonantly amplifies the betatron motion of the train. The,lowest band of dipole modes in the structures are the most harmful in this regard. If the structures in an NLC linac were built with identical cells, so essentially only the synchronous mode (phase velocity = c) in this band would be excited, the blowup would be enormous. To reduce the wakefield to a manageable level, a structure detuning strategy has been developed that exploits the wakefield decoherence that occurs when many modes in the lowest band are excited.In particular, the cells of the structure are designed with a smoothly varying geometry that maintains a constant accelerating mode frequency (1 1.4 GHz) along the structure while producing a Gaussian distribution in frequency of the product of the dipole mode density and the mode coupling strength to the beam. As a result, the integrated dipole wakefield, which evolves in time essentially as the inverse Fourier transform of this product, also falls off in a Gaussian manner.A full-scale (1.8 m long) prototype X-band structure has been built with this detuning strategy and successfully operated at high power [2]. The structure parameters were chosen to reduce the wakefield generated by one bunch by about two orders of magnitude within the 1.4 ns period between bunches in the NLC design. The geometry of its 206 cells are such that if one periodic structure were made from each cell type, the resulting density, dn/dv, of the lowest-band synchronous mode frequencies, v, of the 206 structures would be Gaussian with G,/V = 2.596, a central frequency of 15.1 GHz and a +20, truncation of its tails. To achieve this distribution, the cells vary in iris radius (5.72 to 3.90 mm), iris thickness (1 to 2 mm), and cavity radius (11.44 to 10.68 mm) along the structure. Although the iris thickness variation is not required to detune the lowest band of dipole modes, it was added to further detune the smaller contributions from the higher bands of dipole modes [3].The variation in the cell geometry is expected to yield a dipole mode density,...

In this paper we present methods for studying and controlling transverse cou--pled bunch instabilities. Our primary motivation is the study of damping rings for next-generation linear colliders in which many bunches are damped in the same ring simultaneously, however, the methods presented are also applicable to other situations. .-The theory developed here treats the motion of the bunch centroids, since the coherent dipole modes of coupled-bunch oscillation are expected to be strongly -dominant. A formalism to obtain the n normal modes of oscillation of n bunches -is developed. The imaginary part of the frequency of each normal mode determines its stability. However, not only the long term stability of each oscillation mode, but Laplace transform method, using the eigenmodes and corresponding eigenfrequencies found by the normal modes formalism, and (2) computer tracking, using a localizedkick approximation. Examples are given for damping ring designs appropriate to a linear collider of about 0.5 to 1.0 TeV center of mass energy.