(4 THE ANALYSIS OF TRANSVERSE BEAM TAIL DISTRIBUTIONS OF BUNCHES WITH NON-GAUSSIAN SHAPES*
M. Avilov, Seeman, J. T. · University of North Texas Digital Library (University of North Texas) · 1992
The characterization of transverse particle distributions of bunches with non-Gaussian shapes is difficult due to a wide variety of possibilities [l]. Without knowing additional information one can tit a distribution using first-, second-, third-, and higher order moments [2]. These moments can then be used to describe beam shape changes along the accelerator, but with limited knowledge of the physics which caused‘the perturbed shape. However, when the cause of the non-Gaussian distribution is known, a more detailed description of the particle distribution can be constructed. In the Qanford Linear Collider (SLC) non-Gaussian distributions are produced by transverse wakefields in the 3000 m linac. 1 TRANSVERSE TAIL PARAMETERIZATION The effects of transverse wakefields can be calculated given the transverse equation of motion of the particles in the bunch. A!? ~(2,s) + k2 (2,s) x(z,s) = ds2 I” dz ’ h(z’)W(z’-z) x(z’,s), where x is the transverse offset from the accelerator axis, s is the distance along the accelerator, z is the longitudinal distance along the bunch, k is the lattice strength, y = E/mc2, h is the longitudinal particle density, re is the classical radius of the electron, and W is the transverse wakefield which depends on the longitudinal separation of the particle generating the fields and the particle sensing the fields. The solution of this equation shows that oscillating leading particles drive trailing particles to larger amplitudes, generating non-Gaussian distributions 131. A schematic view of such a transverse tail is shown in Figure 1, where the particle centroids move farther and farther off-axis near the end of the bunch. Also, with very strong wakefields or with special conditions used to reduce wakefield emittance growth (BNS damping), the transverse tails can spread out over circles in transverse phase space.