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Author: Publisher: ISBN: Category : Languages : en Pages :
Book Description
The problem of cumulative beam break up in a periodic linac for a general impedance is discussed, with the effects of acceleration included. The transverse equations of motion for a set of identical point like bunches moving along the length of the linac are cast into a simple form using a smooth approximation. This results in a working formula that is used to analyze beam breakup. Explicit expressions for the transverse motion in the case of a single resonance impedance are found using saddle point integration. This is done first with no external focusing, and again in the strong focusing limit.
Author: Publisher: ISBN: Category : Languages : en Pages :
Book Description
The problem of cumulative beam break up in a periodic linac for a general impedance is discussed, with the effects of acceleration included. The transverse equations of motion for a set of identical point like bunches moving along the length of the linac are cast into a simple form using a smooth approximation. This results in a working formula that is used to analyze beam breakup. Explicit expressions for the transverse motion in the case of a single resonance impedance are found using saddle point integration. This is done first with no external focusing, and again in the strong focusing limit.
Author: Publisher: ISBN: Category : Languages : en Pages :
Book Description
Numerical simulation indicates that cumulative beam breakup (BBU) instability is not a concern to SNS SC linac. First, simulation is carried out for CW operation mode where the driving harmonics are those with frequency multiples of bunch frequency 402.5 MHz. Even when the median HOM frequency is exactly on resonance with multiples of bunch frequency of 402.5 MHz, the cavity-to-cavity HOM frequency spread can ensure operation of linac. Second, in the case of pulsed operation mode, additional driving harmonics of 1 MHz and 60 Hz are added on top of those of CW mode. The shunt impedance of these additional modes is relatively small. BBU is not a concern also for pulsed mode operation, as is verified for a few most dangerous modes. More systematic analysis of BBU of pulsed mode operation is done by Sundelin et al [1] and presented at this conference.
Author: Publisher: ISBN: Category : Languages : en Pages : 2060
Book Description
Multipass beam breakup, a transverse beam instability generated by coherent excitation of cavity higher order modes in a recirculating linac, is a particular concern in designs utilizing superconducting technology. In this paper, an analytic model is presented that includes a description of this effect for a distribution of cavities along the linac with several recirculations in an impulse approximation. For N passes and M cvities, solution of the resulting equations reduces in general to finding M zeros of a 2(N-1) dimensional determinant or equivalently the M eigenvalues of an M-dimensional matrix. The parametric dependence of this system on higher order mode frequencies and Q, lattice functions, and transit times is discussed. Numerical examples are presented to clarify these issues and to model the CEBAF superconducting linac, where threshold currents are found to exceed design currents by more than an order of magnitude.
Author: Publisher: ISBN: Category : Languages : en Pages : 15
Book Description
We describe here a study of a single bunch Beam Break Up (BBU) instability for a proposed Berkeley fast x-ray facility based on a recirculating linac [1]. The recirculating linac employs a 600 MeV superconducting RF linear accelerator and the electron beam energy of H"2.5 GeV is reached over four beam passes through the linac. A 120 MeV superconducting RF linear accelerator is used as an injector to the recirculating linac. The machine parameters are listed in Appendix A. The equation describing the transverse displacement x(s, z) of the electrons in an accelerated bunch, as a function of their longitudinal position within the bunch z, can be written in the form [2]: d/ds[[gamma](s) dx/ds] + k2(s)[gamma](s)x(s, z) = r0+"sub z}{sup {infinity}}[rho](z')W{sub {perpendicular}}(z'-z)x(s, z')dz' (1) where [gamma] is the relativistic factor, k the focusing strength, r0 the classical electron radius, [rho] the bunch density, W{sub {perpendicular}} the transverse wake function per unit length and s indicates the position along the linac. We assume infinitesimally small transverse beam dimensions (a good approximation, when the bunch dimensions are much less than the size of the beam pipe), so that x has to be interpreted as the displacement of the centre of a bunch slice. We also assume a bunch length much less than the betatron wavelength, therefore the displacement in the RHS of Eq.(1) is not retarded and, finally, we use an average transverse wake function obtained averaging the calculated short range wake of a single cavity [2] over the linac length. At first we consider the effect associated with a displacement of the electron bunch at the injection into the perfectly aligned linac. Later we extend the analysis to the case of misalignments of the linac RF cavities and cryomodules. Throughout the paper we compare the results obtained to the output of a simple tracking code, written as a Mathematical notebook. In order to keep the analytical expressions reasonably simple, we model the linac length as entirely filled with RF cavities (thus neglecting all the drift spaces, accounting for as much as one third of the total length). This causes the wakefield intensity used in the analysis to be bigger than the actual value and the average accelerating gradient to be smaller. It is shown in the paper that this corresponds to a conservative estimate of the BBU growth.
Author: Publisher: ISBN: Category : Languages : en Pages : 4
Book Description
An analytic model of cumulative beam breakup has been developed which is applicable to both low-velocity ion and high-energy electron linear accelerators. The model includes arbitrary velocity, acceleration, focusing, initial conditions, beam-cavity resonances, and variable cavity geometry and spacing along the accelerator. The model involves a continuum approximation'' in which the transverse kicks in momentum imparted by the cavities are smoothed over the length of the linac. The resulting equation of transverse motion is solved via the WKBJ method. Specific examples are discussed which correspond to limiting cases of the solution. 16 refs.
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