The letters "Y" and "y" denote a wake field element. The element length is always zero and it does not participate in any optics calculations except tracking. While usually single bunch calculations are implied, multi-bunch calculations can be performed. To achieve that, the initial longitudinal distribution needs to be split on bunches and the wavelength of accelerating wave needs to correspond to the bunch-to-bunch distance. The first parameter in the element definition line determines the plane of the wake field: 0: both transverse planes (axial symmetric wake), 1: x-plane, 2: y-plane, 3: longitudinal plane. The second parameter determines the scaling to be applied to the data read from a text file which determines a dependence of the wake field on longitudinal coordinate. The last parameter FileRef is the reference number to an external file which must be determined in the file reference section (see Input language description). The external file has to consist of two columns determining the wake strength on the longitudinal coordinate. The first column determines the longitudinal coordinate in cm and the second one the wake strength in arbitrary units. Positive sign of the strength corresponds defocusing for transverse wakes, and deceleration for longitudinal wake. The longitudinal coordinate must start from zero and grow monotonically. The wake field is considered to be zero at negative coordinates. The length of the data must exceed the total longitudinal spread of the particles (bunch or beam length). The wake field strength needs to be normalized so that the momentum change excited at given longitudinal coordinate by all particles located at zero longitudinal coordinate would be equal to the product of the value in the file for this coordinate and the amplitude determined by the second parameter of the element definition. The value of momentum change has to be expressed in eV/c. The program interpolates the wake-field at intermediate points using cubical spline. Usually 10-20 points per oscillation length of the wake function are sufficient to get decent accuracy. The accuracy of computations of wake-function grows with number of particles participating in tracking. Numerical experiments show that 500 particles yield about 10% accuracy for the longitudinal wake of a Gaussian bunch. 50000 particles should be adequate in most cases. The example below illustrates how to define transverse and longitudinal wake elements. The wake functions in the file have the standard definition: $$ c\Delta p_\parallel(s) = Ne^2 \int_s^\infty W_\parallel(s'-s)\rho(s') ds' \;\;\; \int_{-\infty}^{\infty} \rho(s')ds' = 1 $$ $$ c\Delta p_x(s) = Ne^2 x \int_s^\infty W_x(s'-s)\rho(s') ds' $$ They have dimensions 1/cm for longitudinal and 1/cm^2 for transverse degrees of freedom.
Example: Transverse and longitudinal wake-fields for a cavity # Wake field definition $Npart=2e11; # Number of particles # Amplitude calculation for the wake field expressed in inverse cm $AwakeL=300 * 4.8e-10 * $Npart; file reference start 1 LongWake.dat 2 TransvWake.dat file reference end begin list # Longitudinal wake-field element definition yLSCcav plane=3 Scale=$AwakeL FileRef=1 # Transverse wake-field element definition yTrSCcav plane=0 Scale=$AwakeL FileRef=2