W-RF cavity (pi-mode standing wave)

Parameter Description Argument Order Argument Name Units Default Value
Total Length 1 cm
Voltage 2 A MV 0.0
Phase 3 phase deg 0.0
Wavelength 4 WaveL cm 0.0
Field Data 5 FileRef

The letters "W" and "w" denote an axial symmetric accelerating cavity. The first parameter is the total length of the cavity. The second parameter is the total accelerating voltage of the cavity for on-crest acceleration. The phase is expressed with repect to the accelerating phase relative to the on-crest acceleration phase; a the positive phase implies that a particle goes through the cavity after the voltage reaches its maximum. WaveL determines the wave length of the accelerating voltage in vacuum $(\lambda=c/f)$. 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 consists of two columns determining the amplitude of the standing wave accelerating field along cavity axis. The first column is the longitudinal coordinate and the second one the longitudinal electric field value (with sign). The program interpolates the field at intermediate points using cubic splines. Usually 10-15 points per cell is sufficient to get decent accuracy. The relative dependence of the field is only important, the program chooses required amplitude itself. The coordinate must be monotonically increasing. The difference between the coordinates of the last and first point must be equal to the cavity length. The program finds the transfer matrix using the third order Runge-Kutta method. Accuracy and number of steps are determined by View|Control menu. The accuracy is determined by a difference of the transfer matrix determinant from one. If accuracy is not achieved the program pops-up a message window. To keep the transfer matrix M symplectic, M21 and M43 are corrected to make each of the $2\times 2$ sub-determinants equal to unity.

Example: 
# cavity with total length of 70 cm and accelerating voltage of 2.5 MeV. The cavity field is determined in the external file C:\OPTIM\CAVITY\cav2.DAT. Accelerating phase is equal to zero (on crest acceleration).
file reference start
1 C:\OPTIM\CAVITY\cav1.DAT 
3 C:\OPTIM\CAVITY\cav2.DAT 
file reference end
...
wAq2       	L[cm]=70        A[MeV]=2.5       Phase[deg]=0  WaveL[cm]=20 FileRef=3