1. Summary of my work in September and my plan What I have done and my status –Finished programming and fixed some bugs of the preliminary version of the XSIF to SAD Translator, successfully applied the program to the translation of the RTML, Main Linac and BDS lattice deck files. (Presented in the BDS meeting of September 13, 2006) –Made some tracking studies on the ATF2 lattice by using SAD, such as the lattice deck files from version 3.1 to 3.4.1 and from version ff3.7.1 to ff3.8.3. –Made some studies on the higher order terms of the transfer matrix, some of the results will be shown later. My plan

2. Some study results of the higher order terms of the transfer matrix In six dimensional phase space, the change of the coordinate vector X i = (x, x’, y, y’, △ l, δ) is driven by the first order transfer matrix R such that X i out = R ij X j in. The second, third and so on terms are included in a similar manner, X i out = R ij X j in + T ijk X j in X k in + U ijkn X j in X k in X n in + …… In studying the final focus system, it is important to know the higher order terms such as T122, T126, and so on, since some of them have a large effect on the beam size. In SAD, there is no such function to calculate the higher order terms now, so some post process programs need to be written.

3. Kuroda-san write a simple program to calculate the higher order term T111, which is based on the following method: 1) Track particles with different initial conditions; 2) Fit the results to obtain the higher order term. But, the problem of Kuroda-san calculation is the accuracy, since if I change the initial conditions, different calculation results will be given. For example, for the calculation of T 111, we only change the initial condition of x. When the initial value of x is 1e-4, the fitted value of T 111 is - 47.88415128090774, while when the initial value of x is 1e- 6, the value of T 111 is 9.608780161841832. (Both smaller and larger change of initial conditions will produce wrong results, but the appropriate value of initial condition is difficult to estimate.)

4. On the basis of Kuroda-san’s program, I also wrote a program to calculate the value of T ijk when i = j = k. In my program, the initial conditions can be changed automatically until a convergence of the calculated T ijk is obtained. But, the calculated value of the T ijk depends on the stop condition of the automatic change of the initial condition, sometimes the calculation may fail. For example, if I set the stop condition to be Abs[Tijk/coeff[3]- 1]=>0.001, the calculated value of T 111 is 9.608780161841832, while if I set the stop condition to be Abs[Tijk/coeff[3]-1]=>0.0001, the calculation will fail. In addition, using my program to calculate T 111 and T 222 is OK, while for T 333, T 444, T 555 and T 666, the program will fail. More detail studies on the calculation method of higher order terms in SAD need to be done.

5. My plan To study the calculation method of the higher order terms of transfer matrix in SAD (started). To make some studies on the ATF2 beam dynamics (Started). To make some studies on the ILC beam dynamics by using different simulation codes (Just started). To explore and understand the XSIFParser source files maintained by PT, then make the XSIF to SAD translator by using Visual Fortran language (will be started). To write my own code (will be started). ……