# Minutes of 76th FFIR/BDSIM meeting on 7/21/2004

The meeting was held in a room of 425 at KEK, 10:00-11:00, 7/21/2004. We discussed on the electron capture threshold in the LINAC and Final focus system.
## (1) Electron capture threshold in the LINAC (T. Yamamura)

(transparencies, 4 pages, pdf, 2.5MB)
Yamamura analytically derived the capture threshold by integrating an equation of motion; m d(γ&beta)/dt=E_{o}sin k(x-t). where one dimentional motion is only considered in longitudinal direction (x) . The capture condition is β_{f}=1 at end of the integration. Therefore, E_{o} > mk/(1+cos &Phi_{i}), where &Phi_{i} is initial phase in (x-t) . The minimal E_{o}, i.e. threshold gradient, should be mk/2 .
At the x-band LINAC, E_{o} > 61.0MV/m .

He also had a simulation study in two cases of sine-wave and "MAFIA-field" in the accelerating structure, where the accelerating gradient is 65MV/m. He calculated the final phase (&Phi_{f}) after 10ns as a function of the initial phase (&Phi_{i}) . For the sine-wave, the &Phi_{f} distribution is symmetric at &Phi_{i}=&pi.
However, the "MAFIA-field" has complicated distribution which can not be intuitively understood. So, he is requested for more detailed investigation in the "MAFIA-field" calculation.

(transparencies, 1 page, pdf, 24KB)
Kuroda estimated longitudinal position (dz), field strength (dk) and rotational (d&theta) errors of sextupole magnets (SD0, SF1, SD4, SF5 and SF6) in the FF system, which blow up beam sizes by 50% in both directions at IP. i.e. 1.5&sigma^{*}_{x}=300nm and 1.5&sigma^{*}_{y}=4nm. These errors are expected to affect on the beam sizes at IP.
The dz has no significant effect on the beam sizes, i.e. it can be greater than 100 um.
The smallest dk error is 0.73-0.76 at SD0 and SD4, and the smallest d&theta one is 1 mrad at SD0, SF1 and SD4.

### The next meeting will be on 8 September, 2004,10:00 - at 3 gokan, 425 .