field index

[jarnovandewalle]

Dear Didier,

I have a question about the BEND element in TRACEWIN.
We have a beam which is (on purpose) off-centered on a quadrupole. Thus, the quadrupole acts effectively as a combined function dipole.
Trying to 're-interprete' the field index (-R/B.dB/dr) in this context, I came up -for this case- to a value of N = 830 and blindly plugged this value into the parameters of the BEND element in TRACEWIN. That actually worked as it should ... the beam is bent as is should and the focusing is also as expected.

But how is the transfer matrix calculated ? In attachement, I copy-paste some snapshots from the manual and the input parameters & transfer matrix of this BEND element. The matrix element which is a cosine is > 1 ... so obviously not corrct ...
Could you clarify what transfer matrix is used in the case of large N values ?

Many thanks in advance & kind regards
Jarno

[Didier]

Dear jarno,

Yes, you are right, the manual only shows the matrix for an index (n) less than 1.
For a higher index and n>0 then kx=sqrt((n-1)*h2)) and cos(...) and sin(...) is replaced by cosh(...) and sinh(..)

Regards,

Didier