Coupling in ibsEmittance

[Skamarokha]

How does ibsEmittance distributes emittance with coupling flag? In my MAD-X calculations I assumed that coupling between emittances works as
e0 = ex + ey; ex = e0(1+coupling); ey = ex*coupling. Here e0 is in my opinion should be ex0 from twissOutput, ex and ey coupled emittances. With my total emittance 73 pm for coupling=1 I would expect to get both coupled emittances ex=ey=73/2 pm, but I get somthing around 48 pm.

[michael_borland]

Mikhail,

The formula you quote is incorrect when the horizontal damping partition number Jx is not 1. The correct formula is ex=ex0/(1+K*Jy/Jx), ey=K*ex.

For example, for APS-U we have ex0=44.3 pm and Jx=2.21. With K=1, we get ex=ey=30.5 pm

--Michael

[Skamarokha]

But what about the sum rule of coupled emittances? If we were to use coupling as you discribed sum of coupled emittances won't be equal to uncoupled horizontal emittance from twissOutput for ideal lattice.

[michael_borland]

Mikhail,

The "sum rule" is only correct when Jx=1. If Jx>1, the sum of the emittances is always greater than the natural emittance.

--Michael

[Skamarokha]

Understood. Thank you for a quick reply.