Elegant users forum

Hi,

for tracking at resonance tune, i.e. Qx=Qy and for a example lattice just with two Quadrupoles and drifts, I dont expect any emittance changes...
this is my lattice:

"mqd: MULT, KnL =-0.2169824517, order = 1
mqf: MULT, KnL = 0.2169824517, order = 1
drift1:DRIF, L = 0.65
quad1:Line=(mqd)
drift2 : DRIF, L =2.6
quad2:line =(mqf)
drift3 : DRIF, L = 9.65

fodo1cell : line = (drift1,quad1,drift2,quad2,drift3)
use,fodo1cell
return
"

After running tracking

"
&run_control
n_passes = 5000000
&end

&bunched_beam
n_particles_per_bunch = 1000
bunch=..\bunch\track_UNIELLIPSE_Emittances_Div_by_4.bun
use_twiss_command_values = 1
emit_x = 8.75e-06
emit_y = 3.75e-06
distribution_cutoff[0] = 1, 1
distribution_type[0] = "uniform-ellipse", "uniform-ellipse"
enforce_rms_values[0] = 1, 1
limit_in_4d = 1
&end

&track
&end
"

I found the there is some changes in the emittances, emi_x increases and emi_y decreases.
I checked it already for kquad and edrift, some thing happened.
Do you have any idea where this emittance changes come?

Regards,
Youssef

Youssef,

The problem seems to be that when using the exact Hamiltonian (the default in elegant), there is "hidden" coupling between x and y motion. In particular, to compute the changes in x and y, we have to compute the slopes x' and y' from the momenta qx and qy. As you can see in equation 6 of LS-356, the transformations involve coordinates from both planes. When using the expanded Hamiltonian, the transformations involve coordinates from a single plane only.

You can see this by using KQUAD elements and setting EXPAND_HAMILTONIAN=1. (MULT has the same parameter, but there's a bug in its implementation.)

The bottom line is that x and y emittances are not separately preserved when using the exact Hamiltonian. Presumably this is made worse by sitting on the coupling resonance, though I didn't check that.

--Michael