reflecting-match lattice in elegant

[yuehao]

Hi,

I have a question on calculating the twiss parameter of a lattice with reflected mirror boundary condition:
beta_start=beta_end
alpha_start=-alpha_end
eta_start=eta_end
etap_start=-etap_end

Is there a simple way to do it in elegant?

Thanks a lot,
Yue

[michael_borland]

Yue,

I've never tried this, but I think this will work:

CELL: line=(...)
REF: REFLECT
RCELL: line=(CELL,REF)

where CELL is the cell you want to match to the conditions you described. Using RCELL and matched=1 in &twiss_output should give the results you want.

--Michael

[yuehao]

Thank you, Michael. The Reflect element does the job magically.

However, there is one more question. When calculating the twiss_output in this case, the twiss parameter has more than one solution.

For this reflected symmetry case, the 1D matrix of the lattice only has two degree of freedom. The other two are killed by symplecticity and symmetry.
And the matrix looks (d and b are free parameter):
m11=d m12=b
m21=(d^2-1)/b m22=d

Meanwhile the same matrix can be expressed in twiss parameter: start->(beta, alpha) end->(beta, -alpha) and phase advance phi
the matrix element are:
m11=cos(phi)+alpha*sin(phi) m12=beta*sin(phi)
m21=(alpha*alpha-1)sin(phi)+2*alpha*cos(phi))/beta m22=cos(phi)+alpha*sin(phi)

so the beta, alpha and phi has infinity solutions. Is there a way to give more input to determine the twiss parameter?

Thanks,
Yue