PTC_TWISS A_ Initialization

Initialization is done in subroutine initmap that is contained in subroutine ptc_twiss

The A_ map is inside variable A_script_probe as its field A_script_probe%x . A_script_probe is of of type probe_8 and it is defined in the scope of subroutine ptc_twiss

There are 2 use cases

1. Transfer lines with provided initial parameters:
   1. Initialisation with Twiss parameters (beta, alpha and dispersion)
   2. A_ linear coefficients are read from a table, enabled with option initial_ascript_manual=true
   3. option initial_matrix_manual=true
   4. option initial_matrix_table=true
   5. option initial_moments_manual=true
   6. option initial_map_manual=true
2. Closed solution of rings

Transfer lines with provided initial parameters

1. Initialisation with Twiss parameters (beta and alpha) It is activated when betx and bety passed to ptc_twiss are bigger than zero and all the options initial_* are false.

   It is implemented in subroutine readinitialtwiss.

   • It reads the arguments passed to ptc_twiss

     • Orbit
     • For transverse planes beta, alpha, dispersion
     • For longitudinal beta and alpha

   • Beta and alpha is scaled with the reference momentum

      do i=1,c_%nd
        be(i)= beta(i)/(1_dp+orbit(5))
        al(i)=alpha(i)/(1_dp+orbit(5))
     enddo

• Orbit is put as constant part of the map

    A_script_probe%x=orbit

• The polynomials for each of transverse variables are built as follows

    do i=1,c_%nd
       A_script_probe%x(2*i-1)= orbit(2*i-1) +
          sqrt(be(i)) * morph((one.mono.(2*i-1))    )
       A_script_probe%x(2*i)  = orbit(2*i)   +
         (one/sqrt(be(i)) * (morph(  (one.mono.(2*i)) )-(al(i)) * morph((one.mono.(2*i-1)))))
    enddo

Closed solution of rings

To obtain a closed solution an identity map is tracked. In 6D case it is made of 6 polynomials. Each polynomial has the form

MAP(n) = Vn_closedorbit + 1*Vn

The map is tracked around the layout. The resulting map is normalized with