``Incorrectly'' fixing the problem using nonsymplectic lattice function

In a true nonsymplectic system, it is possible to define lattice functions which are primarily ``beta'' in nature and another group which is ``eta'' in nature. The first group can be used to compute the effect on the complex part of the eigenvalues when a force is applied. The other group are connected to the change of the damping as a function of the force. There is a relation between these functions which the basis for connecting Chao's formalism to Sands formalism.

Obviously these lattice functions are periodic.

$$\underbrace{\left\langle{{x}_{1}^{2}}\right\rangle}\limits_{{\tt ... ...^{-1}-{A}_{16}{A}_{52}^{-1}}\right)}\limits_{{\tt bet(3)}}^{}{\varepsilon }_{3}$$ (6.3)

!!!!!!!!!!   Tracking a probe_8 to beam sizes around the ring using emittances and super-lattices functions  !!!!!!!!!!

 call kanalnummer(mf,"beam_xx_inf_using_emittances_ripken.dat")
 
 state=default0+radiation0+envelope0
 xs0=x     ! closed orbit intializing a probe
 m=nf%a_t  ! damapspin set to A
 xs=xs0+m  ! Probe_8 = closed orbit probe + Identity
 
  p=>als%start 
 
 id=(m%m.sub.1)**(-1)
 bet(1)=(m%m%v(1).sub.'1')*(id%v(2).sub.'01')-(m%m%v(1).sub.'01')*(id%v(1).sub.'01')
 bet(2)=(m%m%v(1).sub.'001')*(id%v(4).sub.'01')-(m%m%v(1).sub.'0001')*(id%v(3).sub.'01')
 bet(3)=(m%m%v(1).sub.'00001')*(id%v(6).sub.'01')-(m%m%v(1).sub.'000001')*(id%v(5).sub.'01')
 sizes(1,1)=(bet(1)*nf%emittance(1)+bet(2)*nf%emittance(2)+bet(3)*nf%emittance(3)) 
 write(mf,*) p%mag%name, sizes(1,1)

do i=1,als%n
 call track_probe(als,xs,state,fibre1=i,fibre2=i+1) 
 m=xs
 id=(m%m.sub.1)**(-1)
 bet(1)=(m%m%v(1).sub.'1')*(id%v(2).sub.'01')-(m%m%v(1).sub.'01')*(id%v(1).sub.'01')
 bet(2)=(m%m%v(1).sub.'001')*(id%v(4).sub.'01')-(m%m%v(1).sub.'0001')*(id%v(3).sub.'01')
 bet(3)=(m%m%v(1).sub.'00001')*(id%v(6).sub.'01')-(m%m%v(1).sub.'000001')*(id%v(5).sub.'01')
 sizes(1,1)=(bet(1)*nf%emittance(1)+bet(2)*nf%emittance(2)+bet(3)*nf%emittance(3)) 
 p=>p%next
 write(mf,*) p%mag%name, sizes(1,1)
enddo
close(mf)


!!!!!!!!!!   End of Tracking a probe_8 to beam sizes around the ring using emittances and super-lattices functions  !!!!!!!!!!