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Tracking a Quantum Envelope and computing the equilibrium sizes

These routines must track a polymorphic probe; PROBE_8. 4.2.6

  type probe_8
     type(real_8) x(6)     ! Polymorphic orbital ray
     type(spinor_8) s(3)   ! Polymorphic spin
     type(rf_phasor_8) AC  ! Modulation 
      real(dp) E_ij(6,6)   !  Envelope kick
!   stuff for exception
     logical u
     type(integration_node),pointer :: lost_node
  end type probe_8

The probe_8 contains implicitely the linear map $\bgroup\color{black}$M$\egroup$ in the polymorph $\bgroup\color{black}$x(6)$\egroup$ .

$\displaystyle {\Sigma}^{f}$

$\textstyle =$

$\displaystyle M\left({{\Sigma}^{0}+E}\right){M}^{\dagger } ; {\Sigma}_{ij}= \left\langle{{x}_{i}{x}_{j}}\right\rangle$

(6.1)

!!!!!!!!!!   Tracking a probe_8 to get the map   !!!!!!!!!!
 state=default0+radiation0+envelope0
 xs0=x     ! closed orbit intializing a probe
 m=1       ! damapspin set to identity
 xs=xs0+m  ! Probe_8 = closed orbit probe + Identity

call track_probe(als,xs,state,fibre1=1)
m=xs       ! damapspin = Probe_8 
nf=m       ! normal_spin = damapspin (Normalization including spin (if present) or radiation
           ! envelope if present. (Spin without radiation)
write(6,*) nf%n%tune(1:3)
write(6,*) nf%emittance
write(6,*) nf%s_ij0(1,1),nf%s_ij0(5,5)
!!!!!!!!!!  end Tracking a probe_8  to get the map     !!!!!!!!!!

nf is of type normal_spin. It normalises the orbital map, spin and radiation.

  type normal_spin
     type(normalform) N   ! regular orbital normal form
     type(damapspin) a1   ! brings to fixed point
     type(damapspin) ar   ! normalises around the fixed point
     type(damapspin) as   ! pure spin map 
     type(damapspin) a_t  ! !! (a_t%m,a_t%s) = (a1%m, I ) o (I ,as%s) o (ar%m,I)
!!!  extra info
     integer M(NDIM,NRESO),MS(NRESO),NRES  ! orbital and spin resonances to be left in the map
     type(real_8) n0(3)     ! n0 vector
     type(real_8) theta0    !  angle for the matrix around the orbit (analogous to linear tunes)
!!!Envelope
     real(dp) s_ij0(6,6)  !  equilibrium beam sizes
     real(dp) emittance(3),tune(3),damping(3)   ! equilibrium emittances (partially well defined only for infinitesimal damping)
     logical(lp) AUTO,STOCHASTIC
     real(dp)  KICK(3)   ! fake kicks for tracking stochastically
     real(dp)  STOCH(6,6)  ! Diagonalized of stochastic part of map for tracking stochastically
  end type normal_spin

Frank Schmidt 2010-10-15