Invariant Spin field with Normal Form

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Invariant Spin field with Normal Form

$\bgroup\color{black}${T}_{1}= \left({{M}_{1},{S}_{1}}\right)$\egroup$ is made of an orbital $\bgroup\color{black}$M_1$\egroup$ and a position dependent spin matrix $\bgroup\color{black}$S_1$\egroup$ .

$\displaystyle \underbrace{\left({{M}_{2},{S}_{2}}\right)}\limits_{{T}_{2}}^{}\c... ...s_{{T}_{1}}^{}= \left({{M}_{2}\circ {M}_{1},{S}_{2}\circ {M}_{1}{S}_{1}}\right)$

(8.1)

In the library FPP, spin-orbital maps are of type ``damapsin.''

 
  ID_S=1   
  XS=XS0+ID_S     
      
WRITE(6,*)" Computing a one-turn spin taylor map "
CALL TRACK_PROBE(ALS,XS,STATE,FIBRE1=1)
ID_S=XS

WRITE(6,*)" Doing a Spin-Orbital Normal Form: NF_S=ID_S "
NF_S=ID_S

The Taylor map ID_S is of type ``damapspin'': it is a spin orbital map. It is identity in both the spin part and the orbital part. Then the orbital closed orbit is added to it. The map is tracked for one-turn. The map NF_S is of type ``normal_spin.'' Both the orbital and the spin are normalized. (See FPP documentation)

Frank Schmidt 2010-10-15