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.
!!!!!!!!!! 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 !!!!!!!!!!