By Etienne Forest
This booklet illustrates a idea well matched to monitoring codes, which the writer has built through the years. monitoring codes now play a vital position within the layout and operation of particle accelerators. the speculation is totally defined step-by-step with equations and real codes that the reader can collect and run with freely to be had compilers.
In this publication, the writer pursues an in depth process in response to finite “s”-maps, considering that this is often extra normal so long as monitoring codes stay on the centre of accelerator layout. The hierarchical nature of software program imposes a hierarchy that places map-based perturbation idea above the other equipment. The map-based method, probably mockingly, permits eventually an implementation of the Deprit-Guignard-Schoch algorithms extra devoted than whatever present in the normal literature. This hierarchy of equipment isn't really a private selection: it follows logically from monitoring codes overloaded with a truncated strength sequence algebra package.
After defining abstractly and in short what a monitoring code is, the writer illustrates lots of the accelerator perturbation thought utilizing a precise code: PTC. This booklet could seem like a guide for PTC; in spite of the fact that, the reader is inspired to discover different instruments besides. The presence of an exact code guarantees that readers could have a device with which they could attempt their figuring out. Codes and examples might be to be had from a number of websites considering that PTC is in MAD-X (CERN) and BMAD (Cornell).
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Additional resources for From Tracking Code to Analysis: Generalised Courant-Snyder Theory for Any Accelerator Model
E-5_dp,fibre1=1) ! (2) id=1 ! (3) ! map is set to identity ! map is added to closed orbit and put into the 6 polymorphs y(1:6)=closed_orbit(1:6)+id ! (4) call propagate(als,y(1:6),state,fibre1=1) ! (5) one_turn_map=y(1:6) ! Six polymorphs are promoted to Taylor maps closed_orbit=y ! (6) ! (7) call ! (8a) c_normal(one_turn_map,normal_form) write(6,’(1/,a50,1/)’)"Canonical Transformation coming from Normal Form" call print(normal_form%a_t,6) ! 0_dp; ! (9a) if(courant_snyder_teng_edwards) then write(6,’(1/,a50,1/)’) "Courant-Snyder Canonical Transformation " else write(6,’(1/,a50,1/)’) "Anti-Courant-Snyder Canonical Transformation " endif call print(a_1,6,prec) !
8a) c_normal(one_turn_map,normal_form) write(6,’(1/,a50,1/)’)"Canonical Transformation coming from Normal Form" call print(normal_form%a_t,6) ! 0_dp; ! (9a) if(courant_snyder_teng_edwards) then write(6,’(1/,a50,1/)’) "Courant-Snyder Canonical Transformation " else write(6,’(1/,a50,1/)’) "Anti-Courant-Snyder Canonical Transformation " endif call print(a_1,6,prec) ! (9b) Line (5) is the usual propagation that gives the one-turn map. Lines (8a,b) is the result of the normal form: it provides a certain form for as “randomly” chosen by the 38 2 The Linear Transverse Normal Form: One Degree of Freedom programmer of the normal form routine.
The reader is invited to comment it out. , a non-symplectic map such as the map of a classical electron in a radiation source. In that case one must define the normal form to be a “affine dilation,” a damped rotation whose complex eigenvalues are slightly under the unit circle. 34 2 The Linear Transverse Normal Form: One Degree of Freedom Fig. 1 Pictorial view of the phase advance recipe for the (non)linear calculation of the transformation as that depends only on the one-turn map m s at location s.