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[Licence| Download | New Version Template] adgr_v1_0.gz(34 Kbytes)
Manuscript Title: NERO: a code for the nonlinear evaluation of resonances in one-turn mappings.
Authors: E. Todesco, M. Gemmi, M. Giovannozzi
Program title: NERO
Catalogue identifier: ADGR_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 106(1997)169
Programming language: Fortran.
Computer: Alphavax 3000/500.
Operating system: VMS, UNIX.
RAM: 1.2M words
Keywords: Particle physics, Elementary, Accelerator, Symplectic maps, One-turn betatronic maps, Normal forms, Resonances.
Classification: 11.10.

Nature of problem:
This code allows one to reconstruct the dynamics in phase space of a four-dimensional symplectic mapping using the perturbative approach. The position of the network of resonances and their strength are evaluated via analytical methods. This approach is complementary to numerical methods for the analysis of the global dynamics in phase space. It can be useful for evaluating the relevance of the nonlinear effects in betatronic motion of hadron accelerators.

Solution method:
Given a symplectic map in the neighbourhood of an elliptic fixed point, the code evaluates both the nonresonant and the resonant perturbative series (normal forms). For each resonant normal form, the interpolating Hamiltonian is computed and the position and the stability of the resonant orbits and the width of the islands are evaluated; this analysis is carried out through the direct inspection of the coefficients of the interpolating Hamiltonian. All the computations are carried out at an arbitrary order that can be specified by the user; the first significant perturbative order is taken as a first guess, and then a Newton method is used to evaluate the higher orders effect.

Running time:
30 seconds for the test run (phase space analysis up to order 8, with all resonances up to order 9) on Alphavax 3000/500.