danf 0.2.0

Differential Algebra Normal Forms for symplectic maps

DANF

Differential Algebra Normal Forms for symplectic maps, built on DACEyPy.

Computes amplitude-dependent tune shifts (detuning coefficients) of nonlinear symplectic maps via order-by-order normal form transformation in the complex eigenvector basis.

Installation

pip install danf

Quick Start

import numpy as np
from daceypy import DA
from danf import NormalForm
from danf.elements import rotation, thin_sext, compose

# Initialize DA engine: order 7, 2 variables (x, px)
DA.init(7, 2)

# Build a one-turn map: rotation (tune 0.31) + sextupole kick (k2L = 1.0)
one_turn = compose(rotation(0.31), thin_sext(1.0))

# Compute the normal form
nf = NormalForm(one_turn)
nf.compute()

print(f"Tune: {nf.tunes[0]:.6f}")
print(f"dnu/dJ: {nf.detuning['dnux_dJx']:.8f}")

API

NormalForm(da_map)

Main class. Takes a list of DA objects (the symplectic map components) and computes the nonlinear normal form.

• nf.compute() - run the full computation
• nf.tunes - linear tunes
• nf.detuning - dict of amplitude-dependent tune shift coefficients

danf.elements

Convenience functions for building DA maps: rotation, thin_sext, thin_quad, thin_oct, drift, compose.

compute_detuning_1d(da_x, da_px, tune)

Low-level function for 1D normal form computation. Takes map components in normalized (Floquet) coordinates.

Cross-Validation

Results verified against COSY INFINITY v10.2 (DANF procedure) to 10 significant figures:

Quantity	DANF (Python)	COSY INFINITY
dnu/dJ	+0.0121104226	+0.0121104226