diff --git a/mbtrack2/tracking/element.py b/mbtrack2/tracking/element.py
index d065078533ab0b5e9d789338e47b170fa63c75f2..6cba19d9a98df12587a5b4f78313b29c61cbd8c1 100644
--- a/mbtrack2/tracking/element.py
+++ b/mbtrack2/tracking/element.py
@@ -6,7 +6,6 @@ included in the tracking.
"""
import numpy as np
-import at
from abc import ABCMeta, abstractmethod
from functools import wraps
from copy import deepcopy
@@ -176,14 +175,20 @@ class TransverseMap(Element):
phase_advance_y = 2*np.pi * (self.ring.tune[1] +
self.ring.chro[1]*bunch["delta"])
else:
+ Jx = (self.ring.optics.local_gamma[0] * bunch['x']**2) + \
+ (2*self.ring.optics.local_alpha[0] * bunch['x']*bunch['xp']) + \
+ (self.ring.optics.local_beta[0] * bunch['xp']**2)
+ Jy = (self.ring.optics.local_gamma[1] * bunch['y']**2) + \
+ (2*self.ring.optics.local_alpha[1] * bunch['y']*bunch['yp']) + \
+ (self.ring.optics.local_beta[1] * bunch['yp']**2)
phase_advance_x = 2*np.pi * (self.ring.tune[0] +
self.ring.chro[0]*bunch["delta"] +
- self.adts_poly[0](bunch['x']) +
- self.adts_poly[2](bunch['y']))
+ self.adts_poly[0](Jx) +
+ self.adts_poly[2](Jy))
phase_advance_y = 2*np.pi * (self.ring.tune[1] +
self.ring.chro[1]*bunch["delta"] +
- self.adts_poly[1](bunch['x']) +
- self.adts_poly[3](bunch['y']))
+ self.adts_poly[1](Jx) +
+ self.adts_poly[3](Jy))
# 6x6 matrix corresponding to (x, xp, delta, y, yp, delta)
matrix = np.zeros((6,6,len(bunch)))
@@ -282,9 +287,11 @@ class TransverseMapSector(Element):
self.ring = ring
self.alpha0 = alpha0
self.beta0 = beta0
+ self.gamma0 = (1 + self.alpha0**2)/self.beta0
self.dispersion0 = dispersion0
self.alpha1 = alpha1
self.beta1 = beta1
+ self.gamma1 = (1 + self.alpha1**2)/self.beta1
self.dispersion1 = dispersion1
self.tune_diff = phase_diff / (2*np.pi)
self.chro_diff = chro_diff
@@ -315,14 +322,20 @@ class TransverseMapSector(Element):
phase_advance_y = 2*np.pi * (self.tune_diff[1] +
self.chro_diff[1]*bunch["delta"])
else:
+ Jx = (self.gamma0[0] * bunch['x']**2) + \
+ (2*self.alpha0[0] * bunch['x']*self['xp']) + \
+ (self.beta0[0] * bunch['xp']**2)
+ Jy = (self.gamma0[1] * bunch['y']**2) + \
+ (2*self.alpha0[1] * bunch['y']*bunch['yp']) + \
+ (self.beta0[1] * bunch['yp']**2)
phase_advance_x = 2*np.pi * (self.tune_diff[0] +
self.chro_diff[0]*bunch["delta"] +
- self.adts_poly[0](bunch['x']) +
- self.adts_poly[2](bunch['y']))
+ self.adts_poly[0](Jx) +
+ self.adts_poly[2](Jy))
phase_advance_y = 2*np.pi * (self.tune_diff[1] +
self.chro_diff[1]*bunch["delta"] +
- self.adts_poly[1](bunch['x']) +
- self.adts_poly[3](bunch['y']))
+ self.adts_poly[1](Jx) +
+ self.adts_poly[3](Jy))
# 6x6 matrix corresponding to (x, xp, delta, y, yp, delta)
matrix = np.zeros((6,6,len(bunch)))
@@ -379,7 +392,7 @@ def transverse_map_sector_generator(ring, positions):
List of TransverseMapSector elements.
"""
-
+ import at
def _compute_chro(ring, pos, dp=1e-4):
lat = deepcopy(ring.optics.lattice)
lat.append(at.Marker("END"))
diff --git a/mbtrack2/tracking/synchrotron.py b/mbtrack2/tracking/synchrotron.py
index 17460077f3ef755f52c1a0defb7ae54ee1975088..1c34b086e16dad2733fedd468d41b645616fec15 100644
--- a/mbtrack2/tracking/synchrotron.py
+++ b/mbtrack2/tracking/synchrotron.py
@@ -47,13 +47,13 @@ class Synchrotron:
The order of the elements strictly needs to be
[coef_xx, coef_yx, coef_xy, coef_yy], where x and y denote the horizontal
and the vertical plane, respectively, and coef_PQ means the polynomial's
- coefficients of the ADTS in plane P due to the offset in plane Q.
+ coefficients of the ADTS in plane P due to the amplitude in plane Q.
- For example, if the tune shift in y due to the offset x is characterized
- by the equation dQy(x) = 3*x**2 + 2*x + 1, then coef_yx takes the form
- np.array([3, 2, 1]).
+ For example, if the tune shift in y due to the Courant-Snyder invariant
+ Jx is characterized by the equation dQy(x) = 3*Jx**2 + 2*Jx + 1, then
+ coef_yx takes the form np.array([3, 2, 1]).
- Use None, to exclude the ADTS calculation.
+ Use None, to exclude the ADTS from calculation.
Attributes
----------
@@ -296,3 +296,20 @@ class Synchrotron:
tuneS = np.sqrt( - (Vrf / self.E0) * (self.h * self.ac) / (2*np.pi)
* np.cos(phase) )
return tuneS
+
+ def get_adts(self):
+ """
+ Compute and add Amplitude-Dependent Tune Shifts (ADTS) sextupolar
+ componenet from AT lattice.
+ """
+ import at
+ if self.optics.use_local_values:
+ raise ValueError("ADTS needs to be provided manualy as no AT" +
+ " lattice file is loaded.")
+
+ det = at.physics.nonlinear.gen_detuning_elem(self.optics.lattice)
+ coef_xx = np.array([det.A1/2, 0])
+ coef_yx = np.array([det.A2/2, 0])
+ coef_xy = np.array([det.A2/2, 0])
+ coef_yy = np.array([det.A3/2, 0])
+ self.adts = [coef_xx, coef_yx, coef_xy, coef_yy]