From 344cd6a229382b5b60eba74cb71dc51c13840e90 Mon Sep 17 00:00:00 2001
From: Gamelin Alexis <alexis.gamelin@synchrotron-soleil.fr>
Date: Fri, 23 Jun 2023 15:40:47 +0200
Subject: [PATCH] Add higher order momentum compaction factor
Add mcf_order optional parameter for Synchrotron class to prodivde higher-orders momentum compaction factor.
Add Synchrotron.get_mcf_order method to compute momentum compaction factor up to 3rd order from AT lattice.
Modify Synchrotron.eta to use higher order mcf.
Improve Synchrotron docstrings.
Change LongitudinalMap to use Synchrotron.eta.
---
mbtrack2/tracking/element.py | 2 +-
mbtrack2/tracking/synchrotron.py | 106 ++++++++++++++++++++++++++++---
2 files changed, 99 insertions(+), 9 deletions(-)
diff --git a/mbtrack2/tracking/element.py b/mbtrack2/tracking/element.py
index 6cba19d..231ba25 100644
--- a/mbtrack2/tracking/element.py
+++ b/mbtrack2/tracking/element.py
@@ -91,7 +91,7 @@ class LongitudinalMap(Element):
bunch : Bunch or Beam object
"""
bunch["delta"] -= self.ring.U0 / self.ring.E0
- bunch["tau"] += self.ring.ac * self.ring.T0 * bunch["delta"]
+ bunch["tau"] += self.ring.eta(bunch["delta"]) * self.ring.T0 * bunch["delta"]
class SynchrotronRadiation(Element):
"""
diff --git a/mbtrack2/tracking/synchrotron.py b/mbtrack2/tracking/synchrotron.py
index 1c34b08..236f34e 100644
--- a/mbtrack2/tracking/synchrotron.py
+++ b/mbtrack2/tracking/synchrotron.py
@@ -4,6 +4,7 @@ Module where the Synchrotron class is defined.
"""
import numpy as np
+import matplotlib.pyplot as plt
from scipy.constants import c, e
class Synchrotron:
@@ -54,6 +55,12 @@ class Synchrotron:
coef_yx takes the form np.array([3, 2, 1]).
Use None, to exclude the ADTS from calculation.
+ mcf_order : array, optional
+ Higher-orders momentum compaction factor in decreasing powers.
+ Input here the coefficients considering only the derivatives and which
+ do not include any factorial factor.
+ The 1st order should be included in the array and be at the last
+ position.
Attributes
----------
@@ -75,16 +82,24 @@ class Synchrotron:
Relativistic Lorentz gamma.
beta : float
Relativistic Lorentz beta.
- eta : float
- Momentum compaction.
- sigma : array of shape (4,)
- RMS beam size at equilibrium in [m].
Methods
-------
synchrotron_tune(Vrf)
Compute synchrotron tune from RF voltage.
sigma(position)
+ Return the RMS beam size at equilibrium in [m].
+ eta(delta)
+ Momentum compaction taking into account higher orders if provided in
+ mcf_order.
+ mcf(delta)
+ Momentum compaction factor taking into account higher orders if
+ provided in mcf_order.
+ get_adts()
+ Compute and add Amplitude-Dependent Tune Shifts (ADTS) sextupolar
+ componenet from AT lattice.
+ get_mcf_order()
+ Compute momentum compaction factor up to 3rd order from AT lattice.
"""
def __init__(self, h, optics, particle, **kwargs):
self._h = h
@@ -111,7 +126,8 @@ class Synchrotron:
self.sigma_0 = kwargs.get('sigma_0') # Natural bunch length [s]
self.emit = kwargs.get('emit') # X/Y emittances in [m.rad]
self.adts = kwargs.get('adts') # Amplitude-Dependent Tune Shift (ADTS)
-
+ self.mcf_order = kwargs.get('mcf_order', self.ac) # Higher-orders momentum compaction factor
+
@property
def h(self):
"""Harmonic number"""
@@ -231,9 +247,32 @@ class Synchrotron:
self.gamma = value/(self.particle.mass*c**2/e)
@property
- def eta(self):
- """Momentum compaction"""
- return self.ac - 1/(self.gamma**2)
+ def mcf_order(self):
+ """Higher-orders momentum compaction factor"""
+ return self._mcf_order
+
+ @mcf_order.setter
+ def mcf_order(self, value):
+ self._mcf_order = value
+ self.mcf = np.poly1d(self.mcf_order)
+
+ def eta(self, delta=0):
+ """
+ Momentum compaction taking into account higher orders if provided in
+ mcf_order.
+
+ Parameters
+ ----------
+ delta : float or array like bunch["delta"], optional
+ Relative energy deviation. The default is 0.
+
+ Returns
+ -------
+ float or array
+ Momentum compaction.
+
+ """
+ return self.mcf(delta) - 1/(self.gamma**2)
def sigma(self, position=None):
"""
@@ -313,3 +352,54 @@ class Synchrotron:
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]
+
+ def get_mcf_order(self, add=True, show_fit=False):
+ """
+ Compute momentum compaction factor up to 3rd order from AT lattice.
+
+ Parameters
+ ----------
+ add : bool, optional
+ If True, add the computed coefficient to the Synchrotron object.
+ If False, the result is returned.
+ The default is True.
+ show_fit : bool, optional
+ If True, show a plot with the data and fit.
+ The default is False.
+
+ Return
+ ------
+ pvalue : array, optional
+ Momentum compaction factor up to 3rd order
+ """
+ import at
+ if self.optics.use_local_values:
+ raise ValueError("ADTS needs to be provided manualy as no AT" +
+ " lattice file is loaded.")
+ deltamin = -1e-4
+ deltamax = 1e-4
+
+ delta = np.linspace(deltamin, deltamax, 7)
+ delta4eval = np.linspace(deltamin, deltamax, 21)
+ alpha = np.zeros_like(delta)
+
+ for i in range(len(delta)):
+ alpha[i] = at.physics.revolution.get_mcf(self.optics.lattice,
+ delta[i])
+ pvalue = np.polyfit(delta, alpha, 2)
+
+ if show_fit:
+ pvalue = np.polyfit(delta, alpha, 2)
+ palpha = np.polyval(pvalue, delta4eval)
+
+ plt.plot(delta*100, alpha,'k.')
+ plt.grid()
+ plt.plot(delta4eval*100,palpha,'r')
+ plt.xlabel('Energy (%)')
+ plt.ylabel('Momemtum compaction factor')
+ plt.legend(['Data', 'polyfit'])
+
+ if add:
+ self.mcf_order = pvalue
+ else:
+ return pvalue
--
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