From 14ac2edc094955fb1d6c6ef74bfd739d17217163 Mon Sep 17 00:00:00 2001
From: Alexis Gamelin <alexis.gamelin@synchrotron-soleil.fr>
Date: Mon, 3 Jun 2024 15:21:58 +0200
Subject: [PATCH] Add form factor contribution to lcbi_growth_rate_mode
---
mbtrack2/instability/instabilities.py | 39 ++++++++++++++++++++++-----
1 file changed, 32 insertions(+), 7 deletions(-)
diff --git a/mbtrack2/instability/instabilities.py b/mbtrack2/instability/instabilities.py
index 692c465..ec4425e 100644
--- a/mbtrack2/instability/instabilities.py
+++ b/mbtrack2/instability/instabilities.py
@@ -103,10 +103,11 @@ def lcbi_growth_rate_mode(ring,
fr=None,
RL=None,
QL=None,
- Z=None):
+ Z=None,
+ bunch_length=None):
"""
Compute the longitudinal coupled bunch instability growth rate driven by
- an impedance for a given coupled bunch mode mu [1].
+ an impedance for a given coupled bunch mode mu [1-2].
Use either a list of resonators (fr, RL, QL) or an Impedance object (Z).
@@ -131,6 +132,10 @@ def lcbi_growth_rate_mode(ring,
Loaded quality factor of the resonator.
Z : Impedance, optional
Longitunial impedance to consider.
+ bunch_length : float, optional
+ Bunch length in [s].
+ Used to computed the form factor for a resonator impedance if given.
+ Default is None.
Returns
-------
@@ -142,9 +147,12 @@ def lcbi_growth_rate_mode(ring,
[1] : Eq. 51 p139 of Akai, Kazunori. "RF System for Electron Storage
Rings." Physics And Engineering Of High Performance Electron Storage Rings
And Application Of Superconducting Technology. 2002. 118-149.
+
+ [2] : Tavares, P. F., et al. "Beam-based characterization of higher-order-mode
+ driven coupled-bunch instabilities in a fourth-generation storage ring."
+ NIM A (2022): 165945.
"""
-
if synchrotron_tune is None and Vrf is None:
raise ValueError("Either synchrotron_tune or Vrf is needed.")
if synchrotron_tune is None:
@@ -188,8 +196,15 @@ def lcbi_growth_rate_mode(ring,
n1 = np.arange(1, n_max)
omega_p = ring.omega0 * (n0*M + mu + nu_s)
omega_m = ring.omega0 * (n1*M - mu - nu_s)
+
+ if bunch_length is None:
+ FFp = 1
+ FFm = 1
+ else:
+ FFp = np.exp(-(omega_p * bunch_length)**2)
+ FFm = np.exp(-(omega_m * bunch_length)**2)
- sum_val = np.sum(omega_p * Zr(omega_p)) - np.sum(omega_m * Zr(omega_m))
+ sum_val = np.sum(omega_p * Zr(omega_p) * FFp) - np.sum(omega_m * Zr(omega_m) * FFm)
return factor * sum_val
@@ -202,10 +217,11 @@ def lcbi_growth_rate(ring,
fr=None,
RL=None,
QL=None,
- Z=None):
+ Z=None,
+ bunch_length=None):
"""
Compute the maximum growth rate for longitudinal coupled bunch instability
- driven an impedance [1].
+ driven an impedance [1-2].
Use either a list of resonators (fr, RL, QL) or an Impedance object (Z).
@@ -228,6 +244,10 @@ def lcbi_growth_rate(ring,
Loaded quality factor of the HOM.
Z : Impedance, optional
Longitunial impedance to consider.
+ bunch_length : float, optional
+ Bunch length in [s].
+ Used to computed the form factor for a resonator impedance if given.
+ Default is None.
Returns
-------
@@ -245,6 +265,10 @@ def lcbi_growth_rate(ring,
[1] : Eq. 51 p139 of Akai, Kazunori. "RF System for Electron Storage
Rings." Physics And Engineering Of High Performance Electron Storage Rings
And Application Of Superconducting Technology. 2002. 118-149.
+
+ [2] : Tavares, P. F., et al. "Beam-based characterization of higher-order-mode
+ driven coupled-bunch instabilities in a fourth-generation storage ring."
+ NIM A (2022): 165945.
"""
growth_rates = np.zeros(M)
@@ -259,7 +283,8 @@ def lcbi_growth_rate(ring,
fr=fr,
RL=RL,
QL=QL,
- Z=Z)
+ Z=Z,
+ bunch_length=bunch_length)
growth_rate = np.max(growth_rates)
mu = np.argmax(growth_rates)
--
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