From ed09e1a165ba00fb5771f35dae2a1e9d4e746951 Mon Sep 17 00:00:00 2001
From: KeonHKim <alphaover2pi@korea.ac.kr>
Date: Sat, 20 Jul 2024 23:56:36 +0900
Subject: [PATCH] Add a reference for the fundamental theorem of beam loading
---
mbtrack2/impedance/resistive_wall.py | 22 ++++++++++++++--------
1 file changed, 14 insertions(+), 8 deletions(-)
diff --git a/mbtrack2/impedance/resistive_wall.py b/mbtrack2/impedance/resistive_wall.py
index 5dffbad..dcee93e 100644
--- a/mbtrack2/impedance/resistive_wall.py
+++ b/mbtrack2/impedance/resistive_wall.py
@@ -45,7 +45,8 @@ class CircularResistiveWall(WakeField):
Resistive wall WakeField element for a circular beam pipe.
Impedance from approximated formulas from Eq. (2.77) of Chao book [1].
- Wake function formulas from [2, 3].
+ Wake function formulas from [2, 3] and the fundamental theorem of
+ beam loading from [4].
Parameters
----------
@@ -67,7 +68,7 @@ class CircularResistiveWall(WakeField):
----------
[1] : Chao, A. W. (1993). Physics of collective beam instabilities in high
energy accelerators. Wiley.
- [2] : Ivanyan, Mikayel I. and Tsakanov, Vasili M. "Analytical treatment of
+ [2] : Ivanyan, Mikayel I., and Vasili M. Tsakanov. "Analytical treatment of
resistive wake potentials in round pipes." Nuclear Instruments and Methods
in Physics Research Section A: Accelerators, Spectrometers, Detectors and
Associated Equipment 522, no. 3 (2004): 223-229.
@@ -75,6 +76,9 @@ class CircularResistiveWall(WakeField):
interbunch collective beam motions in storage rings." Nuclear Instruments
and Methods in Physics Research Section A: Accelerators, Spectrometers,
Detectors and Associated Equipment 806 (2016): 221-230.
+ [4] : Zotter, Bruno W., and Semyon A. Kheifets (1998). Impedances and wakes
+ in high-energy particle accelerators. World Scientific.
+
"""
@@ -129,9 +133,9 @@ class CircularResistiveWall(WakeField):
The approxmiated expression is valid if the time is large compared
to the characteristic time t0.
- Eq. (11) in [1] is completely equivalent to Eq. (22) in [2].
+ Eq. (11) in [1] is completely identical to Eq. (22) in [2].
- The fundamental theorem of beam loading is applied for the exact
+ The fundamental theorem of beam loading [3] is applied for the exact
expression of the longitudinal wake function: Wl(0) = Wl(0+)/2.
Parameters
@@ -148,7 +152,7 @@ class CircularResistiveWall(WakeField):
References
----------
- [1] : Ivanyan, Mikayel I. and Tsakanov, Vasili M. "Analytical treatment of
+ [1] : Ivanyan, Mikayel I., and Vasili M. Tsakanov. "Analytical treatment of
resistive wake potentials in round pipes." Nuclear Instruments and Methods
in Physics Research Section A: Accelerators, Spectrometers, Detectors and
Associated Equipment 522, no. 3 (2004): 223-229.
@@ -156,6 +160,8 @@ class CircularResistiveWall(WakeField):
interbunch collective beam motions in storage rings." Nuclear Instruments
and Methods in Physics Research Section A: Accelerators, Spectrometers,
Detectors and Associated Equipment 806 (2016): 221-230.
+ [3] : Zotter, Bruno W., and Semyon A. Kheifets (1998). Impedances and wakes
+ in high-energy particle accelerators. World Scientific.
"""
wl = np.zeros_like(time)
idx1 = time < 0
@@ -179,7 +185,7 @@ class CircularResistiveWall(WakeField):
The approxmiated expression is valid if the time is large compared
to the characteristic time t0.
- Eq. (11) in [1] is completely equivalent to Eq. (25) in [2].
+ Eq. (11) in [1] is completely identical to Eq. (25) in [2].
Corrected the typos in the last two terms in exact expression
(Eq. (11), of [1]).
@@ -193,11 +199,11 @@ class CircularResistiveWall(WakeField):
Returns
-------
wt : array of float
- Transverse wake function in [V/C].
+ Transverse wake function in [V/C/m].
References
----------
- [1] : Ivanyan, Mikayel I. and Tsakanov, Vasili M. "Analytical treatment of
+ [1] : Ivanyan, Mikayel I., and Vasili M. Tsakanov. "Analytical treatment of
resistive wake potentials in round pipes." Nuclear Instruments and Methods
in Physics Research Section A: Accelerators, Spectrometers, Detectors and
Associated Equipment 522, no. 3 (2004): 223-229.
--
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