Add a reference for the fundamental theorem of beam loading

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.