Add RWMBI growth rate and threshold calculation + correct typos

collective_effects/__init__.py

@@ -6,6 +6,7 @@ Created on Tue Jan 14 12:25:30 2020
 """
 
 from mbtrack2.collective_effects.instabilities import mbi_threshold, cbi_threshold, lcbi_growth_rate_mode, lcbi_growth_rate
+from mbtrack2.collective_effects.instabilities import rwmbi_growth_rate, rwmbi_threshold
 from mbtrack2.collective_effects.resistive_wall import (skin_depth, CircularResistiveWall, Coating)
 from mbtrack2.collective_effects.resonator import Resonator, PureInductive, PureResistive
 from mbtrack2.collective_effects.tapers import StupakovRectangularTaper, StupakovCircularTaper

collective_effects/impedance_model.py

@@ -25,7 +25,7 @@ class ImpedanceModel(Element):
     ring : Synchrotron object
     wakefield_list : list of WakeField objects
         WakeFields to add to the model.
-    wakefiled_postions : list
+    wakefiled_positions : list
         Longitudinal positions corresponding to the added Wakfields.
     
     Attributes
@@ -45,9 +45,9 @@ class ImpedanceModel(Element):
     
     Methods
     -------
-    add(wakefield_list, wakefiled_postions)
+    add(wakefield_list, wakefiled_positions)
         Add elements to the model.
-    add_multiple_elements(wakefield, wakefiled_postions)
+    add_multiple_elements(wakefield, wakefiled_positions)
         Add the same element at different locations to the model.
     sum_elements()
         Sum all WakeFields into self.sum.
@@ -63,14 +63,14 @@ class ImpedanceModel(Element):
         Plot the contributions of different kind of WakeFields.
     """
     
-    def __init__(self, ring, wakefield_list=None, wakefiled_postions=None):
+    def __init__(self, ring, wakefield_list=None, wakefiled_positions=None):
         self.ring = ring
         self.optics = self.ring.optics
         self.wakefields = []
         self.positions = np.array([])
         self.names = np.array([])
         self.sum_names = np.array([])
-        self.add(wakefield_list, wakefiled_postions)
+        self.add(wakefield_list, wakefiled_positions)
         
     def track(self, beam):
         """
@@ -152,7 +152,7 @@ class ImpedanceModel(Element):
         for name in self.names:
             self.sum_by_name(name)
                     
-    def add(self, wakefield_list, wakefiled_postions):
+    def add(self, wakefield_list, wakefiled_positions):
         """
         Add elements to the model.
 
@@ -160,19 +160,19 @@ class ImpedanceModel(Element):
         ----------
         wakefield_list : list of WakeField objects
             WakeFields to add to the model.
-        wakefiled_postions : list
+        wakefiled_positions : list
             Longitudinal positions corresponding to the added Wakfields.
         """
-        if (wakefield_list is not None) and (wakefiled_postions is not None):
+        if (wakefield_list is not None) and (wakefiled_positions is not None):
             for wakefield in wakefield_list:
                 self.wakefields.append(wakefield)
                 
-            for position in wakefiled_postions:
+            for position in wakefiled_positions:
                 self.positions = np.append(self.positions, position)
                 
         self.update_name_list()
                 
-    def add_multiple_elements(self, wakefield, wakefiled_postions):
+    def add_multiple_elements(self, wakefield, wakefiled_positions):
         """
         Add the same element at different locations to the model.
 
@@ -180,10 +180,10 @@ class ImpedanceModel(Element):
         ----------
         WakeField : WakeField object
             WakeField to add to the model.
-        wakefiled_postions : list
+        wakefiled_positions : list
             Longitudinal positions corresponding to the added Wakfield.
         """
-        for position in wakefiled_postions:
+        for position in wakefiled_positions:
             self.positions = np.append(self.positions, position)
             self.wakefields.append(wakefield)
             

collective_effects/instabilities.py

@@ -8,6 +8,7 @@ General calculations about instabilities
 import numpy as np
 import matplotlib.pyplot as plt
 from scipy.constants import c, m_e, e, pi, epsilon_0
+import math
 
 def mbi_threshold(ring, sigma, R, b):
     """
@@ -251,6 +252,105 @@ def plot_critical_mass(ring, bunch_charge, bunch_spacing, n_points=1e4):
     ax.set_xlabel("Longitudinal position [m]")
     
     return fig
+    
+def rwmbi_growth_rate(ring, current, beff, rho_material, plane='x'):
+    """
+    Compute the growth rate of the transverse coupled-bunch instability induced
+    by resistive wall impedance [1].
+
+    Parameters
+    ----------
+    ring : Synchrotron object
+    current : float
+        Total beam current in [A].
+    beff : float
+        Effective radius of the vacuum chamber in [m].
+    rho_material : float
+        Resistivity of the chamber's wall material in [Ohm.m].
+    plane : str, optional
+        The plane in which the instability will be computed. Use 'x' for the 
+        horizontal plane, and 'y' for the vertical.
+
+    Reference
+    ---------
+    [1] Eq. (31) in R. Nagaoka and K. L. F. Bane, "Collective effects in a
+    diffraction-limited storage ring", J. Synchrotron Rad. Vol 21, 2014. pp.937-960 
+
+    """
+    plane_dict = {'x':0, 'y':1}
+    index = plane_dict[plane]
+    beta0 = ring.optics.local_beta[index]
+    omega0 = ring.omega0
+    E0 = ring.E0
+    R = ring.L/(2*np.pi)
+    frac_tune, int_tune = math.modf(ring.tune[index])
+    Z0 = 377.7 # Vacuum impedance [Ohm]
+    
+    gr = (beta0*omega0*current*R) /(4*np.pi*E0*beff**3) * ((2*c*Z0*rho_material) / ((1-frac_tune)*omega0))**0.5
+    
+    return gr
+
+def rwmbi_threshold(ring, beff, rho_material, plane='x'):
+    """
+    Compute the threshold current of the transverse coupled-bunch instability 
+    induced by resistive wall impedance [1].
+
+    Parameters
+    ----------
+    ring : Synchrotron object
+    beff : float
+        Effective radius of the vacuum chamber in [m].
+    rho_material : float
+        Resistivity of the chamber's wall material in [Ohm.m].
+    plane : str, optional
+        The plane in which the instability will be computed. Use 'x' for the 
+        horizontal plane, and 'y' for the vertical.
+
+    Reference
+    ---------
+    [1] Eq. (32) in R. Nagaoka and K. L. F. Bane, "Collective effects in a
+    diffraction-limited storage ring", J. Synchrotron Rad. Vol 21, 2014. pp.937-960 
+
+    """
+    plane_dict = {'x':0, 'y':1}
+    index = plane_dict[plane]
+    beta0 = ring.optics.local_beta[index]
+    omega0 = ring.omega0
+    E0 = ring.E0
+    tau_rad = ring.tau[index]
+    frac_tune, int_tune = math.modf(ring.tune[index])
+    Z0 = 377.7 # Vacuum impedance [Ohm]
+    
+    Ith = (4*np.pi*E0*beff**3) / (c*beta0*tau_rad) * (((1-frac_tune)*omega0) / (2*c*Z0*rho_material))**0.5
+    
+    return Ith
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
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+    
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+    
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+    
     
     
     
\ No newline at end of file

tracking/wakepotential.py

@@ -703,7 +703,7 @@ class LongRangeResistiveWall(Element):
         of mass with respect to center of the RF bucket number 0 at turn j.
         Turn 0 corresponds to the tracked turn.
         
-        Postive time corresponds to past events and negative time to future 
+        Positive time corresponds to past events and negative time to future 
         events.
 
         Parameters