[Fix] Typo for vacuum impedance

mbtrack2/instability/instabilities.py

@@ -5,7 +5,7 @@ General calculations about instability thresholds.
 
 import numpy as np
 import matplotlib.pyplot as plt
-from scipy.constants import c, m_e, e, pi, epsilon_0
+from scipy.constants import c, m_e, e, pi, epsilon_0, mu_0
 import math
 
 def mbi_threshold(ring, sigma, R, b):
@@ -308,7 +308,7 @@ def rwmbi_growth_rate(ring, current, beff, rho_material, plane='x'):
     E0 = ring.E0
     R = ring.L/(2*np.pi)
     frac_tune, int_tune = math.modf(ring.tune[index])
-    Z0 = 377.7 # Vacuum impedance [Ohm]
+    Z0 = mu_0*c
     
     gr = (beta0*omega0*current*R) /(4*np.pi*E0*beff**3) * ((2*c*Z0*rho_material) / ((1-frac_tune)*omega0))**0.5
     
@@ -343,7 +343,7 @@ def rwmbi_threshold(ring, beff, rho_material, plane='x'):
     E0 = ring.E0
     tau_rad = ring.tau[index]
     frac_tune, int_tune = math.modf(ring.tune[index])
-    Z0 = 377.7 # Vacuum impedance [Ohm]
+    Z0 = mu_0*c
     
     Ith = (4*np.pi*E0*beff**3) / (c*beta0*tau_rad) * (((1-frac_tune)*omega0) / (2*c*Z0*rho_material))**0.5