Emittance calculation

Hello, There are a few changes that need to be verified. I've changed the way emittance is computed. For nonzero dispersion, it gives the correct results. When dispersion is included, I think the difference is minimal for realistic values. But I am not sure.

• Calculation of emittances and CS invariants for nonzero dispersion (based on PyHEADTAIL "cobra" functions)
• Different ion species data in impedance.ions

mbtrack2/tracking/particles.py

@@ -293,11 +293,13 @@ class Bunch:
         Return the average Courant-Snyder invariant of each plane.
 
         """
-        Jx = (self.ring.optics.local_gamma[0] * self['x']**2) + \
-              (2*self.ring.optics.local_alpha[0] * self['x'])*self['xp'] + \
+        xb = self['x'] - self['delta'] * self.ring.optics.local_dispersion[0]
+        yy = self['y'] - self['delta'] * self.ring.optics.local_dispersion[2]
+        Jx = (self.ring.optics.local_gamma[0] * xb**2) + \
+              (2*self.ring.optics.local_alpha[0] *xb)*self['xp'] + \
               (self.ring.optics.local_beta[0] * self['xp']**2)
-        Jy = (self.ring.optics.local_gamma[1] * self['y']**2) + \
-              (2*self.ring.optics.local_alpha[1] * self['y']*self['yp']) + \
+        Jy = (self.ring.optics.local_gamma[1] * yb**2) + \
+              (2*self.ring.optics.local_alpha[1] * yb*self['yp']) + \
               (self.ring.optics.local_beta[1] * self['yp']**2)
         Js = (self.ring.long_gamma * self['tau']**2) + \
               (2*self.ring.long_alpha * self['tau']*self['delta']) + \