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/instability/ions.py

@@ -31,7 +31,7 @@ def ion_cross_section(ring, ion):
     by a relativistic electron using the relativistic Bethe asymptotic formula
     [1].
 
-    Values of M02 and C02 from [2] and [3] (values of constants are independent of beam energy).
+    Values of M02 and C02 from [2-4] (values of constants are independent of beam energy).
 
     Parameters
     ----------
@@ -52,6 +52,9 @@ def ion_cross_section(ring, ion):
     [2] : P. F. Tavares, "Bremsstrahlung detection of ions trapped in the EPA
     electron beam", Part. Accel. 43 (1993).
     [3] : A. G. Mathewson, S. Zhang, "Beam-gas ionisation cross sections at 7.0 TEV", CERN Tech. rep. Vacuum-Technical-Note-96-01. https://cds.cern.ch/record/1489148/
+    [4] : F. Rieke and W. Prepejchal, "Ionization Cross Sections of Gaseous 
+    Atoms and Molecules for High-Energy Electrons and Positrons", 
+    Phys. Rev. A 6, 1507 (1972).
 
     """
     if ion == "CO":
@@ -66,6 +69,9 @@ def ion_cross_section(ring, ion):
     elif ion == "CH4":
         M02 = 4.23
         C0 = 42.85
+    elif ion == "H20":
+        M02 = 3.24
+        C0 = 32.26
     else:
         raise NotImplementedError
 
@@ -235,6 +241,10 @@ def fast_beam_ion(
         A = 28
     elif ion == "H2":
         A = 2
+    elif ion == "H2O":
+        A = 16
+    elif ion == "CO2":
+        A = 44
 
     sigma_i = ion_cross_section(ring, ion)