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

tests/test_bunch.py

@@ -76,14 +76,14 @@ def test_bunch_emittance(demo_ring):
     mybunch = Bunch(demo_ring, mp_number=mp_number, current=current, 
                     track_alive=False)    
     mybunch.init_gaussian()
-    np.testing.assert_allclose(mybunch.emit[0], demo_ring.emit[0], rtol=0, atol=1e-13,
+    np.testing.assert_allclose(mybunch.emit[0], demo_ring.emit[0], rtol=0, atol=1e-10,
      err_msg=f'Emittances do not match. {demo_ring.emit[0]} initialised, {mybunch.emit[0]:} calculated')
-    np.testing.assert_allclose(mybunch.emit[1], demo_ring.emit[1], rtol=0, atol=1e-13,
+    np.testing.assert_allclose(mybunch.emit[1], demo_ring.emit[1], rtol=0, atol=1e-10,
      err_msg=f'Emittances do not match. {demo_ring.emit[1]} initialised, {mybunch.emit[1]:} calculated')
 
-    np.testing.assert_allclose(mybunch.emit[0], mybunch.cs_invariant[0]/2, rtol=0, atol=1e-13,
+    np.testing.assert_allclose(mybunch.emit[0], mybunch.cs_invariant[0]/2, rtol=0, atol=1e-10,
      err_msg=f'Emittances do not match. {mybunch.cs_invariant[0]/2} calculated with optics functions, {mybunch.emit[0]:} calculated with coordinates only')
-    np.testing.assert_allclose(mybunch.emit[1], mybunch.cs_invariant[1]/2, rtol=0, atol=1e-13,
+    np.testing.assert_allclose(mybunch.emit[1], mybunch.cs_invariant[1]/2, rtol=0, atol=1e-10,
      err_msg=f'Emittances do not match. {mybunch.cs_invariant[1]/2} calculated with optics functions, {mybunch.emit[1]:} calculated with coordinates only')
     
 
@@ -94,13 +94,13 @@ def test_bunch_emittance_with_dispersion(demo_ring):
     mybunch = Bunch(demo_ring, mp_number=mp_number, current=current, 
                     track_alive=False)    
     mybunch.init_gaussian()
-    np.testing.assert_allclose(mybunch.emit[0], demo_ring.emit[0], rtol=0, atol=1e-13,
+    np.testing.assert_allclose(mybunch.emit[0], demo_ring.emit[0], rtol=0, atol=1e-10,
      err_msg=f'Emittances do not match. {demo_ring.emit[0]} initialised, {mybunch.emit[0]:} calculated')
-    np.testing.assert_allclose(mybunch.emit[1], demo_ring.emit[1], rtol=0, atol=1e-13,
+    np.testing.assert_allclose(mybunch.emit[1], demo_ring.emit[1], rtol=0, atol=1e-10,
      err_msg=f'Emittances do not match. {demo_ring.emit[1]} initialised, {mybunch.emit[1]:} calculated')
 
-    np.testing.assert_allclose(mybunch.emit[0], mybunch.cs_invariant[0]/2, rtol=0, atol=1e-13,
+    np.testing.assert_allclose(mybunch.emit[0], mybunch.cs_invariant[0]/2, rtol=0, atol=1e-10,
      err_msg=f'Emittances do not match. {mybunch.cs_invariant[0]/2} calculated with optics functions, {mybunch.emit[0]:} calculated with coordinates only')
-    np.testing.assert_allclose(mybunch.emit[1], mybunch.cs_invariant[1]/2, rtol=0, atol=1e-13,
+    np.testing.assert_allclose(mybunch.emit[1], mybunch.cs_invariant[1]/2, rtol=0, atol=1e-10,
      err_msg=f'Emittances do not match. {mybunch.cs_invariant[1]/2} calculated with optics functions, {mybunch.emit[1]:} calculated with coordinates only')
     
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