Update SP_Relativity.py with functions emit_geo and emit_norm which return the...

Update SP_Relativity.py with functions emit_geo and emit_norm which return the geometrical and normalized emittances

ess/SP_Relativity.py

 '''
 renamed variables not to have a variable with the same name as the fuction the variable is used within
 -- ME. 2018-07-23
+
+added geometrical and normalized emittance calculations
+-- ME. 2019-02-19
 '''
 from scipy import constants
 
@@ -127,3 +130,50 @@ def energy(gamma_beta, mass=proton_mass_in_MeV):
         e = mass * (-1 + 1 / (1 - gamma_beta ** 2) ** 0.5)
     return e
 
+def emit_geo(u_up_array):
+    '''
+    parameters
+    ----------
+    u_up_array: array like
+        a 2D array containing that has u_up_array[:,:2] as coordinates in u and u'
+        
+    returns
+    -------
+    geometrical emittance of the distribution/array in units of pi.mm.mrad
+    '''
+    u_shift = u_up_array[:,0]      #  x
+    up_shift = u_up_array[:,1]     #  x'
+    u = u_shift - np.average(u_shift)
+    up = up_shift - np.average(up_shift)
+    u2 = np.square(u)        #  x2
+    u2ave = np.average(u2)   # <x2> 
+    print(u2ave)
+    up2 = np.square(up)      #  x'2
+    up2ave = np.average(up2) # <x'2>
+    print(up2ave)
+    uup = np.multiply(u, up)      #  x.x'  
+    uupave = np.average(uup) # <x.x'>
+    uupave2 = uupave**2      # <x.x'>2
+    print(uupave2)
+    emit2 = (u2ave * up2ave) - uupave2
+    emit = np.sqrt(emit2)
+    return emit
+
+def emit_norm(u_up_array, gamma):
+    '''
+    parameters
+    ----------
+    u_up_array: array like
+        a 2D array containing that has u_up_array[:,:2] as coordinates in u and u'
+    gamma: float
+        relativistic gamma of the particles in the beam
+    returns
+    -------
+    normalized emittance of the distribution/array in units of pi.mm.mrad
+    '''
+    #from ess import SP_Relativity as spr
+    bt = spr.beta_from_gamma(gamma)
+    geo_emit = emit_geo(u_up_array)
+    emit = bt * gamma * geo_emit
+    return emit
+