[#85] Created function to calculate Natural broadening

aurora/line_broaden.py

@@ -99,7 +99,7 @@ def _get_Doppler(
         np.sqrt(2.0 * (dphysics['Ti_eV'] * cnt.e) / mass)
         / cnt. c
         * (cnt.c / wave_A)
-        ) # [Hz], dim(trs,)
+        ) # [m/AA * Hz], dim(trs,)
 
     # set a variable delta lambda based on the width of the broadening
     _dlam_A = wave_A**2 / cnt.c * dnu_g * 5  # [AA], dim(trs,), 5 standard deviations
@@ -156,4 +156,104 @@ def _get_Doppler(
     #        spec[typ] += comp
     #        spec_tot += comp
     #
-    #return line_shape
+    #return line_shape
+
+def _get_Natural(
+    # Settings
+    dphysics=None,
+    # ADF15 file
+    wave_A=None,
+    ):
+    '''
+    INPUTS: dphysics -- [dict], necessary physics information
+                NOTE: The expected form is keys for each central
+                wavelength of interst with its associated Einstein
+                coefficient as a float. This is so that a user won't
+                need to provide a data for every transition in the
+                ADF15 file.
+
+                !!! It is assumed you know, at least very closely,
+                the exact wavelength stored in your ADF15 file
+
+                i.e., If one wishes to explore the impact of Natural
+                broadening on the w, x, y, z lines for He-like Kr, the
+                input dictionary would look like --
+                dphysics = {
+                    '0.9454': 1.529e15, # [1/s], w line
+                    '0.9471': 9.327e10, # [1/s], x line
+                    '0.9518': 3.945e14, # [1/s], y line
+                    '0.9552': 5.715e9,  # [1/s], z line
+                    }
+
+            wave_A -- [list], dim(trs,), [AA], 
+                transition central wavelength
+
+    OUTPUTS: [dict], line shape
+                i) 'lam_profs_A' -- [AA], dim(trs,nlamb), 
+                        wavelength mesh for each transition
+                ii) 'theta' -- [1/AA], dim(trs, nlamb),
+                        line shape for each transition
+
+
+    '''
+
+    # Initializes output
+    lams_profs_A = np.zeros((len(wave_A), 100)) # [AA], dim(trs, nlamb)
+    theta = np.zeros((len(wave_A), 100)) # [1/AA], dim(trs, nlamb)
+
+    # Tolerance on wavelength match
+    tol = 1e-4 # [AA]
+
+    # Loop over transitions of interest
+    for lmb in dphysics.keys():
+        # Finds transitions of interst in ADF15 file
+        ind = np.where(
+            (wave_A >= lmb -tol)
+            & (wave_A <= lamb+tol)
+            )[0]
+
+        # Error check
+        if len(ind) == 0:
+            print('NO TRANSITION FOUND FOR LAMBDA= '+str(lmb))
+            continue
+
+        # Characteristic time for transitions
+        tau = 2/dphysics[lmb] # [s]
+
+        # FWHM
+        dnu = 1/(np.pi*tau) # [Hz]
+
+        # Loop over transitions
+        for ii in ind:
+            # set a variable delta lambda based on the width of the broadening
+            _dlam_A = (
+                wave_A[ii]**2 / (cnt.c*1e10) 
+                * dnu * 5  
+                )# [AA], dim(trs,), 5 standard deviations
+
+            # Wavelength mesh
+            lams_profs_A[ii,:] = np.linspace(
+                wave_A[ii] - _dlam_A, 
+                wave_A[ii] + _dlam_A, 
+                100) # [AA], dim(,nlamb)
+
+            # Lorentz profile
+            theta[ii,:] = 1/(
+                1+ (
+                    (1/lam_profs_A[ii,:] - 1/ wave_A[ii])
+                    * cnt.c*1e10
+                    * 2*np.pi*tau
+                    )**2
+                ) # [], dim(,nlamb)
+
+            # Normalization
+            theta[ii,:] *= 2* tau # [1/Hz]
+
+            # Fixes units
+            theta[ii,:] *= (cnt.c*1e10)/wave_A[ii]**2 # [1/AA]
+
+    # Output line shape and wavelength mesh
+    return {
+        'lams_profs_A': lams_profs_A,   # [AA], dim(trs,nlamb)
+        'theta': theta,                 # [1/AA], dim(trs,nlamb)
+        }