def sigma_t(iso, T=300.0, E_g=None, E_n=None, phi_n=None):
"""Calculates the total neutron cross-section for an isotope.
.. math::
\\sigma_{s, g} = \\sum_{h} \\sigma_{s, g\\to h}
Args:
* iso (int or str): An isotope to calculate the total cross-section for.
Keyword Args:
If any of these are None-valued, values from the cache are used.
* T (float): Tempurature of the target material [kelvin].
* E_g (sequence of floats): New, lower fidelity energy group structure [MeV]
that is of length G+1. Ordered from lowest-to-highest energy.
* E_n (sequence of floats): higher resolution energy group structure [MeV]
that is of length N+1. Ordered from lowest-to-highest energy.
* phi_n (sequence of floats): The high-fidelity flux [n/cm^2/s] to collapse the fission
cross-section over. Length N. Ordered from lowest-to-highest energy.
Returns:
* sig_t_g (numpy array): A numpy array of the total cross-section.
"""
# Ensure that the low-fidelity group structure is in the cache
if E_n is not None:
xs_cache['E_n'] = E_n
if E_g is not None:
xs_cache['E_g'] = E_g
if phi_n is not None:
xs_cache['phi_n'] = phi_n
# Get the total XS
iso_zz = isoname.mixed_2_zzaaam(iso)
sigma_a_g_iso_zz = 'sigma_a_g_{0}'.format(iso_zz)
sigma_s_g_iso_zz_T = 'sigma_t_g_{0}_{1}'.format(iso_zz, T)
sigma_t_g_iso_zz_T = 'sigma_t_g_{0}_{1}'.format(iso_zz, T)
# Don't recalculate anything if you don't have to
if sigma_t_g_iso_zz_T in xs_cache:
return xs_cache[sigma_t_g_iso_zz_T]
# This calculation requires the abosorption cross-section
if sigma_a_g_iso_zz not in xs_cache:
xs_cache[sigma_a_g_iso_zz] = sigma_a(iso, E_g, E_n, phi_n)
# This calculation requires the scattering cross-section
if sigma_s_g_iso_zz_T not in xs_cache:
xs_cache[sigma_s_g_iso_zz_T] = sigma_s(iso, T, E_g, E_n, phi_n)
# Sum over all h indeces
sig_t_g = xs_cache[sigma_a_g_iso_zz] + xs_cache[sigma_s_g_iso_zz_T]
# Put this value back into the cache, with the appropriate label
xs_cache[sigma_t_g_iso_zz_T] = sig_t_g
return sig_t_g
def sigma_reaction(iso, rx, E_g=None, E_n=None, phi_n=None):
"""Calculates the neutron absorption reaction cross-section for an isotope for a new, lower resolution
group structure using a higher fidelity flux. Note that g indexes G, n indexes N, and G < N.
Note: This always pulls the absorption reaction cross-section out of the nuc_data library.
Args:
* iso (int or str): An isotope to calculate the absorption cross-section for.
* rx (str): Reaction key. ('gamma', 'alpha', 'p', etc.)
Keyword Args:
If any of these are None-valued, values from the cache are used.
* E_g (sequence of floats): New, lower fidelity energy group structure [MeV]
that is of length G+1. Ordered from lowest-to-highest energy.
* E_n (sequence of floats): higher resolution energy group structure [MeV]
that is of length N+1. Ordered from lowest-to-highest energy.
* phi_n (sequence of floats): The high-fidelity flux [n/cm^2/s] to collapse the fission
cross-section over. Length N. Ordered from lowest-to-highest energy.
Returns:
* sigma_rx_g (numpy array): A numpy array of the collapsed absorption cross-section.
"""
# Ensure that the low-fidelity group structure is in the cache
if E_n is not None:
xs_cache['E_n'] = E_n
if E_g is not None:
xs_cache['E_g'] = E_g
if phi_n is not None:
xs_cache['phi_n'] = phi_n
# Get the absorption XS
iso_zz = isoname.mixed_2_zzaaam(iso)
sigma_rx_n_iso_zz = 'sigma_rx_{1}_n_{0}'.format(iso_zz, rx)
sigma_rx_g_iso_zz = 'sigma_rx_{1}_g_{0}'.format(iso_zz, rx)
# Don't recalculate anything if you don't have to
if sigma_rx_g_iso_zz in xs_cache:
return xs_cache[sigma_rx_g_iso_zz]
else:
sigma_rx_n = xs_cache[sigma_rx_n_iso_zz]
# Perform the group collapse, knowing that the right data is in the cache
sigma_rx_g = partial_group_collapse(sigma_rx_n)
# Put this value back into the cache, with the appropriate label
xs_cache[sigma_rx_g_iso_zz] = sigma_rx_g
return sigma_rx_g
def convolve_initial_fuel_form(stream, chem_form):
"""Convolves a heavy metal mass stream with a chemical form. The chemical
form is a dictionary that should have an "IHM" key, whose value gets replaced
with the fuel mass stream in the resultant isovec.
Args:
* `stream` (MassStream [see bright]): An initial heavy metal mass stream.
* `chem_form` (dict): The chemical form of the fuel. For instance UOX
would be represented by ``{80160: 2.0, "IHM": 1.0}`` while a metal fuel
would simply be ``{"IHM": 1.0}``.
Returns:
* `isovec` (dict): Normalized, mass-weighted isotopic vector of the initial fuel form.
* `AW` (float): Atomic weight of the fuel mass stream (ie, just the IHM).
* `MW` (float): Molecular weight of the chemical form after the fuel stream has been
inserted into it. This should always be greater than or equal to AW.
"""
AW = stream.atomic_weight()
# Calculate the MW
if "IHM" not in chem_form:
raise KeyError("The fuel chemical form must contain the key 'IHM'.")
MW = 0.0
for key in chem_form:
if key == "IHM":
MW += chem_form[key] * AW
else:
key_aw = isoname.nuc_weight(key)
MW += chem_form[key] * key_aw
AW_over_MW = AW / MW
# Calculate the isotopic vector
isovec = {}
for key in chem_form:
if key == "IHM":
comp = stream.comp
for iso in comp:
isovec[iso] = comp[iso] * AW_over_MW
else:
key_zz = isoname.mixed_2_zzaaam(key)
key_aw = isoname.nuc_weight_zzaaam(key_zz)
isovec[key_zz] = chem_form[key] * key_aw / MW
return isovec, AW, MW
def nist_2_zzaaam(nist_iso):
"""Converts a NIST style isotope to a zzaaam style.
Args:
* nist_iso (str): A nist isotope.
Returns:
* iso_zz (int): a zzaaam isotope.
"""
m = re.match(nist_iso_pattern, nist_iso)
if m.group(1) == "":
elem = m.group(2).upper()
iso_zz = isoname.LLzz[elem] * 10000
else:
iso_zz = isoname.mixed_2_zzaaam(m.group(2) + m.group(1))
return iso_zz
def cell_power(Material, SpecificPower, CellVolume, Density):
"""Calculates the power from a given unit cell.
Args:
* `Material` (dict): Normalized material dictionary; e.g. UOX, Metal (weight fraction, NOT atom fraction).
* `SpecificPower` (float): Specific power of material [MW / kgIHM].
* `CellVolume` (float): Unit cell volume that material occupies [cm^3].
* `Density` (float): Density of material [g / cm^3].
Returns:
* `Power` (float): The power coming from this fuel cell [MW].
"""
WeightFracIHM = 0.0
for iso in Material.keys():
if not ( isoname.zzLL[ isoname.mixed_2_zzaaam(iso)/10000 ] in isoname.ACT ):
continue
WeightFracIHM = WeightFracIHM + Material[iso]
return SpecificPower * (10.0**-3) * Density * WeightFracIHM * CellVolume
def test_mixed_2_zzaaam(self):
assert_equal(isoname.mixed_2_zzaaam(20040), 20040)
assert_equal(isoname.mixed_2_zzaaam("PU239"), 942390)
assert_equal(isoname.mixed_2_zzaaam(95642), 952421)
def chi(iso, E_g=None, E_n=None, phi_n=None):
"""Calculates the neutron fission energy spectrum for an isotope for a new, lower resolution
group structure using a higher fidelity flux. Note that g indexes G, n indexes N, and G < N.
Args:
* iso (int or str): An isotope to calculate the fission energy spectrum for.
Keyword Args:
If any of these are None-valued, values from the cache are used.
* E_g (sequence of floats): New, lower fidelity energy group structure [MeV]
that is of length G+1. Ordered from lowest-to-highest energy.
* E_n (sequence of floats): higher resolution energy group structure [MeV]
that is of length N+1. Ordered from lowest-to-highest energy.
* phi_n (sequence of floats): The high-fidelity flux [n/cm^2/s] to collapse the fission
cross-section over. Length N. Ordered from lowest-to-highest energy.
Returns:
* chi_g (numpy array): A numpy array of the fission energy spectrum.
"""
# Ensure that the low-fidelity group structure is in the cache
if E_n is not None:
xs_cache['E_n'] = E_n
if E_g is not None:
xs_cache['E_g'] = E_g
if phi_n is not None:
xs_cache['phi_n'] = phi_n
# Get the fission XS
iso_zz = isoname.mixed_2_zzaaam(iso)
chi_g_iso_zz = 'chi_g_{0}'.format(iso_zz)
# Don't recalculate anything if you don't have to
if chi_g_iso_zz in xs_cache:
return xs_cache[chi_g_iso_zz]
# Get the the set of isotopes we know we need chi for.
if 'fissionable_isos' not in xs_cache:
with tb.openFile(nuc_data, 'r') as f:
fi = set(f.root.neutron.xs_mg.fission.cols.iso_zz)
xs_cache['fissionable_isos'] = fi
fissionable_isos = xs_cache['fissionable_isos']
if (iso_zz not in fissionable_isos) and (86 <= iso_zz/10000):
fissionable_isos.add(iso_zz)
# Perform the group collapse on a continuous chi
nE = 101
G = len(xs_cache['E_g']) - 1
chi_g = np.zeros(G, dtype=float)
if (iso_zz in fissionable_isos):
for g in range(G):
E_space = np.logspace(np.log10(xs_cache['E_g'][g]), np.log10(xs_cache['E_g'][g+1]), nE)
dnumer = _chi(E_space)
numer = integrate.trapz(dnumer, E_space)
denom = (xs_cache['E_g'][g+1] - xs_cache['E_g'][g])
chi_g[g] = (numer / denom)
# renormalize chi
chi_g = chi_g / chi_g.sum()
# Put this value back into the cache, with the appropriate label
xs_cache[chi_g_iso_zz] = chi_g
return chi_g
def sigma_s_gh(iso, T, E_g=None, E_n=None, phi_n=None):
"""Calculates the neutron scattering cross-section kernel for an isotope for a new, lower resolution
group structure using a higher fidelity flux. Note that g, h index G, n indexes N, and G < N.
g is for the incident energy and h is for the exiting energy.
.. math::
\\sigma_{s, g\\to h} = \\frac{\\int_{E_g}^{E_{g+1}} \\int_{E_h}^{E_{h+1}} \\sigma_s(E) P(E \\to E^\\prime) \\phi(E) dE^\\prime dE}
{\\int_{E_g}^{E_{g+1}} \\phi(E) dE}
Note: This always pulls the scattering length out of the nuc_data library.
Args:
* iso (int or str): An isotope to calculate the fission cross-section for.
* T (float): Tempurature of the target material [kelvin].
Keyword Args:
If any of these are None-valued, values from the cache are used.
* E_g (sequence of floats): New, lower fidelity energy group structure [MeV]
that is of length G+1. Ordered from lowest-to-highest energy.
* E_n (sequence of floats): higher resolution energy group structure [MeV]
that is of length N+1. Ordered from lowest-to-highest energy.
* phi_n (sequence of floats): The high-fidelity flux [n/cm^2/s] to collapse the fission
cross-section over. Length N. Ordered from lowest-to-highest energy.
Returns:
* sig_s_gh (numpy array): A numpy array of the scattering kernel.
"""
# Ensure that the low-fidelity group structure is in the cache
if E_n is not None:
xs_cache['E_n'] = E_n
if E_g is not None:
xs_cache['E_g'] = E_g
if phi_n is not None:
xs_cache['phi_n'] = phi_n
# Get the fission XS
iso_zz = isoname.mixed_2_zzaaam(iso)
sigma_s_gh_iso_zz_T = 'sigma_s_gh_{0}_{1}'.format(iso_zz, T)
# Don't recalculate anything if you don't have to
if sigma_s_gh_iso_zz_T in xs_cache:
return xs_cache[sigma_s_gh_iso_zz_T]
# Get some needed data
G = len(xs_cache['E_g']) - 1
b = xs_cache['b_{0}'.format(iso_zz)]
M_A = xs_cache['M_A_{0}'.format(iso_zz)]
# Initialize the scattering kernel
sig_s_gh = np.zeros((G, G), dtype=float)
# Calculate all values of the kernel
for g, h in product(range(G), range(G)):
# Numerator inetgration term
dnumer = lambda _E_prime, _E: sigma_s_E(_E, b, M_A, T) * P(_E, _E_prime, M_A, T) * xs_cache['phi_g'][g]
# Integral
nE = 26
E_space = np.logspace(np.log10(xs_cache['E_g'][g]), np.log10(xs_cache['E_g'][g+1]), nE)
E_prime_space = np.logspace(np.log10(xs_cache['E_g'][h]), np.log10(xs_cache['E_g'][h+1]), nE)
numer = msmintegrate.dbltrapz(dnumer, E_space, E_prime_space)
# Denominator term, analytically integrated
denom = xs_cache['phi_g'][g] * (xs_cache['E_g'][g+1] - xs_cache['E_g'][g])
# Cross section value
sig_s_gh[g, h] = numer / denom
# Put this value back into the cache, with the appropriate label
xs_cache[sigma_s_gh_iso_zz_T] = sig_s_gh
return sig_s_gh
