def set_hydro_num(self, T, ndens):
"""Sets the matrix of momentum relaxation collsion rates formulated
in the above reference for a system described by hydrodynamics, i.e.
only a single temperature is avaliable.
Parameters
----------
T : float
System temperature in units of energy/kb
ndens : (N,) np.ndarray
Number density of each ion species in units of 1/length^{3}.
"""
leff = get_leff(T, T, self.zsolver.zbars, ndens, self.cd, o=self.o)
#set each upper triangular nu to g
for i in range(ndens.shape[0]):
for j in range(i, ndens.shape[0]):
self.nu[i, j] = self.zsolver.zbars[i]*self.zsolver.zbars[j]
self.nu[i,j] = self.nu[i,j]*self.cd['e']*self.cd['e']
self.nu[i,j] = self.cd['kc']*self.nu[i,j]/leff/(self.cd['kb']*T)
self.nu = 128.0*np.pi*np.pi*get_calk(1, 1, self.nu)/3.0/np.power(2*np.pi, 1.5)
#set each lower triangular element to its upper triangular equivalent
for i in range(ndens.shape[0]):
for j in range(i, ndens.shape[0]):
self.nu[i,j] = self.nu[i,j]*np.power(self.zsolver.zbars[i]*\
self.zsolver.zbars[j]*self.cd['e']*self.cd['e'], 2.0)
self.nu[i,j] = self.nu[i,j]*np.sqrt(self.mass[i]*self.mass[j])
self.nu[i,j] = self.nu[i,j]/np.sqrt((self.mass[i] + self.mass[j]))
self.nu[i,j] = ndens[i]*ndens[j]*self.nu[i,j]
self.nu[i,j] = self.nu[i,j]/np.power(self.cd['kb']*T, 1.5)
self.nu[j,i] = self.nu[i,j]
for i in range(ndens.shape[0]):
self.nu[i, :] = self.cd['kc']*self.cd['kc']*self.nu[i, :]/(self.mass[i]*ndens[i])
def get_kinetic_num(Te, T, Zbar, ndens, mass, cd, o=3):
"""Returns the matrix of momentum relaxation collsion rates formulated
in the above reference for a system described by kinetics, i.e.
each ion species has its own temperature.
Parameters
----------
Te : float
System electron temperature.
T : (N,) np.ndarray
System ion temperatures in units of energy/kb
Zbar : (N,) np.ndarray
The effective charge of each ion species in units of electron
charge.
ndens : (N,) np.ndarray
Number density of each ion species in units of 1/length^{3}.
cd : dict
A dictionary holding all of the fundamental constants in the same
units as the other input args (`ndens`, `T`, `masses`). Must have
the following keys: na, kb, e, g, hbar, c, kc, me, mp.
mass : (N,) np.ndarray
Mass of each species.
o : {3, 1, 2}, optional
Order of approximation to use. 1->appx with max 2.5% relative error,
2->appx with max 1.1% relative error, and 3->'exact' (with fermi
integral fits).
Returns
-------
nu : (N, N) np.ndarray
The collision frequencies between each species.
"""
leff = get_leff(Te, T, Zbar, ndens, cd, o=o)
nu = np.zeros((ndens.shape[0], ndens.shape[0]), dtype=ndens.dtype)
#set each upper triangular nu to g
for i in range(ndens.shape[0]):
for j in range(i, ndens.shape[0]):
nu[i,
j] = Zbar[i] * Zbar[j] * cd['e'] * cd['e'] * (mass[i] + mass[j])
nu[i, j] = nu[i, j] / leff / (cd['kb'] *
(mass[i] * T[j] + mass[j] * T[i]))
nu = 128.0 * np.pi * np.pi * get_calk(1, 1, nu) / 3.0 / np.power(
2 * np.pi, 1.5)
#set each lower triangular element to its upper triangular equivalent
for i in range(ndens.shape[0]):
for j in range(i, ndens.shape[0]):
nu[i, j] = nu[i, j] * np.power(
Zbar[i] * Zbar[j] * cd['e'] * cd['e'], 2.0)
nu[i,
j] = nu[i, j] * np.sqrt(mass[i] * mass[j]) * (mass[i] + mass[j])
nu[i, j] = ndens[i] * ndens[j] * nu[i, j]
nu[i, j] = nu[i, j] / np.power(
cd['kb'] * (mass[i] * T[j] + mass[j] * T[i]), 1.5)
nu[j, i] = nu[i, j]
for i in range(ndens.shape[0]):
nu[i, :] = nu[i, :] / (mass[i] * ndens[i])
return nu