Transport equations

transportEqs.py

# impact parameter
def impact_param(temperature, ionization=1.0):
    """
    impact parameter for classical Coulomb collision ()
    default is electron species against ion with ionization = 1.0
    inputs:
    temperature (eV)
    ionization (dimless)
    """
    vel = vTh(temperature=temperature, species='e')
    param = ionization * plsmc.qe**2 / (4 * np.pi * plsmc.epsilon0 * plsmc.me * vel**2)
    return param

# Coulomb logarithm (dimless)
# note: need to change to 'ee', 'ie', and 'ii' species
def coul_log(temperature, density, ionization=1.0):
    """
    Coulomb logarithm (dimless)
    default is ionization 1.0
    inputs:
    temperature (eV)
    density (cm^-3)
    ionization (dimless)
    """
    dLength = debye_length(temperature=temperature, density=density)
    param = impact_param(temperature=temperature, ionization=ionization)
    cLog = np.log( dLength / param )
    return cLog

# collision frequency (Hz)
# need to adjust to accept electron and/or ion temperature in vThermal
# check that ee frequency is correct!
def coll_freq(density, temperature, ionization=1.0, species='ii', massIon=-1):
    """
    Collision frequency (Hz)
    default is ion-ion collisions with ionization 1.0
    inputs:
    density(cm^-3)
    temperature (eV)
    ionization (dimless)
    """
    density_conv = 1e6  # convert density from cm^-3 to m^-3
    if species == 'ii':
        param = impact_param(temperature=temperature, ionization=ionization)
        cLog = coul_log(temperature=temperature, density=density, 
                        ionization=ionization)
        vel = vTh(temperature=temperature, species='i', massIon=massIon)
        freq = density * density_conv * vel * 6 * np.pi * param**2 * cLog
    elif species == 'ee':
        param = impact_param(temperature=temperature, ionization=ionization)
        cLog = coul_log(temperature=temperature, density=density, 
                        ionization=ionization)
        vel = vTh(temperature=temperature, species='e')
        freq = density * density_conv * vel * 6 * np.pi * param**2 * cLog
    return freq

# mean free path (m)
# allow for inputing ion and electron temperature independently
# for now it's Te=Ti
def mfp(density, temperature, ionization=1.0, species='ii', massIon=-1):
    """
    Collisional mean free path (m)
    Default is ion-ion collision with ionization 1.0
    inputs:
    density (cm^-3)
    temperature (eV)
    ion mass (kg)
    """
    if species == 'ee':
        vel = vTh(temperature=temperature, species='e')
        freq = coll_freq(density, temperature, ionization=ionization,
                         species='ee')
        length = vel / freq
    elif species == 'ie':
        # !!! is it correct to only use electron thermal velocity here?
        vel = vTh(temperature=temperature, species='e')
        freq = coll_freq(density, temperature, ionization=ionization,
                         species='ii', massIon=massIon)
        temp_rat = 1.0
        length = vel / (freq * (massIon/(2*plsmc.me))**0.5 * (temp_rat)**(3.0/2.0))
    elif species == 'ii':
        vel = vTh(temperature=temperature, species='i', massIon=massIon)
        freq = coll_freq(density, temperature, ionization=ionization,
                         species='ii', massIon=massIon)
        length = vel / freq
    return length

# particle mobility in electric field (m^2/(V s))
def mobility(density, temperature, ionization=1.0, species='i', massIon=-1):
    """
    Electrical mobility (m^2/(V s))
    default is ion with ionization 1.0
    input:
    temperature (eV)
    density (cm^-3)
    ionization (dimless)
    ion mass (kg)
    """
    if species == 'e':
        freq = coll_freq(density, temperature, ionization=ionization,
                         species='ee')
        mob = plsmc.qe / (plsmc.me * freq)
    elif species == 'i':
        freq = coll_freq(density, temperature, ionization=ionization,
                         species='ii', massIon=massIon)
        mob = ionization * plsmc.qe / (massIon * freq)
    return mob

# Knudsen number
def knudsen(density, temperature, length, ionization=1.0, species='ee', massIon=-1):
    """
    Knudsen number (dimless)
    default species is e-e with ionization 1.0
    inputs:
    density (cm^-3)
    temperature (eV)
    ionization (dimless)
    characteristic length (m)
    ion mass (kg)
    """
    if species == 'ee':
        path = mfp(density=density, temperature=temperature,
                   ionization=ionization, species='ee')
        kn = path / length
    elif species == 'ie':
        path = mfp(density=density, temperature=temperature,
                   ionization=ionization, species='ie', massIon=massIon)
        kn = path / length
    elif species == 'ii':
        path = mfp(density=density, temperature=temperature,
                   ionization=ionization, species='ii', massIon=massIon)
        kn = path / length
    return kn