def plutonium_to_time(pu, flux_average, phi_0, pu_0):
    """Approximate time in units of plutonium
    
    With the assumption that plutonium-per-unit-fluence is constant for 
    an average batch of fuel (one simulation), the total plutonium 
    over several subsequent batches is related to the operating time
    of the reactor via a linear equation.
    
    Parameters
    ----------
    pu : float
        Plutonium density in g cm-3.
    flux_average : float
        Average flux in the reactor in s-1 cm-2.
    phi_0 : float
        Fluence of an average batch in cm-2.
    pu_0 : float
        Plutonium density of an average batch in g cm-3.
    
    Returns
    -------
    t : float
        Total irradiation time in s.
    """
    t = pu * phi_0 / pu_0 / flux_average
    return t