def J_p(Ep, norm=1.0, alpha=2.0):
    """
    Defines the particle distribution of the protons as a power law.

    Parameters
    ----------
    - Ep = E_proton (GeV)
    - alpha = slope
    - norm = the normalization (at 1 GeV) in units of cm^-3 GeV-1

    Outputs
    --------
    - The particle distribution in units of 1/GeV/cm^-3
    """

    return norm*(Ep/1.0)**(-alpha)