is modeled with the galactic-center dipole field, where the field is penetrating the galactic plane, and is written as [@gkss10] $$\label{eq:Bp}
B_{{\rm p},z}(z) =\mu_{\rm p}(1-3(z/r)^2)/r^3,$$ where $r=(x^2+y^2+z^2)^{1/2}$. For Model 2, we set $\mu_{\rm p}$ to a value such that the strength $B_{{\rm p},z}(z)\sim 1.0~{\rm \mu G}$ around $(x,y)=(0,8.5)$ in kpc while it is absent for other models. The second parameter is the scale height of cosmic-ray electron density. The cosmic-ray electron density is written as [@sun08] $$\label{eq:Cp}
C(z) \propto C_0 \exp(-|z|/h_{\rm c}),$$ where $C_0=0.0001$ ${\rm cm^{-3}}$ and the scale height $h_{\rm c}=1$ kpc for Models 1, 2 and 4 and $3$ kpc for Model 3. The third parameter is the scale height of thermal electron density of the thick disk component, which is given by [@cl02] $$\label{eq:ne}
n_1(z) \propto n_1 {\rm sech^2}(z/h_1),$$ where $n_1=0.02$ ${\rm cm^{-3}}$ and the scale height $h_1=1$ kpc for Models 1, 2 and 3 and $3$ kpc for Model 4.

Result {#section:3}
======

Complexity of FDF {#subsection:3.1}
-----------------

In this subsection, we show some examples of FDFs of galaxies of Model 1. First, we calculate FDFs of a single grid in $x$-$y$ plane ($16~{\rm pc} \times 16~{\rm pc}$) which corresponds to a beam size of $0.3''\times 