We employ the fluid wave simulation model which has been developed by Kim and Lee (2003). Similar to previous wave simulations (Kim et al., 2008), the background magnetic field *B*_{0} and the electron density *N*_{e} are assumed to be constants with *N*_{e} = 3 cm^{−3}, and *B*_{0} = 86 nT at Mercury. The ambient magnetic field, **B**_{0}, lies in the *z* direction and the inhomogeneity is introduced in the *x* direction. Since the Mercury’s magnetopause is located near 1.4 R_{
m
} (Anderson et al., 2011), we assumed a shorter radial distance of 1 R_{
m
} than the magnetopause location in *x* direction, where R_{
m
} is the Mercury’s radius. To save computing time, electron mass is assumed to be *m*_{e} = *m*_{
H
}/100. We limit ourselves to harmonic variations in the *y* and *z* and all waves are proportional to exp(*ik*_{
y
}*y*+*ik*_{
z
}*z*), where *k*_{
y
} and *k*_{
z
} are the given *y* and *z* direction wavenumbers. For simplicity, *k*_{
y
} is assumed to be 0 and *k*_{
z
} = 2*π*/*L*_{
z
}, where *L*_{
z
} = 1 R_{
m
}, which is similar to the field line length of *L*_{
z
} = 0.93 at *L* = 1.5 in dipole coordinate. The simulation is driven by imposing an impulse in *E*_{
y
} at *X* =0 during the interval 0 ≤ *τ* ≤ 2, where *X* = *x*/*L*_{
x
}, *τ* = *t*/*t*_{ci}, and *t*_{ci} = 2*π*/*ω*_{ci}. The simulation is run from *τ* = 0–60 and the boundaries become perfect reflectors after the impulsive stimulus ends (*τ* = 2), thus the total energy in the box model will remain constant in time after this interval.

Because H^{+} and He^{+} are major ions at Mercury (Zurbuchen et al., 2008, 2011) and waves near the He^{2+} gy-rofrequency are observed (Boardsen et al., 2009a, b), we adopt an electron-H^{+}-He^{2+}-He^{+} plasma and the electron density is also assumed to be sum of the ion densities. For simplicity, the He^{2+} density ratio to electron density (*η*He2 = *N*_{He2}/*N*_{e}) is assumed to be 0.025, however, in order to see the multi-ion effects easily, we assume decreasing He^{+} density ratio in space. Figure 1(a) shows the ion density ratio to electron density (*η*_{ion} = *N*_{ion}/*N*_{e}) profile. We assumed the H^{+} density ratio (*η*H) increases from 0 at *X* = 0 to 0.95 at *X* = 1 while He^{+} density (*η*He) decreases from 0.95 to 0. Using this profile, we calculate the normalized critical frequencies to *ω*_{ci} (Ω = *ω*/*ω*_{ci}), such as cutoffs Ω_{L(R)} (where ) and ion-ion hybrid (and Alfvén) resonances (Ω_{ii} and Ω_{
A
}) frequencies. These frequencies are plotted in Fig. 1(b) and shaded regions represent frequency stop-bands where waves are evanescent. Different from the two-ion case predicted by Kim et al. (2008), the IIH resonance modes in between the proton and heaviest ion gyrofrequencies split into the two branches of Ω_{ii−1} (where ) and Ω_{ii −2} (where ). Here, Ω_{ii −1} decreases from 1 to 0.527 and Ω_{ii −2} decreases from 0.486 to 0.312. When the impulsive input is excited at *X* =0, most waves in these resonance frequency ranges encounter the resonance location without cutoffs. In this case, the maximum absorption can increase up to 100% (Lee et al., 2008; Kim et al., 2011). However, below most waves except between the local cutoff of Ω_{R} = 0.124 and resonance frequency of Ω = 0.143 at *X* = 0 cannot propagate toward the resonances. Therefore, if the wave power is not enough large to penetrate the wave stop gap, the mode conversion at the Alfvén resonance does not occur.

We store time histories of the electromagnetic fields at each grid point in *X* during the simulation running time of 0 < *τ* < 60 and obtain the wave power spectra through the fast Fourier transform. Figure 2 shows the wave spectra of (a) *B*_{
x
} (radial component), which is and (b) *B*_{
y
} (azimuthal component).

In this figure, harmonics of the global cavity modes appear in both components near Ω = 0.14 which is in between Ω_{
L
} < Ω < Ω_{
A
}, and Ω = 0.32, 0.38, and 0.51 which are larger than the local Ω_{
R
}. In contrast with the global cavity wave modes, the continuous spectrum appears only in azimuthal component of *B*_{
y
}. For , there are two continuous bands whose frequencies decrease with increasing *X*. These continuous spectrum are impulsively excited by the broadband compressional source at *X* = 0 and corresponds to the IIH resonant conditions of Ω_{ii−1} and Ω_{ii−2}. For , power enhancement of *B*_{
y
} only occurs at Ω = 0.14 near *X* = 0. This mode is associated with Alfvén resonance. Different to Ω_{ii−1} and Ω_{ii−2}, most waves in the frequency range of Ω_{
A
} at *X* = 0 cannot propagate into the simulation domain as shown in Fig. 1(b) but some wave energy can directly reach Ω_{
A
} near *X* = 0.

Figure 2 also shows that each resonant wave mode branches have different power at different locations. Resonant waves at Ω_{ii−1} have strong power in wide range 0 ≤ *X* ≤ 0.95, while waves at Ω_{ii−2} are strong for 0.6 ≤ *X* ≤ 0.85 but weak for 0 ≤ *X* < 0.6. Moreover, the Alfvén resonance mode (Ω_{
A
}) occurs only near *X* ≈ 0. Therefore, single or multiple frequencies of mode-converted wave can be detected at certain locations. For instance, two mode-converted waves can be detected at *X* = 0.06 (Ω_{high} = Ω_{ii−1} ≈ 0.93 and Ω_{low} = Ω_{
A
} ≈ 0.16) and *X* = 0.7 (Ω_{high} = Ω_{ii−1} ≈ 0.57 and Ω_{low} = Ω_{ii−2} ≈ 0.44) while a single frequency of mode-converted wave (Ω_{high} = Ω_{ii−1} ≈ 0.8) can be observed at *X* = 0.2 (these frequencies are marked as open circles in Fig. 2(b)). In order to examine the coupling properties, we plot the time histories of *B*_{
x
} and *B*_{
y
} in Fig. 3, which are obtained using the inverse Fourier transforms. In this figure, the first and second panels are wave time histories of higher (Ω_{high}) and lower frequencies (Ω_{low}) of magnetic azimuthal component (*B*_{
y
}) at (a) *X* = 0.06, (b) 0.2, and (c) 0.7, respectively. We also plot the wave time histories of the azimuthal (*B*_{
y
}) and radial (*B*_{
x
}) components in the third and fourth panels of Fig. 3 that show superposition of two resonant waves of Ω_{high} and Ω_{low}. However, because only one resonant wave mode is dominant at *X* = 0.2, the second panel is remained as blank.

Similar to the previous multi-ion simulation study by Kim et al. (2008), wave azimuthal components with single frequency grow in time as shown in the first and second panels of Fig. 3. When mode-converted waves contain two different frequencies, waves can show modulation of the amplitude in time. For *X* = 0.06, because frequency ratio of two resonant waves Ω_{high}/ Ω_{low} is 6.27 and the amplitude of Ω_{low} is greater than Ω_{high}, wave amplitude beating is not significantly appeared in the third panel. Different to case of *X* = 0.06, for *X* = 0.7 in Fig. 3(c), Ω_{high}/Ω_{low} = 1.31 and the wave amplitudes are similar for both frequencies, therefore, the amplitude beating in time is clearly shown in the third panel of Fig. 3(c). In this case, when two wave amplitudes are assumed to be the same and constant in time, the beat period *T*_{beat} can be approximated to be 1/(ΔΩ) ≈ 7.7, which is consistent with the simulation results. In contrast to the increase of the azimuthal component (*B*_{
y
}), the radial component (*B*_{
x
}) damps for two mode-converted waves (fourth panels in Figs. 3(a) and (c)) and for a single mode (Fig. 3(b)). When there are two mode-converted waves appeared at the same location in Fig. 3(a) and (c), *B*_{
x
} also show wave amplitude beating with damping in time.