On the Alfvén wave cut-off in partly ionized collisional plasmas

Abstract

The cut-off of the Alfvén wave, caused by plasma collisions with neutrals in multi-component partially ionized plasmas, is discussed. Full multi-component theory is used, and similarities and differences regarding the classic magnetohydrodynamic theory are presented. It is shown that the cut-off in partially ionized plasma in principle may remain the same as predicted in classic magnetohydrodynamic works, although multi-component theory also yields some essential differences. Due to electric field, the ion motion is intrinsically two-dimensional and this results in additional forced oscillations of neutrals. One new small parameter, containing the ion inertial length, appears in the multi-component theory. This new small parameter is missing in the magnetohydrodynamic description, and it turns out that for some parameters it may be greater than the ions-to-neutrals density ratio which is the only small parameter in the magnetohydrodynamic description. Due to this the Alfvén wave behavior can become much different as compared to classic magnetohydrodynamic results. It is shown also that in plasmas with unmagnetized ions, Alfvén waves cannot be excited. This by all means applies to the solar photosphere where the ion collision frequency may be far above the ion gyro-frequency.

Frozen-In Magnetic Field Lines and Alfvén Wave Generation in Weakly Ionized Plasma

“…According to Soler et al (2013), the results of Vranjes et al (2008) and Tsap, Stepanov, and Kopylova (2011) agree if we correctly specify the initial conditions. In particular, Tsap, Stepanov, and Kopylova (2011) took the equal initial velocities of ions in contrast to Vranjes et al (2008). Zaqarashvili, Khodachenko, and Soler (2013) suggested that the weak wave flux obtained by Vranjes et al (2008) might be caused by the weak magnetic field strength B adopted in this work.…”

“…However, Soler et al (2013) (see also Vranjes and Kono, 2014) again came to the conclusion, however, that the Alfvén flux may strongly depend on the initial velocity of ions. According to Soler et al (2013), the results of Vranjes et al (2008) and Tsap, Stepanov, and Kopylova (2011) agree if we correctly specify the initial conditions. In particular, Tsap, Stepanov, and Kopylova (2011) took the equal initial velocities of ions in contrast to Vranjes et al (2008).…”

“…In particular, Tsap, Stepanov, and Kopylova (2011) took the equal initial velocities of ions in contrast to Vranjes et al (2008). Zaqarashvili, Khodachenko, and Soler (2013) suggested that the weak wave flux obtained by Vranjes et al (2008) might be caused by the weak magnetic field strength B adopted in this work. They pointed out that the magnetic field B of the photospheric tubes is on the order of kG and not hundreds of G. This suggests that "Alfvén waves are excited inside flux tubes only, but not outside the tubes, where the magnetic field is relatively weak".…”

“…Following Vranjes et al (2008), Kopylova (2011), andSoler et al (2013) and using standard notation, we can write the linearized momentum equations for electrons (e), ions (i), and neutrals (a) of the hydrogen plasma −en e δE − en e c δv e × B = 0;…”

“…Therefore any indications concerning this problem have a great interest. Vranjes et al (2008) recently used the three-fluid equations and came to the conclusion that the energy flux of Alfvén waves in the photosphere F must be many orders of magnitude lower than its generally accepted value that follows from the well-known relation F = ρδv 2 v A /2, where ρ is the plasma density, δv is the amplitude of the transverse velocity, and v A is the Alfvén velocity. This is explained by the low degree of ionization of the photospheric plasma (∼ 10 −4 ).…”