1.7 Waves in question in this thesis
1.7.1 Ion acoustic waves
ion temperature is lesser than 1. In a series of papers, Backrud et al. (2004, 2005a,b),have analyzed the Cluster observation of ion acoustic waves in auroral region and they have found that broadband wave emissions are a combination of various linear waves and ion acoustic waves are observed in small regions of auroral plasma without suprathermal electron, whose energies are of the order of tens of eV. The electric field which was observed has a significant parallel component in all the events considered.
Ion acoustic waves were observed in the plasma modeled by hot and cool electron along with positive ions, Jones et al. (1975). They have summarized that presence of even small fraction of cold electrons drastically affect the properties of ion acoustic waves. Ion acoustic waves were also observed in a two component magnetized plasma for oblique prop- agation(Lee and Kan, 1981). The space plasmas are often characterized by non-thermal dis- tributions such as kappa-distribution as has been discussed by Thorne and Summers (1991).
They employed the kappa distribution to study the electrostatic waves in a hot unmagnetized plasma and have shown that damping of ion-acoustic waves is strongly dependent on the ion temperature and high-energetic tail of non-thermal distribution only has a slight effect on the damping. This work was latter extended to incorporate the kappa-Maxwellian distribution function Hellberg and Mace (2002). In a magnetized plasma comprising of cold ions and kappa electrons, Sultana et al. (2010) have shown that there is a decrease in the frequency of ion acoustic waves with the increase in the angle of propagation and decrease in the value of superthermality index. It was shown by Hadi et al. (2017) that the ion acoustic modes gets damped in a non-thermal plasma modeled by Cairn’s distribution with the increase in the non-thermality factor. With the aid of kinetic theory in a plasma modeled by singly ionized electrons, drifting helium ions and drifting protons, Rehman et al. (2018b) have shown that phase speed of ion acoustic waves increases with the increase in the drift velocity. Moreover, plasma density and temperature does not affect the phase speed to the extend effected by streaming.
In a multi ion plasma, two different kinds of ion acoustic wave modes can be seen- slow ion acoustic mode and fast ion acoustic mode (Andr´e, 1985; Mishra and Chhabra, 1996). The phase speed of the slow mode lies between the thermal speeds of the two ion species, whereas for the fast mode it lies between thermal speeds of the hotter ions and the electrons (Nsengiyumva et al., 2014). The evidence for this mode came into light while
studying the propagation and damping of ion wave in a plasma comprising of electron and two ions (D'Angelo et al., 1966). Fast ion acoustic modes have decreased Landau damping rate compared with that of slow ion acoustic mode (D'Angelo et al., 1966; Yoshimura et al., 1997; Misra et al., 2012). This hints at possible application of slow ion acoustic wave for heating of ions in a plasma. In a plasma comprising of proton and oxygen beam along with background hot electron, Bergmann et al. (1988) had shown that there exist slow and fast ion acoustic mode. They had found that for the fast waves the dissipation due to Landau damping is negligible on account of higher phase velocity of fast modes compared with the ion ther- mal velocity. The slow modes propagate with a frequency below the negative ion frequency and they do propagate without any instability. In auroral region, Freja satellite measured broadband extremely low frequency (BB-ELF) plasma wave in high-resolution (Seyler and Wahlund, 1996; Wahlund et al., 1998). Seyler and Wahlund (1996) have differentiated the wave regime of propagation of electrostatic plasma waves on the basis of propagation angle lesser or greater thanε =pm
e/mi, where the angle is with respect to magnetic field. Waves with propagation angles greater than ε correspond to either the electrostatic ion cyclotron wave or the shorter wavelength oblique ion acoustic wave, which are termed as fast ion cy- clotron or fast ion acoustic waves respectively. On the other hand, waves propagating at an- gles less thanεcorrespond to the inertial Alfven wave which is called the slow ion cyclotron wave and in the short wavelength limit is called the slow ion acoustic wave. Numerical and experimental analysis of ion acoustic waves in a four component plasma comprising of elec- tron, F-, SF−6 and a positive ion species (Ar+or Xe+) were undertaken by Ichiki et al. (2001).
They had found the coexistence of fast ion acoustic mode and slow ion acoustic mode in this plasma and also speculate the possibility of existence of fast and slow ion acoustic modes in single negative ion plasma. The existence of fast and slow ion acoustic modes were also reported in plasma comprising of positive and negative ions, electrons and immobile dust (Misra et al., 2012). Shahmansouri and Tribeche (2014) investigated the properties of ion acoustic waves in bi-ion plasma comprising of hot and cold ion and kappa electron and found out that the plasma supports fast ion acoustic mode and slow ion acoustic mode. When the thermal effects are neglected, the system supports only fast mode.