Spiky parallel electrostatic ion cyclotron and ion acoustic waves

Abstract

Abstract.One of the interesting observations from the FAST satellite is the detection of strong spiky waveforms in the parallel electric field in association with ion cyclotron oscillations in the perpendicular electric fields. We report here an analytical model of the coupled nonlinear ion cyclotron and ion-acoustic waves, which could explain the observations. Using the fluid equations for the plasma consisting of warm electrons and cold ions, a nonlinear wave equation is derived in the rest frame of the propagating wave for any direction of propagation oblique to the ambient magnetic field. The equilibrium bulk flow of ions is also included in the model to mimic the field-aligned current. Depending on the wave Mach number M defined by M = V /C s with V and C s being the wave phase velocity and ion-acoustic speed, respectively, we find a range of solutions varying from a sinusoidal wave form for small amplitudes and low M to sawtooth and highly spiky waveforms for nearly parallel propagation. The results from the model are compared with the satellite observations.

Nonlinear ion-acoustic (IA) waves driven in a cylindrically symmetric flow

“…This result reproduces the results obtained by Reddy et al (2002); Bharuthram et al (2002) in Cartesian coordinates. This indicates that the features of nonlinear waves are strengthened increasingly with stronger drifts of azimuthal flows.…”

“…Their studies were followed by, e.g., Nakamura & Sugai (1996); Chatterjee & Roychoudhury (1997); Das et al (2000); Jovanovic & Shukla (2000); Mamun & Shukla (2002). Particularly, Reddy et al (2002); Bharuthram et al (2002); Ma & Hirose (2009) not only verified that the nonlinear structures originate from a coupling between the IC and IA modes, but also obtained the three waveforms reported firstly by Temerin et al (1979). The authors found that the nonlinear shapes change from a sinusoidal IC/IA structure of small amplitudes at low Mach numbers to sawtooth and then bipolar/spiky waveforms of large amplitudes at higher Mach numbers in parallel propagations.…”

Some theoretical models for solitary structures of boundary layer waves

“…The 3-D simulations of electron-beam driven electron holes indicate that, initially a large number of electron holes are formed. They merge continuously, and at a later time, only a few electron holes are left and they decay by emitting low-frequency whistler waves (Singh, 2002). However, only a fraction of the possible parametric space where solitary structure can exist has been simulated.…”

“…Implications of these two-dimensional localized solutions to the observed solitary structures needs to be explored. Reddy et al (2002) have developed an analytical model of the coupled nonlinear ion cyclotron and ion-acoustic waves, which could explain the FAST observations (Ergun et al, 1998) of strong, spiky waveforms in the parallel electric field, in association with ion cyclotron oscillations in the perpendicular electric fields. Using the fluid equations for the plasma consisting of warm electrons and cold ions, a nonlinear wave equation is derived in the rest frame of the propagating wave for any direction of propagation oblique to the ambient magnetic field.…”

“…Equation (2) has been solved numerically by Reddy et al (2002) over a wide parametric space. For nearly parallel propagation, the electric field is found to exhibit a variety of waveforms, for example, sinusoidal, sawtooth or highly spiky waveforms, depending upon the driving amplitude E 0 , Mach number M, and the bulk flow velocity v 0 .…”