Plasma Physics in Active Wave Ionosphere Interaction

The following sections are included:

• Dedication
• Preface
• List of Figures
• Contents

The following sections are included:

• Introduction
  • Collective phenomena
• Description of Plasma
  • Single particle description (for the discreteness phenomena)
  • Kinetic description (for discreteness as well as collective phenomena)
  • Fluid description
  • Self-consistent description
• Problems

Plasma is a dielectric medium, which supports three types of waves including electromagnetic (EM), electrostatic (ES), as well as hybrid:

• EM wave is a transverse wave (i.e., TEM); it carries two fields, electric field E and magnetic field H, which are perpendicular to each other and also to the wave propagation direction referred by the wavevector k, i.e., E⊥H⊥k, where $K=\stackrel{\wedge }{K}\left(2\pi /\lambda \right)$ and λ is the wavelength; the wavenumber k = 2π/λ infers the number of waves in unit length; thus ∇ · E = 0, i.e., n_e = n_i = n₀, there is no space charge associated with EM waves. However, the wave electric field will drive a current in plasma. Thus, TEM wave is governed only by the two curl equations in Maxwell’s equations. The induced current density J appearing in the curl equation of the Ampere’s law modifies the wave fields self-consistently as well as the wave propagation properties.
• ES wave is a longitudinal wave; it carries only electric field E, which is parallel to the wave propagation direction, i.e., E‖k, and thus H = 0. Therefore, the wave is governed only by the divergence equation (Gauss’law) for the electric field. In this case, a scalar potential ϕ can be introduced to define E = − ∇ ϕ, which converses the divergence equation to the Possion’s equation ∇²ϕ = −e(n_i − n_e)/ε₀.
• Hybrid wave is neither transverse nor longitudinal and exists in magneto plasma; the wave electric field has an angle other than 0° or 90° with respect to the propagation direction. Generally, the full set of Maxwell’ equations is needed to specify the wave; some simplification, based on its nature tending to be EM or ES, may be introduced. In the high-frequency domain, ions are immobile, only electron plasma responds to the wave fields; on the other hand, quasi-neutral condition in the density perturbations may be assumed in the low-frequency domain. Hybrid waves are also plasma modes…

A homogeneous and stationary plasma in uniform dc magnetic field ${\text{B}}_0\widehat{\text{z}}$ is considered; it has a phase space density distribution f_a0(v) in each species “a”. In the presence of an electric field disturbance δE = E₁ exp[i(k · r − ωt)], the linearized Vlasov equation (1.18b) is expressed explicitly to be

The following sections are included:

• Background
• Wave Propagation in the Bottomside of the Ionosphere
  • Solution of the wave equation near a turning point
  • Swelling effect of wave propagation to a reflection layer
• Ray Tracing in Inhomogeneous Media
  • A planar stratified medium
  • General formulation
  • Ray trajectory equations
  • Examples
• Mode Conversion
  • Modes flowing in the spectral regions bounded by the dispersion curves
  • Linear mode conversion
  • Nonlinear mode conversion
• Mode Coupling
• Quasi-linear Diffusion and Effective Temperature
• Problems

Ionospheric heating by powerful HF waves transmitted from the ground is a platform for experimental and theoretical investigation of wave–wave and wave–particle interactions in magneto plasma. Considerable advancement toward the understanding of nonlinear plasma processes has been recognized through the observations of various heating-induced phenomena at Arecibo, Puerto Rico, Tromso, Norway, Gakona, Alaska, and elsewhere. The facility is also applied to explore new technological innovations, such as an ionospheric very-low-frequency (VLF) transmitter for underwater communications and for conditioning the magnetosphere…

The following sections are included:

• Physical Mechanism
  • Parametric decay instability
  • Oscillating two-stream instability
  • Langmuir (upper hybrid) cascade
• Formulation
  • Equations for high-frequency plasma waves
  • Derivation of the coupled mode equation for the Langmuir/upper hybrid sideband
  • One fluid equations
  • Derivation of the coupled mode equation for the low-frequency decay mode
• Manley–Rowe Relations
  • Coupled mode equation for the electromagnetic pump
  • Coupled mode equations for the Langmuir wave and ion acoustic wave
  • Rate equations for the amplitudes of the three waves
  • Energy densities of the waves
  • Demonstration of Manley–Rowe relations
  • Analysis
• Problems

Decays of an O-mode EM dipole pump E_p(ω₀, k_p =0) into Langmuir/upper hybrid sidebands ϕ_±(ω_±, k_±) and purely growing/FAI decay mode or ion acoustic/lower hybrid decay mode n_s(ω_s, k_s) in the spatial region below the high frequency (HF) reflection height/upper hybrid resonance layer are studied; ϕ_± and ns denote the sidebands’ electrostatic potentials and decay mode’s density perturbation, respectively, and ϕ₋ is neglected in the three wave coupling (e.g., Parametric decay instability (PDI). Applying the same notations in the two cases of (6.1a) and (6.1b), the frequency and wavevector matching conditions (6.1) become

Parametric decay instability (PDI) and oscillating two-stream instability (OTSI) and the subsequent plasma wave cascades via follow-up parametric instability processes generate Langmuir waves and upper hybrid waves and broaden their frequency and wavenumber spectra. Although these instabilities can excite plasma waves with an angular distribution around the geomagnetic field, Langmuir waves propagating closely parallel to the geomagnetic field are dominant with the largest growth rates and upper hybrid waves are polarized closely perpendicular to the geomagnetic field to form standing waves. These dominant ones will grow to high intensity and aggregate together, the nonlinearity slows down wave dispersion. The self-induced density perturbations provide nonlinear feedback to modulate the envelopes of the aggregations; consequently, linear plasma waves evolve to nonlinear plasma waves…

The following sections are included:

• Background
• Very- Low-Frequency Radiation of Modulated Ionospheric Electrojet
  • Formulation of electrojet modulation
  • Electron heating
  • Electron heat loss in collisions
  • Numerical model of very- low-frequency wave radiated by heater-modulated electrojet
  • Numerical results
• Very- Low-Frequency Wave Generation by Beating of Two High-Frequency Heater Waves
  • Beating current
  • Operation of the high-frequency transmitter array for beat wave generation
  • Radiation field of the beat wave
• Experiments and Results of Beat Wave Generation
• Problems

The following sections are included:

• Bibliography
• Index