Electrostatic ion cyclotron, beam‐plasma, and lower hybrid waves excited by an electron beam

Abstract

The excitation of waves at frequencies ω < ωlh, where ωlh is the lower hybrid (LH) frequency, by a low‐energy electron beam is examined under the electrostatic approximation; the frequency range ω < ωlh includes the ion cyclotron frequencies (Ωi) and their harmonics in a multi‐ion plasma. Since the beam velocity Vb ≫ νte, the electron thermal velocity, the excited waves have phase velocities Vp ≃ Vb ≫ νte. Thus, the background electrons can be treated as cold, and the electron density fluctuations are small. In the limit of cold ion approximation, the excited waves are either the ion cyclotron resonance cone (ICRC) waves or the beam‐plasma (B‐P) mode. Both of these waves show stop bands near the gyrofrequencies of the constituent ions. The ICRC waves are limited to the highest gyrofrequency while the B‐P mode propagates even beyond it. A comparison of the characteristics of the electrostatic ICRC waves with those determined from a full electromagnetic treatment at frequencies ω < Ωi shows that the electrostatic approximation is valid when beam energy is low (∼100 eV) and for relatively more energetic beams the validity holds good only when the perpendicular wave number k⊥ is sufficiently large (k⊥ > 10³Ω(H+)/C, Ω being the H+ gyrofrequency, and C the velocity of light in vacuum). Warm ion effects on the waves are examined; when K⊥ = k⊥rl(H+) > 0.3, where rl(H+) is the H+ Larmor radius in a He+‐H+ plasma, the excited waves are the electrostatic‐ion cyclotron (EIC) waves. Because of their phase velocity Vp ≫ νte, these EIC waves are pure ion Bernstein (PIB) waves. The characteristics of the electron beam‐excited PIB waves are compared with their counterpart, the neutralized ion Bernstein (NIB) waves, which are EIC waves excited by drifting bulk electrons. The consideration of electrostatic waves in the frequency band Ω(H+) < ω < ωlh shows that the B‐P waves with k⊥rl(H+) ≪ 1 have considerably larger temporal growth rates than the EIC waves. The interconnections between LH and B‐P waves are found to be similar to those between EIC and B‐P waves; B‐P waves have long perpendicular wavelengths (λ⊥ while EIC and LH waves have comparatively much shorter ones. The relevance of ICRC and PIB waves to satellite observations of waves in the ELF band is discussed. The B‐P waves appear to be similar to the electrostatic broadband noise emissions in the frequency range from below the ion cyclotron frequency to the lower hybrid frequency observed from various satellites in the auroral and cusp regions.