Wave breaking through phase mixing of a variant of Lower Hybrid Modes in cold electron-ion plasma

The wave breaking through a process called phase mixing of low frequency

lower hybrid modes is investigated in the frequency range Ω_ci ≪ ω ≪ Ω_ce ,

where Ω_ci = eB₀ /m_i c and Ω_ce = eB₀ /m_e c are cyclotron frequencies of ions and

electrons, respectively. The dispersion relation shows the existence of a variant

of lower hybrid modes whose nonlinear evolution is studied analytically. Our

interests is in the plasma environments like pulsars where the magnetic field

is so strong that the condition Ω_c ≫ 1 holds and also in the weak magnetic

field limit (for instance, ionosphere) where Ω _c ≪ 1 holds (Ω _c = Ω_ce /ω_pe ). In

the range Ω_ci ≪ ω ≪ Ω_ce it is justified to treat the ions as un-magnetized and

treat the contribution of electron inertia in the x-component to be

negligible. The dispersion relation for such mode can be written as ω² = ω²_pi / (1 + Ω²_pe / Ω²_ce )

(where ω_pe = 4πn₀ e² /m_e and ω_pi = 4πn₀ e²/m_i ). We employ perturbation

expansion technique to investigate the space time evolution of such mode in

the frequency range considered. Such nonlinear analysis shows that the excited

wave breaks at arbitrarily small amplitudes via the process of phase mixing. An

estimate of the phase mixing time is provided which is found to increase as we

increase the strength of the applied magnetic field. The results are of relevance

to the field of space science and laboratory experiment.