Theoretical Investigation of Langmuir Wave Instability in Irradiated Dusty Plasmas

M. K. Islam 1), Y. Nakashima

Plasma Research Center, University of Tsukuba, Tsukuba, Ibaraki 305-8577, Japan
1) Institute of Nuclear Science and Technology, Atomic Energy Research Establishment, Ganakbari, Savar, Dhaka 1349, (GPO Box: 3787, Dhaka 1000), Bangladesh

Presence of the dynamics of dust grains in a plasma can modify the existing plasma modes or may introduce new low frequency eigenmodes [1]. Moreover, the dust charge fluctuation oscillation can be sustained by the low frequency perturbation and usually leads the damping of these modes [2]. A different mechanism of sustaining high frequency dust charge fluctuation oscillation by the combined effect of high frequency perturbation and photoelectron emission is considered. The piled up electrons on a dust grain due to Langmuir wave (LW) perturbation can be swept out by photoelectric effect. The photoelectrons will then collide with another dust grain in a time τ. The dispersion relation of the LW in collisional and irradiated dusty plasma with dust charge fluctuation is given by

ω = ±(ωpe2+K2Ce2)1/2 - iνe/2 + i{2e(1+K2λDe2)}-1(ndo/neo) [|Ieo| + |Ipeo(τ=o)| {exp (-νeτ) -1}],

where ωpe and λDe are plasma frequency and Debye length of electron, respectively. Electron thermal velocity, Ce = (kBTe/me)1/2. Quantities, K, νe, njo, kB, and e, Te, and me are propagation constant, electron neutral collisional frequency, equilibrium density of species j, Boltzmann constant, and charge, temperature, and mass of electron, respectively. Ieo and Ipeo(τ=o) [= - eneo{2(ħν-Φ)/me}1/2] are the equilibrium electron and photoelectron currents, respectively. The dispersion relation will hold for the plasma with negatively charged grains provided: Ieo = -πr2e (8kBTe/πme)1/2neo exp(eφfo/kBTe) and for positively charged grains provided: Ieo = -πr2e (8kBTe/πme)1/2neo (1 + eφfo/kBTe). Quantities, ħ, ν, Φ, r, and φfo are Planck's constant, irradiation frequency, work function, grain radius, and equilibrium potential difference between grain and adjacent plasma, respectively.

Thus, LW (1st term in rhs) can be unstable due to dust charge fluctuation effect (3rd term in rhs) in irradiated dusty plasma, provided collisional damping (2nd term in rhs) is negligible. In a collisionless plasma, dust charge fluctuation effect depends on |Ieo|, ndo, and neo. This investigation clarifies many phenomena related with high frequency mode both in laboratory and natural dusty plasmas.

References

[1] P. K. Shukla, Phys. Plasmas, 8 (2001) 1791
[2] M. R. Jana, A. Sen, and P. K. Kaw, Phys. Rev. E, 48 (1993) 3930