Proton Cyclotron Instability Threshold Condition of Suprathermal Protons by Kappa Distribution

Observation has clearly shown that natural space plasmas generally possess a pronounced non-Maxwellian high-energy tail distribution that can be well modeled by a kappa distribution. In this study we investigate the proton cyclotron wave instability driven by the temperature anisotropy （T⊥/TH 〉1） of suprathermal protons modeled with a typical kappa distribution in the magnetosheath. It is found that as in the case for a regular bi-Maxwellian, the supratherreal proton temperature anisotropy is subject to the threshold condition of this proton cyclotron instability and the instability threshold condition satisfies a general form T⊥/T｜｜ - 1 = S/β｜｜^α, with a very narrow range of the fitting parameters： 0.40 ≤ α ≤ 0.45, and a relatively sensitive variation 0.27 ≤ S ≤ 0.65, over 0.01 ≤β｜｜ 〈 10. Furthermore, the difference in threshold conditions between the kappa distribution and the bi-Maxwellian distribution is found to be small for a relatively strong growth but becomes relatively obvious for a weak wave growth. The results may provide a deeper insight into the physics of this instability threshold for the proton cyclotron waves.

Scalings for the Alfvén-cyclotron instability in a bi-kappa plasma

The particle velocity distribution in space plasma usually exhibits a non-Maxwellian high-energy tail that can be well modeled by kappa distributions.In this study,we focus on the growth rates of the Alfvén-cyclotron instability driven by ion temperature anisotropy in a kappa plasma.By solving the kinetic linear dispersion equation,we explore the sensitivity of growth rates to the spectral indexκof a bi-kappa distribution under different plasma conditions,including a variety of plasma beta β_(hp) and temperature anisotropy A_(hp) values of hot protons.Furthermore,a concise,analytic scaling formula is derived that relates the dimensionless maximum growth rate to three independent variables:the spectral index and the plasma beta and temperature anisotropy of hot protons.Our results show that as theκ-value increases,the instability bandwidth narrows and the maximum growth rate increases significantly.For higherβ_(hp)and A_(hp)′the maximum instability undergoes a sharp increase as well.When our fits of dimensionless maximum growth rates are compared with solutions to kinetic linear dispersion theory,the results generally exhibit good agreement between them.Especially under the circumstances of largeκ-values and highβ_(hp)and A_(hp)′the scalings of maximum growth rates primarily accurately model the numerical solutions.Our analytic expressions can readily be used in large-scale models of the Earth’s magnetosphere to understand wave generation due to the Alfvén-cyclotron instability.

Dispersion and damping rate of Langmuir wave in space plasma with regularized Kappa distributed electrons

The dispersion of Langmuir wave(LW)in an unmagnetized collisionless plasma with regularized Kappa distributed electrons is investigated from the kinetic theory.The frequency and damping rate of LW are analyzed for the parameters relating to the source region of a typeⅢsolar radio burst.It is found that the linear behavior of LW is greatly modified by the suprathermal indexκand the exponential cutoff parameterα.In the regionκ<1.5,the damping rate of LW will be much larger than the one with Maxwellian distributed electrons.Hence,the nonlinear process of LW in lowκregion may exhibit different properties in comparison with the one in largeκregion.

Oblique collisional effects of dust acoustic waves in unmagnetized dusty plasma

Effects of oblique collisions of the dust acoustic(DA)waves in dusty plasma are studied by considering unmagnetized fully ionized plasma.The plasma consists of inertial warm negatively charged massive dusts,positively charged dusts,superthermal kappa distributed electrons,and isothermal ions.The extended Poincaré–Lighthill–Kuo(e PLK)method is employed for the drivation of two-sided Korteweg–de Vries(KdV)equations(KdVEs).The Kd V soliton solutions are derived by using the hyperbolic secant method.The effects of superthermality index of electrons,temperature ratio of isothermal ion to electron,and the density ratio of isothermal ions to negatively charged massive dusts on nonlinear coefficients are investigated.The effects of oblique collision on amplitude,phase shift,and potential profile of right traveling solitons of DA waves are also studied.The study reveals that the new nonlinear wave structures are produced in the colliding region due to head-on collision of the two counter propagating DA waves.The nonlinearity is found to decrease with the increasing density ratio of ion to negative dust in the critical region.The phase shifts decrease(increase)with increasing the temperature ratio of ion to electron(κe).The hump(compressive,κe<κec)and dipshaped(rarefactive,κe>κec)solitons are produced depending on the angle(θ)of oblique collision between the two waves.

Nonplanar dust acoustic solitary and rogue waves in an ion beam plasma with superthermal electrons and ions

The propagation characteristics of dust acoustic solitary and rogue waves are investigated in an unmagnetized ion beam plasma with electrons and ions following kappa-type distribution in nonplanar geometry. The reductive perturbation method （RPM） is employed to derive the cylindrical/spherical Korteweg-de Vries （KdV） equation, which is further transformed into standard KdV equation by neglecting the geometrical effects. Using new stretching coordinates, nonlinear Schrrdinger equation （NLSE） has been derived from the standard KdV equation to study the different order rational solutions of dust acoustic rogue waves （DARWs）. The impact of various physical parameters on the characteristics of dust acoustic solitary waves （DASWs） is elaborated specifically in nonplanar geometry. Further, the effects of ion beam and superthermality of electrons/ions on the characteristics of DARWs are studied. The results obtained in the present investigation may be useful in comprehending a variety of phenomena in Earth＇s magnetosphere polar cap region where the presence of positive ion beam has been detected and also in other regions of space/astrophysical environments where dust along with superthermal electrons and ions exists.

Nonlinear Dust Acoustic Waves in a Magnetized Dusty Plasma with Trapped and Superthermal Electrons

In this work, the effects of superthermal and trapped electrons on the oblique propa- gation of nonlinear dust-acoustic waves in a magnetized dusty （complex） plasma are investigated. The dynamic of electrons is simulated by the generalized Lorentzian （k） distribution function （DF）. The dust grains are cold and their dynamics are simulated by hydrodynamic equations. Using the standard reductive perturbation technique （RPT） a nonlinear modified Korteweg-de Vries （mKdV） equation is derived. Two types of solitary waves; fast and slow dust acoustic solitons, exist in this plasma. Calculations reveal that compressive solitary structures are likely to propagate in this plasma where dust grains are negatively （or positively） charged. The properties of dust acoustic solitons （DASs） are also investigated numerically.