Non-linear electrostatic waves in pair-ion plasmas - National Centre ...

Dissipative shocks and solitons in Pair-ion PlasmasThe Poisson equation is written as follows,2 2∂ ϕ ∂ ϕ+ = n − −n2 2+∂x∂ywhere+β = T−/ T+μμ, η+ -= −and ηλ( λ )have been defined.v D+sIn fully ionized gas, the coefficient of viscosity in the absence of magnetic field isgiven by5 / 2 1/ 2−15T±Aiμ ±= 2.21×10gm / cm sec Braginskii (1962)4Z lnΛUsing reductive perturbation method, the perturbed quantities can be expandedabout their equilibrium values in powers of ε such thatv D−snvα(1)(2)23= 1+εnα+ ε nα+ ε nα(3)+ ....(1) 2 (2) 3 (3)α= εuα+ ε uα+ ε uα+ ....3/ 2 (1) 5 / 2 (2) 7 / 2 (3)α= ε vα+ ε vα+ ε vαuϕFor weak dissipation,(1) 2 (2) 3 (3)= εϕ + ε ϕ + ε ϕ+ ......η = ε 1/ 2η± 0±where η 0±is+ ....0 (1)28