Erratum: “Ion acoustic shock waves in presence of superthermal electrons and interaction of classical positron beam” [Phys. Plasmas 19, 032302 (2012)]

Shah, Asif; Mahmood, S.; Haque, Q.

doi:10.1063/1.4745865

The flow velocities of the plasma species of the paper¹ are normalized by the electron thermal speed $(\sqrt{T_{e} / m_{e}}) .$ Therefore, a normalization parameter $R = m_{e} / m_{i}$ must appear in each of the Eqs. (2), (9), and (11) and coefficients $A_{1}, A_{2}, A_{3}$ of Eq. (15) of Ref. 1. The Eqs. (2), (9), and (11) and coefficients $A_{1}, A_{2}, A_{3}$ of the Eq. (15) of the paper¹ are correctly expressed by the following mathematical expressions:

\frac{\partial u_{i}}{\partial t} + u_{i} \frac{\partial u_{i}}{\partial x} + R \frac{\partial ϕ}{\partial x} - η_{i 0} \frac{\partial^{2} u_{i}}{\partial x^{2}} = 0,

(2)

u_{i}^{(1)} = \frac{R ϕ^{(1)}}{λ_{0}}, n_{i}^{(1)} = \frac{R (1 - p) ϕ^{(1)}}{λ_{0}^{2}},

(9)

\frac{\partial u_{i}^{(1)}}{\partial τ} - λ_{0} \frac{\partial u_{i}^{(2)}}{\partial ξ} + u_{i}^{(1)} \frac{\partial u_{i}^{(1)}}{\partial ξ} + \frac{R \partial ϕ^{(2)}}{\partial ξ} - η_{i 0} \frac{\partial^{2} u_{i}^{(1)}}{\partial x^{2}} = 0,

(11)

A_{1} = [\frac{2 R (1 - p)}{λ_{0}^{3}} + \frac{2 p (λ_{0} - u_{p b 0})}{{({(λ_{0} - u_{p b 0})}^{2} - χ)}^{2}}],

(15A1)

A_{2} = [\frac{3 R^{2} (1 - p)}{λ_{0}^{4}} - \frac{(4 κ_{e}^{2} - 1)}{{(2 κ_{e} - 3)}^{2}} + \frac{3 p {(λ_{0} - u_{p b 0})}^{2}}{{({(λ_{0} - u_{p b 0})}^{2} - χ)}^{3}} - \frac{χ p}{{({(λ_{0} - u_{p b 0})}^{2} - χ)}^{3}}],

(15A2)

A_{3} = [\frac{η_{i 0} (1 - p) R}{λ_{0}^{3}}] .

(15A3)

The effects of various plasma parameters on the propagation of shock wave are also explored numerically and exhibited graphically. Figure 1 shows that at the higher value of electron kappa parameter (⁠ $κ_{e}$ ⁠), the shock wave amplitude is flourished. The role of positron to electron temperature ratio (⁠ $T_{p} / T_{e}$ ⁠) on shock structure is presented in Fig. 2. It is noticed that any increase in the positron to electron temperature ratio causes the shock amplitude to diminish in the considered plasma system. It is not difficult to interpret from Fig. 3 that the shock wave amplitude escalates with an enhancement of the positron beam concentration (p). However, the peak amplitude of the shock wave declines remarkably with an upsurge in the positron beam streaming speed (⁠ $u_{p b 0}$ ⁠), as displayed in Fig. 4. Our results are similar to the findings of Ref. 1.

FIG. 1.

View large Download slide

The effect of electron kappa parameter (⁠ $κ_{e}$ ⁠) on structure of shock wave is explored. The other parameters are p = 0.25, $χ = 0.1, u_{p b 0} = 0.02, η_{i 0} = 0.5$ ⁠, and v = 0.001.

FIG. 2.

View large Download slide

The effect of positron to electron temperature ratio (⁠ $χ = T_{p} / T_{e}$ ⁠) on structure of shock wave is shown. The other parameters are p = 0.25, $κ_{e} = 5, u_{p b 0} = 0.01, η_{i 0} = 0.5$ ⁠, and v = 0.001.

FIG. 3.

View large Download slide

The effect of positron beam concentration (p) on structure of shockwave is presented. The other parameters are $χ = 0.1, κ_{e} = 3, u_{p b 0} = 0.01, η_{i 0} = 0.4$ ⁠, and v = 0.001.

FIG. 4.

View large Download slide

The effect of positron beam streaming speed (⁠ $u_{p b 0}$ ⁠) on peak amplitude of shock wave is exhibited. The other parameters are $χ = 0.2, κ_{e} = 3$ ⁠, p = 0.1, $η_{i 0} = 0.5$ ⁠, and v = 1.

REFERENCES

1.

A.

Shah

,

S.

Mahmood

, and

Q.

Haque

,

Phys. Plasmas

19

,

032302

(

2012

).

https://doi.org/10.1063/1.3684659

Google Scholar

Crossref

View Original Article

2012

American Institute of Physics

Erratum: “Ion acoustic shock waves in presence of superthermal electrons and interaction of classical positron beam” [Phys. Plasmas 19, 032302 (2012)]

REFERENCES

Citing articles via

Submit your article

Sign up for alerts

Resources

Explore

pubs.aip.org

Connect with AIP Publishing

Erratum: “Ion acoustic shock waves in presence of superthermal electrons and interaction of classical positron beam” [Phys. Plasmas 19, 032302 (2012)]

REFERENCES

Citing articles via

Submit your article

Sign up for alerts

Resources

Explore

pubs.aip.org

Connect with AIP Publishing

This Feature Is Available To Subscribers Only