Diffusion and heat conductivity in the weakly ionized plasma with power-law q-distributions in nonextensive statistics

Ji, Xiaoxuan; Du, Jiulin

doi:10.1016/j.physa.2019.01.046

Cited by 11 publications

(25 citation statements)

References 21 publications

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“…Based on the above facts of weakly ionized plasma, the Boltzmann equation of transport together with further simplification of the collision integral are used to study transport properties of weakly ionized plasmas. It can be written as the generalized Boltzmann equation,

\frac{\partial f_{α}}{\partial t} + v \cdot \nabla f_{α} + \frac{Q_{α}}{m_{α}} [E + c^{- 1} (v \times B)] \cdot \nabla_{v} f_{α} = C_{κ} (f_{α}),

where f α ≡ f α ( r , v , t ) is the single‐particle velocity distribution function at time t , velocity v , and position r , and E is the electric field. The subscript α = e , i denotes electrons and ions, respectively.…”

Section: The Generalized Boltzmann Equation Of Transport and The κ‐Dimentioning

confidence: 99%

“…Following the line of refs [], the κ ‐collision term is considered the generalized Krook model based on the κ ‐distribution. In the first‐order approximation of Chapman‐Enskog expansion for the velocity distribution functions in the weakly ionized, magnetized, and κ ‐distributed plasma, we let the velocity distribution function be

f_{α} = f_{κ, α}^{((), 0)} + f_{κ, α}^{((), 1)}

, where the stationary‐state distribution function is taken as the κ ‐distribution for the α th component, namely,

f_{κ, α}^{((), 0)} (r, v) = f_{κ, α} (r, v) = n_{α} B_{κ, α} {([], 1 + A_{κ, α} {[v - u]}^{2})}^{- (κ_{α} + 1)}

with…”

Section: The Generalized Boltzmann Equation Of Transport and The κ‐Dimentioning

confidence: 99%

“…Equations (23)–(26) show that these transport coefficients depend strongly on the κ ‐parameter and the magnetic field. When the magnetic field is equal to zero, the Righi‐Leduc coefficient Equation (24) and the Hall Dufour coefficient Equation (26) disappear, and the transverse thermal conductivity Equation (23) and the Dufour coefficient Equation (25) obtain the shape for the plasma without magnetic field . When we take the parameter κ → ∞, they recover to the standard forms in the plasma with a Maxwellian velocity distribution, namely,

K_{⊥, α}^{normal∞} = \frac{5 n_{α} ν_{α} k_{B}^{2} T_{α}}{2 m_{α} (ν_{α}^{2} + ω_{B, α}^{2})}, K_{\land, α}^{normal∞} = \frac{5 n_{α} k_{B}^{2} T_{α} ω_{B, α}}{2 m_{α} (ν_{α}^{2} + ω_{B, α}^{2})},

D_{ρ ⊥, α}^{normal∞} = \frac{5 ν_{α} n_{α} k_{B}^{2} T_{α}^{2}}{m_{α} (ν_{α}^{2} + ω_{B, α}^{2})}, D_{ρ \land, α}^{normal∞} = \frac{5 n_{α} k_{B}^{2} T_{α}^{2} ω_{B, α}}{m_{α} (ν_{α}^{2} + ω_{B, α}^{2})} .

…”

Section: Thermal Conductivity and Dufour Effectmentioning

confidence: 99%

“…In order to more clearly demonstrate the roles of the κ ‐parameter, as well as of the magnetic field, we relate the coefficients of Equations (23)–(26) to the thermal conductivity and Dufour coefficient in the unmagnetized Maxwellian plasma,

K_{α}^{normal∞} = \frac{5 n_{α} k_{B}^{2} T_{α}}{2 m_{α} ν_{α}}, D_{ρ, α}^{normal∞} = \frac{5 n_{α} k_{B}^{2} T_{α}^{2}}{m_{α} ν_{α}} .

…”

Section: Thermal Conductivity and Dufour Effectmentioning

confidence: 99%

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Heat conductivity and Dufour effect in the weakly ionized, magnetized, and kappa‐distributed plasma

Xia

2020

Contributions to Plasma Physics

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By using the generalized Boltzmann equation of transport and the first‐order approximation of Chapman‐Enskog expansion on the κ‐distribution function, we study the thermal conductivity and Dufour effect in the weakly ionized and magnetized plasma. We show that the thermal conductivity and Dufour coefficient in the κ‐distributed plasma are significantly different from those in the Maxwell‐distributed plasma, and the transverse thermal conductivity and Dufour coefficient in the κ‐distributed plasma are generally greater than those in the Maxwell‐distributed plasma, and the Righi‐Leduc coefficient and Hall Dufour coefficient in the κ‐distributed plasma are also generally greater than those in the Maxwell‐distributed plasma.

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\frac{\partial f_{α}}{\partial t} + v \cdot \nabla f_{α} + \frac{Q_{α}}{m_{α}} [E + c^{- 1} (v \times B)] \cdot \nabla_{v} f_{α} = C_{κ} (f_{α}),

Section: The Generalized Boltzmann Equation Of Transport and The κ‐Dimentioning

confidence: 99%

f_{α} = f_{κ, α}^{((), 0)} + f_{κ, α}^{((), 1)}

, where the stationary‐state distribution function is taken as the κ ‐distribution for the α th component, namely,

f_{κ, α}^{((), 0)} (r, v) = f_{κ, α} (r, v) = n_{α} B_{κ, α} {([], 1 + A_{κ, α} {[v - u]}^{2})}^{- (κ_{α} + 1)}

with…”

Section: The Generalized Boltzmann Equation Of Transport and The κ‐Dimentioning

confidence: 99%

K_{⊥, α}^{normal∞} = \frac{5 n_{α} ν_{α} k_{B}^{2} T_{α}}{2 m_{α} (ν_{α}^{2} + ω_{B, α}^{2})}, K_{\land, α}^{normal∞} = \frac{5 n_{α} k_{B}^{2} T_{α} ω_{B, α}}{2 m_{α} (ν_{α}^{2} + ω_{B, α}^{2})},

D_{ρ ⊥, α}^{normal∞} = \frac{5 ν_{α} n_{α} k_{B}^{2} T_{α}^{2}}{m_{α} (ν_{α}^{2} + ω_{B, α}^{2})}, D_{ρ \land, α}^{normal∞} = \frac{5 n_{α} k_{B}^{2} T_{α}^{2} ω_{B, α}}{m_{α} (ν_{α}^{2} + ω_{B, α}^{2})} .

…”

Section: Thermal Conductivity and Dufour Effectmentioning

confidence: 99%

K_{α}^{normal∞} = \frac{5 n_{α} k_{B}^{2} T_{α}}{2 m_{α} ν_{α}}, D_{ρ, α}^{normal∞} = \frac{5 n_{α} k_{B}^{2} T_{α}^{2}}{m_{α} ν_{α}} .

…”

Section: Thermal Conductivity and Dufour Effectmentioning

confidence: 99%

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Heat conductivity and Dufour effect in the weakly ionized, magnetized, and kappa‐distributed plasma

Xia

2020

Contributions to Plasma Physics

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“…In fact, for the transport processes of nonequilibrium complex plasmas, the average collision frequencies depend on the velocity/energy distributions of the particles, but are often assumed to be a constant. [14][15][16][17][18][19] As we known, non-Maxwellian and/or power-law velocity and/or energy distributions are ubiquitous in many nonequilibrium complex plasmas. For example, the famous κ-and κ-like velocity/energy distributions exist widely in astrophysical and space plasmas.…”

Section: Intronductionmentioning

confidence: 99%

The collision frequency of electron‐neutral‐particle in the weakly ionized plasma with the power‐law velocity distribution

Sun

2020

Contributions to Plasma Physics

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We study the collision frequency of electron-neutral-particle in the weakly ionized plasma with the power-law velocity q-distribution and derive the formulation of the average collision frequency. We find that the average collision frequency in the q-distributed plasma also depends strongly on the q-parameter and thus is generally different from that in the Maxwell-distributed plasma, which therefore modifies the transport coefficients in the previous studies of the weakly ionized plasmas with the power-law velocity distributions.

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The collision frequencies of charged particles in the complex plasmas with the non-Maxwellian velocity distributions

2022

Indian J Phys

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Diffusion and heat conductivity in the weakly ionized plasma with power-law q-distributions in nonextensive statistics

Cited by 11 publications

References 21 publications

Heat conductivity and Dufour effect in the weakly ionized, magnetized, and kappa‐distributed plasma

Heat conductivity and Dufour effect in the weakly ionized, magnetized, and kappa‐distributed plasma

The collision frequency of electron‐neutral‐particle in the weakly ionized plasma with the power‐law velocity distribution

The collision frequencies of charged particles in the complex plasmas with the non-Maxwellian velocity distributions

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