Reflection and transmission of plasma waves at the interface of crystallites

Латышев, А. В.; Yushkanov, А. А.

doi:10.1134/s096554250707010x

Cited by 6 publications

(15 citation statements)

References 2 publications

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“…In Table 1, column I contains the values of the isothermal slip coefficient calculated by the modified method of discrete ordinates [8], column IV contains the values given in [7], and columns II (the zeroth-order approximation) and III (the first-order approximation) contain the values obtained here. It follows from formulas (4.12) and (4.18) that K v (q) = √ π/q as q → 0; this relation exactly coincides with the well-known result obtained by Cercignani [11].…”

Section: The Problem With a Mirror Boundary Conditionmentioning

confidence: 99%

“…We present Table 2, where column I contains the values obtained in [8] by numerical methods, columns II and III contain the values calculated here by the zeroth-and first-order approximation formulas (5.15) and (5.16), and column IV contains the values given in [7]. Analyzing the values in Table 2 shows that already in the zeroth-order approximation, the method developed here ensures an accuracy of at least 1% in the entire range of q.…”

Section: Thermal Slip Problemmentioning

confidence: 99%

“…As is known [2], [5], and [7], the Kramers problem with the Maxwell condition on the wall reduces to solving the boundary value problem…”

Section: The Bhatnagar-gross-krook Equationmentioning

confidence: 99%

“…A method for solving boundary value problems with the Maxwell condition based on calculating approximate solutions of the singular integral equations was also proposed in [7]. In contrast to the method considered in [7], a distinguishing feature of the method proposed here is the coincidence with the exact results obtained as q → 0 and at q = 1, i.e., in the cases where the accommodation coefficient of the tangential momentum takes the limit values: q = 0 corresponds to purely mirror scattering of molecules at the wall, and q = 1 corresponds to completely diffusion scattering.…”

Section: Introductionmentioning

confidence: 99%

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The Method of Singular Equations in Boundary Value Problems in Kinetic Theory

Латышев¹,

Yushkanov²

2005

Theor Math Phys

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We develop a new effective method for solving boundary value problems in kinetic theory. The method permits solving boundary value problems for mirror and diffusive boundary conditions with an arbitrary accuracy and is based on the idea of reducing the original problem to two problems of which one has a diffusion boundary condition for the reflection of molecules from the wall and the other has a mirror boundary condition. We illustrate this method with two classical problems in kinetic theory : the Kramers problem (isothermal slip) and the thermal slip problem. We use the Bhatnagar-Gross-Krook equation (with a constant collision frequency) and the Williams equation (with a collision frequency proportional to the molecular velocity).

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Section: The Problem With a Mirror Boundary Conditionmentioning

confidence: 99%

Section: Thermal Slip Problemmentioning

confidence: 99%

“…As is known [2], [5], and [7], the Kramers problem with the Maxwell condition on the wall reduces to solving the boundary value problem…”

Section: The Bhatnagar-gross-krook Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Method of Singular Equations in Boundary Value Problems in Kinetic Theory

Латышев¹,

Yushkanov²

2005

Theor Math Phys

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“…It's well known that specularity coefficient q is a very important factor in the kinetic skin effect theory [7] - [9]. The limiting cases q = 0 (diffuse surface scattering of electrons) and q = 1 (specular surface scattering of electrons) are only very special cases.…”

Section: Introductionmentioning

confidence: 99%

Skin effect with arbitrary specularity in Maxwellian plasma

Латышев

Yushkanov

2010

Journal of Mathematical Physics

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The problem of skin effect with arbitrary specularity in maxwellian plasma with specular-diffuse boundary conditions is solved. New analytical method is developed that makes it possible to obtain a solution up to an arbitrary degree of accuracy. The method is based on the idea of symmetric continuation of not only the electric field, but also electron distribution function. The solution is obtained in a form of von Neumann series.

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Degenerate plasma in a half-space under an external electric field

Латышев

Yushkanov

2006

Theor Math Phys

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An analytic solution is found for the problem on the behavior of a collisional plasma in a variable external electric field. We elucidate the structure of the screened electric field and investigate the case where the frequency of the external field is close to the plasma oscillation frequency (resonance). We show that there are two near-surface layers where the behavior of the screened field differs essentially.

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Reflection and transmission of plasma waves at the interface of crystallites

Cited by 6 publications

References 2 publications

The Method of Singular Equations in Boundary Value Problems in Kinetic Theory

The Method of Singular Equations in Boundary Value Problems in Kinetic Theory

Skin effect with arbitrary specularity in Maxwellian plasma

Degenerate plasma in a half-space under an external electric field

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