Self-similar and asymptotic solutions for a one-dimensional Vlasov beam

Burgan, J. R.; Feix, Marc; Fijalkow, E.; Munier, A.

doi:10.1017/s0022377800000635

Cited by 26 publications

(24 citation statements)

References 3 publications

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“…Some time decay is known for the three-dimensional analogue of (1.1)( [6], [7], [9]). Also, there are time decay results for (1.1) (in dimension one) when the plasma is monocharged (set g ≡ 0) ( [1], [2], [12]). In this work two species of particles with opposite charge are considered, thus the methods used in these references do not apply.…”

Section: Dedication and Introductionmentioning

confidence: 99%

Time decay for solutions to one-dimensional two component plasma equations

2009

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Dedicated to Professor Walter Strauss on his 70th birthday1. Dedication and introduction. We represent three generations of students: Bob Glassey, Walter's student finishing at Brown in 1972, Jack Schaeffer, Bob's student finishing at Indiana University in 1983, and Steve Pankavich, Jack's student finishing at Carnegie Mellon in 2005. We have all thrived professionally from our association with Walter and are delighted to dedicate this note to him on the occasion of his 70th birthday. The problem we study below concerns the asymptotic behavior of solutions, an area to which Walter has contributed greatly.The motion of a collisionless plasma is described by the Vlasov-Maxwell system. If we neglect magnetic effects we then have the Vlasov-Poisson system (VP). We can also consider the effect of large velocities and solutions to the relativistic Vlasov-Poisson system (RVP). We will study both systems in one space and one momentum dimension with two species of oppositely charged particles. We further assume that each system is neutral , which means that the average value of the density ρ vanishes (see below). The

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Section: Dedication and Introductionmentioning

confidence: 99%

Time decay for solutions to one-dimensional two component plasma equations

2009

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“…Some time decay is known for the three-dimensional analog of (1) [3][4][5]. Also, there are time decay results for (1) (in dimension 1) when the plasma is monocharged (set g ≡ 0) [6][7][8]. In the work that follows, two species of particles with opposite charge are considered, thus the methods used in [6][7][8] do not apply.…”

Section: Introductionmentioning

confidence: 99%

Decay in time for a one‐dimensional two‐component plasma

Glassey¹,

Pankavich²,

Schaeffer³

2008

Math Methods in App Sciences

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“…The Vlasov-Poisson system has been studied extensively in the case where F (v) = 0 and solutions tend to zero as |x| → ∞, both for the one-dimensional problem and the more difficult, three-dimensional problem. Most of the literature involving the one-dimensional Vlasov-Poisson system focus on time asymptotics, such as [2] and [3]. Much more work has been done concerning the three-dimensional problem.…”

Section: Introductionmentioning

confidence: 99%

Explicit solutions of the one‐dimensional Vlasov–Poisson system with infinite mass

Pankavich

2007

Math Methods in App Sciences

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SUMMARYA collisionless plasma is modelled by the Vlasov-Poisson system in one dimension. A fixed background of positive charge, dependent only upon velocity, is assumed and the situation in which the mobile negative ions balance the positive charge as |x| → ∞ is considered. Thus, the total positive charge and the total negative charge are infinite. In this paper, the charge density of the system is shown to be compactly supported. More importantly, both the electric field and the number density are determined explicitly for large values of |x|.

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Self-similar and asymptotic solutions for a one-dimensional Vlasov beam

Abstract: Rescaling transformations bringing friction terms in the new equation are used to obtain the asymptotic solution of a one-dimensional, one-species beam. It is shown that for all possible initial conditions this asymptotic solution coincides with the self-similar solution.

Cited by 26 publications

References 3 publications

Time decay for solutions to one-dimensional two component plasma equations

Time decay for solutions to one-dimensional two component plasma equations

Decay in time for a one‐dimensional two‐component plasma

Explicit solutions of the one‐dimensional Vlasov–Poisson system with infinite mass

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