Effect of a large-amplitude wave on the one-dimensional velocity distribution of particles in a linearized Fokker-Planck collisional plasma

Jukka Heikkinen, Timo Pättikangas

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Abstract

The evolution of a one-dimensional velocity distribution is studied in the presence of a monochromatic large-amplitude periodic force which is turned on adiabatically. The periodic Vlasov-Poisson equations are solved in the presence of a linearized Fokker-Planck collision term. For a constant driving force, the system is found to approach, after transient oscillations, a steady state which is maintained by one wave at the driving frequency. This is in contrast to the result in the absence of collisions where the steady state tends to be supported by several waves. An analytical solution for the steady-state distribution function in the presence of a driven large-amplitude wave is obtained by a Hamiltonian approach. The distribution function is expanded in powers of a small parameter Γ proportional to the collision strength. From the expansion, the zeroth order term is shown to give the space-averaged distribution function correct to first order in Γ. Comparison with the results of the simulations and of the harmonics expansion method shows that the solution estimates the distribution with good accuracy. The plateau in the wave trapping regime is analyzed, and the current driven by the large-amplitude traveling wave is determined.
Original languageEnglish
Pages (from-to)2208-2216
Number of pages9
JournalPhysical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume50
Issue number3
DOIs
Publication statusPublished - 1994
MoE publication typeA1 Journal article-refereed

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collisional plasmas
Fokker-Planck
Velocity Distribution
Plasma
velocity distribution
Distribution Function
Collision
distribution functions
collisions
transient oscillations
Vlasov-Poisson Equations
expansion
Steady-state Distribution
Zeroth
Term
Driving Force
Poisson equation
Trapping
traveling waves
Small Parameter

Cite this

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title = "Effect of a large-amplitude wave on the one-dimensional velocity distribution of particles in a linearized Fokker-Planck collisional plasma",
abstract = "The evolution of a one-dimensional velocity distribution is studied in the presence of a monochromatic large-amplitude periodic force which is turned on adiabatically. The periodic Vlasov-Poisson equations are solved in the presence of a linearized Fokker-Planck collision term. For a constant driving force, the system is found to approach, after transient oscillations, a steady state which is maintained by one wave at the driving frequency. This is in contrast to the result in the absence of collisions where the steady state tends to be supported by several waves. An analytical solution for the steady-state distribution function in the presence of a driven large-amplitude wave is obtained by a Hamiltonian approach. The distribution function is expanded in powers of a small parameter Γ proportional to the collision strength. From the expansion, the zeroth order term is shown to give the space-averaged distribution function correct to first order in Γ. Comparison with the results of the simulations and of the harmonics expansion method shows that the solution estimates the distribution with good accuracy. The plateau in the wave trapping regime is analyzed, and the current driven by the large-amplitude traveling wave is determined.",
author = "Jukka Heikkinen and Timo P{\"a}ttikangas",
note = "Project code: ENE0630",
year = "1994",
doi = "10.1103/PhysRevE.50.2208",
language = "English",
volume = "50",
pages = "2208--2216",
journal = "Physical review E",
issn = "2470-0045",
publisher = "American Physical Society",
number = "3",

}

TY - JOUR

T1 - Effect of a large-amplitude wave on the one-dimensional velocity distribution of particles in a linearized Fokker-Planck collisional plasma

AU - Heikkinen, Jukka

AU - Pättikangas, Timo

N1 - Project code: ENE0630

PY - 1994

Y1 - 1994

N2 - The evolution of a one-dimensional velocity distribution is studied in the presence of a monochromatic large-amplitude periodic force which is turned on adiabatically. The periodic Vlasov-Poisson equations are solved in the presence of a linearized Fokker-Planck collision term. For a constant driving force, the system is found to approach, after transient oscillations, a steady state which is maintained by one wave at the driving frequency. This is in contrast to the result in the absence of collisions where the steady state tends to be supported by several waves. An analytical solution for the steady-state distribution function in the presence of a driven large-amplitude wave is obtained by a Hamiltonian approach. The distribution function is expanded in powers of a small parameter Γ proportional to the collision strength. From the expansion, the zeroth order term is shown to give the space-averaged distribution function correct to first order in Γ. Comparison with the results of the simulations and of the harmonics expansion method shows that the solution estimates the distribution with good accuracy. The plateau in the wave trapping regime is analyzed, and the current driven by the large-amplitude traveling wave is determined.

AB - The evolution of a one-dimensional velocity distribution is studied in the presence of a monochromatic large-amplitude periodic force which is turned on adiabatically. The periodic Vlasov-Poisson equations are solved in the presence of a linearized Fokker-Planck collision term. For a constant driving force, the system is found to approach, after transient oscillations, a steady state which is maintained by one wave at the driving frequency. This is in contrast to the result in the absence of collisions where the steady state tends to be supported by several waves. An analytical solution for the steady-state distribution function in the presence of a driven large-amplitude wave is obtained by a Hamiltonian approach. The distribution function is expanded in powers of a small parameter Γ proportional to the collision strength. From the expansion, the zeroth order term is shown to give the space-averaged distribution function correct to first order in Γ. Comparison with the results of the simulations and of the harmonics expansion method shows that the solution estimates the distribution with good accuracy. The plateau in the wave trapping regime is analyzed, and the current driven by the large-amplitude traveling wave is determined.

U2 - 10.1103/PhysRevE.50.2208

DO - 10.1103/PhysRevE.50.2208

M3 - Article

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SN - 2470-0045

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