Numerische Integration der nichtlinearen Vlasov-Gleichung

The VLASOV equation, i. e. the BOLTZMANN equation without collision term, was numerically integrated as an initial value problem together with the second MAXWELL equation for a one-dimensional electron plasma with smeared-out ion background. The initial values were taken as a MAXWELLian distribution in velocity space and a cosine distribution in position, resulting in a sinusform for the electric field.The LANDAU damping of the total energy of the electric field turned out to be valid for times larger than those given by a formal estimation of the validity of the linear solution. For still later times, the decay rate of the electric energy is less than that given by LANDAU damping.The period of validity of LANDAU damping was computed by estimating the influence of the trapped particles. As a non-linear effect the first harmonic of the electric field builds up within this period. The growth of the first harmonic is faster for larger wave numbers k.

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A solvable model of Vlasov-kinetic plasma turbulence in Fourier–Hermite phase space

Journal of Plasma Physics ◽

10.1017/s0022377818000089 ◽

2018 ◽

Vol 84 (1) ◽

Cited By ~ 12

Author(s):

T. Adkins ◽

A. A. Schekochihin

Keyword(s):

Phase Space ◽

Electric Field ◽

Landau Equation ◽

Electric Energy ◽

Solvable Model ◽

Chaotic Advection ◽

Phase Mixing ◽

One Dimensional ◽

Kolmogorov Scale ◽

The One

A class of simple kinetic systems is considered, described by the one-dimensional Vlasov–Landau equation with Poisson or Boltzmann electrostatic response and an energy source. Assuming a stochastic electric field, a solvable model is constructed for the phase-space turbulence of the particle distribution. The model is a kinetic analogue of the Kraichnan–Batchelor model of chaotic advection. The solution of the model is found in Fourier–Hermite space and shows that the free-energy flux from low to high Hermite moments is suppressed, with phase mixing cancelled on average by anti-phase-mixing (stochastic plasma echo). This implies that Landau damping is an ineffective route to dissipation (i.e. to thermalisation of electric energy via velocity space). The full Fourier–Hermite spectrum is derived. Its asymptotics are $m^{-3/2}$ at low wavenumbers and high Hermite moments ($m$) and $m^{-1/2}k^{-2}$ at low Hermite moments and high wavenumbers ($k$). These conclusions hold at wavenumbers below a certain cutoff (analogue of Kolmogorov scale), which increases with the amplitude of the stochastic electric field and scales as inverse square of the collision rate. The energy distribution and flows in phase space are a simple and, therefore, useful example of competition between phase mixing and nonlinear dynamics in kinetic turbulence, reminiscent of more realistic but more complicated multi-dimensional systems that have not so far been amenable to complete analytical solution.

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Electron acceleration by a localized electric field

Laser and Particle Beams ◽

10.1017/s0263034600002123 ◽

1986 ◽

Vol 4 (3-4) ◽

pp. 439-452 ◽

Cited By ~ 1

Author(s):

D. Galmiche ◽

J. P. Nicolle ◽

D. Pesme

Keyword(s):

Particle Acceleration ◽

Electric Field ◽

Plasma Wave ◽

Electron Acceleration ◽

Landau Damping ◽

One Dimensional ◽

Convective Regime ◽

Electric Structure ◽

Electron Distributions

The acceleration of test electrons by a resonant, one—dimensional electric structure is studied in the convective regime with the Zakharov equations. Depending on the nonlinearity level the particle acceleration is due to diffusion or trapping by the plasma wave. Electron distributions are obtained and compared with 1-D particle code results. Influence of Landau damping formulation is discussed.

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One-Dimensional Poisson Calculation for Electrically Controlled Band Bending in GaAs/AlGaAs Heterostructure

Journal of Nanoscience and Nanotechnology ◽

10.1166/jnn.2020.17559 ◽

2020 ◽

Vol 20 (7) ◽

pp. 4428-4431

Author(s):

Hyungkook Choi ◽

Minsoo Kim ◽

Ji-Yun Moon ◽

Jae-Hyun Lee ◽

Seok-Kyun Son

Keyword(s):

Electric Field ◽

Electron Gas ◽

Dimensional Electron ◽

Metal Gate ◽

Modulation Doping ◽

Band Bending ◽

One Dimensional ◽

Surface Metal ◽

Dimensional Electron Gas ◽

Electrically Modulated

Here, we describe the band-bending situation for introducing electrons in an undoped GaAs and AlGaAs quantum well. Our calculation has shown that an externally applied electric field can modulate two-dimensional electron gas (2DEG) without standard modulation doping. The topic of electrically modulated 2DEG has only background impurities, no intentional dopants, so scattering or dephasing by background potential fluctuations should be much reduced. Using our calculation, it is straightforward to confine carriers (in the range of 1010~1011 cm−2), when the external electric field is more than threshold voltage, 4 V to the surface metal gate.

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