Effects of nonthermal electrons on plasma expansion into vacuum

Bennaceur-Doumaz, D.; Bara, Djemai; Benkhelifa, El-Amine; Djebli, M.

doi:10.1063/1.4906776

Cited by 18 publications

(7 citation statements)

References 36 publications

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“…At the moving boundaries where quasi-neutrality down, inclusion of Poisson's equation around the discontinuities may lead to localized short wavelength oscillations (Gurevich & Pitaevsky 1975). Additionally, we note that a variety of instabilities may arise with the introduction of multiple ion species (Gurevich, Par & Pitaevski 1973;Elkamash & Kourakis 2016), non-Maxwellian electron distributions (True 1981;Bennaceur-Doumaz et al 2015) and magnetic fields (Gurevich & Pitaevsky 1975;García-Rubio et al 2016). All of these auxiliary effects are beyond the scope of the present study.…”

Section: Appendix a Review Of Self-similar Formulationmentioning

confidence: 83%

“…Semi-analytic models with a more accurate portrayal of the ion front boundary layer (Mora 2003;Medvedev 2011) have shown that the self-similar domain of validity can be extended earlier in time and further in space. Many variations of this problem, beyond the scope of the present discussion, include non-isothermal expansion (Mora & Pellat 1979;Grismayer et al 2008), non-Maxwellian initial distributions (Gurevich & Meshcherkin 1981a;True 1981;Akbari-Moghanjoughi 2015;Bennaceur-Doumaz et al 2015), magnetic fields (García-Rubio, Ruocco & Sanz 2016) and multiple ion species (Elkamash & Kourakis 2016). Some attention has been given to the case of a finite plasma (Medvedev 2005;Murakami & Basko 2006), but still with infinite boundary conditions in the vacuum.…”

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confidence: 98%

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Plasma expansion towards an electrically insulated surface

Rhodes

Farrell

2020

J. Plasma Phys.

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The problem of plasma expansion into a vacuum is revisited with the addition of a finite boundary condition; an electrically insulated surface. As plasma expands towards a charge-accumulating surface, the leading electron cloud charges the surface negatively, which in turn repels electrons and attracts ions. This plasma–surface interaction is shown to result in a feedback process which accelerates the plasma expansion. In addition, we examine the decrease in (negative) surface potential and associated near-surface electron density. To investigate this plasma coupling with an electrically floating surface, we develop an analytic model including four neighbouring plasma regions: (i) undisturbed plasma, (ii) quasi-neutral self-similar expansion, (iii) ion front boundary layer and (iv) electron cloud. A key innovation in our approach is a self-contained analytic approximation of the ion front boundary layer, providing a spatially continuous electric field model for the early phase of bounded plasma expansion.

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Section: Appendix a Review Of Self-similar Formulationmentioning

confidence: 83%

mentioning

confidence: 98%

Plasma expansion towards an electrically insulated surface

Rhodes

Farrell

2020

J. Plasma Phys.

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“…The distribution of those electrons accelerated at the vacuum-plasma interface is of importance for ion acceleration processes at the rear side of a target with finite width, and it is of interest for the models describing ion acceleration. [70][71][72][73][74][75][76][77][78][79][80][81][82][83] The evolution shown in Fig. 12, illustrating how the most energetic electron penetrate into the dense plasma, are therefore of particular relevance for relatively thin target foils for which the cutoff in the electron momentum remains 'preserved' till the arrival of the fastest electrons at the rear face.…”

Section: Discussionmentioning

confidence: 99%

On the non-thermal nature of distributions of electrons accelerated by high intensity lasers at the vacuum-plasma interface

et al. 2019

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The distribution function of electrons accelerated by intense laser pulses at steep vacuumplasma interfaces is investigated by using Fokker-Planck equation and methods from extreme statistics. The energy spectrum of electrons penetrating into the dense plasma after being accelerated at the interface and in the pre-plasma shows systematically cutoff-like decrease in the momentum component p x /m e c along the laser propagation axis. While the distribution associated to the kinetic energy spectrum (E kin ) is often approximated by a thermal distribution, F(E kin ) ∝ exp(−E kin /T h ), with a hot particle temperature T h , the nature of the distribution close to the cutoff is clearly non-thermal. Electron distributions are analyzed here from two-dimensional Particle-in-Cell simulations. Via a comparison with solutions derived from a Fokker-Planck equation and based on Chirikov's standard map models, we find that the electron distributions show a clear signature of stochastic heating, due to repeated acceleration in the standing wave in the pre-plasma. Further analysis of the solutions to the Fokker-Planck equation allows us to describe the cutoff seen in the momentum p of the distributions F(p), which can be expressed as a function of time τ in the form F(p, τ) ∝ [(p max − p)/δ p] exp −2p 3 /9τ , portraying a time-dependent cutoff at p → p max . This implies that the energetic tail of the distribution belongs to the maximum domain of attraction of the Weibull law, which means that the probability to find highenergy electrons varies abruptly near p max . The variance of physical observables sensitive to the high-energy tail is consequently considerably higher than when assuming thermal distribution. a)

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“…At this point, we need to adopt an explicit form of the distribution function. There are several reasonable options, such as the κ or Vasyliunas distribution function [39][40][41][42], the Tsallis distribution function [43][44][45], a super-Gaussian [46,47], a Maxwellian with a supra-thermal component [48] or a Jüttner distribution with a superimposed shift in the momentum [49]. Here, we choose a Cairns-like distribution function.…”

Section: Non-equilibrium Relativistic Distribution Functionmentioning

confidence: 99%

Non-equilibrium effects in a relativistic plasma sheath model

2020

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Plasma sheaths characterized by electrons with relativistic energies and far from thermodynamic equilibrium are governed by a rich and largely unexplored physics. A reliable kinetic description of relativistic non-equilibrium plasma sheaths-besides its interest from a fundamental point of view-is crucial to many application, from controlled nuclear fusion to laser-driven particle acceleration. Sheath models proposed in the literature adopt either relativistic equilibrium distribution functions or non-relativistic non-equilibrium distribution functions, making it impossible to properly capture the physics involved when both relativistic and non-equilibrium effects are important. Here we tackle this issue by solving the electrostatic Vlasov-Poisson equations with a new class of fully-relativistic distribution functions that can describe non-equilibrium features via a real scalar parameter. After having discussed the general properties of the distribution functions and the resulting plasma sheath model, we establish an approach to investigate the effect of non-equilibrium solely. Then, we apply our approach to describe laser-plasma ion acceleration in the target normal sheath acceleration scheme. Results show how different degrees of non-equilibrium lead to the formation of sheaths with significantly different features, thereby having a relevant impact on the ion acceleration process. We believe that this approach can offer a deeper understanding of relativistic plasma sheaths, opening new perspectives in view of their applications.2 In a kinetic description, an equilibrium plasma state is any stationary state that cancels out the collision integral in the transport equation (or, equivalently, that makes the entropy production rate vanish) and is solution of the transport equation itself. Any other state-even if stationary-is of non-equilibrium.

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Effects of nonthermal electrons on plasma expansion into vacuum

Cited by 18 publications

References 36 publications

Plasma expansion towards an electrically insulated surface

Plasma expansion towards an electrically insulated surface

On the non-thermal nature of distributions of electrons accelerated by high intensity lasers at the vacuum-plasma interface

Non-equilibrium effects in a relativistic plasma sheath model

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