Variational solutions of the Vlasov equation and Landau damping in nuclear matter

1989 ◽  
Vol 495 (1-2) ◽  
pp. 193-200 ◽  
Author(s):  
João da Providência
1998 ◽  
Vol 59 (4) ◽  
pp. 611-618 ◽  
Author(s):  
I. PRIGOGINE ◽  
T. PETROSKY

The well-known van Kampen–Case treatment of the Vlasov equation leads to a spectrum on the real axis. In this paper we show that, by going to a ‘rigged’ Hilbert space, we can derive a spectral representation that is complex and breaks time symmetry. This leads to a semigroup description in which the decay rates due to the Landau damping appear explicitly in the spectrum. Moreover, we can then define an entropy. In this way, the relation between Landau damping and irreversibility is made explicit. The analogy with the well-known Friedrichs model is stressed.


2020 ◽  
Vol 80 (12) ◽  
Author(s):  
Fabio Moretti ◽  
Flavio Bombacigno ◽  
Giovanni Montani

AbstractWe establish the possibility of Landau damping for gravitational scalar waves which propagate in a non-collisional gas of particles. In particular, under the hypothesis of homogeneity and isotropy, we describe the medium at the equilibrium with a Jüttner–Maxwell distribution, and we analytically determine the damping rate from the Vlasov equation. We find that damping occurs only if the phase velocity of the wave is subluminal throughout the propagation within the medium. Finally, we investigate relativistic media in cosmological settings by adopting numerical techniques.


1989 ◽  
Vol 500 (2) ◽  
pp. 301-307 ◽  
Author(s):  
D.M. Brink ◽  
J. Da Providencia

2021 ◽  
Author(s):  
Simon Lautenbach ◽  
Rainer Grauer

<p>Collisionless plasmas, mostly present in astrophysical and space environments, often require a kinetic treatment given by the Vlasov equation. Unfortunately, the six-dimensional Vlasov equation is inherently expensive to compute and usually can only be solved on very small parts of the considered spatial domain. However, in some cases, e.g. magnetic reconnection, it is sufficient to solve the Vlasov equation in a localized domain and solve the remaining domain with appropriate fluid models. We present an adaptive hierarchical treatment of collisionless plasmas ranging from fully kinetic, to a 10-moment fluid model incorporating a simplified treatment of Landau damping, to a 5-moment fluid description. To account for separation of electron and ion physics, hybrid stages of mixed electron and ion models are also allowed. As a proof of concept, the full physics-adaptive hierarchy is applied to the Geospace Environmental Modeling (GEM) challenge of magnetic reconnection.</p>


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