24 research outputs found
Fast growing instabilities for non-parallel flows
Unstable modes growing when two plasma shells cross over a background plasma
at arbitrary angle , are investigated using a non-relativistic three
cold fluids model. Parallel flows with are slightly more unstable
than anti-parallel ones with . The case is as
unstable as the one, but the fastest growing modes are oblique.
While the most unstable wave vector varies with orientation, its growth rate
slightly evolves and there is no such thing as a stable configuration. A number
of exact results can be derived, especially for the case.Comment: 4 pages, 3 figures, to appear in Phys. Lett.
How large can the electron to proton mass ratio be in Particle-In-Cell simulations of unstable systems?
Particle-in-cell (PIC) simulations are widely used as a tool to investigate
instabilities that develop between a collisionless plasma and beams of charged
particles. However, even on contemporary supercomputers, it is not always
possible to resolve the ion dynamics in more than one spatial dimension with
such simulations. The ion mass is thus reduced below 1836 electron masses,
which can affect the plasma dynamics during the initial exponential growth
phase of the instability and during the subsequent nonlinear saturation. The
goal of this article is to assess how far the electron to ion mass ratio can be
increased, without changing qualitatively the physics. It is first demonstrated
that there can be no exact similarity law, which balances a change of the mass
ratio with that of another plasma parameter, leaving the physics unchanged.
Restricting then the analysis to the linear phase, a criterion allowing to
define a maximum ratio is explicated in terms of the hierarchy of the linear
unstable modes. The criterion is applied to the case of a relativistic electron
beam crossing an unmagnetized electron-ion plasma.Comment: To appear in Physics of Plasma
Early out-of-equilibrium beam-plasma evolution
We solve analytically the out-of-equilibrium initial stage that follows the
injection of a radially finite electron beam into a plasma at rest and test it
against particle-in-cell simulations. For initial large beam edge gradients and
not too large beam radius, compared to the electron skin depth, the electron
beam is shown to evolve into a ring structure. For low enough transverse
temperatures, the filamentation instability eventually proceeds and saturates
when transverse isotropy is reached. The analysis accounts for the variety of
very recent experimental beam transverse observations.Comment: to appear in Phys. Rev. Letter
Characterization of the initial filamentation of a relativistic electron beam passing through a plasma
The linear instability that induces a relativistic electron beam passing
through a return plasma current to filament transversely is often related to
some filamentation mode with wave vector normal to the beam or confused with
Weibel modes. We show that these modes may not be relevant in this matter and
identify the most unstable mode on the two-stream/filamentation branch as the
main trigger for filamentation. This sets both the characteristic transverse
and longitudinal filamentation scales in the non-resistive initial stage.Comment: 4 page, 3 figures, to appear in PR
Instabilities for a relativistic electron beam interacting with a laser irradiated plasma
The effects of a radiation field (RF) on the unstable modes developed in
relativistic electron beam--plasma interaction are investigated assuming that
, where is the frequency of the RF and
is the plasma frequency. These unstable modes are parametrically
coupled to each other due to the RF and are a mix between two--stream and
parametric instabilities. The dispersion equations are derived by the
linearization of the kinetic equations for a beam--plasma system as well as the
Maxwell equations. In order to highlight the effect of the radiation field we
present a comparison of our analytical and numerical results obtained for
nonzero RF with those for vanishing RF. Assuming that the drift velocity
of the beam is parallel to the wave vector of the
excitations two particular transversal and parallel configurations of the
polarization vector of the RF with respect to are
considered in detail. It is shown that in both geometries resonant and
nonresonant couplings between different modes are possible. The largest growth
rates are expected at the transversal configuration when is
perpendicular to . In this case it is demonstrated that in general
the spectrum of the unstable modes in -- plane is split into two
distinct domains with long and short wavelengths, where the unstable modes are
mainly sensitive to the beam or the RF parameters, respectively. In parallel
configuration, , and at short wavelengths
the growth rates of the unstable modes are sensitive to both beam and RF
parameters remaining insensitive to the RF at long wavelengths.Comment: 23 pages, 5 figure
Two-stream-like instability in dilute hot relativistic beams and astrophysical relativistic shocks
Relativistic collisionless shocks are believed to be efficient particle
accelerators. Nonlinear outcome of the interaction of accelerated particles
that run ahead of the shock, the so-called "precursor", with the unperturbed
plasma of the shock upstream, is thought to facilitate additional acceleration
of these particles and to possibly modify the hydrodynamic structure of the
shock. We explore here the linear growth of kinetic modes appearing in the
precursor-upstream interaction in relativistic shocks propagating in non and
weakly magnetized plasmas: electrostatic two-stream parallel mode and
electrostatic oblique modes. These modes are of particular interest because
they are the fastest growing modes known in this type of system. Using a
simplified distribution function for a dilute ultra-relativistic beam that is
relativistically hot in its own rest frame, yet has momenta that are narrowly
collimated in the frame of the cold upstream plasma into which it propagates,
we identify the fastest growing mode in the full -space and calculate its
growth rate. We consider all types of plasma (pairs and ions-electrons) and
beam (charged and charge-neutral). We find that unstable electrostatic modes
are present in any type of plasma and for any shock parameters. We further find
that two modes, one parallel () and the other one oblique (), are competing for dominance and that either one may dominate the
growth rate in different regions of the phase space. The dominant mode is
determined mostly by the perpendicular spread of the accelerated particle
momenta in the upstream frame, which reflects the shock Lorentz factor. The
parallel mode becomes more dominant in shocks with lower Lorentz factors (i.e.,
with larger momentum spreads). We briefly discuss possible implications of our
results for external shocks in gamma-ray burst sources
Robustness of the filamentation instability as shock mediator in arbitrarily oriented magnetic field
The filamentation instability (sometimes also referred to as "Weibel") is a
key process in many astrophysical scenario. In the Fireball model for Gamma Ray
Bursts, this instability is believed to mediate collisionless shock formation
from the collision of two plasma shells. It has been known for long that a flow
aligned magnetic field can completely cancel this instability. We show here
that in the general case where there is an angle between the field and the
flow, the filamentation instability can never be stabilized, regardless of the
field strength. The presented model analyzes the stability of two symmetric
counter-streaming cold electron/proton plasma shells. Relativistic effects are
accounted for, and various exact analytical results are derived. This result
guarantees the occurrence of the instability in realistic settings fulfilling
the cold approximation.Comment: To appear in Physics of Plasmas Letter
Index
The interest in relativistic beam-plasma instabilities has been greatly rejuvenated over the past two decades by novel concepts in laboratory and space plasmas. Recent advances in this long-standing field are here reviewed from both theoretical and numerical points of view. The primary focus is on the two-dimensional spectrum of unstable electromagnetic waves growing within relativistic, unmagnetized, and uniform electron beam-plasma systems. Although the goal is to provide a unified picture of all instability classes at play, emphasis is put on the potentially dominant waves propagating obliquely to the beam direction, which have received little attention over the years. First, the basic derivation of the general dielectric function of a kinetic relativistic plasma is recalled. Next, an overview of two-dimensional unstable spectra associated with various beam-plasma distribution functions is given. Both cold-fluid and kinetic linear theory results are reported, the latter being based on waterbag and Maxwell–Jüttner model distributions. The main properties of the competing modes (developing parallel, transverse, and oblique to the beam) are given, and their respective region of dominance in the system parameter space is explained. Later sections address particle-in-cell numerical simulations and the nonlinear evolution of multidimensional beam-plasma systems. The elementary structures generated by the various instability classes are first discussed in the case of reduced-geometry systems. Validation of linear theory is then illustrated in detail for large-scale systems, as is the multistaged character of the nonlinear phase. Finally, a collection of closely related beam-plasma problems involving additional physical effects is presented, and worthwhile directions of future research are outlined.Original Publication: Antoine Bret, Laurent Gremillet and Mark Eric Dieckmann, Multidimensional electron beam-plasma instabilities in the relativistic regime, 2010, Physics of Plasmas, (17), 12, 120501-1-120501-36. http://dx.doi.org/10.1063/1.3514586 Copyright: American Institute of Physics http://www.aip.org/</p