1,535 research outputs found
Solving Vlasov Equations Using NRxx Method
In this paper, we propose a moment method to numerically solve the Vlasov
equations using the framework of the NRxx method developed in [6, 8, 7] for the
Boltzmann equation. Due to the same convection term of the Boltzmann equation
and the Vlasov equation, it is very convenient to use the moment expansion in
the NRxx method to approximate the distribution function in the Vlasov
equations. The moment closure recently presented in [5] is applied to achieve
the globally hyperbolicity so that the local well-posedness of the moment
system is attained. This makes our simulations using high order moment
expansion accessible in the case of the distribution far away from the
equilibrium which appears very often in the solution of the Vlasov equations.
With the moment expansion of the distribution function, the acceleration in the
velocity space results in an ordinary differential system of the macroscopic
velocity, thus is easy to be handled. The numerical method we developed can
keep both the mass and the momentum conserved. We carry out the simulations of
both the Vlasov-Poisson equations and the Vlasov-Poisson-BGK equations to study
the linear Landau damping. The numerical convergence is exhibited in terms of
the moment number and the spatial grid size, respectively. The variation of
discretized energy as well as the dependence of the recurrence time on moment
order is investigated. The linear Landau damping is well captured for different
wave numbers and collision frequencies. We find that the Landau damping rate
linearly and monotonically converges in the spatial grid size. The results are
in perfect agreement with the theoretic data in the collisionless case
Diffuse PeV neutrinos from gamma-ray bursts
The IceCube collaboration recently reported the potential detection of two
cascade neutrino events in the energy range 1-10 PeV. We study the possibility
that these PeV neutrinos are produced by gamma-ray bursts (GRBs), paying
special attention to the contribution by untriggered GRBs that elude detection
due to their low photon flux. Based on the luminosity function, rate
distribution with redshift and spectral properties of GRBs, we generate, using
Monte-Carlo simulation, a GRB sample that reproduce the observed fluence
distribution of Fermi/GBM GRBs and an accompanying sample of untriggered GRBs
simultaneously. The neutrino flux of every individual GRBs is calculated in the
standard internal shock scenario, so that the accumulative flux of the whole
samples can be obtained. We find that the neutrino flux in PeV energies
produced by untriggered GRBs is about 2 times higher than that produced by the
triggered ones. Considering the existing IceCube limit on the neutrino flux of
triggered GRBs, we find that the total flux of triggered and untriggered GRBs
can reach at most a level of ~10^-9 GeV cm^-2 s^-1 sr^-1, which is insufficient
to account for the reported two PeV neutrinos. Possible contributions to
diffuse neutrinos by low-luminosity GRBs and the earliest population of GRBs
are also discussed.Comment: Accepted by ApJ, one more figure added to show the contribution to
the diffuse neutrino flux by untriggered GRBs with different luminosity,
results and conclusions unchange
On the origin of >10 GeV photons in gamma-ray burst afterglows
Fermi/LAT has detected long-lasting high-energy photons (>100 MeV) from
gamma-ray bursts (GRBs), with the highest energy photons reaching about 100
GeV. One proposed scenario is that they are produced by high-energy electrons
accelerated in GRB forward shocks via synchrotron radiation. We study the
maximum synchrotron photon energy in this scenario, considering the properties
of the microturbluence magnetic fields behind the shock, as revealed by recent
Particle-in-Cell simulations and theoretical analyses of relativistic
collisionless shocks. Due to the small-scale nature of the micro-turbulent
magnetic field, the Bohm acceleration approximation breaks down at such high
energies. This effect leads to a typical maximum synchrotron photon of a few
GeV at 100 s after the burst and this maximum synchrotron photon energy
decreases quickly with time. We show that the fast decrease of the maximum
synchrotron photon energy leads to a fast decay of the synchrotron flux. The
10-100 GeV photons detected after the prompt phase can not be produced by the
synchrotron mechanism. They could originate from the synchrotron self-Compton
emission of the early afterglow if the circum-burst density is sufficiently
large, or from the external inverse-Compton process in the presence of central
X-ray emission, such as X-ray flares and prompt high-latitude X-ray emission.Comment: 13 pages, 3 figures, accepted by ApJ Letter
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