1,937 research outputs found
Ultrashort light bullets described by the two-dimensional sine-Gordon equation
By using a reductive perturbation technique applied to a two-level model,
this study puts forward a generic two-dimensional sine-Gordon evolution
equation governing the propagation of femtosecond spatiotemporal optical
solitons in Kerr media beyond the slowly varying envelope approximation. Direct
numerical simulations show that, in contrast to the long-wave approximation, no
collapse occurs, and that robust (2+1)-dimensional ultrashort light bullets may
form from adequately chosen few-cycle input spatiotemporal wave forms. In
contrast to the case of quadratic nonlinearity, the light bullets oscillate in
both space and time and are therefore not steady-state lumps
The molecular ion in a magnetic field
A detailed study of the low-lying electronic states
{}^1\Si,{}^3\Si,{}^3\Pi,{}^3\De of the molecular ion in parallel
to a magnetic field configuration (when \al-particle and proton are situated
on the same magnetic line) is carried out for G in
the Born-Oppenheimer approximation. The variational method is employed using a
physically adequate trial function. It is shown that the parallel configuration
is stable with respect to small deviations for \Si-states. The quantum
numbers of the ground state depend on the magnetic field strength. The ground
state evolves from the spin-singlet {}^1\Si state for small magnetic fields
a.u. to the spin-triplet {}^3\Si unbound state for
intermediate fields and to the spin-triplet strongly bound state for a.u. When the molecular ion exists, it is stable with
respect to a dissociation.Comment: 13 pages, 5 figures, 4 table
Charged Hydrogenic, Helium and Helium-Hydrogenic Molecular Chains in a Strong Magnetic Field
A non-relativistic classification of charged molecular hydrogenic, helium and
mixed helium-hydrogenic chains with one or two electrons which can exist in a
strong magnetic field G is given. It is shown that for
both cases at the strongest studied magnetic fields the longest
hydrogenic chain contains at most five protons indicating to the existence of
the and ions, respectively. In the case of the
helium chains the longest chains can exist at the strongest studied magnetic
fields with three and four \al-particles for cases, respectively. For
mixed helium-hydrogenic chains the number of heavy centers can reach five for
highest magnetic fields studied. In general, for a fixed magnetic field
two-electron chains are more bound than one-electron ones.Comment: 32 pages, 2 figures, 9 table
Effects of Line-tying on Magnetohydrodynamic Instabilities and Current Sheet Formation
An overview of some recent progress on magnetohydrodynamic stability and
current sheet formation in a line-tied system is given. Key results on the
linear stability of the ideal internal kink mode and resistive tearing mode are
summarized. For nonlinear problems, a counterexample to the recent
demonstration of current sheet formation by Low \emph{et al}. [B. C. Low and
\AA. M. Janse, Astrophys. J. \textbf{696}, 821 (2009)] is presented, and the
governing equations for quasi-static evolution of a boundary driven, line-tied
magnetic field are derived. Some open questions and possible strategies to
resolve them are discussed.Comment: To appear in Phys. Plasma
Extended Scaling Laws in Numerical Simulations of MHD Turbulence
Magnetised turbulence is ubiquitous in astrophysical systems, where it
notoriously spans a broad range of spatial scales. Phenomenological theories of
MHD turbulence describe the self-similar dynamics of turbulent fluctuations in
the inertial range of scales. Numerical simulations serve to guide and test
these theories. However, the computational power that is currently available
restricts the simulations to Reynolds numbers that are significantly smaller
than those in astrophysical settings. In order to increase computational
efficiency and, therefore, probe a larger range of scales, one often takes into
account the fundamental anisotropy of field-guided MHD turbulence, with
gradients being much slower in the field-parallel direction. The simulations
are then optimised by employing the reduced MHD equations and relaxing the
field-parallel numerical resolution. In this work we explore a different
possibility. We propose that there exist certain quantities that are remarkably
stable with respect to the Reynolds number. As an illustration, we study the
alignment angle between the magnetic and velocity fluctuations in MHD
turbulence, measured as the ratio of two specially constructed structure
functions. We find that the scaling of this ratio can be extended surprisingly
well into the regime of relatively low Reynolds number. However, the extended
scaling becomes easily spoiled when the dissipation range in the simulations is
under-resolved. Thus, taking the numerical optimisation methods too far can
lead to spurious numerical effects and erroneous representation of the physics
of MHD turbulence, which in turn can affect our ability to correctly identify
the physical mechanisms that are operating astrophysical systems
Magnetohydrodynamic Turbulent Cascade of Coronal Loop Magnetic Fields
The Parker model for coronal heating is investigated through a high
resolution simulation. An inertial range is resolved where fluctuating magnetic
energy E_M (k_perp) \propto k_\perp^{-2.7} exceeds kinetic energy E_K (k_\perp)
\propto k_\perp^{-0.6}. Increments scale as \delta b_\ell \simeq \ell^{-0.85}
and \delta u_\ell \simeq \ell^{+0.2} with velocity increasing at small scales,
indicating that magnetic reconnection plays a prime role in this turbulent
system. We show that spectral energy transport is akin to standard
magnetohydrodynamic (MHD) turbulence even for a system of reconnecting current
sheets sustained by the boundary. In this new MHD turbulent cascade, kinetic
energy flows are negligible while cross-field flows are enhanced, and through a
series of "reflections" between the two fields, cascade more than half of the
total spectral energy flow.Comment: 5 pages, 5 figures, to appear in Physical Review E - Rapid. Com
Renormalized non-modal theory of the kinetic drift instability of plasma shear flows
The linear and renormalized nonlinear kinetic theory of drift instability of
plasma shear flow across the magnetic field, which has the Kelvin's method of
shearing modes or so-called non-modal approach as its foundation, is developed.
The developed theory proves that the time-dependent effect of the finite ion
Larmor radius is the key effect, which is responsible for the suppression of
drift turbulence in an inhomogeneous electric field. This effect leads to the
non-modal decrease of the frequency and growth rate of the unstable drift
perturbations with time. We find that turbulent scattering of the ion gyrophase
is the dominant effect, which determines extremely rapid suppression of drift
turbulence in shear flow
The Spectral Slope and Kolmogorov Constant of MHD turbulence
The spectral slope of strong MHD turbulence has recently been a matter of
controversy. While Goldreich-Sridhar model (1995) predicts Kolmogorov's -5/3
slope of turbulence, shallower slopes were often reported by numerical studies.
We argue that earlier numerics was affected by driving due to a diffuse
locality of energy transfer in MHD case. Our highest-resolution simulation
(3072^2x1024) has been able to reach the asymptotic -5/3 regime of the energy
slope. Additionally, we found that so-called dynamic alignment, proposed in the
model with -3/2 slope, saturates and therefore can not affect asymptotic slope.
The observation of the asymptotic regime allowed us to measure Kolmogorov
constant C_KA=3.2+-0.2 for purely Alfv\'enic turbulence and C_K=4.1+-0.3 for
full MHD turbulence. These values are much higher than the hydrodynamic value
of 1.64. The larger value of Kolmogorov constant is an indication of a fairly
inefficient energy transfer and, as we show in this Letter, is in theoretical
agreement with our observation of diffuse locality. We also explain what has
been missing in numerical studies that reported shallower slopes.Comment: 5 pages 3 figure
- …