A three-dimensional code for muon propagation through the rock: MUSIC

We present a new three-dimensional Monte-Carlo code MUSIC (MUon SImulation Code) for muon propagation through the rock. All processes of muon interaction with matter with high energy loss (including the knock-on electron production) are treated as stochastic processes. The angular deviation and lateral displacement of muons due to multiple scattering, as well as bremsstrahlung, pair production and inelastic scattering are taken into account. The code has been applied to obtain the energy distribution and angular and lateral deviations of single muons at different depths underground. The muon multiplicity distributions obtained with MUSIC and CORSIKA (Extensive Air Shower simulation code) are also presented. We discuss the systematic uncertainties of the results due to different muon bremsstrahlung cross-sections.     

Energy loss of protons in the molecular oxygen

A theoretical study of the proton loss function in the molecular oxygen based on the most appropriate elastic and inelastic cross-sections is made. The earlier results of the loss function are modified for ionization, charge exchange and elastic scattering. The present results are in good agreement with experiment.     

Formation of zebra patterns of solar microwave bursts as a result of propagation of radio waves through the inhomogeneous corona

The geoefficiency of solar bursts is diagnosed using the dynamic radio emission spectrum. At certain time intervals, the spectrum exhibits nearly parallel narrow-band emission strips termed the zebra pattern. Although there are many hypotheses of its origin, all of them do not take into account changes in the signal parameters upon signal propagation through the solar corona. Our analysis shows that the propagation effects form a dynamic spectrum that contains a zebra pattern. The properties of the modeled spectrum are shown to coincide with the basic properties of the observed spectrum. It is clarified that the spike structure of strips is a natural consequence of the interference of radio waves, and the occurrence of this structure is considered to be evidence in favor of the interference nature of the zebra pattern formation. Consequently, the zebra pattern can be formed not in the radiation source itself, but rather can arise as a result of propagation of radio waves through an inhomogeneous refracting medium of the solar corona.     

Viscous computations of resonant absorption of MHD waves in flux tubes by fem

A numerical code is presented for computing the stationary state of resonant absorption of MHD waves in cylindrical flux tubes in linear, compressible, and viscous MHD. The full viscosity stress tensor is included in the code with the five viscosity coefficients as given by Braginskii (1965). Also non-zero plasma pressure effects are taken into account, and the finite elements discretization with the Galerkin method has been used. The implementation of the stress tensor and the numerical accuracy of the tensorial viscous MHD code are scrutinized in test case. The test case involves the absorption of waves in cylindrical flux tubes considered by Lou (1990) and Goossens and Poedts (1992) in the context of absorption of acoustic oscillations. The results for the absorption rates obtained with the tensorial viscous code agree completely with the results obtained by Lou in a scalar viscous MHD and by Goossens and Poedts in resistive MHD. This verifies not only the complicated tensor viscous code but again proves that the absorption rate is independent of the actual dissipation mechanism.     

Induced Raman scattering in pulsar magnetospheres

It is shown that induced Raman scattering of electromagnetic waves in the strongly magnetized electron–positron plasma of pulsar magnetospheres may be important for wave propagation and as an effective saturation mechanism for electromagnetic instabilities. The frequencies at which strong Raman scattering occurs in the outer parts of a magnetosphere fall into the observed radio band. The typical threshold intensities for the strong Raman scattering are of the order of the observed intensities, implying that pulsar magnetospheres may be optically thick to Raman scattering of electromagnetic waves.     

Seismic scattering and shallow structure of the moon in oceanus procellarum

Long, reverberating trains of seismic waves produced by impacts and moonquakes may be interpreted in terms of scattering in a surface layer overlying a non-scattering elastic medium. Model seismic experiments are used to qualitatively demonstrate the correctness of the interpretation. Three types of seismograms are found, near impact, far impact and moonquake. Only near impact and moonquake seismograms contain independent information. Details are given in the paper of the modelling of the scattering processes by the theory of diffusion.Interpretation of moonquake and artificial impact seismograms in two frequency bands from the Apollo 12 site indicates that the scattering layer is 25 km thick, with a Q of 5000. The mean distance between scatterers is approximately 5 km at 25 km depth and approximately 2 km at 14 km depth; the density of scatterers appears to be high near the surface, decreasing with depth. This may indicate that the scatterers are associated with cratering, or are cracks that anneal with depth. Most of the scattered energy is in the form of scattered surface waves.Communication presented at the Lunar Science Institute Conference on Geophysical and Geochemical Exploration of the Moon and Planets, January 10–12, 1973.     

Fluctuations of density and waves in nonlinear nuclear reactions in stellar cores

The space correlation of fluctuation of density in the nuclear reaction system inside the stars is investigated by using the theory of a generating function. Referring to the dynamical rate equation, we have introduced the gravitational force and temperature gradient terms into master equation of the probability distribution function of density, and a generalized master equation has been obtained. We take P-PI reactions of hydrogen-burning in the solar core as an example to solve this master equation for infinite medium. A series of waves have been obtained. The first branch is the average density wave which has already been obtained from the dynamical rate equation. Other branches describe the propagation of the fluctuation moments of the local density. They represent the propagation processes of the local distortion of the probability distribution function. Stability of the system may be related to an increase and decay of the waves. We have analysed the phase velocity of these waves.     

The radiation force on small particles

A more complete expression for the radiation force on a small particle in the solar system is given which includes the effect of asymmetry of the thermal reradiation and also of inelastic scattering such as fluorescence. Both the Poynting-Robertson drag and the Yarkovsky effect are affected by such asymmetries and are incorporated into the formalism. For non-spherical particles the direction of the radiation force will no longer coincide with the solar irradiation.     

Lorentz scattering of interplanetary dust

Charged dust grains in a turbulent magnetic field will see a Lorentz force due to the convection of the solar magnetic field past them at the solar wind velocity. Since the sign of this magnetic field is randomly varying, the direction of the force will be random, and the net effect will be to randomly scatter the orbital elements of these particles. The square roots of the mean square change in semimajor axis, inclination, and eccentricity are determined as a function of the particles' original orbital elements. Particles 3 μm in radius and smaller will have their motions strongly perturbed or dominated by Lorentz scattering. This scattering will have an effect comparable to, or greater than, the Poynting-Robertson effect on these particles for time scales comparable to their Poynting-Robertson lifetimes.     

MHD waves at a spherical interface modelling EIT waves

Eruptive events such as flares and coronal mass ejections (CMEs) are known to generate global waves propagating over distances comparable to the solar radius in different layers of the solar atmosphere. Here we investigate the propagation of coronal EIT waves, modelled as fast magnetoacoustic modes propagating at a spherical interface in the presence of a purely radial magnetic field. Based on a simplified equilibrium we derive the dispersion relation of the waves. The generation and propagation of EIT waves at the spherical interface is studied numerically for different values of spherical degree and preliminary conclusions are reached regarding the properties of EIT waves. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The analogy between sunquakes and water waves

To investigate the seismic waves generated at the surface of the convection zone by a sunquake, the solar convection zone is modeled as an incompressible fluid layer of finite depth which is excited by a pressure pulse just above the solar surface. Solutions for the surface displacement ζ as a function of time are obtained by solving the linearized Euler equations for wave propagation in an inviscid, incompressible fluid. Approximate solutions are derived using the method of stationary phase and formulas are obtained for the position of the wave crests versus time and the decay of the wave amplitude versus distance. Despite the very simple nature of the model, the resulting time–distance relation is found to exhibit the correct order of magnitude when compared to the observations of the flare initiated sunquake of 9 July 1996. However, the water wave model cannot fully explain the observations because, for one thing, the distance in between successive wave crests is greater than that seen in the observations. One may conclude that the sunquake is probably composed primarily of acoustic waves, that is, p modes and not f modes.     

Validation of numerical codes for impact and explosion cratering: Impacts on strengthless and metal targets

Abstract— Over the last few decades, rapid improvement of computer capabilities has allowed impact cratering to be modeled with increasing complexity and realism, and has paved the way for a new era of numerical modeling of the impact process, including full, three‐dimensional (3D) simulations. When properly benchmarked and validated against observation, computer models offer a powerful tool for understanding the mechanics of impact crater formation. This work presents results from the first phase of a project to benchmark and validate shock codes. A variety of 2D and 3D codes were used in this study, from commercial products like AUTODYN, to codes developed within the scientific community like SOVA, SPH, ZEUS‐MP, iSALE, and codes developed at U.S. National Laboratories like CTH, SAGE/RAGE, and ALE3D. Benchmark calculations of shock wave propagation in aluminum‐on‐aluminum impacts were performed to examine the agreement between codes for simple idealized problems. The benchmark simulations show that variability in code results is to be expected due to differences in the underlying solution algorithm of each code, artificial stability parameters, spatial and temporal resolution, and material models. Overall, the inter‐code variability in peak shock pressure as a function of distance is around 10 to 20%. In general, if the impactor is resolved by at least 20 cells across its radius, the underestimation of peak shock pressure due to spatial resolution is less than 10%. In addition to the benchmark tests, three validation tests were performed to examine the ability of the codes to reproduce the time evolution of crater radius and depth observed in vertical laboratory impacts in water and two well‐characterized aluminum alloys. Results from these calculations are in good agreement with experiments. There appears to be a general tendency of shock physics codes to underestimate the radius of the forming crater. Overall, the discrepancy between the model and experiment results is between 10 and 20%, similar to the inter‐code variability.     

Dynamic phenomena in the chromospheric layer of a sunspot

We have studied running penumbral waves, umbral oscillations, umbral flashes and their interrelations from H observations of a large isolated sunspot. Using a subtraction image processing technique we removed the sharp intensity gradient between the umbra and the penumbra and enhanced the low contrast, fine features. We observed running penumbral waves which started in umbral elements with a size of a few arcseconds, covered the umbra and subsequently propagated through the penumbra. The period of the waves was 190 s and the mean propagation velocity was about 15 km s^–1. We detected intense brightenings, located between umbral elements from where waves started, which had the characteristics of umbral flashes. There are indications that umbral flashes are related to the propagation of the waves through the umbra and their coupling. The subtraction images also show considerable fine structure in the chromospheric umbra, with size between 0.3 and 0.8.     

Kinetic equations for neutrino spin- and type-oscillations in a medium

Quantum kinetic equations for the distribution function of massive Dirac neutrinos have been obtained. They describe neutrino spin- and type-oscillations in a medium. The processes of elastic and inelastic scattering of neutrinos with medium components as well as -processes have been taken into account. Applications of developed equations for stellar collapse are discussed.     

Quantum string theory in curved space-times

A general method to quantize strings in curved space-times is exposed. It treats the space-time metric exactly and the string excitations small as compared with the energy scale of the geometry. The method is applied to cosmological (de Sitter) and black-hole (Schwarzschild) geometries. The critical dimension decreases in one for de Sitter and stays unaltered for black-holes as compared with flat space-time values. Bogoliubov transformations in the context of string theory are derived and the Bogoliubov coefficients describing elastic and inelastic scattering and excitation of modes are computed explicitely. The string-black-hole cross section is derived and a pair mode creation phenomena is found. The quantization and scattering of strings in shockwave geometries (ultrarelativistic boosted black-holes or Aichelburg-Sexl space time) is found to be exactly solvable.     

Polarization of Microwave Radio Emission of Flare-Producing Solar Active Regions

On the basis of our multiwavelength observations made with the one-dimensional RATAN-600 radio telescope, we study the inversion of the circular polarization in the solar microwave emission at different frequencies. The inversion is detected in the emission of flare-producing active regions (FPARs) at various stages of their development, starting from the pre-flare stage. During the latest 23rd solar cycle maximum, numerous FPARs revealed spectral inhomogeneities in their polarized microwave radiation (Bogod and Tokhchukova, 2003, Astron. Lett. 29, 263). Here, we discuss a particular case of such inhomogeneities, the frequency-dependent double inversion of the sign of circular polarization, which probably reflects some essential processes in FPARs. We consider several mechanisms for the double inversion: linear interaction of waves in the region of a quasitransverse magnetic field, the propagation of waves through a region of zero magnetic field, the scattering of radio waves on waves of high-frequency plasma turbulence, the influence of the current fibrils on the propagation of the radio emission, and the magnetic “dips,” in which the direction of magnetic field lines changes the sign relative to the observer. All of them have shortcomings, but the last mechanism explains the observations the best.     

A Kinetic Model of Coronal Heating and Acceleration by Ion-Cyclotron Waves: Preliminary Results

We present a kinetic model of the heating and acceleration of coronal protons by outward-propagating ion-cyclotron waves on open, radial magnetic flux tubes. In contrast to fluid models which typically insist on bi-Maxwellian distributions and which spread the wave energy and momentum over the entire proton population, this model follows the kinetic evolution of the collisionless proton distribution function in response to the combination of the resonant wave-particle interaction and external forces. The approximation is made that pitch-angle scattering by the waves is faster than all other processes, resulting in proton distributions which are uniform over the resonant surfaces in velocity space. We further assume, in this preliminary version, that the waves are dispersionless so these resonant surfaces are portions of spheres centered on the radial sum of the Alfvén speed and the proton bulk speed. We incorporate the fact that only those protons with radial speeds less than the bulk speed will be resonant with outward-propagating waves, so this rapid interaction acts only on the sunward half of the distribution. Despite this limitation, we find that the strong perpendicular heating of the resonant particles, coupled with the mirror force, results in substantial outward acceleration of the entire distribution. The proton distribution evolves towards an incomplete shell in velocity space, and appears vastly different from the distributions assumed in fluid models. Evidence of these distinctive distributions should be observable by instruments on Solar Probe.     

Coronal loop heating by discrete Alfvén waves

We have modeled the solar coronal active loop heating by discrete Alfvén waves. Discrete Alfvén waves (DAW) are a new class of Alfvén waves which can be described by the two-fluid model with finite ion-cyclotron frequency, or the MHD model with plasma current along the magnetic field line as shown by Appert, Vaclavik, and Villar (1984). We have modeled the coronal loop as a semi-toroidal plasma with the major toroidal radius much larger than the plasma radius. We have shown that the absorption of discrete Alfvén waves by the plasma through viscosity can account for at least 30% of the coronal heating rate density of 10^–4 J m^–3 s^–1.     

彗木相撞中的波动

1994年7月18日至24日期间，彗星苏梅克-列维9(SL-9)的超过20块碎片与木星发生了相撞．哈勃空间望远镜(HST)拍摄到的图像揭示了木星大气对撞击的动力学响应．具有重要意义的是观测到5个撞击点周围的圆环，它们以450米／秒的常速度向外运动．环的圆形性表明它们是波．因为对于不同大小的撞击，波速是常量，可以推断出传播速度与爆炸能量无关．这意味着这些波动是线性波．评述现行理论所使用的3类候选波，亦即惯性引力波、声波和地震波，介绍的重点是前面两种．     

The dynamical effects of supernovae on the interstellar medium

An interstellar cloud suddenly overrun by a supernova blast wave experiences a very rapid increase in boundary pressure. A shock wave propagates into the cloud. As a preliminary investigation, the propagation of spherical shock waves in an adiabatic medium is studied numerically.