On the Fay identity for KdV tau functions and the identity for the Wronskian of squared solutions of Sturm-Liouville equation

We show that the well known identity for the Wronskian of squared solutions of a Sturm-Liouville equation follows from the Fay identity. We also study some odd-order (($2^n -1$)-order, $n = 2, 3, ...$) identities which are specific for tau functions, related to the KdV hierarchy.Comment: Amstex, 13 page

Hadron Generator and Atmospheric Seasonal Variation Influence on Cosmic Ray Ionization computed with CORSIKA Code

Recently an essential progress in development of physical models for cosmic ray induced ionization in the atmosphere is achieved. Basically, the models are full target, i.e. based on Monte Carlo simulation of an electromagnetic-muon-nucleon cascade in the atmosphere. In general, the contribution of proton nuclei in those models is highlighted, i.e. primary cosmic ray $\alpha$-particles and heavy nuclei are neglected or scaled to protons. The development of cosmic ray induced atmospheric cascade is sensitive to the energy and mass of the primary cosmic ray particle. The largest uncertainties in Monte Carlo simulations of a cascade in the Earth atmosphere are due to assumed hadron interaction models, the so-called hadron generators. In the work presented here we compare the ionization yield functions $Y$ for primary cosmic ray nuclei, such as protons, $\alpha$-particles, Oxygen and Iron nuclei, assuming different hadron interaction models. The computations are fulfilled with the CORSIKA 6.9 code using GHEISHA 2002, FLUKA 2011, UrQMD hadron generators for energy below 80 GeV/nucleon and QGSJET II for energy above 80 GeV/nucleon. The observed difference between hadron generators is widely discussed. The influence of different atmospheric parametrizations, namely US standard atmosphere, US standard atmosphere winter and summer profiles on ion production rate is studied. Assuming realistic primary cosmic ray mass composition, the ion production rate is obtained at several rigidity cut-offs - from 1 GV (high latitudes) to 15 GV (equatorial latitudes) using various hadron generators. The computations are compared with experimental data. A conclusion concerning the consistency of the hadron generators is stated.Comment: 24 pages, 11 figures, extended version of paper accpted for publication in JAST

Energetic particle influence on the Earth's atmosphere

This manuscript gives an up-to-date and comprehensive overview of the effects of energetic particle precipitation (EPP) onto the whole atmosphere, from the lower thermosphere/mesosphere through the stratosphere and troposphere, to the surface. The paper summarizes the different sources and energies of particles, principally galactic cosmic rays (GCRs), solar energetic particles (SEPs) and energetic electron precipitation (EEP). All the proposed mechanisms by which EPP can affect the atmosphere are discussed, including chemical changes in the upper atmosphere and lower thermosphere, chemistry-dynamics feedbacks, the global electric circuit and cloud formation. The role of energetic particles in Earth’s atmosphere is a multi-disciplinary problem that requires expertise from a range of scientific backgrounds. To assist with this synergy, summary tables are provided, which are intended to evaluate the level of current knowledge of the effects of energetic particles on processes in the entire atmosphere

Influence of forbush effect on atmospheric ionization due to solar energtic particles

Abstract High-energy precipitating particles of cosmic origin viz. cosmic ray (CR) protons of heavier nuclei of galactic and/or solar origin induce complicated nuclear-electromagnetic-lepton cascades in the Earth’s atmosphere, eventually leading to an ionization of the ambient air. The induced by CRs ionization is related to possible effect of precipitating particles on physico-chemical processes in the atmosphere. These effects can be considerably enhanced during solar proton events. While the contribution of galactic CRs to ion production in the atmosphere is slightly variable throughout a solar cycle, relativistic solar particles could produce a significant excess of electron-ion pair production, particularly over polar caps. This effect is strong on short time scales. On the other hand, depressions of the galactic CR flux, that is, Forbush decreases, can significantly impact on induced ionization. The sequence of three ground level enhancements (GLEs) 65, 66 and 67 in October-November 2003, specifically GLE 66 occurred during a giant Forbush decrease, provides unique opportunity to study impact ionization on enhanced manner and extended time scale, explicitly considering the reduced galactic CR flux. Using Monte Carlo simulations and appropriate solar proton spectra we computed the ion production rate and the corresponding ionization effect in the Earth atmosphere during GLE 66 which occurred on 29 October 2003

Ionization effects in the middle stratosphere due to cosmic rays during strong GLE events

Abstract An important topic in the field of solar-terrestrial and space physics is the highly discussed possible effect of cosmic ray (CR) particles on atmospheric chemistry and physics, specifically by induced ionization. In most of the recently developed models, the induced by CRs atmospheric ionization plays a significant role. Nowadays, it is clear that the contribution of galactic cosmic ray particles to electron-ion production in the atmosphere slightly varies with the solar modulation and transient effects. On the other hand, high energy solar particles could produce complicated hadron-electromagnetic-muon cascade in the atmosphere of the Earth and significantly enhance the electron-ion pair production, particularly over polar caps. This effect is usually strong on a short time scales, being more important in the region of Regener–Pfotzer maximum. However, for some atmospheric chemistry and physics purposes it is important to estimate the ionization effect in the middle stratosphere. The Ground Level Enhancement GLE 59 on Bastille Day 14 of July 2000 and the maverick GLE 70 on 13 December 2006 are among the strongest recorded events during the previous solar cycle 23. Herein, using recently proposed full target Monte Carlo simulation and previously derived high energy solar particles energy spectra we estimated the electron-ion production rate and corresponding ionization effect in the Earth middle stratosphere during two moderately strong ground level enhancement events

Ionization effect in the region of Regener–Pfotzer Maximum due to cosmic rays during halloween GLE events in October–November 2003

Abstract One of the main drivers of the possible effect of cosmic ray particles on atmospheric physics and chemistry is connected to the Induced Atmospheric Ionization (IAI) due to high-energy precipitating particles. IAI by cosmic rays, which can be considerably enhanced during solar proton events, was extensively discussed over the last decade. In most of the recent models, IAI plays a key role on the physics and chemistry of the atmosphere, specifically on minor constituents. It is known that the contribution of galactic cosmic ray particles to ion production in the atmosphere is nearly constant, slightly influenced by the solar activity. On the other hand, the relativistic solar particles could produce a significant excess of ion pair production, particularly over polar caps. This effect is normally strong at short time scales. The sequence of three ground level enhancements GLE 65, 66 & 67 in October–November 2003 gives an unique opportunity to study impact ionization on enhanced manner and extended time scale. Using Monte Carlo simulation and derived solar proton spectra, we computed the ion production and the corresponding ionization effect in the Earth atmosphere in the region of Regener–Pfotzer maximum during the so-called Halloween events in October–November 2003