Corrections for regular identification of high energy positive particles in experimental data using lobachevsky space

New methods of materials irradiation with high energy (≥ 1 MeV) charged particles

The known systems of radial equations describing the relativistic hydrogen atom on the base of the Dirac equation in Lobachevsky hyperbolic space is solved. The relevant 2-nd order differential equation has six regular singular points, its solutions of Frobenius type are constructed explicitly. To produce the quantization rule for energy values we have used the known condition for determination of the transcendental Frobenius solutions. This defines the energy spectrum which is physically interpretable and similar to the spectrum arising for the scalar Klein-Fock-Gordon equation in Lobachevsky space. In the present paper, exact analytical solutions referring to this spectrum are constructed. Convergence of the series involved is proved analytically and numerically. Squared integrability of the solutions is demonstrated numerically. It is shown that the spectrum coincides precisely with that previously found within the semi-classical approximation.

8 - Particle Accelerators

Chapter 8 - Particle Accelerators

As requirements for satellite on-board processing throughput continue to increase, users of radiation tolerant electronics are driven to ever decreasing feature sizes. As device feature sizes drop below the current radiation hardened capabilities of 130 nm one should include more of the high-energy space environment in the analysis of the potential effects. The effects due to particle showers produced by very high-energy celestial gamma-rays and charged particles have been neglected to date because of their low numbers, but small feature size large area devices may have susceptibilities. Above an energy of 30 MeV, the primary photon interaction with matter is pair production. These particles in turn interact producing an electromagnetic shower. The result of such an interaction is that many charged particles will pass through the system at one time. The integrated flux is approximately 10 photons/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> /day with each photon producing two or more charged daughter particles. Since the incident particles are photons they are not affected by the Earth's magnetic field and the integrated rate will be approximately the same for any orbit. An interaction anywhere on the space vehicle, primary structure, subsystem enclosures, or actual electronic parts will produce a shower that can affect any components downstream of it. There is a definite need to study this problem. The NASA gamma-ray large area space telescope, to be launched in the spring of 2008, will be the most sophisticated Gamma- ray telescope ever flown. GLAST is a pair conversion telescope which measures the direction and energy of the daughter products of the incident photon using a silicon strip tracker and CsI calorimeter. It will provide detailed information on both celestial and Earth albedo Gamma-rays as well as providing additional detail on the charged particle environment in low Earth orbit through its on-board and ground segment charged particle rejection capabilities.

Based on their unique resistance to various space parameters, Bacillus endospores are one of the model systems used for astrobiological studies. In this study, spores of B. subtilis were used to study the effects of galactic cosmic radiation (GCR) on spore survival and induced mutagenesis. In interplanetary space, outside Earth's protective magnetic field, spore-containing rocks would be exposed to bombardment by high-energy charged particle radiation from galactic sources and from the Sun, which consists of photons (X-rays, gamma rays), protons, electrons, and heavy, high-energy charged (HZE) particles. B. subtilis spores were irradiated with X-rays and accelerated heavy ions (helium, carbon, silicon and iron) in the linear energy transfer (LET) range of 2-200 keV/mum. Spore survival and the rate of the induced mutations to rifampicin resistance (Rif(R)) depended on the LET of the applied species of ions and radiation, whereas the exposure to high-energy charged particles, for example, iron ions, led to a low level of spore survival and increased frequency of mutation to Rif(R) compared to low-energy charged particles and X-rays. Twenty-one Rif(R) mutant spores were isolated from X-ray and heavy ion-irradiated samples. Nucleotide sequencing located the Rif(R) mutations in the rpoB gene encoding the beta-subunit of RNA polymerase. Most mutations were primarily found in Cluster I and were predicted to result in amino acid changes at residues Q469L, A478V, and H482P/Y. Four previously undescribed alleles in B. subtilis rpoB were isolated: L467P, R484P, and A488P in Cluster I and H507R in the spacer between Clusters I and II. The spectrum of Rif(R) mutations arising from spores exposed to components of GCR is distinctly different from those of spores exposed to simulated space vacuum and martian conditions.

Introduction. Cosmic rays – high-energy charged particles (electrons, protons, heavier nuclei) – constantly bombard the Earth’s atmosphere and generate showers of secondary cosmic rays, in particular, high-energy muons. Muons have high mean range even in materials with high density, therefore they are an effective source of signals for tomographic studies of large-scale objects up to hundreds of meters and even up to kilometers. In particular, muon tomography is now the only method for remotely studying the spatial distribution of various components of nuclear reactors. In this paper a scheme for studying the structure of a nuclear-dangerous accumulation in the destroyed fourth reactor of the Chornobyl NPP with the help of muon tomography is proposed. Methods. Primary cosmic rays reach the Earth’s atmosphere, interact with atmospheric nuclei (N, O, etc.) and, as a result of nuclear cascades, generate showers of secondary particles. These include the muon flux. Since our atmosphere is constantly bombarded by cosmic rays, the flux of muons is constantly coming from the atmosphere to the Earth’s surface and due to the high energy of muons (from 1 GeV to tens of TeV), they have a high penetration power and can penetrate underground to depths of hundreds of meters and up to several kilometers into solid rocks. At the same time, due to energy losses and scattering, the integral intensity of muons decreases depending on the passed column density X as the product of the density of the medium ρ by the passed distance L: X(L)=ρ∙L. Position-sensitive muon detectors, in particular, hodoscopes, record the integral intensity of muons at a certain solid angle and, using the integral intensity map, allow to reproduce the value of X – the distribution of the absorbing substance along the line of sight. Based on observations of an object from several locations with different zenith and azimuth angles, it is possible to reproduce a 3D distribution of absorbers in the object. Results. A method for muon tomography using to determine the internal structure of the melt of fuel-containing materials, in particular, a nuclear-dangerous accumulation in the destroyed fourth reactor of the Chornobyl nuclear power plant, is proposed. The integral intensity of muons with momentum p&gt;1.12 GeV/c at the zenith angle of 75° (the observation direction of the hodoscope) is I(&gt;p=1.12 GeV/c)=6.90·10-4 cm-2∙s-1∙sr-1. The number of muons recorded in the solid angle (pixels in the sky) δΩ=1.0·10−3 sr with an effective area of Σ=5.76 cm2∙sr and an observation time of 100 days (8.64·106 s) would be Nμ =3.43·104. If there is an absorbing object with a density ρ, length L and the corresponding column density X(L)=ρ∙L on the line of sight of the telescope, then when a layer of concrete 10 m thick, muons with an initial momentum of p&gt;5 GeV/c will fall on the detector. If the density of the absorbing object – a nuclear-dangerous cluster – is equal to 5 g/cm3, muons with an initial momentum of p&gt;10.4 GeV/c, integral intensity I(&gt;p=10.4 GeV/c)=2.65·10-4 cm-2∙s -1∙sr-1, and the number of registered muons – 1.32·104. That is, the sensitivity of the proposed method is sufficient to confidently determine the internal structure of the melt of fuel-containing materials. Conclusions. Muon tomography is currently the only effective method for remote study of the spatial distribution of nuclear reactor components. In this paper a scheme for studying the structure of a nuclear-dangerous accumulation in the destroyed fourth reactor of the Chornobyl NPP with the help of muon tomography is proposed. It is shown that for the specified parameters of the hodoscope, it is possible to perform muon tomography of the reactor with an observation time from one location of about 100 days.

In this discussion, we first try to define the cases where analysis by irradiation with charged particles requires the use of relatively high energy beams, e.g from a cyclotron or from a Tandem Van de Graaff. It seems that the most important method using high energy charged particles, is activation analysis. We describe the important features of this method, we compare them with those of other methods, and we try to show the important role it plays in two important fields : -The analysis of traces -The elaboration of reference materials.

Some classical and quantum-mechanical problems previously studied in Lobachevsky space are generalized to the extended Lobachevsky space (unification of the real, imaginary Lobachevsky spaces and absolute). Solutions of the Schrodinger equation with Coulomb potential in two coordinate systems of the imaginary Lobachevsky space are considered. The problem of motion of a charged particle in the homogeneous magnetic field in the imaginary Lobachevsky space is treated both classically and quantum mechanically. In the classical case, Hamilton-Jacoby equation is solved by separation of variables, and constraints for integrals of motion are derived. In the quantum case, solutions of Klein-Fock-Gordon equation are found.

8 - Particle Accelerators

Particle Accelerators

УДК 514.13, 515.12, 513.83, 517.5 Розглянуто узагальнення задачі про тінь у гіперболічному просторі. Цю задачу можна розглядати як задачу про знаходження умов, які забезпечують належність точок до узагальнено опуклої оболонки сім'ї множин. Визначено граничні значення параметрів, при яких одні й ті ж конфігурації куль забезпечують належність точки до узагальнено опуклої оболонки куль в евклідовому й гіперболічному просторах. Крім куль розглянуто сім'ї орикуль, а також комбінації куль і орикуль.

ALICE [1] is one of the four experiments presently under construction for the Large Hadron Collider (LHC) at CERN in Geneva. ALICE is a general-purpose heavy-ion experiment designed to study the physics of strongly interacting nuclear matter and the quark-gluon plasma in nucleus-nucleus collisions. At a maximum cms energy of 5.5 TeV per nucleon in Pb-Pb collisions, up to 8000 charged particles per unit rapidity are produced within a central collision. Owing to the enormous particle multiplicity per event, very specific requirements are made on the performance of the detectors, the electronics and the data acquisition. The ALICE TPC, operated in a solenoid of 0.5 T, is the main detector of the ALICE experiment for tracking, momentum measurement and particle identification of charged particles. In conjunction with the Transition Radiation Detector (TRD), the Inner Tracking System (ITS), Cherenkov counters (HMPID) and Multi-gap Resistive Plate Chambers for time of flight (TOF), the TPC will provide identification of leptonic and hadronic particles in the momentum range from 0.5 to 10 GeV/c.

Chromosome aberrations induced by high-energy charged particles in normal human lymphocytes and human fibroblasts have been investigated. The charged particles included 250 MeV/nucleon protons, 290 MeV/nucleon carbon ions and 1 GeV/nucleon iron ions. The energies of the charged particles were higher than in most of the studies reported in the literature. Lymphocytes were stimulated to grow immediately after irradiation, while fibroblasts were incubated at 37 degrees C for 24 h for repair. Chromosomes were collected at the first mitosis after irradiation and chromosome aberrations were scored using the fluorescence in situ hybridization (FISH) technique with a whole-chromosome 4 probe. Chromosome aberrations were classified as reciprocal exchanges, incomplete exchanges, deletions and complex exchanges. The relative biological effectiveness (RBE) for each type of aberration was calculated by dividing a dose of 4 Gy by the dose of the charged particles producing the same effect as 4 Gy of gamma rays. Results of this study showed that complex aberrations have the highest RBE for radiation of high linear energy transfer (LET) for human lymphocytes, but for fibroblasts, the greatest effect was for incomplete exchanges. For both lymphocytes and fibroblasts, iron ions induced a similar fraction of aberrant cells.

Unique characteristics of bulk radiation chemical reactions induced by high energy charged particle suggest strongly non-homogeneous process of the reactions limited in an ion track, and giving also the estimate of the size of spatial distribution ranging a few to tens nm. Herein, the high-energy charged particles become only the candidate of ionizing radiation which can cause “stoichiometric” chemical reactions in an ion track via condensed reactive intermediates in the area, and enable to produce “a nanomaterial” by “a particle”. The process called as “Single Particle Nanofabrication Technique” has been realized and utilized miniaturization of a variety of polymeric materials, suggesting versatile nature of the technique for nanofabrication. The visualization of the produced 1-dimensional nanomaterials are demonstrated in the present chapter, as well as the totally theoretical model of the energy distribution in an ion tack giving good interpretation to the sizes of produced nanomaterials. The present technique has been realized by a “charged particle”, but the size of the field of chemical reactions has also been revealed to be defined by the target polymer materials themselves. This is suggestive that the present methodology is neither “top-down” nor “bottom-up” approaches in the miniaturization of materials and nanotechnologies, but a unique and versatile tool for nanomaterials fabrication.