Trapping Conditions Research Articles

Simplified coaxial ion trap: Simulation-based geometry optimization, unidirectional ejection, and trapping conditions

We have simulated the design and performance of the simplified coaxial ion trap – a dual ion trap mass spectrometer consisting of an outer simplified toroidal trap and an inner cylindrical trap. The device can perform tandem mass analysis by initially trapping ions in the toroidal region, and then transferring ions mass-selectively to the cylindrical region where they can be fragmented, isolated, and mass-scanned. The key benefit of the coaxial trap is the ability to store and retain the original ion population in the toroidal region while tandem mass analysis is being done in the cylindrical region for a selected mass. This study models a miniaturized simplified coaxial ion trap using the ion trajectory simulation software, SIMION, and characterizes its performance in terms of mass resolution and selectivity of transfer from toroidal to cylindrical regions, ion ejection direction from the toroidal trap, and trapping efficiency in the cylindrical trap. Mass resolution was maximized with a slightly positive octopole term in the toroidal trapping region, and the desired inward radial ejection of ions was achieved with a positive hexapole term. We demonstrate the possibility to obtain an optimized electric field for a given aspect ratio of the toroidal trap by varying only three geometric parameters. Simulated mass resolution from the optimized geometry was 0.3 Da for aspect ratio 8. The trapping efficiency was found to be affected by RF and AC voltages, RF phase, as well as the pressure. A mismatch between the kinetic energy of transferred ions and the RF phase in the cylindrical trap at the time of transfer was found to account for most of the ion loss during transfer. The intricate dependence of trapping efficiency on a number of operational variables was found to lead to trade-offs between itself and other operational parameters such as mass resolution and transfer efficiency. The results demonstrate successful operation of the simplified coaxial trap and reveal the geometric and operational constraints to be considered in its operation.

Experimental Investigation of Melting Process of Encapsulation Phase Change Material in Spiral Shell and Tube Heat Exchanger

Phase change materials are potentially able to store significant amounts of heat energy at almost constant temperatures, especially during the melting and freezing process. These materials enable us to design the individual thermal energy storage systems (TESS). However, several methods have been proposed to solve low thermal conductivity of PCMs, one of which is encapsulating the material in a heat-conducting membrane. In this research, non-welded steel capsules with unique sealing have been manipulated. A Hermetic-Sealed Chamber is fabricated to investigate the heat transfer from a hot fluid to PCMs. The hot fluid is circulated through the spiral coil and Encapsulated PCMs are embedded in shell side. In two different test, static water and trapped air as intermediate fluids are used between the interior system's wall and the cylindrical capsules. The results show that during the heat storage period, combined heat transfer mechanism and mostly through radiation has played a pivotal role when using trapped air. On the other hand, in different flow regimes, a comparison between the total heat transfer coefficients of different tests show that in trapped air condition (Test 2), values of coefficients are almost 1 to 3 times greater than when the water is used (Test 1). Therefore, by considering case of trapped air and integrating this study with solar technologies as a heat source of hot fluid is an excellent way for building energy at any geographical locations.

A 3-D numerical simulation of fatigue crack growth in an alumino thermite welded UIC60 rail joint under different loading conditions

In this article, a UIC60 rail AT weldment with appropriate rail and weld geometry on two-parent rail tracks as per Indian Railways is analysed separately under vertical and lateral loads, applying FEM. Stresses in an alumino-thermite welded rail is measured using finite element analysis. The results of operating condition on the development of fatigue cracks in rail welds are investigated. A 3-D elastoplastic material basis analysis has performed on a CAD assembly model for this purpose. A wheel-rail track model is used to simulate for the allocation of high stresses field in the weldment on the rail under intense service conditions for the welded straight track. Damage mechanics approaches are also used to assess the stress allocation on weld and wheel interaction along with the influence on fatigue lifecycle. The crack's variables like of displacement and stress intensity factors (SIFs) are calculated at crack tip in finite element model to measure crack propagation patterns and the rate of growth, considering two crack and its comparison for different modes. Also the trapped fluid condition due to weather and its influence on crack has been discussed. As friction rate of the contact area between rail weld and wheels increases, formation of crack 1 initiates, and the growth of crack-2 accelerates. Friction of contact patch and the fracture surface have opposite effects on fatigue life. Wet-lubrication are useful for crack friction reduction and can be used as a catalytic factor for SIF on mode II, but this liquid may flow into crack-1 and creates wedge effect. The SIF of opening mode in crack-1 abruptly rises as a result the crack's spread-up, and the fracture becomes deeper. Increasing friction force reduces slip on the fracture crack surfaces, thus reduction in crack propagation. Fracture mechanics fundamentals are used to find the growth of fatigue cracks in weld zone. To measure the progress rate of fatigue crack and SIFs, updated Paris model is used with ANSYS academic.

Aeolian sand accumulation and land desertification over the past 1,500 years as revealed by two aeolian dunes in the Beiluhe Basin on interior Qinghai-Tibet Plateau, SW China

As an important region of desertification in China, the Qinghai-Tibetan Plateau (QTP) has attracted great attention. However, the study of land desertification history at the millennia-scale on the interior plateau is grossly inadequate. In a severely and rapidly desertifying area in the Beiluhe Basin on the interior QTP, grain-size distributions, sand particle morphologies, and 7 available optically stimulated luminescence (OSL) ages of sand sediment from two fixed aeolian dunes were obtained by several laboratory tests. Combining these results with plateau paleoclimate and contemporary aeolian sand activities in several adjacent regions, two phases of evident enhanced aeolian sand accumulation corresponding to desert expansion over the past 1500 years in the study region were identified. The first enhanced phase (850–700 a B.P.) might have been closely related to suitable trapping of denser vegetation cover and degradation of permafrost on the QTP as a consequence of warm and wet climates. Reactivation of local older sediments caused by cold and dry climates might have been responsible for the second enhanced phase (1400–1200 a B.P.). Permafrost plays an important role in aeolian sand accumulation and desertification on the QTP. However, expansion (or degradation) of permafrost has not always prevented (or promoted) aeolian desertification development on the QTP since the Last Glaciation Maximum (LGM, 21–14–12 ka B.P.). The effects of permafrost on aeolian desertification are governed by numerous factors such as preceding and current climate conditions, locations of permafrost and aeolian sand activity, and trap conditions due to vegetation and topography.

Determination of 9 kinds of volatile halogenated alkane and chlorobenzene compounds in water by gas chromatography-mass spectrometry with purge and trap method

In this study, in the face of water environmental pollution, a more simple and efficient detection method was obtained for simultaneous determination of 9 kinds of volatile halogenated alkane and chlorobenzene compounds in water by PT/GCMS. By optimizing the purge and trap conditions, the optimal experimental conditions were obtained as follows: purge time was 15 min, purge temperature was 35 °C, purge velocity was 40 mL/min, desorption time was 2 min, desorption temperature was 240 °C. The linearity of the method was good, and the correlation coefficients were all greater than 0.999. The minimum detection limit(MDL) of the method was 0.1 μg/L. The average recovery rate ranged from 85.4 %~102.1 % in surface water and drinking water with relative standard deviation (RSD) ranged from 5.3 %-9.2 % in the spiked concentration levels of 5 μg/L and 10 μg/L. This method has the advantages of simple operation, good separation effect, rapid detection, high recovery and good precision, and can simultaneously meet the requirements of 9 kinds of volatile organic compounds detection in drinking water and surface water. This work provides a new method for the detection of volatile organic compounds in water and will have great significance for the detection of water quality.

Whistlers in Micro Ducts

AbstractObservations from satellites demonstrate that small‐scale, localized packages of VLF waves are frequently detected inside the field‐aligned density depletions (low‐density ducts) and enhancements (high‐density ducts) with comparable sizes. Because the conditions for the wave trapping in these inhomogeneities depend on the parameters of the wave and the duct, the information about the background media can be used to find parameters of the wave trapped in the duct. We present results from the modeling study of the propagation of VLF whistler‐mode waves in the field‐aligned density inhomogeneities with the perpendicular sizes comparable to (and even less than) one perpendicular wavelength of the wave inside the duct. Simulations of the electron‐MHD model reproduce in good quantitative detail observations from the satellites and let us identify perpendicular and parallel wavelengths of the waves trapped in the ducts. Simulations also reveal the conditions causing trapping of the oblique VLF waves in the low‐density and high‐density ducts with the transverse size comparable with the perpendicular wavelength of the smallest (and most oblique) wave inside the duct.

Interpretation of Mineralization in the Western Carpathians (Polish Segment)—A Tectonic Mélange Approach

Quartz, carbonates and other minerals as e.g., realgar are present in veins and caverns in sedimentary rocks in the Western Carpathians. In the Polish segment, they have been characterized from the mineralogical, petrologic, and geochemical points of view, as well as fluid inclusions. Their characters are discussed from perspective of a description of particular types of chaotic complexes—the tectonic mélange zones, distinguished in the Western Carpathian area over the last two decades. The mélange zones are considered to be geochemical systems open to fluid flow, a site for mineral crystallization and/or migration zones of hydrocarbons and mineralized waters. In this context the tectonic mélange in the Jabłonki/Rabe vicinity (SE Poland, the Bieszczady region) in comparison to that of the Mszana Dolna tectonic window area are proposed as the examples. The trapping conditions of fluids (brine and methane) in the minerals in the mélange zones appear to have been 180–205 °C and ~550–570 bars, and 220 °C and 500 bars for calcite and quartz, respectively. The general trend of the increase in temperatures and pressures from west towards east and south-east in the mélange zones points to an increase in the degree of exhumation of different parts of the Carpathians.

The formation of wide exoKuiper belts from migrating dust traps

ABSTRACT The question of what determines the width of Kuiper belt analogues (exoKuiper belts) is an open one. If solved, this understanding would provide valuable insights into the architecture, dynamics, and formation of exoplanetary systems. Recent observations by ALMA have revealed an apparent paradox in this field, the presence of radially narrow belts in protoplanetary discs that are likely the birthplaces of planetesimals, and exoKuiper belts nearly four times as wide in mature systems. If the parent planetesimals of this type of debris disc indeed form in these narrow protoplanetary rings via streaming instability where dust is trapped, we propose that this width dichotomy could naturally arise if these dust traps form planetesimals whilst migrating radially, e.g. as caused by a migrating planet. Using the dust evolution software dustpy, we find that if the initial protoplanetary disc and trap conditions favour planetesimal formation, dust can still effectively accumulate and form planetesimals as the trap moves. This leads to a positive correlation between the inward radial speed and final planetesimal belt width, forming belts up to ∼100au over 10 Myr of evolution. We show that although planetesimal formation is most efficient in low-viscosity (α = 10−4) discs with steep dust traps to trigger the streaming instability, the large widths of most observed planetesimal belts constrain α to values ≥4 × 10−4 at tens of au, otherwise the traps cannot migrate far enough. Additionally, the large spread in the widths and radii of exoKuiper belts could be due to different trap migration speeds (or protoplanetary disc lifetimes) and different starting locations, respectively. Our work serves as a first step to link exoKuiper belts and rings in protoplanetary discs.

Analysis of tight oil accumulation conditions and prediction of sweet spots in Ordos Basin: A case study

Tight sandstone reservoirs are widely developed in the Mesozoic Yanchang Formation of the Ordos Basin, China. There is a lack of understanding on the sedimentary setting, source-reservoir relationship and oil accumulation conditions in this area. In this study, through the comprehensive analysis of the distribution of tight oil, we evaluated the properties and petrological features of reservoir, geochemical characteristics of source rocks, the source-reservoir relationship, as well as the trapping, preservation and accumulation conditions of tight oil in the Chang 7 Member, and predicted the sweet spots of tight oil in the study area. The results show that the Chang 7 Member is a typical low-porosity and ultra-low permeability reservoir with great tightness, small pore throat and high capillary pressure, and must have been of near-source accumulation. The source rocks are mainly developed in the Chang 73 submember, and the reservoirs mainly occur in the Chang 71 and Chang 72 submembers, forming a combination mode of “lower source rock and upper reservoir”. Sandbodies with good connectivity and fractures being well developed in local areas are the main hydrocarbon transport systems. The abnormal high pressure caused by hydrocarbon generation and pressurization is the main driving force of tight oil accumulation. The mode of hydrocarbon transportation is dominated by the vertical or lateral migration from underlying source rocks or adjacent source rocks to reservoirs within a short distance. Following the integrated evaluation of lithology, physical properties and oil saturation of reservoirs and geochemical characteristics of source rocks, we grouped the sweet spots of Chang 7 Member into three types: Type I, Type II and Type III. Among others, the Type I sweet spots are the best in terms of porosity, permeability and source rock thickness and hydrocarbon enrichment which should be the focus of oilfield development. This study lays an important foundation for the economic and efficient development of tight oil in the Chang 7 Member of Heshui area, and has important implications on tight sandstone reservoirs in other regions of Ordos Basin in China.

Formation of Diagenetic Minerals in the Carboniferous Rock Complex from the Fore-Sudetic Monocline (SW Poland): Fluid Inclusion, Isotopic and Raman Constraints

The paper presents the latest state of knowledge on clastic sedimentary rocks from the Carboniferous complex in the SW part of the Polish Lowlands, studied to help determine their potential prospectivity for the occurrence of oil and/or gas deposits. Rocks were analyzed with respect to the petrographic-mineralogical characteristics of the Carboniferous deposits, their diagenesis, determinations of pressure-temperature conditions of mineral formation and the hydrocarbon occurrence. Analyses were carried out on samples from four selected boreholes in the Fore-Sudetic Monocline. After microscopic analysis of rocks and minerals in thin sections, the following techniques were used: luminescence analysis (UV, blue light), microthermometric analysis of fluid inclusions in double-sided polished wafers, cathodoluminescence analysis, electron scanning microscope studies, XRD analyses, stable isotopic analyses (carbon, oxygen) on calcite and dolomite-ankerite and Raman spectra of fluid inclusions. Orthochemical components, such as carbonates and authigenic quartz, that form cements or fill the veins cutting the sample material have been studied. Fluid inclusion data in quartz and carbonates result in homogenization temperatures of 74–233 °C. The Raman analysis gives temperature estimations for the organic matter of about 164 °C and 197 °C, depending on the borehole, which points to a low coalification degree. The post-sedimentary processes of compaction, cementation and diagenetic dissolution under eo- and meso-diagenetic conditions to temperatures of over 160 °C influenced the present character of the deposits. P-T conditions of brines and methane trapping have been estimated to be ~850–920 bars and 185–210 °C (vein calcite) and ~1140 bars and 220 °C (Fe-dolomite/ankerite). Therefore, locally, temperatures might have been higher (>200 °C), which may be a symptom of local regional metamorphism of a very low degree.

Dielectrophoretic Trapping for Nanoparticles, High-Molecule-Weight DNA, and SYBR Gold Using Polyimide-Based Printed Circuit Board

Microelectrodes for electrokinetic detection have been employed to manipulate and collect nanomaterials and biomaterials. However, the process of microelectrode patterning has been researched in the semiconductor fabrication process, which is expensive and time-consuming. Here, we demonstrate dielectrophoretic trapping of 200 nm fluorescent polystyrene nanoparticles and λ-deoxyribonucleic acid with SYBR gold using dielectrophoretic trapping onto an interdigitated circular electrode (ICE). For dielectrophoretic trapping, an ICE is designed and an ordered flexible printed circuit board (FPCB), possessing a non-porous polyimide substrate, is constructed. The ICE FPCB could identify the dielectrophoretic trapping conditions and simulate them by the finite element method. The fluorescent molecules in the ICE FPCB are dielectrophoretically trapped at the finger edges of the ICE when a peak-to-peak voltage of 12 V is applied at 6 kHz for 15-20 min. Moreover, monitoring of the dielectrophoretic trapping effect of SYBR gold eliminated the false negative detection error.

Insights into Elution of Anion Exchange Cartridges: Opening the Path toward Aliphatic 18F-Radiolabeling of Base-Sensitive Tracers.

Aliphatic nucleophilic substitution (SN2) with [18F]fluoride is the most widely applied method to prepare 18F-labeled positron emission tomography (PET) tracers. Strong basic conditions commonly used during 18F-labeling procedures inherently limit or prohibit labeling of base-sensitive scaffolds. The high basicity stems from the tradition to trap [18F]fluoride on anion exchange cartridges and elute it afterward with basic anions. This sequence is used to facilitate the transfer of [18F]fluoride from an aqueous to an aprotic organic, polar reaction medium, which is beneficial for SN2 reactions. Furthermore, this sequence also removes cationic radioactive contaminations from cyclotron-irradiated [18O]water from which [18F]fluoride is produced. In this study, we developed an efficient elution procedure resulting in low basicity that permits SN2 18F-labeling of base-sensitive scaffolds. Extensive screening of trapping and elution conditions (>1000 experiments) and studying their influence on the radiochemical yield (RCY) allowed us to identify a suitable procedure for this. Using this procedure, four PET tracers and three synthons could be radiolabeled in substantially higher RCYs (up to 2.5-fold) compared to those of previously published procedures, even from lower precursor amounts. Encouraged by these results, we applied our low-basicity method to the radiolabeling of highly base-sensitive tetrazines, which cannot be labeled using state-of-art direct aliphatic 18F-labeling procedures. Labeling succeeded in RCYs of up to 20%. We believe that our findings facilitate PET tracer development by opening the path toward simple and direct SN2 18F fluorination of base-sensitive substrates.

Impact of geometry on the magnetic flux trapping of superconducting accelerating cavities

Controlling trapped magnetic flux in superconducting radiofrequency (RF) cavities is of crucial importance in modern accelerator projects. In order to study flux trapping efficiency and sensitiv- ity of surface resistance, dedicated experiments have been carried out on different types of low-\b{eta} superconducting accelerating cavities. Even under almost full trapping conditions, we found that the measured magnetic sensitivities of these cavity geometries were significantly lower than the theoretical values predicted by commonly-used models based on local material properties. This must be resolved by taking account of geometrical effects of flux trapping and flux oscillation under RF surface current in such cavity shape. In this paper, we propose a new approach to convolute the influence of geometries. We point out a puzzling contradiction between sample measurements and recent cavity experiments, which leads to two different hypotheses to simulate oscillating flux trapped in the cavity surface. A critical reconsideration of flux oscillation by the RF Lorentz force, compared with temperature mapping studies in elliptical cavities, favoured the results of previous sample measurements, which suggested preferential flux trapping of normal component to the cavity inner surface. Based on this observation, we builded a new model to our experimental results and the discrepancy between old theory and data were resolved.

Forensically relevant blow flies (Diptera: Calliphoridae) of Central Connecticut, USA

Connecticut and the Northeastern United States in general, lacks forensically relevant entomological survey data. To determine which forensically relevant calliphorid (blow flies, Diptera: Calliphoridae) and non-calliphorid species dominate Connecticut, 5 traps using pork bait were set out 7 times over a 2-year period to collect adult and immature specimens. Insects collected from human corpses in this region were also tabulated to collaborate the forensic relevance of trapped specimens. The survey identified a total of 8 species of blow flies of the Lucilia and Calliphora genera, 6 of which colonized the baits, and 5 of which have been found to colonize human corpses in the area. Non-calliphorid genera Sarcophaga and Muscina were also found to be colonizers of the baited traps but in relatively lower numbers. Trap sites differed significantly in the degree of urbanization which was determined by using GIS mapping to classify a 1 kilometer (km) radius around each site using land use and the percent of urban impervious surfaces. The 1 km radius revealed the highly fragmented nature of the immediate habitats of the trap sites and no habitat or seasonal preference was demonstrated by blow flies under these trap conditions. Temperature was the one variable which significantly affected the number of flies trapped and the colonizing species. All trapped species have been described previously as widespread and common in the United States and as synanthropic. Further research in this region should trap at the constantly changing extreme ends of the urban–rural gradient and in the colder temperatures of winter to explore the limits of the flexibility of these blow fly species.

Multilevel Laser Induced Continuum Structure.

Laser-induced-continuum-structure (LICS) allows for coherent control techniques to be applied in a Raman type system with an intermediate continuum state. The standard LICS problem involves two bound states coupled to one or more continua. In this paper, we discuss the simplest non-trivial multistate generalization of LICS which couples two bound levels, each composed of two degenerate states through a common continuum state. We reduce the complexity of the system by switching to a rotated basis of the bound states, in which different sub-systems of lower dimension evolve independently. We derive the trapping condition and explore the dynamics of the sub-systems under different initial conditions.

Transient Permeabilization of Living Cells: Combining Shear Flow and Acoustofluidic Trapping for the Facilitated Uptake of Molecules

Here, we present a novel approach for the transient permeabilization of cells. We combined laminar shear flow in a microchannel with chaotic advection employing surface acoustic waves. First, as a fundamental result on the one hand, and as a kind of reference measurement for the more complex acoustofluidic approach on the other hand, we studied the permeabilization of cells in pure shear flow in a microchannel with Y-geometry. As a proof of principle, we used fluorescent dyes as model drugs and investigated their internalization into HeLa cells. We found that drug uptake scaled non-linearly with flow rate and thus shear stress. For calcein, we obtained a maximal enhancement factor of about 12 at an optimum flow rate of Q = 500 µL/h in the geometry used here compared to static incubation. This result is discussed in the light of structural phase transitions of lipid membranes accompanied by non-linear effects, as the plasma membrane is the main barrier to overcome. Second, we demonstrated the enhanced permeabilization of acoustically trapped cells in surface acoustic wave induced vortices in a microchannel, with an enhancement factor of about 18 compared to quasi-static incubation. Moreover, we optimized the trapping conditions regarding flow rate, the power level of the surface acoustic wave, and trapping time. Finally, we showed that our method is not limited to small molecules but can also be applied to compounds with higher molecular weight.

Research on the ions’ axial temperature of a sympathetically-cooled 113Cd+ ion crystal* *Project supported by the Beijing Natural Science Foundation (Grant No. 1202011), the Tsinghua University Initiative Scientific Research Program, the National Natural Science Foundation of China (Grant No. 12073015), and the National Key Research and Development Program of China (Grant No. 2016YFA0302101).

Molecular dynamics simulation of a sympathetically-cooled 113Cd+ ion crystal system is achieved. Moreover, the relationship between ions’ axial temperature and different electric parameters, including radio frequency voltage and end-cap voltage is depicted. Under stable trapping condition, optimum radio frequency voltage, corresponding to minimum temperature and the highest cooling efficiency, is obtained. The temperature is positively correlated with end-cap voltage. The relationship is also confirmed by a sympathetically-cooled 113Cd+ microwave clock. The pseudo-potential model is used to illustrate the relationship and influence mechanism. A reasonable index, indicating ions’ temperature, is proposed to quickly estimate the relative ions’ temperature. The investigation is helpful for ion crystal investigation, such as spatial configuration manipulation, sympathetic cooling efficiency enhancement, and temporal evolution.

Observation of a non-Hermitian phase transition in an optical quantum gas.

Quantum gases of light, such as photon or polariton condensates in optical microcavities, are collective quantum systems enabling a tailoring of dissipation from, for example, cavity loss. This characteristic makes them a tool to study dissipative phases, an emerging subject in quantum many-body physics. We experimentally demonstrate a non-Hermitian phase transition of a photon Bose-Einstein condensate to a dissipative phase characterized by a biexponential decay of the condensate's second-order coherence. The phase transition occurs because of the emergence of an exceptional point in the quantum gas. Although Bose-Einstein condensation is usually connected to lasing by a smooth crossover, the observed phase transition separates the biexponential phase from both lasing and an intermediate, oscillatory condensate regime. Our approach can be used to study a wide class of dissipative quantum phases in topological or lattice systems.

A dissipative quantum gas of light

Quantum Optics Our textbook understanding of quantum systems tends to come from modeling these systems isolated from the environment. However, an emerging focus is understanding how many-body quantum systems behave when interacting with their surroundings and how they subsequently become dissipative, or non-Hermitian, systems. Ozturk et al. formed a quantum condensate of light by trapping photons in an optical cavity, a system that is naturally dissipative. By altering the trapping conditions, they demonstrated that the system provides a powerful platform with which to explore the complex dynamics and phase transitions occurring in dissipative quantum systems. Science , this issue p. [88][1] [1]: /lookup/doi/10.1126/science.abe9869

Scatter-free acceleration of particles by interaction with plasma shock waves in the interstellar medium

ABSTRACTScatter-free acceleration is investigated for a test particle thrusted by a moving magnetized cloud in the presence of the uniform interstellar magnetic field. It is found that depending on the orientation of the background magnetic field, three different scenarios occur for the interacting particle. In some cases, the particle reflects into space with a negligible increase in energy. Otherwise, the particle is either trapped at the wavefront or is injected inside the cloud. The trapped particle moves with the cloud and gains energy through the magnetic trapping acceleration mechanism, which is already investigated in previous reports. The injected particle accelerates through a different mechanism, which is introduced in this paper as the spiral acceleration. In this mechanism, the particle moves in a spiral path and gains energy by the convective electric field of the cloud. The radius of the spiral increases as the particle gains more energy and the process continues until the particle is located inside the cloud. Since in most cases the trapping condition is not satisfied, the spiral acceleration mechanism is of great importance.