Particle energisation in a collapsing magnetic trap model : the relativistic regime

The authors acknowledge financial support by the UK’s Science and Technology Facilities Council through a Doctoral Training Grant (SEO) and Consolidated Grant ST/K000950/1 (SEO and TN).Context. In solar flares, a large number of charged particles is accelerated to high energies. By which physical processes this is achieved is one of the main open problems in solar physics. It has been suggested that during a flare, regions of the rapidly relaxing magnetic field can form a collapsing magnetic trap (CMT) and that this trap may contribute to particle energisation. Aims. In this Research Note we focus on a particular analytical CMT model based on kinematic magnetohydrodynamics. Previous investigations of particle acceleration for this CMT model focused on the non-relativistic energy regime. It is the specific aim of this Research Note to extend the previous work to relativistic particle energies. Methods. Particle orbits were calculated numerically using the relativistic guiding centre equations. We also calculated particle orbits using the non-relativistic guiding centre equations for comparison. Results. For mildly relativistic energies the relativistic and non-relativistic particle orbits mainly agree well, but clear deviations are seen for higher energies. In particular, the final particle energies obtained from the relativistic calculations are systematically lower than the energies reached from the corresponding non-relativistic calculations, and the mirror points of the relativistic orbits are systematically higher than for the corresponding non-relativistic orbits. Conclusions. While the overall behaviour of particle orbits in CMTs does not differ qualitatively when using the relativistic guiding centre equations, there are a few systematic quantitative differences between relativistic and non-relativistic particle dynamics.Publisher PDFPeer reviewe

Stochastic And Modified Sequent Peak Algorithm For Reservoir Planning Analysis Considering Performance Indices

This study is on modeling the critical period and total storage capacity of reservoir systems employing performance criteria and synthetic data generation technique. Three sites in the Southern part of Peninsular Malaysia are selected as conceptual reservoirs to be the case studies: Johor at Rantau Panjang; Melaka at Pantai Belimbing and Muar at Buluh Kasap gauging stations. Statistical data analysis of both annual and monthly streamflow data of the study sites is carried out prior to the time series analysis. The tests are implemented for testing consistency, stationarity, randomness and determining the most appropriate probability distribution function of the historical data. Subsequently, Auto-regressive lag one, AR(1), coupled with Valencia-Schaake (V-S) disaggregation model are applied to generate synthetic streamflow data. In the next stage, the modified Sequent Peak Algorithm (SPA) is employed for the Storage-yield planning analysis of reservoir systems at different demands, reliability and vulnerability performance metrics employing the synthetic streamflow data. The results show that the reliability and vulnerability metrics are significant in critical period and storage capacity modeling. Subsequently, using the simulation results, new regression equations are developed to model the critical period and total storage capacity of study systems individually and three systems together applying standard demand parameter, reliability and vulnerability performance measures and coefficient of variation and skewness of annual flows. The R2 obtained over the complete range of the critical period and storage capacity prediction is high, being 0.9810 and 0.9856, respectively for the three systems together. Hence, the obtained equations could reproduce the simulated critical period and storage capacity for different demands, reliability and vulnerability indices efficiently

Agricultural mechanisation systems analysis: tractor power selection for tillage operations

Primary tillage largely dictates the power requirement on an arable farm. As power and machinery costs continue to rise, it is important to provide a sound management base for the optimum selection of tractor size. A tractor power selection programme has been developed by examining a single operation for a single crop, namely, ploughing for cereals.The tractor power selection programme comprises seven essential sections each of which an be used separately and independently depending on the type of the output required. The even major steps are the prediction of soil moisture, soil workability, soil strength, tractor performance, plough draught and system cost and the selection of a limited number of suitable tractor plough combinations.For the prediction of daily fluctuations of soil moisture content, the amount of water rained by the soil is balanced against the amount of water lost. Water added to the soil in he form of precipitation and irrigation is lost by means of evapotranspiration, drainage and surface run -off. Potential evaporation is calculated by means of an empirical equation sing mean monthly air temperature and converted to actual evaporation from the soil and transpiration from vegetation where present. Factors are incorporated to correct for the dryness of the soil, the duration and intensity of precipitation and the stage of the crop which is covering the soil. Daily values of drainage flux was calculated from the hydraulic conductivicies and moisture content of the soil at saturation and field capacity and soil moisture content prior to commencement of drying. Existing empirical procedures were utilised to calculate run -off.By analysing the predicted soil moisture contents, each calendar day can be assigned as suitable for farm work (a work day) or unsuitable for a given operation (non -work day). As oil workability varies from soil to soil, machine to machine and farm manager to farm manager, the adoption of a unique soil moisture value to differentiate between soil workability and unworkability is unrealistic. A procedure has therefore been adopted to enable the number if work days to be calculated at different levels of soil moisture content or workability criteria. The data is analysed for a number of years (up to 20) and then the cumulated number years on which a given day was a work day or a non -work day with a given workability criterion was determined for different probability levels. This data is of direct relevance lot only to machinery planning but also to irrigation planning and for timeliness penalty evaluation.Soil strength in terms of the cone penetrometer resistance or cone index of the soil at a given soil workability criterion level is predicted by an empirical equation containing soil bulk density. The cone index influences the pull produced by the tractor for a given set of tyre and deflection data and the tractor power required. It also affects the draught requirements of the plough of given dimensions, tail angle, number of bodies and depth of cut.The cost of owning a machinery system is calculated in the form of the present annual cost, taking into account the effect of inflation and interest rate by using discounted cash flows. the purchase prices of tractors and implements were related to the average price per unit of power and per unit width of plough, respectively. Crop loss or timeliness penalties through delayed operations are also determined.Finally, the various different ploughing systems with different sizes of tractors and Ploughs and at different operations speeds are examined and a small number of suitable systems are presented in a form which enables the farmer or farm manager to take into account other critique management parameters of his particular farm business