PERIODIC SOLUTIONS TO ELECTRON BEAMS FOCUSING SYSTEM

In this paper, we study a mathematical model of electron beam focusing system. We prove the existence of periodic solutions to the model using homotopy method.

Focused electron beam transport through a long narrow metal tube at elevated pressures in the forevacuum range

We present here our investigations of the features of focused electron beam transport in free space at elevated pressures of a few pascals.We have explored the effect of the beam accelerating voltage,operating gas pressure,and magnetic focusing upon the trajectory of beam electrons in the crossover region,in particular on the beam convergence and divergence angles.It is shown that for the forevacuum pressure range of 2-5 Pa explored,a distinctive feature of the propagation of a focused electron beam with a current of up to 20 mA at an accelerating voltage of 10-20 kV is the difference in the angles of convergence(before the focus)and divergence(after the focus).Whereas at a low pressure of 2 Pa the divergence angle is smaller than the convergence angle,as the pressure increases the divergence angle increases and for pressures greater than 5 Pa the divergence angle is greater than the convergence angle.The results obtained were used in experiments on electron beam transport through a long narrow metal tube with a diameter of 5.8-9.2 mm and length of 10-30 cm.We show that for a 30 cm long tube of 7.5 mm diameter,the focused beam transmission can exceed 70%.

Characterization of 3D pore nanostructure and stress-dependent permeability of organic-rich shales in northern Guizhou Depression,China

The three-dimensional(3D)pore structures and permeability of shale are critical for forecasting gas production capacity and guiding pressure differential control in practical reservoir extraction.However,few investigations have analyzed the effects of microscopic organic matter(OM)morphology and 3D pore nanostructures on the stress sensitivity,which are precisely the most unique and controlling factors of reservoir quality in shales.In this study,ultra-high nanoscale-resolution imaging experiments,i.e.focused ion beam-scanning electron microscopy(FIB-SEMs),were conducted on two organic-rich shale samples from Longmaxi and Wufeng Formations in northern Guizhou Depression,China.Pore morphology,porosity of 3D pore nanostructures,pore size distribution,and connectivity of the six selected regions of interest(including clump-shaped OMs,interstitial OMs,framboidal pyrite,and microfractures)were qualitatively and quantitatively characterized.Pulse decay permeability(PDP)measurement was used to investigate the variation patterns of stress-dependent permeability and stress sensitivity of shales under different confining pressures and pore pressures,and the results were then used to calculate the Biot coefficients for the two shale formations.The results showed that the samples have high OM porosity and 85%of the OM pores have the radius of less than 40 nm.The OM morphology and pore structure characteristics of the Longmaxi and Wufeng Formations were distinctly different.In particular,the OM in the Wufeng Formation samples developed some OM pores with radius larger than500 nm,which significantly improved the connectivity.The macroscopic permeability strongly depends on the permeability of OM pores.The stress sensitivity of permeability of Wufeng Formation was significantly lower than that of Longmaxi Formation,due to the differences in OM morphology and pore structures.The Biot coefficients of 0.729 and 0.697 were obtained for the Longmaxi and Wufeng Formations,respectively.