Fluidization and bubbling behavior of potash particles in a deep fluidized bed

Most existing models for predicting bubble size and bubble frequency have been developed for freely bubbling fluidized beds.Accurate prediction of bubbling behavior in deep fluidized beds,however,has been a challenge due to the higher degree of bubble coalescence and break up,high probability of the slugging regime,partial fluidization,and chaotic behavior in the bubbling regime.In this work,the bubbling and fluidization behavior of potash particles was investigated in a deep fluidized bed employing a twin-plane electrical capacitance tomography(ECT)system.Solid volume fraction,average bubble velocity,average bubble diameter,and bubble frequency in both bubbling and slugging regimes were measured at two different bed height ratios(H/D=3.5 and H/D=3.78).This work is the first to illustrate a sequential view of bubbles at different superficial gas velocities in a fluidized bed.The results show that both the bubble diameter and rising velocity increased with increasing the superficial gas velocity for the two bed heights,with larger values observed in the deeper bed compared to the shallower one.Predicted values for bubble diameter,bubble rise velocity and bubble frequency from different models are compared with the experimental data obtained from the ECT system in this work.Good agreement has been achieved between the values predicted by the previous models and the experimental data for the bubble diameter and bubble rise velocity with an average absolute deviation of 16%and 15%for the bed height of 49 cm and 13%and 8%for the bed height of 53 cm,respectively.

Monoenergetic electron parameters in a spheroid bubble model

A reliable analytical expression for the potential of plasma waves with phase velocities near the speed of light is derived.The presented spheroid cavity model is more consistent than the previous spherical and ellipsoidal models and it explains the mono-energetic electron trajectory more accurately,especially at the relativistic region.The maximum energy of electrons is calculated and it is shown that the maximum energy of the spheroid model is less than that of the spherical model.The electron energy spectrum is also calculated and it is found that the energy distribution ratio of electrons △E/E for the spheroid model under the conditions reported here is half that of the spherical model and it is in good agreement with the experimental value in the same conditions.As a result,the quasi-mono-energetic electron output beam interacting with the laser plasma can be more appropriately described with this model.

Electron trajectory evaluation in laser-plasma interaction for effective output beam

Using the ellipsoidal cavity model, the quasi-monoenergetic electron output beam in laser-plasma interaction is described. By the cavity regime the quality of electron beam is improved in comparison with those generated from other methods such as periodic plasma wave field, spheroidal cavity regime and plasma channel guided acceleration. Trajectory of electron motion is described as hyperbolic, parabolic or elliptic paths. We find that the self-generated electron bunch has a smaller energy width and more effective gain in energy spectrum. Initial condition for the ellipsoidal cavity is determined by laser-plasma parameters. The electron trajectory is influenced by its position, energy and cavity electrostatic potential.

Pulse chirping effect on controlling the transverse cavity oscillations in nonlinear bubble regime

The propagation of an intense laser pulse in an under-dense plasma induces a plasma wake that is suitable for the acceleration of electrons to relativistic energies. For an ultra-intense laser pulse which has a longitudinal size shorter than the plasma wavelength, λp, instead of a periodic plasma wave, a cavity free from cold plasma electrons, called a bubble, is formed behind the laser pulse. An intense charge separation electric field inside the moving bubble can capture the electrons at the base of the bubble and accelerate them with a narrow energy spread. In the nonlinear bubble regime, due to localized depletion at the front of the pulse during its propagation through the plasma, the phase shift between carrier waves and pulse envelope plays an important role in plasma response. The carrier–envelope phase（CEP） breaks down the symmetric transverse ponderomotive force of the laser pulse that makes the bubble structure unstable. Our studies using a series of two-dimensional（2D） particle-in-cell（PIC） simulations show that the frequency-chirped laser pulses are more effective in controlling the pulse depletion rate and consequently the effect of the CEP in the bubble regime. The results indicate that the utilization of a positively chirped laser pulse leads to an increase in rate of erosion of the leading edge of the pulse that rapidly results in the formation of a steep intensity gradient at the front of the pulse. A more unstable bubble structure, the self-injections in different positions, and high dark current are the results of using a positively chirped laser pulse. For a negatively chirped laser pulse, the pulse depletion process is compensated during the propagation of the pulse in plasma in such a way that results in a more stable bubble shape and therefore, a localized electron bunch is produced during the acceleration process. As a result, by the proper choice of chirping, one can tune the number of self-injected electrons, the size of accelerated bunch and its energy spectrum to the values required for practical applications.