Study On Acceleration Of Electrons By A Laser Pulse With Phase Modulated

We presented a method to modulate the phase of a laser pulse and investigate the acceleration of electrons in such radiation fields. The numerical calculating based on a full3D relativity test particle model and a theoretical analysis of a simplified model and the simulation s by PIC show us that the modulated pulse can accelerate electrons efficiently; the energy gain of the electrons can increase1-2orders.The modulation is along the transverse profile of the laser, with phase incensement△φ for each incensement of△r and the gradient is described by parameter s. After modulation the laser is split into a set of beam lets and when an electron is oscillating in the fields, the displacement of the electron will bring additional phases which is an equivalent that the electron feels a lower phase speed of the laser and can keep up with the fields and accelerated by the fields with less phase slip and gain much more energy. The phase speed of field that an electron feels can be modified by s. Smaller s creates higher phase speed and the electron can reach higher speed. But the analytical solution of the transverse moment of the electron indicates that this will happen provide that the initial energy of the electron is beyond a certain threshold and this threshold which will increase when s decrease. There is another solution of the transverse moment of the electron results lower final energy but need lower initial energy. The final energy of this second solution increases as s increase in a certain range. These two solutions have their own energy range without overlap when s is less than a critical value sc.When a electron is initially with lower energy, its final energy is limited by the second solution and cannot be accelerated to high energy. When s increases and become s> sc, two ranges will overlap and the movement of the electron can be described by two solutions and the electron can be well accelerated to large energy gain.Theoretically when the condition s> sc is satisfied, smaller s will bring higher energy gain, but smaller s also require proper initial phase of the electron which maybe only a narrow window of the phase space, thus few electrons can be well accelerated. Our analytical solution reveals that a slightly increase of s though reduce the final energy gain but increase the width of the window of the proper phase and more electrons will be well accelerated and increase the average energy of an electron beam. So there may be a optimized value for s to achieve good acceleration. This conclusion is confirmed by the numerical study base on a test particle model.In our test particle model, the beam lets generated by the modulation are treated with the method of geometrical optics; no diffraction and interference are considered. Such a model may be enough when the interaction distance is small. When the interaction distance increases, diffraction and interference of the beam lets cannot be neglected. To investigation with more consideration, we developed a2D3V particle-in-cell code with modern algorithms to simulate the propagation of the laser which naturally include the effect of diffraction and interference. Using the PIC code we simulated the acceleration of electrons by a pulse with phase modulated and the data shows that the electrons can be accelerated to high energy and the average energy gain is increased1-order and some electrons gain energy2-order higher than that of the pulse without modulation. The simulation is coinciding to what we have discussed above.We also study the acceleration of electrons by a circular polarized pulse with phase echelon modulated. By analysis of a simplified model and the numerical investigation of a test particle model we found that the acceleration in the direction of the modulation is similar to a linear polarized pulse, but in orthogonal direction there is a new mechanism to accelerate electron. This mechanism is related to the broken of the symmetry of the dynamics in the direction of modulation and after an oscillation in the orthogonal direction the electron can get some energy due to the asymmetry of the dynamics and they can be accumulated. This mechanism is not so sensitive to the initial phase of an electron. PIC simulations by VORPAL indicate that at the beginner of the acceleration more electrons are well accelerated than a linear polarized pulse and the total energy fold increased as well, the acceleration in the direction orthogonal to the modulation direction plays an important role.