It is demonstrated that the performance of the self-modulated proton driver plasma wakefield accelerator (SM-PDPWA) is strongly affected by the reduced phase velocity of the plasma wave. Using analytical theory and particle-in-cell simulations, we show that the reduction is largest during the linear stage of self-modulation. As the instability nonlinearly saturates, the phase velocity approaches that of the driver. The deleterious effects of the wake's dynamics on the maximum energy gain of accelerated electrons can be avoided using side-injections of electrons, or by controlling the wake's phase velocity by smooth plasma density gradients.

An accurate description of noise levels is of crucial importance for the correct simulation of instabilitydriven processes, such as the density modulation of a long proton bunch traversing a plasma. To insure that the correct instability develops, a seed field must be larger than the cumulative shot noise. We develop an analytical theory of the noise field and compare it with multidimensional simulations. We find that the natural noise wakefield generated in a plasma by the CERN Super Proton Synchrotron bunches is very low, at the level of 10 kV=m. This fortunate fact eases the requirements on the seed. Our threedimensional simulations show that even a few tens MeV electron bunch precursor of a very moderate intensity is sufficient to seed the proton bunch self-modulation in plasma.

Generation of collimated, quasi-monoenergetic electron beams (peak energy ~17-22MeV, divergence ~10mrad, energy spread ~20%) by interaction of Ti:sapphire laser pulse of 200fs duration, focussed to an intensity of ~ 2.1×10 18 W/cm 2 ,with an under-dense (density~3.6×10 19 to ~1.1×10 20 cm -3 ) He gas-jet plasma was observed. Two stages of selffocusing of the laser pulse in the plasma were observed. Two groups of accelerated electrons were also observed associated with these stages of the channeling and is attributed to the betatron resonance acceleration mechanism. This is supported by 2D PIC simulations performed using code EPOCH and a detailed theoretical analysis which shows that present experimental conditions are more favorable for betatron resonance acceleration and generation of collimated, quasi-thermal/quasi-monoenergetic electron beams.

Terahertz radiation is investigated using nonlinear interaction of a laser beat wave with a density-modulated medium of graphite nanoparticles. A beam-decentering parameter, b, is used to modify the polarizing field’s profile to produce different-shaped laser pulse envelopes, e.g. Gaussian, top head, ring-shaped and cosh-Gaussian. The normal vectors corresponding to the basal planes of graphite nanoparticles are considered to be aligned parallel and perpendicular to the polarization of the propagating laser pulse. The electronic cloud of the graphite nanoparticles acquires a nonlinear oscillatory velocity under the influence of a nonlinear force that produces a strong nonlinear current at the beat-wave frequency ( ω T = ω 1 − ω 2 ) . The strong nonlinear current allows the emission of radiation in the terahertz frequency regime. The terahertz radiation intensifies and attains a peak value when the laser beat-wave frequency ( ω T ) equals the plasmon frequency ω p of the nanoparticles. The terahertz radiation’s amplitude is enhanced by up to the fourth order of magnitude in the case of a cosh-Gaussian laser pulse, when the beam-decentering parameter, b, equals 5. The present numerical results reveal that by changing the shape of a laser pulse and the properties of nanoparticles, one can control and tune the THz emission.

The propagation of an intense short pulse laser, Gaussian in time, in plasma is studied when the quiver velocity of the electron approaches the velocity of light. The group velocity of the pulse is an increasing function of intensity; hence the peak of the pulse travels faster than the front causing pulse front sharpening. Further, the non-linear refractive index of the plasma acquires a radial profile with a maximum on the axis, causing self-focussing of the pulse. The peak of the pulse converges more rapidly than the front of the pulse. This leads to an enhancement in the group of the peak causing stronger pulse front sharpening.