## Description of PhD work

A new era of laser-matter interaction is born as a consequence of continuous growth of laser technology. The generation of these intense lasers promised variety of applications like nuclear phenomenon, generation of high energy ion beams, intense x-ray generation, tabletop particle accelerators, laser induced fusion, generation of giant magnetic fields inside plasma, high resolution imaging and precision laser machining etc. In this thesis we studied three different aspects related to the subject, namely laser interaction with (a) solid targets, (b) atomic clusters and the (c) laser induced ion acceleration.

(a) We have developed a generalized model for laser-matter interaction which is valid for wide range of laser pulse durations (femtoseconds to nanoseconds) and wide range of laser intensities. The model is based on the solutions of wave propagation equations in a medium with complex dielectric constant. The wave equations are solved numerically using matrix method. The dielectric constant is obtained from Drude’s free electron gas model while the collision frequency is obtained as an harmonic mean of Spitzer’s formula valid at high temperature and phonon scattering model valid at low temperature. The model is used to obtain absorption profile for linear, exponential and parabolic density profiles and results are compared with analytical and semi analytical models. It is also shown that the model discussed above easily converges to well known Fresnel’s limit for case of abrupt vacuum target interface.

In order to be able to simulate various laser-plasma interaction experiments, we have coupled this absorption model with an existing one dimensional multi-group radiation hydrodynamic code. A non local thermodynamic equilibrium (NLTE) model is used to calculate energy dependent radiation opacities and quotidian equation of state (EOS) model is used to generate EOS data. Number of experiments on laser-plasma interaction with pulse duration varying from 150 fs to 5 ps and laser intensities varying from 1012 W/cm2 to 1017 W/cm2 are simulated and results are found to be in good agreement with experiments.

(b) A model for the interaction of laser with atomic clusters is also developed, which considers the radial non-uniformities during cluster expansion. We have calculated the laser absorption by solving the Helmholtz equation for a stratified sphere using a recursive algorithm. The model includes three types of ionization mechanisms, namely, tunnelling ionization, collisional ionization and ponderomotive ionization. Furthermore, collisional ionization is calculated by using a numerical fitted formula for the gases of low atomic numbers (≤28) while Lotz formula is used for higher Z elements. Hydrodynamics is treated by solving the conservation of mass, momentum and energy equations in 1D Lagrangian geometry. Shocks are treated by Von-neumann artificial viscosity mechanism.

We have retrieved the uniform density results by modelling the cluster as a one region sphere. It is seen that the spatial non-uniformities play a vital role in absorption dynamics. In case of uniform density model, the resonance occurs only once but in our case, the resonance point keeps moving in space and time giving higher absorption. For example, for a laser intensity of 5×1015 W/cm2 , the laser absorption increases by a factor of 40 as compared to the uniform density model. Effect of pulse duration on the laser absorption is also studied. It is observed that there is an optimum pulse duration for maximum absorption. It is further observed that the uniform density model over predicts the effect of pulse duration.

(c) We have also carried out the study of laser interaction with preformed plasma leading to the laser induced ion acceleration. Contemporary state of the art lasers are capable of accelerating electrons and ions to relativistic energies with a tabletop setup. Conventional linear accelerators will take kilometres of space to achieve similar energies. The limitation of linear accelerators arises because of the threshold magnetic field which the constituent materials can tolerate. On the other hand, laser induced accelerators exploit the plasma properties to accelerate the charge particles to relativistic energies.

A number of mechanisms are discussed which are responsible for the acceleration of ions to relativistic energies. Target normal sheath acceleration (TNSA), laser break out afterburner (BOA), coulomb explosion of atomic cluster, collisionless electrostatic shock (CES), etc. are few of the various mechanisms for the laser induced ion acceleration. However, the dominance of particular mechanism depends on the laser and plasma conditions.

We have studied the effect of initial plasma density on the energetics of the laser accelerated ions. For this purpose a one dimensional fully electromagnetic PIC code is used. We found in our studies that the initial plasma density plays an important role in generation of high energy particles. For the case of constant initial density, an optimum value of density is observed for which we get the maximum acceleration. Similarly, in case of a linear density ramp, an optimum ramp exists for the maximum acceleration. For a laser intensity of 5×1020 W/cm2 (a = 20) a maximum energy of about 1 GeV is observed with optimum density ramp. These observations are understood as a consequence of the multi-stage acceleration mechanism, when all the ions attains a maximum velocity then second phase of acceleration begins which further enhances the energies of ions.

(a) We have developed a generalized model for laser-matter interaction which is valid for wide range of laser pulse durations (femtoseconds to nanoseconds) and wide range of laser intensities. The model is based on the solutions of wave propagation equations in a medium with complex dielectric constant. The wave equations are solved numerically using matrix method. The dielectric constant is obtained from Drude’s free electron gas model while the collision frequency is obtained as an harmonic mean of Spitzer’s formula valid at high temperature and phonon scattering model valid at low temperature. The model is used to obtain absorption profile for linear, exponential and parabolic density profiles and results are compared with analytical and semi analytical models. It is also shown that the model discussed above easily converges to well known Fresnel’s limit for case of abrupt vacuum target interface.

In order to be able to simulate various laser-plasma interaction experiments, we have coupled this absorption model with an existing one dimensional multi-group radiation hydrodynamic code. A non local thermodynamic equilibrium (NLTE) model is used to calculate energy dependent radiation opacities and quotidian equation of state (EOS) model is used to generate EOS data. Number of experiments on laser-plasma interaction with pulse duration varying from 150 fs to 5 ps and laser intensities varying from 1012 W/cm2 to 1017 W/cm2 are simulated and results are found to be in good agreement with experiments.

(b) A model for the interaction of laser with atomic clusters is also developed, which considers the radial non-uniformities during cluster expansion. We have calculated the laser absorption by solving the Helmholtz equation for a stratified sphere using a recursive algorithm. The model includes three types of ionization mechanisms, namely, tunnelling ionization, collisional ionization and ponderomotive ionization. Furthermore, collisional ionization is calculated by using a numerical fitted formula for the gases of low atomic numbers (≤28) while Lotz formula is used for higher Z elements. Hydrodynamics is treated by solving the conservation of mass, momentum and energy equations in 1D Lagrangian geometry. Shocks are treated by Von-neumann artificial viscosity mechanism.

We have retrieved the uniform density results by modelling the cluster as a one region sphere. It is seen that the spatial non-uniformities play a vital role in absorption dynamics. In case of uniform density model, the resonance occurs only once but in our case, the resonance point keeps moving in space and time giving higher absorption. For example, for a laser intensity of 5×1015 W/cm2 , the laser absorption increases by a factor of 40 as compared to the uniform density model. Effect of pulse duration on the laser absorption is also studied. It is observed that there is an optimum pulse duration for maximum absorption. It is further observed that the uniform density model over predicts the effect of pulse duration.

(c) We have also carried out the study of laser interaction with preformed plasma leading to the laser induced ion acceleration. Contemporary state of the art lasers are capable of accelerating electrons and ions to relativistic energies with a tabletop setup. Conventional linear accelerators will take kilometres of space to achieve similar energies. The limitation of linear accelerators arises because of the threshold magnetic field which the constituent materials can tolerate. On the other hand, laser induced accelerators exploit the plasma properties to accelerate the charge particles to relativistic energies.

A number of mechanisms are discussed which are responsible for the acceleration of ions to relativistic energies. Target normal sheath acceleration (TNSA), laser break out afterburner (BOA), coulomb explosion of atomic cluster, collisionless electrostatic shock (CES), etc. are few of the various mechanisms for the laser induced ion acceleration. However, the dominance of particular mechanism depends on the laser and plasma conditions.

We have studied the effect of initial plasma density on the energetics of the laser accelerated ions. For this purpose a one dimensional fully electromagnetic PIC code is used. We found in our studies that the initial plasma density plays an important role in generation of high energy particles. For the case of constant initial density, an optimum value of density is observed for which we get the maximum acceleration. Similarly, in case of a linear density ramp, an optimum ramp exists for the maximum acceleration. For a laser intensity of 5×1020 W/cm2 (a = 20) a maximum energy of about 1 GeV is observed with optimum density ramp. These observations are understood as a consequence of the multi-stage acceleration mechanism, when all the ions attains a maximum velocity then second phase of acceleration begins which further enhances the energies of ions.