2016PUPC普林斯顿大学物理竞赛Online真题与答案免费下载-Laser and Plasma Physics








Laser and Plasma Physics Online Part 完整版真题免费下载





The subject of this document is a link between plasma physics and laser physics. More specifically, we will see how we can use plasmas to obtain a very strong laser amplification. We will also try to understand the theory of laser amplification, which is roughly the process of obtaining a very high laser intensity from a lower intensity laser beam. Laser amplification technology has become highly advanced since the 1960’s through methods such as Mode-locking, Q-switching and Chirped Pulse Amplification. These methods have allowed huge improvements in laser intensity, with beams reaching intensities of up to 1020 W/cm2 , in a focused beam. However, these methods are limited by the material which is used to amplify the laser beam. Solid state lasers use amplification medium crystals, such as Titanium–sapphire crystals, or the more common neodymium-doped yttrium aluminium garnet, known as YAG. These materials deteriorate at very high intensities due to the resulting high temperature, so they are limited to a certain maximum laser beam intensity.

In this paper, you will explore a new idea to enhance laser amplification by using a process called Raman-Backscattering. Raman-Backscattering is the process of having a photon hit an atom, excite it to a certain state, and then have another photon be re-emitted at a different frequency from the initial frequency in the direction of the initial incoming atom. This process can roughly turn a long high energy laser pulse into a short, very high intensity laser pulse. (We will actually use two laser beams to obtain this result later in this document.) Instead of a normal amplification medium you will use plasma, which is already broken up into ions and electrons, so it cannot deteriorate further in a high intensity laser. You will work on some small problems to get accustomed to the ideas of oscillations in plasmas and to the idea of Raman Scattering. Finally, you will implement a computer simulation of a method of amplifying laser beams.

1 Introduction

We will start by working with some simple models of plasma oscillations as they will be helpful in seeing how plasma behaves when it interacts with electric fields. We will then discuss some about how magnetic potential relates to laser intensity and we will do a simple model of Raman Scattering.

2 Theory

2.1 Plasma Oscillation

A neutral plasma is defined as a collection of particles: ions and electrons. Ions have positive charge +e> 0 and electrons have negative charge −e< 0. They have equal number densities ne. In the first part of the problem we shall model the small oscillations that happen in cold plasmas (plasmas with negligible thermal motion) because of small disturbances in the arrangement of the electrons and ions.

Imagine a collection of fixed ions. We can consider the ions fixed as they have a much larger mass than the electrons and move very little compared to the electrons. The freely moving electrons have equal density with the ions and fill all the space. Set a 3 axes coordinate system x, y, z. Consider the yz plane and x the axis perpendicular to it. Consider all the electrons with x> 0 to be displaced a distance d in the positive direction, and all the electrons for which x< 0 to be displaced a distance d in the negative direction. (You can ignore transient effects due to this initial displacement and take it as a given.) There will be an excess positive net charge due to the ions in the infinite slab centered at x=0 with width 2d. This charge creates an electric field, which pulls the electrons back towards the origin. This force, which pulls the electrons, creates an oscillatory motion.

Question: Describe the movement of an electron due to this electric field and assume that the ions are stationary. Find the oscillation frequency wpl. Note: consider electrons directly at the border of the slab. Give your answer in terms of ne, electron number density, me, mass of the electron, and e, charge of the electron.