Abstract

A tomographic gas-density diagnostic using a Single-Beam Wollaston Interferometer able to characterize non-symmetric density distributions in gas jets is presented. A real-time tomographic algorithm is able to reconstruct three-dimensional density distributions. A Maximum Likelihood-Expectation Maximization algorithm, an iterative method with good convergence properties compared to simple back projection, is used. With the use of graphical processing units, real-time computation and high resolution are achieved. Two different gas jets are characterized: a kHz, piezo-driven jet for lower densities and a solenoid valve-based jet producing higher densities. While the first jet is used for free electron laser photon beam characterization, the second jet is used in laser wake field acceleration experiments. In this latter application, well-tailored and non-symmetric density distributions produced by a supersonic shock front generated by a razor blade inserted laterally to the gas flow, which breaks cylindrical symmetry, need to be characterized.

Highlights

  • The aim of future advanced accelerator concepts is to use accelerating structures that can sustain higher electric field strengths to downsize the structure compared to conventional microwave cavities.Laser Wake Field Acceleration (LWFA) is one such promising technology, which is being investigated by several research groups around the world

  • The driver pulse excites electron density oscillations, which are co-propagating with the driver almost at the speed of light forming a plasma wave, which is moving with a relativistic phase velocity

  • If the studied object can be assumed to be rotationally symmetric around a central axis, an Abel inversion yields the 3D density distribution from a single phase projection, i.e., a 2D projection obtained in one single observation direction, which is perpendicular to the axis of symmetry

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Summary

Introduction

The aim of future advanced accelerator concepts is to use accelerating structures that can sustain higher electric field strengths to downsize the structure compared to conventional microwave cavities. It has been shown that a density change by a factor of two to three can be achieved by a shock front in supersonic gas jets [3] At such a sharp transition, many electrons are loaded into the same phase-space volume of the plasma wave, which will result in a narrow energy spread of the accelerated electrons. The parameters of the generated electron beam (energy spectrum, charge and duration) critically depend on the plasma wave and its evolution, which in turn is very sensitive to the plasma density distribution With these facts in mind, a precise and fast real-time density measurement is required for controlling the down-ramp process [4] and (when shot-to-shot-fluctuations in the gas jet cannot be sufficiently suppressed) for increasing the shot-to-shot stability of the generated electron beam.

Theory
Estimation of Phase Shift Due to a Gas Jet Density Distribution
Wollaston Interferometer
Objective
Experimental Set-Up for Non-Rotational Measurements
Data Analysis for Interferometry and Real-Time Tomography
Numerical Tools
Tomographic Reconstruction
Maximum Likelihood-Expectation Maximization
Convergence and Error Studies of ML-EM
Real-Time Computation of the Density Reconstruction
Piezo Gas Jet for Free Electron Laser Beam Instrumentation
Solenoid Gas Jet for LWFA
Shock Front Characterization in an LWFA
Error and Stability Analysis
Conclusions
Full Text
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