Momentum Computed Tomography

Various secondary particles will be produced in the collisions of ions,electrons or laser beam with targets of atoms,molecules,clusters or solids.These secondary particles can be photons,electrons or other charged or neutral atoms or molecules,and carry lots of information on the collision dynamics.Various spectrometers have been utilized to measure their energy spectrums or angular distributions.Momentum computed tomography?MCT?was recently proposed by our group as a novel measuring theory.In MCT,the particle momentum is firstly projected onto a position-sensitive detector,giving a series of position spectrums,and the particle momentum distributions are then reconstructed numerically from these position spectrums.The current work enriches and complements the continuous and discrete forms of the MCT projection theory.Based on the intuitional picture of integral domain interception with momentum space,the original theory is firstly expressed into a concise form.By the definition of integral measurement and projection,the strict probabilistic analysis is further accomplished.The explicit projection forms in the cases of multiple particle species and finite collision regions are developed,and more discussions on the strong field approximation are presented.This work lays down clear discretization pictures of the momentum space and the positions spectrums,and constructs the Poisson statistical model.After elaborating the relationship between the maximum a posteriori method and the penalized weighted least square approach,and by observing the momentum space sampling characteristics in the measurement,the author develops an inexact alternating direction method of multipliers to solve the reconstruction problem,which is based on the compressed sensing theory and adopts the second-order three-dimensional total generalized variation as the regularization item.The author develops a program for MCT data analysis,i.e.,the momentum computed tomography iterative reconstruction framework?MCTIRF?.The program is coded in C++programming language and consists of a series of classes.The matrix template class undertakes most of the calculation works in momentum reconstruction,and adopts the OpenMP parallelism and sparse matrix techniques to accelerate the calculation speed.The histogram classes integrate some devoted methods for MCT,including the histogram superposition and slicing methods.The spectrometer simulation classes are capable to calculate the particle trajectories in the spectrometer field and their splat positions on the detector,as well as the integral curves in the particle momentum space.These simulated data can be used as references in studying the reconstruction algorithms and in designing the measuring strategy in online experiments.The projection class is constructed to calculate the projection matrix,and different reconstruction methods can be integrated into MCTIRF expediently.The first spectrometer based on the MCT theory is designed and constructed,which is composed of a stainless steel stand,a target holder,an electrode array,and a?160 mm microchannel plate detector.The target holder,the electrodes and the detector sensitive surface are connected by a series of high-precision resistors,providing the uniform electrostatic field to drive the secondary particles to the detector.A novel double layer strip array resistive anode and four spectroscopy amplifiers are adopted in the detector,which are all designed in this work.Careful and repeated tests are carried out to accommodate their working states with the gain of the microchannel plate.The position resolution of the detector reaches 0.38 mm in 160 Hz counting rate in the test.The detector counting rate is about 1 kHz in the experiment,leading to²%event superposition rate.Numerical experiments on measuring the momentum distributions of C⁺,C₂⁺,and C²⁺ions are carried out with MCTIRF,the parameters of which are based on the currently designed spectrometer.The simulations reconstruct the momentum distribution based on the popular adaptive steepest descent-projection onto convex set algorithm and the inexact alternating direction method of multipliers?IADMM?developed in this work,and compare the reconstruction qualities in different measurement strategies,thus demonstrating the MCT theory,the superior convergence of the IADMM algorithm,and the good stability and efficiency of MCTIRF.Some reconstruction cases when the particle species and the range of the particle momentum spaces are unknown are further discussed.The numerical experiments provide ample references for the online experiment.The online experiment is carried out in the EBIS laboratory,Institute of Modern Physics,Chinese Academy of Sciences,in which 15 keV Ar⁺ions collide with a highly oriented pyrolytic graphite?0001?surface at a 60°incident angle w.r.t.the target surface normal.A series of position spectrums are acquired,and the momentum distributions of C⁺and C₂⁺ions are reconstructed,from which some qualitative conclusions about the reaction process can be drawn.More detail physical analysis still relies on the improvement of the performance of the spectrometer,detector and reconstruction algorithm.