Department Library


Michael Carlson (Senior Thesis, April 2018, Advisor: Ross Spencer )


The shock structure near the skimmer cone of the plasma/vacuum interface of an Inductively Coupled Plasma-Mass Spectrometer (ICP-MS) is computationally modeled using a Direct Simulation Monte Carlo (DSMC) code, FENIX. These shocks are caused by a hypersonic, rarefied gas flow hitting a metal surface. To determine the most accurate simulation of the shocks, three different gas--surface interaction models are tested against existing experimental data. The three interaction models used in this study are the specular, thermal and Cercignani-Lampis-Lord (CLL) models. The specular and thermal models are simpler to implement, but do not result in the correct shock structure. Namely, the specular model conserves too much energy in the reflected particles and does not scatter the particles enough. The thermal model does not conserve enough energy and scatters particles too much. The CLL model requires more time to set up, but results in a more accurate representation of the shock. This additional set up time comes from accommodation coefficients in the CLL model that can be set to approximately represent any surface, with its accompanying roughness and temperature. To find these accommodation coefficients, the simulated shocks need to be matched with experimental data. We found that the specular gas--surface interaction model gave the most accurate shock structure.

Joseph Chandler (Senior Thesis, April 2018, Advisor: Ross Spencer )


Between the skimmer cone and the mass analyzer of an Inductively Coupled Plasma Mass Spectrometer (ICP-MS) lies an electrostatic ion lens. The lens uses a large negative potential to remove the electrons from the plasma and to collimate the ions forming a plasma sheath. By using Boltzmann electrons and collisionless ions to computationally model this interaction, we can calculate the electrostatic potential and ion density near the skimmer cone. Doing this calculation on a cylindrically symmetric grid gives a version of Poisson's equation, which is a second order nonlinear partial differential equation that we try to solve using a successive overrelaxation technique. In this plasma sheath calculation, no pre-sheath is required due to the supersonic velocities of the ions. By calculating the position of the plasma sheath based on different initial conditions we are developing an understanding of how and where this sheath forms in both one and two dimensions.

Carson Evans (Senior Thesis, April 2018, Advisor: Ross Spencer )


The plasma torch of the Inductively Coupled Plasma Mass Spectrometer (ICP) is powered by a 3-turn coil attached to a radio-frequency generator running at 40 MHz. The discharge is started by a Tesla coil that briefly ionizes a small fraction of the argon gas flowing through the coil. After the initial ionization pulse, the RF field produces the electric field that gives the electrons enough energy to heat the argon gas. As the electrons gain energy from the RF field they reach an energy capable of either exciting or ionizing the argon atoms. We are modeling the effect of the RF field on the electrons as well as the effect of collisions between electrons with neutral, excited, and ionized argon and with other electrons. We are also including the possibility of de-excitation argon. Our goal is to see an electron avalanche, a chain reaction where electrons ionizing argon neutrals create more free electrons which in turn ionize more argon.


Matthew R Zachreson (PhD Dissertation, August 2015, Advisor: Ross Spencer )


The inductively coupled plasma mass spectrometer (ICP-MS) has been used in laboratories for many years. The majority of the improvements to the instrument have been done empirically through trial and error. A few fluid models have been made, which have given a general description of the flow through the mass spectrometer interface. However, due to long mean free path effects and other factors, it is very difficult to simulate the flow details well enough to predict how changing the interface design will change the formation of the ion beam. Towards this end, Spencer et al. developed FENIX, a direct simulation Monte Carlo algorithm capable of modeling this transitional flow through the mass spectrometer interface, the transitional flow from disorganized plasma to focused ion beam. Their previous work describes how FENIX simulates the neutral ion flow. While understanding the argon flow is essential to understanding the ICP-MS, the true goal is to improve its analyte detection capabilities. In this work, we develop a model for adding analyte to FENIX and compare it to previously collected experimental data. We also calculate how much ambipolar fields, plasma sheaths, and electron-ion recombination affect the ion beam formation. We find that behind the sampling interface there is no evidence of turbulent mixing. The behavior of the analyte seems to be described simply by convection and diffusion. Also, ambipolar field effects are small and do not significantly affect ion beam formation between the sampler and skimmer cones. We also find that the plasma sheath that forms around the sampling cone does not significantly affect the analyte flow downstream from the skimmer. However, it does thermally insulate the electrons from the sampling cone, which reduces ion-electron recombination. We also develop a model for electron-ion recombination. By comparing it to experimental data, we find that significant amounts of electron-ion recombination occurs just downstream from the sampling interface.


Nicholas J Eyring (Masters Thesis, December 2013, Advisor: Ross Spencer )


A high spatial resolution acoustic directivity acquisition system (ADAS) has been developed to acquire anechoic measurements of the far field radiation of musical instruments that are either remote controlled or played by musicians. Building upon work performed by the BYU Acoustic Research Group in the characterization of loudspeaker directivity, one can rotate a musical instrument with sequential azimuthal angle increments under a fixed semicircular array of microphones while recording repeated notes or sequences of notes. This results in highly detailed and instructive directivity data presented in the form of high-resolution balloon plots. The directivity data and corresponding balloon plots may be shown to vary as functions of time or frequency. This thesis outlines the development of a prototype ADAS and its application to different sources including loudspeakers, a concert grand piano, trombone, flute, and violin. The development of a method of compensating for variations in the played amplitude at subsequent measurement positions using a near-field reference microphone and Frequency Response Functions (FRF) is presented along with the results of its experimental validation. This validation involves a loudspeaker, with known directivity, to simulate a live musician. It radiates both idealized signals and anechoic recordings of musical instruments with random variations in amplitude. The concept of coherence balloon maps and surface averaged coherence are introduced as tools to establish directivity confidence. The method of creating composite directivities for musical instruments is also introduced. A composite directivity comes from combining the directivities of all played partials to approximate what the equivalent directivity from a musical instrument would be if full spectral excitation could be used. The composite directivities are derived from an iterative averaging process that uses coherence as an inclusion criterion. Sample directivity results and discussions of experimental considerations of the piano, trombone, flute, and violin are presented. The research conducted is preliminary and will be further developed by future students to expand and refine the methods presented here.

David Perkins (Senior Thesis, August 2013, Advisor: Ross Spencer )


The National Spherical Torus Experiment (NSTX), underway at Princeton Plasma Physics Laboratory (PPPL), investigates the plasma dynamics in a spherical tokamak to understand the device’s potential as a fusion power generator. Temperature anisotropy, a characteristic that could have substantial effects on the plasma’s overall dynamics, is not well-known in NSTX. The particle code GTC- NEO, a particle-in-cell simulation developed at PPPL, allows for computational diagnosis of temperature anisotropy. The code simulates a tokamak plasma in the neoclassical limit. We present here a computational study of temperature anisotropy in NSTX using GTC- NEO, including spatial temperature anisotropy profiles in varied regimes of particle collision frequency. Results show that anisotropy is less than 5% in NSTX. We observed that temperature anisotropy peaks near the edge of the plasma on the outboard side of the device. The magnitude of this peak varies inversely with collision frequency.


Matthew R Zachreson (Masters Thesis, December 2012, Advisor: Ross Spencer )


The Direct Simulation Monte Carlo algorithm as coded in FENIX is used to model the transport of trace ions in the first vacuum stage of the inductively coupled plasma mass spectrometer. Haibin Ma of the Farnsworth group at Brigham Young University measured two radial trace density profiles: one 0.7 mm upstream of the sampling cone and the other 10 mm downstream. We compare simulation results from FENIX with the experimental results. We find that gas dynamic convection and diffusion are unable to account for the experimentally-measured profile changes from upstream to downstream. Including discharge quenching and ambipolar electric fields, however, makes it possible to account for the way the profiles change.


Steven Schmidt (Capstone, July 2010, Advisor: Ross Spencer )


In order to study the operation of the Inductively Coupled Plasma Mass Spectrometer (ICP-MS), a computer code called FENIX has been developed which implements the Direct Simulation Monte-Carlo simulation method. A history of this project and a description of the recently developed version 10 of this software is presented. This computer code is written in FORTRAN 95 and is designed to run on multiple processors in parallel, the number of which is scalable to the demands of the problem. Recent improvements include algorithms which allow this rescaling to occur in an automated fashion, including automatically reconfiguring the geometry of the problem to work properly with any number of nodes. Also, the simulation of trace particles in addition to the background argon gas particles was re-implemented after this capability was lost when FENIX was rewritten for multiple processors. Finally, a method of simulating the interaction of these trace particles with an ambipolar electric field was developed and implemented into FENIX. These improvements have allowed for research to progress more quickly and with fewer problems. A study of gas flow through the skimmer cone of the ICP-MS was performed utilizing the FENIX 10 computer code which uses the Direct Simulation Monte Carlo (DSMC) method. Velocity distribution data in the region near the skimmer tip was collected in order to analyze the effect that different skimmer cone shapes have on the creation of a beam. This velocity distribution data allowed the shock size as a function of the skimmer shape to be measured. For instance, when the skimmer cone has a conical throat, the shock at the entrance to the skimmer cone is significantly smaller than when the skimmer cone has a cylindrical throat.


Daniel Wilcox (Senior Thesis, April 2009, Advisor: Ross Spencer )


Inductively coupled plasma mass spectrometers contain a sampling cone which accelerates an atmospheric-pressure gas to supersonic speeds. Calculating the flow properties as the gas passes through the cone is challenging because of the difficulty in specifying upstream boundary conditions and because the gas exhibits non-ideal effects as it passes through the cone. To calculate the flow, the Direct Simulation Monte Carlo algorithm was used on the BYU supercomputing cluster using about 200 processors and 600 million simulation particles with a three-week calculation time. Carefully crafted velocity and temperature boundary conditions were necessary. Evidence is presented that the calculated flowfield is a good solution to the problem.


William R Somers (Masters Thesis, August 2008, Advisor: Ross Spencer )


A Direct Simulation Monte Carlo fluid dynamics code named FENIX has been employed to study gas flow-through properties of the inductively coupled plasma mass spectrometer (ICP-MS). Simulation data have been tested against the Navier-Stokes and heat equations in order to see if FENIX functions properly. The Navier-Stokes and heat equations have been constructed from simulation data and are compared term by term. This comparison shows that FENIX is able to correctly reproduce fluid dynamics throughout the ICPMS simulation, with an exception immediately behind the ICP-MS sampler cone, where the continuum criterion for the Navier-Stokes equation is not met. Testing the data produced by Fenix also shows that this DSMC method correctly produces momentum and thermal boundary layer phenomenon as well. FENIX output data produce statistical fluctuations of about 2%. Limitations occur from fitting data near surfaces, incurring a relative error of about 5%, and fitting data to take second derivatives where fluid velocity gradients are steep, introducing a relative error of about 10%.

Charles Woods (Senior Thesis, April 2008, Advisor: Ross Spencer )


We have analyzed the flow of a gas through a cylindrical tube of constant radius for Mach number M<< 1 using both the fluid equations and the Direct Simulation Monte Carlo algorithm (DSMC). We find that the two methods are in good agreement, and for the flow velocity in this non-uniform case we give an approximate analytic solution.


Adam Payne (Senior Thesis, August 2007, Advisor: Ross Spencer )


An implementation of the Direct Simulation Monte Carlo Method has been used to model the behavior of the argon background gas in an Inductively Coupled Plasma-mass spectrometer as it expands supersonically from the sampler cone towards the skimmer cone. Of particular interest is the production of a shock wave as the neutral gasf flows through the nozzle and expands into the downstream vacuum region. Simulations where the skimmer cone is placed well inside the zone of silence will be presented. The results will show that collisional effects from the skimmer cone can trigger a shock in front of the cone. The results will also show that specularly reflecting (frictionless) cones do not produce a shock structure in front of the nozzle. In each simulation, the overall skimming process will be analyzed. Finally, a simulation using a combination of thermal and specular reflections will be presented in a preliminary attempt to more accurately model gas interaction with the cone surfaces.

Melissa Powell (Capstone, December 2007, Advisor: Ross Spencer )


A Malmberg-Penning trap is a cylindrical apparatus which confines non-neutral plasma with an axial magnetic field and negative electric potentials on both ends. Theory predicts that a hollow plasma density profile is unstable, and experiments agree. However, the experimental growth rate of the m=1 diocotron mode of the instability is much larger than the theoretical growth rate, by a factor of around 2-4. We are collaborating with an experimental research group to find the cause for this discrepancy by recreating their Malmberg- Penning trap in our 3D PIC computer simulation. The growth rates of our simulation test cases have remained roughly half that of the experiments. I will report how we successfully parallelized the simulation, allowing the number of plasma particles to be increased to approximately the number of particles in the experiment. The increased number of particles improves the accuracy of the simulation by reducing the noise on the computational grid.

Andrew Sampson (Senior Thesis, August 2007, Advisor: Ross Spencer )


Fenix is a program designed to simulate an inductively coupled plasma mass spectrometer using a particle-in-cell method called Direct Simulation Monte Carlo. Fenix specifically focuses on the supersonic expansion region in the inductively coupled plasma mass spectrometer. I have been working on the introduction of an analyte with the end result of comparing computational results with experimental results. Initial testing has shown similar behavior to the main element within the inductively coupled plasma mass spectrometer, but has also revealed areas that need to be re-evaluated.


Jaron Krogel (Senior Thesis, January 2006, Advisor: Ross Spencer )


The Inductively Coupled Plasma Mass Spectrometer (ICP-MS) is ubiquitous in trace elemental analysis. Recent research demonstrates that background ion content in the analyte sample influences ion transport through the device, impairing its accuracy. Here we present the development and testing of FENIX, a particle-in-cell simulation of the ICP-MS. We outline problems faced in ICP-MS and experimental methods used to investigate the fl.ow properties of the device. We describe the general process of the Direct Simulation Monte Carlo algorithm, and its specific implementation in FENIX. Properties of neutral argon flow in the device are presented, including comparisons with analytical approximations in each major region of the device's first vacuum stage. We conclude that FENIX accurately models neutral gas fl.ow in the complicated device geometry and that further work is necessary (particularly the modeling of a tracer species) before direct comparisons with experimental results can be made.


Donald M. Cannon (Senior Thesis, July 2003, Advisor: Ross Spencer )


James Aamodt Hart (Senior Thesis, April 2003, Advisor: Ross Spencer )


Eric L. Peterson (Honors Thesis, February 2003, Advisor: Ross Spencer )


Lance Smemoe (Capstone, April 2003, Advisor: Ross Spencer, Garth Hill, Jason Dzubak )



Erik C Bard (Masters Thesis, December 2002, Advisor: Ross Spencer )


This work presents an analytical treatment of resonant coupling between a particle undergoing cyclotron oscillation and an electromagnetic (TE) cavity mode of a cylindrical Penning trap. The outcome of the derivation is a closed form solution for the rate of cyclotron damping as well as a time-dependent solution for cyclotron motion and cavity mode evolution. The mode-generation transient is studied and the long-time scale resonant cyclotron damping rate is favorably compared with experimental values taken from a study of cyclotron resonance related phenomena conducted at Harvard University.


Thomas Grant Jenkins (Masters Thesis, December 2000, Advisor: Ross Spencer )


Numerical methods are presented for finding the eigenfunctions (normal modes) and mode frequencies of azimuthally symmetric non-neutral plasmas (confined in a Penning trap) whose axial thickness is much smaller than their radial size. The plasma may be approximated as a charged disk in this limit; the normal modes and frequencies can be found if the surface charge density profile σ(r) of the dis and the trpa bounce frequency profile ω(r) are known. The dependence of the eigenfunctions and equilibrium plasma shapes on non-ideal components of the confining Penning trap fields is discussed. The results of the calculations are compared with the experimental data pf Weimer et al [Phys. Rev. A 49, 3842 (1994)].


Thomas Grant Jenkins (Senior Thesis, April 1999, Advisor: Ross Spencer )



Cavendish McKay (Senior Thesis, April 1997, Advisor: Ross Spencer )


Deborah L Paulson (Masters Thesis, August 1997, Advisor: Ross Spencer )


Global thermal equilibrium computations are presented for non-neutral plasmas whose radial size is much larger than their axial thickness. Axial and radial density profiles are computed for both ideal and non-ideal Penning trap fields. Simple results are obtained in the limits of both low and high central density. Comparison is made to the grid calculations of Mason et al.


Kenneth C Hansen (Masters Thesis, December 1995, Advisor: Ross Spencer )


A study of the linear and nonlinear stages of electrostatic modes in warm, nonneutral plasma is presented. The normal modes of these systems have been studied in cold plasmas by Prasad and O’Neil, Dublin, and Jennings, Spencer, and IIansen. Here, numerical solution to the electrostatic mode equation for warm nonneutral plasma is presented. The solutions are compared with the work mentioned above for cold plasmas and also with other experimental and computational work. The method agrees with other data to within 2 or 3%. For plasmas that are spheroidal, it is found that the mode equation has a continuum that causes singularities in the perturbed potential. These resonances are named “acoustic resonances” because the singularities are a result of the acoustic-like terms in the mode equation. These resonances are found to be result of the model used and not the numerical method. Because the mode frequencies of these systems vary as a function of temperature, it should be possible to use them as a temperature diagnostic. It is found, however, that for the long plasmas studied, the temperature dependence is weak. Slight variations in the experimental plasma shape can account for enough shift in the mode frequencies to make the diagnostic useless. A nonlinear stage of the normal modes for this system may be excited by driving the plasma at one of the mode frequencies. The nonlinear stage is found to consist of number counter streaming solitons equal to the number of axial nodes in the linear mode. Particles trapped by these pulses are accelerated to large velocities and can escape the confinement region. A comparison of the experimental and computational results for these nonlinear modes is given along with additional insight gained from running a particle-in-cell simulation.

Y. E. Young (Honors Thesis, March 1995, Advisor: Ross Spencer )



R. K. Berg (Honors Thesis, April 1994, Advisor: Ross Spencer )



Johnny Kline Jennings (PhD Dissertation, April 1993, Advisor: Ross Spencer )


The low-frequency mode equation of a nonneutral plasma is a hyperbolic partial differential equation inside the plasma and an elliptic equation outside the plasma. This equation can now be solved numerically by directly solving the set of finite difference equations using a banded-matrix inverter that gives highly accurate results for this particular problem. When analyzing plasmas with sharp boundaries, special care must be taken in implementing the matching conditions at the plasma boundary. The results of this solution are compared to the results of a particle simulation and to analytic solutions of special cases discussed by Prasad and O’Neil [3] and by Dubin [4]. We have studied the effect of the wall on the mode frequency of short plasmas and have also looked at the indirect effect of the wall by way of its effect on the shape of the plasma. The direct effect on the frequency is small for radii less than a certain percentage of the wall radius. This percentage is mode dependent and can be estimated by a Gould-Trivelpiece analysis. For large plasma radii, however, Gould-Trivelpiece analysis overestimates the frequency shift. The effect on the shape of the plasma is also small for small radii, and increases as the plasma radius approaches the wall radius. Both effects seem to suggest that the effect of image charge in the trap wall is to lower the oscillation frequency.

Michael B Ottinger (Masters Thesis, December 1993, Advisor: Ross Spencer )


The dispersion relation for a single species plasma confined in a cylindrical chamber is obtained by theory and by computer simulation. It is first shown that the complex dispersion relation can be obtained from the drift-kinetic equation by method of characteristics with the help of the matrix shooting program GOULD. The validity of GOULD is obtained by other means. Next the particle simulation code RATTLE is described. The real part of the dispersion relation from RATTLE is obtained, but the complex part remains elusive. Finally the dispersion relations are compared and it is shown that agree to within 1%.


Jinyun Lin (Masters Thesis, December 1992, Advisor: Ross Spencer )


A 1-D MHD simulation code has been developed and tested for Carbon plasma in a capillary device. With classical transport coefficients, the model has successfully repeated Rocca’s 0-D model results. Although we cannot simulate the rising temperature part of Bogen’s experiment, we are able to obtain about the same cooling rate as his by using non-classical transport multiplication factors. The code will be used to develop a full experimental design for testing the recombination scheme to produce an x-ray laser and to interpret experimental results after the experiment has been built.