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Training and Research Experiences in Nonlinear Dynamics

Nonlinear Dynamics in Charged Particle Beam Systems

Rami Kishek and Brian Beaudoin - University of Maryland Electron Ring

The study of the nonlinear dynamics in charged particle beams at the extreme frontier of intensity is important for many applications. Example applications include high-energy and nuclear physics, materials science (using spallation neutron sources and x-ray free electron lasers and related intense light sources), free electron lasers for directed energy, and future heavy ion-driven inertial fusion concepts. At high intensity, particles experience internal forces from other particles (space charge) that are comparable to the applied external focusing and accelerating forces. The internal space charge forces depend on the constantly-evolving beam distribution and are typically nonlinear. The group operates a world-class experimental research facility: the University of Maryland Electron Ring (UMER), a compact accelerator using low-energy, high-current electron beams to model the dynamics of intense beams.

Projects suitable for undergraduate participation will be centered on relevant scientific issues. Examples are:

  • Experimental investigation of a mutli-stream instability caused by the longitudinal overlap of multiple beams
  • Computational investigation of the chaotic dynamics involved in beam halo formation
  • Electronics design for an acceleration module for UMER

The Charged Particle Beam Group has employed over thirty undergraduate research assistants in recent years, many of whom have appeared as co-authors on scientific publications. Examples include Ksenia Danylevich, Matt Holland, Brian Beaudoin, Matthew Bakalar, Erin Sohr, Nader Behdin, Nana Asare, and Kiersten Ruisard.

Efficient High-Power Radio Frequency (RF) Sources for Applications in Ionospheric HeatingBrian Beaudoin

The Laboratory for High-Power RF sources complements the Charged Particle Beam Group by designing efficient electron sources using novel approaches that minimize energy losses and maximize energy recovery. These sources are a key instrument in the heating of the ionospheric plasma in order to develop new applications that take advantage of the ionosphere as an active plasma medium, improving the performance of trans-ionospheric communications and intelligence.  

Laboratory for Photocathode Research - Eric Montgomery

The Laboratory for Photocathode Research complements work done in the Charged Particle Beam Group by looking at the inception of a charged particle beam just as it is "born" at the photocathode, combining principles from electrodynamics, quantum mechanics, solid state physics, and surface science. Photocathodes are photosensitive materials that are used to generate high brightness and low emittance electron beams: a primary application is as a driver for free electron lasers (FELs). The goal is to fabricate and analyze high quantum efficiency and long lifetime photocathodes through closely coupled experiment and theory.

The laboratory has offered TREND students self-paced as well as collaborative research projects. Hands-on experimentation is conducted within a theoretical framework understandable by motivated students with a sophomore physics or engineering background. Student creativity, responsibility and independence are emphasized.

Research skills developed by prior students include ultrahigh vacuum apparatus operation and design, thin film deposition and measurement, experimental automation in LabVIEW, data analysis and interpretation, machine shop fabrication, and optics bench layout and alignment.

Dr. Montgomery is dedicated to advancing TREND participants in their broader scientific careers through mentoring in public speaking skills, writing skills , conference presentation, and journal publication. Past and present students have received a first authorship and several co-authorships in major journals and conferences for their TREND work. Since 2007, in competition with over 50 other undergraduate interns at UMD, Dr. Montgomery's TREND students have won the top prize (all-expenses-paid conference travel) in three of six years.

Recent TREND projects from the Laboratory for Photocathode Research have included:


Information about nonlinear dynamics in charged particle beam systems can be found at and by contacting Rami Kishek at 301-405-5012 ( or Brian Beaudoin at 301-405-6994 (,). 

Information about the Laboratory for Photocathode Research can be obtained by contacting Eric Montgomery at 301-405-8484 (