REU Site

• The stipend for participation is $700/week, with a 10 week program anticipated.
• Travel to Columbia: participants will receive up to a $500 travel reimbursement for travel to/from New York City.
• American Physical Society Division of Plasma Physics Meeting: participants will receive up to a $800 travel reimbursement for the 2025 meeting, to be held in Long Beach, CA.

• Accommodations in Columbia Housing are included with participation in the program.
• Accommodation dates are: Arrive Sunday June 1st, Depart Sat Aug 9th.
• Accommodations will be a single room in a suite-style residence with a shared kitchen and bathroom space.
• One set of linens will be provided at the program outset.

Students participating in the program will be eligible for the following additional activities. They are described in the Social page.

• A weekly student seminar, where graduate students are asked to provide presentations of their research topics or interests in a manner strongly relatable to the undergraduate students.
• Faculty and external speaker colloquia, in current-day topics of interest.
• Summer social events, hosted by the department or individual members.
• National Laboratory tour, of either Princeton Plasma Physics Laboratory, or Brookhaven National Laboratory.
• End of Summer Poster Symposium, where students can present their work to their colleagues and other members of the plasma group.

Potential Mentors in this area are:

• Prof Elizabeth Paul
• Dr Nikolas Logan
• Dr Chris Hansen

Representative theory and computation projects in magnetically confined plasmas are described below:

• Magnetically confined plasma fusion systems rely on the confinement of the charged fusion products, the alpha particles, for a sufficiently long time that they can deposit their heat in the hot plasma bulk. One magnetic confinement concept, the stellarator, has historically suffered from poor confinement of these alpha particles. Numerical optimization algorithms have recently demonstrated the ability to obtain stellarator magnetic fields that could be candidates for a fusion energy device. This project focuses on improvements in the numerical integration schemes used for evolving the trajectories of alpha particles in a three-dimensional fusion system, enabling more efficient design and modeling of these devices. The student will perform modification of an existing open-source C++ and python library to improve the accuracy and performance of the integration routines. This will be achieved through application of symplectic algorithms, improved parallelism, and other code optimization techniques. The student should have an interest in high-performance computing and scientific computing.
• This project will implement the calculation of a new theoretical limit in the size of “3D” distortions an axisymmetric magnetically confined plasmas can withstand before breaking apart. Devices called “tokamaks” are designed to be donut shaped plasma columns that are symmetric going (toroidally) around the donut. Asymmetries as small as one part in 10,000 smaller than the primary magnetic field can drive “reconnection” of field lines that destroys the otherwise good confinement of these toroidal plasmas. Before this, the plasma is simply distorted and maintains concentric surfaces of magnetic flux in which the magnetic field lines lie without crossing the field lines on neighboring surfaces. Maintaining concentric flux surfaces is essential to the ability of the plasma to retain heat and access high temperature conditions for fusion reactions to occur. At some point, the plasma becomes exponentially sensitive to resistivity and the surfaces fall apart due to any small resistivity. This project will be to implement this theoretical threshold calculation in the Generalized Perturbed Equilibrium Code (GPEC), and predict when this might happen for real experimental tokamak plasmas. An analytical theory for determining the limit at has also been recently developed and this will be compared with the simulated thresholds in GPEC. The outcome will enable specifying the tolerable asymmetry.
• A student would investigate the application of Machine Learning (ML) methods to classify and predict the presence of unwanted plasma instabilities for optimizing the design of magnetically confined plasmas based on the tokamak concept. Avoidance or control of unwanted plasma instabilities is an important design consideration in fusion devices and other engineered plasmas. The “Edge Localized Mode” (ELM) is an example of such an instability, which exists in high-performance tokamak plasmas, and must be avoided in commercial fusion applications. This requires the development of so-called ELM-free regimes that avoid instabilities by carefully regulating energy transport through a variety of approaches. The student would work with their mentor as well as collaborate with Columbia and outside participants of a related SciDAC project investigating this work. They would learn about and apply ML techniques for classification and prediction, including generative approaches similar to those in ChatGPT and other state-of-the-art methods in the ML/AI field. Models will be trained using experimental and high-fidelity simulation, providing an opportunity to learn about a breadth of the methods and their application in plasma physics. Finally, they will attend and participate in subject and plenary meeting for the collaboration, providing additional opportunities to build communication and collaboration skills.

Potential Mentors in this area are:

• Prof Lorenzo Sironi
• Dr Luca Comisso
• Dr Michael Hahn

In the area of plasma astrophysics, some typical projects are described below.

• Magnetic fields on the Sun are measured by making use of the Zeeman effect. The resulting maps of the solar photospheric magnetic field are known as magnetograms. The Zeeman effect refers to the shifts in the energies of atomic energy levels when the atoms are in a magnetic field. These shifts in energy cause lines in the spectrum to split compared to when there is no magnetic field. Additionally, light emitted from the split sub-levels is polarized differently depending on the orientation of the observer to the magnetic field. Most magnetograms are based on polarimetric measurements. But such measurements are slow because the Sun must be imaged using optical filters for four polarization states. The successful applicant will test a method for measuring photospheric magnetic fields relying only on the spectroscopic Zeeman splitting and compare those results to conventional polarimetric measurements to assess the level of agreement.
• The Sun emits a continuous stream of charged particles into space known as the solar wind. The characteristics of the solar wind are measured by satellites near the Earth and those properties vary significantly. For example the wind may be fast or slow or it may contain many or few Alfven plasma waves. One hypothesis is that the solar wind starts off with the same amount of plasma wave energy everywhere, but the Alfven waves are damped more quickly in some solar wind compared to others, and this may also affect other properties such as the wind speed. The successful applicant will study solar wind satellite data to test this hypothesis by measuring the correlations between characteristics of Alfven waves and other properties of the solar wind.
• A variety of plasma waves can be found in the solar corona. Alfven waves are transverse waves in which the magnetic field and the plasma move together. These waves are thought to play an important role in coronal heating by carrying wave energy from lower layers of the Sun into the corona. The corona also supports acoustic waves. Although the acoustic waves carry little energy themselves, they may act as a catalyst for heating the corona by driving reflection and damping the Alfven waves. Acoustic waves can be measured in images of the Sun as intensity fluctuations over time, as the intensity is proportional to the square of the plasma density. The successful applicant will study images of the corona and measure the amplitudes, frequencies, and wavelengths of acoustic waves throughout the solar corona. These data will be used as inputs to a theoretical model to understand how the acoustic waves affect the Alfven waves.

• Participants must be U.S. citizens or permanent residents
• Participants must be enrolled in (but have not yet graduated from) an accredited undergraduate college degree program with a concentration in physics or a related engineering field.
• Participants must be 18 years of age or older at the time of the program

We will collect the following information as part of the application:

• Basic name, educational institution, and demographic information
• A personal statement** (2 page max)
• An unofficial transcript (and your GPA)
• A Curriculum Vitae (2 page max)
• A reference letter (submitted separately)

**You will be requested to provide a personal statement. While this statement can take any format you prefer, you are encouraged to address the following questions in your statement:

1. What are your career plans after your undergraduate / masters degree?
2. What past experience has best prepared you for our REU program?
3. What are your goals for your time in our REU program? Why do you want to work here? Is there a particular activity that interests you?
4. Our group does a mix of computer-based data analysis and modeling, and hands-on projects. Do you have a preference, which, and why?