New study provides understanding of astrophysical plasma dynamics

plasma from a sun-like star in the upper left corner is coming out like a string that swirls like a whirlpool around a dot in the center of the image

Stars, solar systems, and even entire galaxies form when astrophysical plasma — the flowing, molten mix of ions and electrons that makes up 99% of the universe — orbits around a dense object and attaches, or accretes, on to it. Physicists have developed models to explain the dynamics of this process, but in the absence of sending probes to developing stars, the experimental confirmation has been hard to come by.

In a study published in Physical Review Letters September 25, University of Wisconsin–Madison physicists recreated an astrophysical plasma in the lab, allowing them to investigate the plasma dynamics that explain the accretion disk formation. They found that electrons, not the momentum-carrying ions, dominate the magnetic field dynamics in less dense plasmas, a broad category that includes nearly all laboratory astrophysical plasma experiments.

plasma from a sun-like star in the upper left corner is coming out like a string that swirls like a whirlpool around a dot in the center of the image
An artist’s conception of the accretion disk | Credit: P. Marenfeld/NOAO/AURA/NSF

Like water swirling around and down an open drain, plasma in an accretion disk spins faster nearer the heavy object in the center than further away. As the plasma falls inward, it loses angular momentum. A basic physics principle says that angular momentum needs to be conserved, so the faster rotating plasma must be transferring its momentum away from the center.

“This is an outstanding problem in astrophysics — how does that angular momentum get transported in an accretion disk?” says Ken Flanagan, a postdoctoral researcher with the department of physics at UW–Madison and lead author of the study.

The simplest explanation is friction, but it was ruled out when the corresponding accretion times, in some cases, would be longer than the age of the universe. A model developed by theoretical physicists posits that turbulence, or the chaotic changes in plasma flow speeds, can explain the phenomenon on a more realistic time scale.

“So ad hoc, astrophysicists say, ‘Okay, there’s this much turbulence and that explains it,’” Flanagan says. “Which is good, but you need to call in the plasma physicists to piece together where that turbulence comes from.”

Flanagan and colleagues, including UW­–Madison physics professor Cary Forest, wanted to build off an idea that the turbulence was coming from an intrinsic property of some plasmas known as magnetorotational instability. This instability is seen in plasmas that are flowing fastest near the center and are in the presence of a weak magnetic field.

“And it’s lucky because there are weak magnetic fields all around the universe, and the flow profile in the accretion disks is set by the gravitational force,” Flanagan says. “So, we thought this plasma instability could be responsible for turbulence, and it explains how accretion disks work.”

To investigate if this intrinsic plasma instability explained the observation, the researchers turned to the Big Red Ball (BRB), a three-meter-wide hollow sphere with a 3000 magnets at its inner surface and various probes inside. They activate a plasma by ionizing gas inside the BRB, then applying a current to drive its movement.

a 3-meter-diameter sphere, painted red and with tons of probes all around it
The Big Red Ball is one of several pieces of scientific equipment being used to study the fundamental properties of plasma in order to better understand the universe, where the hot, ionized gas is abundant. | Photo by Jeff Miller / UW–Madison)

Because they had previously been encountering problems in driving very fast flows, they tried a new technique to drive the flow across the entire volume of plasma, as opposed to just the edges. Fortuitously, the BRB had magnetic field probes from a previous experiment still attached, and when they activated the plasma under these conditions, they found that this new flow setup amplified the magnetic field strength with a peak at the center nearly twenty times the baseline strength.

“We didn’t expect to see that at all, because usually in plasma physics the simplest model is to think of plasmas as one fluid with the heavier ions dominating momentum,” Flanagan says. “The results suggested that the plasma is in the Hall regime, which means the electrons and their motion are entirely responsible for the plasma moving around magnetic fields.”

If they were correct in assuming it was the Hall effect that was driving magnetic field amplification, the equations governing magnetic fields and electric currents say that if you drive the current in the opposite direction, the strength of the magnetic field would be canceled out. So, they switched the current and measured the magnetic field strength: it was zero, supporting the Hall regime explanation.

While the results are not directly applicable to the plasma accretion disks around, say, a very dense black hole, they do directly impact the earth-bound experiments that attempt to recreate and study them.

“Nearly all plasma astrophysical experiments operate in the Hall regime, and so this sort of large qualitative effect is something you’re going to have to pay attention to when you make these sorts of flows in laboratory astrophysical plasmas,” Flanagan says. “In that sense, this work has a pretty broad impact for lots of different research areas.”

This research was supported in part by the National Science Foundation (#1518115) and by the U.S. Department of Energy (#DE-SC0018266).

New study expands types of physics, engineering problems that can be solved by quantum computers

A well-known quantum algorithm that is useful in studying and solving problems in quantum physics can be applied to problems in classical physics, according to a new study in the journal Physical Review A from University of Wisconsin–Madison assistant professor of physics Jeff Parker.

Quantum algorithms – a set of calculations that are run on a quantum computer as opposed to a classical computer – used for solving problems in physics have mainly focused on questions in quantum physics. The new applications include a range of problems common to physics and engineering, and expands on the types of questions that can be asked in those fields.

profile photo of Jeff Parker
Jeff Parker

“The reason we like quantum computers is that we think there are quantum algorithms that can solve certain kinds of problems very efficiently in ways that classical computers cannot,” Parker says. “This paper presents a new idea for a type of problem that has not been addressed directly in the literature before, but it can be solved efficiently using these same quantum computer types of algorithms.”

The type of problem Parker was investigating is known as generalized eigenvalue problems, which broadly describe trying to find the fundamental frequencies or modes of a system. Solving them is crucial to understanding common physics and engineering questions, such as the stability of a bridge’s design or, more in line with Parker’s research interests, the stability and efficiency of nuclear fusion reactors.

As the system being studied becomes more and more complex — more components moving throughout three-dimensional space — so does the numerical matrix that describes the problem. A simple eigenvalue problem can be solved with a pencil and paper, but researchers have developed computer algorithms to tackle increasingly complex ones. With the supercomputers available today, more and more difficult physics problems are finding solutions.

“If you want to solve a three-dimensional problem, it can be very complex, with a very complicated geometry,” Parker says. “You can do a lot on today’s supercomputers, but there tends to be a limit. Quantum algorithms may be able to break that limit.”

The specific quantum algorithm that Parker studied in this paper, known as quantum phase estimation, had been previously applied to so-called standard eigenvalue problems. However, no one had shown that they could be applied to the generalized eigenvalue problems that are also common in physics. Generalized eigenvalue problems introduce a second matrix that ups the mathematical complexity.

Parker took the quantum algorithm and extended it to generalized eigenvalue problems. He then looked to see what types of matrices could be used in this problem. If the matrix is sparse ­— meaning, if most of the numerical components that make it up are zero — it means this problem could be solved efficiently on a quantum computer.

The study shows that quantum algorithms could be applied to classical physics problems, such as nuclear fusion mirror machines. | Credit: Cary Forest

“What I showed is that there are certain types of generalized eigenvalue problems that do lead to a sparse matrix and therefore could be efficiently solved on a quantum computer,” Parker says. “This type includes the very natural problems that often occur in physics and engineering, so this study provides motivation for applying these quantum algorithms more to generalized eigenvalue problems, because it hasn’t been a big focus so far.”

Parker emphasizes that quantum computers are in their infancy, and these classical physics problems are still best approached through classical computer algorithms.

“This study provides a step in showing that the application of a quantum algorithm to classical physics problems can be useful in the future, and the main advance here is it shows very clearly another type of problem to which quantum algorithms can be applied,” Parker says.

The study was completed in collaboration with Ilon Joseph at Lawrence Livermore National Laboratory. Funding support was provided by the U.S. Department of Energy to Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344 and U.S. DOE Office of Fusion Energy Sciences “Quantum Leap for Fusion Energy Sciences” (FWP SCW1680).

Welcome, Assistant Professor Jeff Parker!

profile photo of Jeff Parker

Have you heard the joke about the lawyer who became a physics professor? Jeff Parker has, but rather than be the punchline, he was always in on the joke. After earning his Ph.D. in plasma physics from Princeton in 2014, Parker enrolled at Stanford Law School to pursue a career in energy and climate policy. “I lasted one year in law school, decided I really didn’t like it and just loved physics, and I wanted to get back to physics research,” Parker says.

After that one year, Parker accepted a postdoctoral fellowship at Lawrence Livermore National Lab, and two years later became a staff scientist there. On July 1, 2020, Parker joined the UW–Madison Physics Department as its newest assistant professor. Here, he will focus his research interests in theoretical plasma astrophysics. To welcome Professor Parker, we sat down for a (virtual) Q+A with him.

What are the main topics or projects that you will focus your research on?

My immediate research program has two main directions.

One area of research is going to be in plasma astrophysics and astrophysical fluid dynamics. This concerns plasmas in space or in the universe, like in the sun, or the origin of magnetic fields in the cosmos and how they shape what we see in the universe.  I will be investigating angular momentum transport by magnetic fields, which can occur in stars, accretion disks around black holes, and planetary interiors.

Another area is topological phases of matter in plasma physics, related to the 2016 Nobel prize on topological insulators, which came out of condensed matter physics. I am applying these ideas for the first time to plasma physics and plasma waves. This is a brand-new field in plasmas and I’m just getting into it, but I think it’s really, really interesting.

You’re in Madison now, and you’re getting started with your research. What is the first thing you’re doing?

One particular project I’m very interested in is the astrophysical fluid dynamics involving angular momentum transport due to magnetic fields. I have developed theory on something that I call magnetic eddy viscosity, which could be important where there are magnetic fields and rotation. This can occur in astrophysical objects like stars or accretion discs or planets. And so where I studied this was in a pretty idealized system, and I’d really like to extend this into more realistic models that are closer to reality that would help us say something more about real object like stars or accretion discs, or potentially could be measured in the laboratory. So, there are these experiments, Prof. Forest has one, and there are other experiments throughout the country or the world that have rotating plasmas or liquid metals. This effect could potentially be seen in those experiments as well, and that is something I’d love to do right away.

Your work is primarily theory and computation. Do you see your work as predicting ideas that would be tested with collaborators in the department?

That is one thing I do hope to do. But I do also enjoy developing theory to better understand plasmas, even if those theories cannot be tested immediately in an experiment. I’m a theoretical physicist at heart, but there are so many great plasma physics experiments at Madison, which enable a close collaboration of theory and experiment. Progress is truly made when you can measure, observe, analyze, and use theory to understand what you see.

What’s one thing you hope students who take a class with you will come away with?

I want students to take away how plasma physics is everywhere, how most of the universe is plasma, and so if we want to understand the universe, we need to understand plasma physics.

What is your favorite element and/or elementary particle?

For elementary particle, I’ll say the neutrino because it’s so mysterious, and mysterious is good for physics. For favorite element, hydrogen and its isotopes because they’re what’s important for fusion.

What hobbies/other interests do you have?

I like to hike, run, and travel.