Optimizing klystrons for cancer therapy
When LaGrange College senior math major Kayla Cline accepted a Research
Experience for Undergraduates (REU) position at North Carolina State University
this past summer, she didn’t realize she would be the only one out of the 40 students
there who had taken a MATLAB course to prepare her for what was ahead.
MATLAB is a high-level language and interactive environment for numerical computation,
visualization and programming. Using it, you can analyze data, develop algorithms
and create models and applications. Kayla says she had a jump on her counterparts
at NC State because her LaGrange College professors offered the class.
“Some of the students in my research group I really learned from because one was
a math and physics double major, and another was a math and engineering double
major,” says Kayla, who is from Cartersville. “But as for MATLAB, some of the students
had learned MATLAB on their own or had it as part of an undergraduate research
experience, but I was the only one who had taken a class. It wasn’t a new concept
Kayla spent 10 weeks at NC State’s REU to do research in applied mathematics.
Two hundred undergraduates across the nation were chosen to participate, with 40
in math. The 40 were split into teams for nine research projects.
Kayla’s group worked with a team from Calabazas Creek Research in California to
research optimization of klystron circuits, notably the Clinac klystron used
in cancer therapy.
“Klystrons are tubes that are wave amplifiers,” Kayla says. “They have applications
ranging from radar to cancer therapy. Anything that has a wave probably has a klystron
When engineers build the klystrons, their wave has to be very exact, with a certain
gain, power and bandwidth, which means their specifications must be precise. Kayla
and her team’s job was to improve the small-signal code to include optimization
of parameters, which has never been done before, and hopefully create a code in
MATLAB so scientists will not have to compute wavelengths manually. Instead, they
will input measurements into the team’s computer program, and their measurements
will be computed for them.
Kayla’s team worked with a computer program known as AJ-Disk, which was created
by Stanford University graduate Aaron Jensen, who now works at the Stanford Linear
“With the AJ-Disk, engineers can punch in what they think their klystrons should
be built like, hit a simulator button and the AJ-Disk will tell them what their
klystrons should be able to do,” Kayla says. “Right now, without the AJ-Disk, it’s
just a guess. With the disk, when you punch in the numbers, it will find the optimal
variables you should punch in to get the kind of klystron you want. It makes the
guessing process automatic.”
Kayla joined LaGrange College graduate George Lankford at NC State, who is working
toward a Ph.D. in applied mathematics. George graduated from LaGrange in 2011.
“George was the graduate student mentor in my research group, and it was great
having a familiar face,” Kayla says.
George and Kayla both went to Stanford University during the summer and visited
Calabazas Creek Research and the Stanford Linear Accelerator Center. The center’s
main building is three miles long and houses a linear accelerator that is powered
by 250 klystrons in a row. They also spoke with Aaron Jensen, inventor of the AJ-Disk.
At LaGrange College, Kayla’s math classes have included a calculus sequence, differential
equations, linear algebra, computational math, data-mining and MATLAB. She’s
also participated in an undergraduate research math experience of differential
equations in math modeling by examining the heating and cooling systems in the
college’s Lewis Library.
She highly recommends the REU, an opportunity she learned about from Drs. Stacey
and Jon Ernstberger, both LaGrange College math professors. Both earned their doctoral
degrees in computational mathematics from NC State and have been instrumental in
preparing both Kayla and George for the NC State experience through the classes
they’ve offered, their guidance through LaGrange College undergraduate research
projects and their accessibility as professors, Kayla says.
Kayla says she planned on becoming a math teacher without going to graduate school
until she experienced math classes at LaGrange College and NC State’s REU.
“I would like to become a math professor at a college one day, but I also really
love research,” she says. “And after grad school, I might love it even more.”
Kayla is continuing to work with her REU group via email throughout her senior
“There’s so much more we have to do,” she says. “For one, in the long run we hope
to optimize the Clinac klystron, which is used for cancer therapy and radiation.
Ultimately, we want to make the klystron smaller and more efficient, so it will
be cheaper to make, and then it will be more available for hospitals to buy.”