Emittance Exchange – The 2nd Ph.D. Project.
Tim Koeth’s Ph.D. at Fermilab was not built around a single narrowly defined experiment. It unfolded over roughly seven years of intensive, hands-on accelerator work, during which he was entrusted with two unusually large experimental projects. The first was Capture Cavity II, where he led and participated deeply in the preparation, assembly, installation, RF commissioning, cryogenic integration and high-gradient testing of a major superconducting RF system. After CCII successfully demonstrated the required high-gradient performance, Fermilab decided that the cavity had become too important to its broader superconducting-RF program to be relocated to the A0 Photoinjector as originally envisioned. Tim therefore had to find a new dissertation project.
That second project became the Emittance Exchange Experiment, or EEX.
Far from being a smaller CCII replacement effort, EEX became another all-encompassing accelerator experiment and ultimately the work on which Tim completed his dissertation. Under the mentorship of Helen Edwards at Fermilab’s A0 Photoinjector, Tim again found himself responsible not merely for analyzing data from an existing machine, but for helping create the experimental apparatus itself. In his dissertation acknowledgements, Tim described Helen as giving him “the educational experience of a lifetime” and credited her direction with bringing him through the completion of the experiment.
The project also represented a direct continuation of Tim’s earlier RF experience. In 1998, Rutgers physicist Gordon Thomson had introduced him to the problem of building a 3.9-GHz resonator for the proposed CKM experiment. That work had brought Tim to Fermilab and into Helen Edwards’ laboratory, where he first became immersed in accelerator RF. As Tim later wrote in his thesis, when that first 3.9-GHz resonator problem was posed, “we had no idea where it would lead.”
Years later, that earlier CKM experience became directly relevant when the EEX experiment required a very different but closely related 3.9-GHz device: a TM110 transverse-deflecting RF cavity.
Designing an accelerator around the physics
The EEX concept was elegant in theory. A transverse-deflecting RF cavity placed in a properly designed dispersive beamline could couple the horizontal and longitudinal phase spaces of an electron bunch, allowing the emittance in those two dimensions to be exchanged. The Fermilab experiment was based on a refinement of earlier theoretical proposals and was intended as a proof-of-principle demonstration of transverse-to-longitudinal emittance exchange.
But turning that theoretical concept into a working accelerator required considerably more than placing a cavity between a few magnets.
Tim had to design the entire EEX beamline around the available A0 Photoinjector space and hardware. That required determining the physical geometry and transport optics; selecting and positioning dipoles and quadrupoles; integrating beam-position monitors, viewing screens, emittance diagnostics, momentum diagnostics and bunch-length instrumentation; and ensuring that the complete arrangement could actually be installed and operated at A0. He developed and used a Trace-3D/Matlab model of the real beamline hardware both as a design tool and later as a guide during measurements of the EEX transport matrix and the actual exchange.
The beamline made extensive use of existing Fermilab hardware. In particular, the four principal dipole magnets forming the two magnetic doglegs were recycled from the bunch compressor of an earlier experiment. These C-frame magnets used trapezoidal and parallelogram pole tips and exploited edge focusing. Their geometry was selected so that the dispersion derivative vanished in the region between the second and third dipoles, precisely where the TM110 cavity was to be located.
This was a crucial point in the experimental logic. The magnetic system established the dispersion, and the dispersion in turn determined the RF field the cavity had to generate. Once Tim had developed the physical beamline, he could derive the required TM110 shear strength. At the cavity location, the design produced approximately 330 mm of dispersion, requiring an integrated longitudinal electric field equivalent to approximately 45 kV at a position 1 mm off axis.
In other words, the RF cavity specification was not arbitrary. It emerged directly from the accelerator optics Tim had designed.
A cavity that would not quite work at room temperature
The next question was how to produce that field.
Fermilab’s superconducting RF program had already developed prototype 3.9-GHz TM110 cavities, originally associated with an RF-separated kaon beam concept. But those devices were not practical for installation in the EEX beamline: no suitable beam-tube cryostat or adequate liquid-helium infrastructure existed for such an application. Since the required EEX field was relatively modest, the decision was made to construct a normal-conducting cavity from oxygen-free high-conductivity copper instead.
That solution created another engineering problem.
At room temperature, the copper cavity did not have enough quality factor to meet the required field, power and mode-separation constraints in a practical geometry. A warm cavity would have required approximately seven cells, but a seven-cell structure would bring adjacent resonant modes too close to the desired π mode, increasing the likelihood of unwanted mode excitation.
Tim’s solution was to cool the copper cavity with liquid nitrogen.
Because the electrical conductivity of high-purity copper increases substantially as its temperature falls, cooling the structure to approximately 80 K increased its unloaded quality factor from about 14,800 to 35,600, a factor of roughly 2.4. That improvement reduced the RF power required and narrowed the resonances sufficiently that a five-cell cavity became practical. Although the calculations suggested that three cells might have been enough, Tim chose a five-cell structure, deliberately providing two additional cells as operating margin against RF-power limitations and other real-world uncertainties.
The result was an unusual accelerator device: a 3.9-GHz, five-cell, normal-conducting copper TM110 cavity designed to operate at liquid-nitrogen temperature.
Building the five-cell TM110 cavity
Designing the cavity electromagnetically was only part of the job. Tim then became deeply involved in turning that design into a working RF structure.
The cavity was fabricated from 2.2-mm-thick OFHC copper half-cells, most of them stamped using tooling originally developed for Fermilab’s C15a niobium cavities. Pairs of half-cells were vacuum brazed together to form RF “dumbbells.” Each dumbbell was then electrically characterized and trimmed at the equator so that the completed structure would arrive at the proper operating frequency after both final tuning and thermal contraction to liquid-nitrogen temperature.
This required careful RF work on essentially every part of the cavity. Tim performed and oversaw the dumbbell measurements, half-cell tuning, end-cell matching and complete-structure characterization. The end cells could not simply be treated as identical copies of the central cells because the beam pipes and couplers perturbed the RF boundary conditions. They therefore had to be reconciled with the main body of the cavity so that the completed five-cell structure behaved as a single coherent resonator with the correct mode spectrum, frequency and field distribution.
The input coupling system required another substantial design effort. Rather than create a completely new high-power coupler, the project repurposed a spare Fermilab/DESY 3.9-GHz third-harmonic superconducting-cavity input coupler, rated for approximately 80 kW pulsed operation. Tim used HFSS modeling to determine the coupler’s longitudinal position and penetration into the beam pipe so that the external Q would properly match the lower Q of the copper cavity. An adjustable low-power room-temperature coupler was used during testing to determine the proper coupling empirically at both warm and cold conditions before the high-power system was finalized.
The low-level RF system also had to be adapted. Fermilab’s existing ESECON controls had been developed around 1.3-GHz superconducting RF, so a dedicated 1.3-to-3.9-GHz up/down-conversion system was built to allow the controller to regulate the TM110 cavity’s phase and amplitude.
Bead pulls, tuning and polarization
Once the cavity was brazed together, Tim faced one of the most labor-intensive parts of the entire project: making the actual field inside the cavity match the intended design.
The team resurrected a Fermilab LINAC bead-pull system, combining an HP8510 network analyzer, stepper motor and a tiny metallic bead that could be pulled longitudinally through the cavity. As the bead passed through each cell, it perturbed the local electromagnetic field, allowing the relative field strength to be mapped.
The first measurements showed roughly 20 percent RMS variation in the field from cell to cell—far too large.
Correcting that imbalance required repeated cycles of RF measurement, mechanical adjustment and remeasurement. Because the available tuning process could effectively move individual cell frequencies in only one direction, each adjustment had to be made cautiously. After more than sixty tuning iterations, the cavity reached less than 2.6 percent RMS variation in peak electric field, essentially at the resolution limit of the measurement system. Even after repeated thermal cycling between room temperature and approximately 80 K, the field flatness remained acceptable.
The TM110 mode brought another complication: polarization. Unlike an ordinary azimuthally symmetric accelerating mode, the dipole mode can exist in two transverse orientations. Tim therefore also had to ensure that the desired polarization was correctly oriented and sufficiently separated in frequency from its orthogonal partner. Measurements showed greater than 5 MHz separation between the two π-mode polarizations, with the asymmetry introduced by the input coupler itself helping to establish the required orientation.
The repeated dumbbell measurements, cell tuning, end-cell matching, coupler studies, bead pulls, polarization measurements and warm-to-cold RF measurements were not peripheral technical chores. They were what transformed the theoretical cavity into an accelerator component capable of doing the required beam physics.
Assembling the EEX Beamline — Ultra-High Vacuum in the Real World
Building the EEX beamline involved considerably more than positioning magnets and bolting accelerator components together. Because the A0 Photoinjector contained a superconducting RF cavity, the entire machine operated under exceptionally stringent ultra-high-vacuum and particulate-cleanliness requirements. The finished beamline ultimately operated at pressures of only a few × 10⁻⁹ Torr, meaning that contamination invisible to the eye—dust, fingerprints, oil, fibers or improperly prepared vacuum surfaces—could compromise accelerator performance.
The beamline was therefore constructed almost like a piece of scientific instrumentation inside a spacecraft. Vacuum components were first cleaned in ultrasonic baths using ultrapure water in a Class 1000 clean room, then blown with dry nitrogen and checked in a Class 10 clean room until the measured population of 10-µm particles fell below background. Wherever possible, the many beamline components—beam-position monitors, diagnostic chambers, vacuum piping, screens, slits and other hardware—were assembled into substantial, roughly table-sized subassemblies under these controlled conditions rather than being assembled piece-by-piece inside the accelerator cave.
Once a clean subassembly had been completed, its open vacuum interfaces were carefully capped and protected so that the cleanliness achieved in the clean room survived transportation. The completed assemblies were then moved to the A0 experimental area and, because of their size and weight and the crowded accelerator geometry, rigged and lowered into position with cranes and lifting equipment. This created an unusual installation problem: the precision cleanliness required for an ultra-high-vacuum accelerator had to be maintained while installing large pieces of machinery in an industrial experimental hall.
The solution was essentially to bring the clean room to the accelerator. After the large subassemblies had been positioned and aligned, portable clean-room enclosures were erected around the connection points. Only inside these localized clean environments were protective caps removed and the final vacuum joints made. Tim’s thesis specifically notes that as much assembly as possible was done in the permanent Class 10 clean room and that the unavoidable final in-situ connections were performed beneath a portable clean room.
After each vacuum section was closed, the work still had to prove itself. The EEX/A0 vacuum system could be divided by gate valves into six independently isolated volumes. Each section was initially evacuated using oil-free, mechanically backed turbomolecular pumps until pressures of approximately 1 × 10⁻⁷ Torr or better were reached. The mechanical pumping system was then isolated and ion pumps took over. Beam operations were permitted only when pressures measured at the ion pumps had fallen to the few × 10⁻⁹ Torr range or below.
This aspect of EEX also illustrates something that can disappear from a published physics result: an accelerator experiment of this complexity depends upon world-class technicians, machinists, vacuum specialists, riggers and engineers. The beamline contained a dense succession of quadrupoles, dipoles, BPMs, viewing stations, slits, the TM110 cavity and spectrometer instrumentation extending over many meters. Installing that apparatus while simultaneously preserving Class-10-level cleanliness and maintaining leak-tight UHV joints was specialized work requiring extraordinary experience and discipline.
Commissioning the machine Tim had built
Even after the cavity was assembled and installed, the experiment was still not finished.
First-beam measurements showed that the transverse deflection was weaker than expected for the applied RF power. Tim and the team traced the shortfall to several practical effects, including less-than-unity coupling, lack of full klystron output, the non-optimal effective cell length and changes in field flatness under cryogenic conditions. The decision to build a five-cell structure with additional operating margin proved valuable. Through further cavity tuning, LLRF adjustment and increased RF power—ultimately around 55 kW—the cavity achieved the gradient required for emittance exchange.
Tim then undertook a systematic characterization of the accelerator itself. Rather than assuming that the beamline was performing the intended exchange because the output beam looked qualitatively different, he measured the full 6 × 6 transport matrix of the EEX system using difference-orbit techniques. Individual input beam coordinates were deliberately varied, and the resulting changes in all six output coordinates were measured. The experimentally determined matrix showed overall good agreement with the calculated EEX transport matrix.
Only after the beamline had been designed, assembled, commissioned, modeled and experimentally characterized could Tim perform the measurement for which the apparatus had been built.
Using a 14.3-MeV, 250-pC electron bunch, he directly measured the electron beam before and after the exchange channel. An incoming longitudinal emittance of 21.1 ± 1.5 mm·mrad appeared as an outgoing horizontal emittance of 20.8 ± 2.0 mm·mrad, effectively a one-to-one exchange within the experimental uncertainty. The complementary measurement found an incoming horizontal emittance of 4.67 ± 0.22 mm·mrad exchanged into an observed longitudinal emittance of 7.06 ± 0.43 mm·mrad, with the discrepancy understood in terms of limitations of the longitudinal diagnostic and an unresolved energy-time correlation.
This work became Tim’s 2009 Rutgers dissertation, An Observation of a Transverse to Longitudinal Emittance Exchange at the Fermilab A0 Photoinjector.
A seven-year experimental apprenticeship
Seen in the context of Tim’s entire Ph.D., EEX was not an isolated dissertation project. It was the second major accelerator system he helped carry from engineering concept through commissioning and experimental operation.
His first major undertaking, Capture Cavity II, had already immersed him in superconducting RF, high-power RF, cryogenics, controls, vacuum, shielding, radiation safety, rigging, installation and the coordination of a large multidisciplinary laboratory team. When circumstances beyond his control made CCII unavailable as his eventual dissertation experiment, he did not simply move to an established beamline and collect enough data to graduate. He effectively began again—with another ambitious accelerator project.
EEX demanded a different but equally broad set of skills: accelerator optics, magnet selection and characterization, beamline layout, electromagnetic cavity design, machining and brazing, RF metrology, cryogenic operation, high- and low-level RF, diagnostics, beam commissioning, transport-matrix measurements and finally the experimental physics itself.
That breadth is what makes Tim’s seven-year Ph.D. experience unusual. By the time he completed his doctorate, he had effectively gone through two major cycles of experimental accelerator development. He had already learned on CCII what it meant to shepherd a large technical system from components to operation; EEX then required him to apply that accumulated experience to a machine whose beamline and central RF device he had to help design essentially from the ground up.
His dissertation was therefore the endpoint not merely of one successful measurement, but of seven years spent learning how accelerators actually get built and made to work.
The progression is particularly striking: from the early 3.9-GHz CKM cavity, to the large-scale superconducting Capture Cavity II project, and finally to the complete EEX beamline and its liquid-nitrogen-cooled five-cell TM110 cavity. Each project added another layer of experimental responsibility. By EEX, Tim was no longer simply learning individual accelerator technologies; he was integrating beam physics, RF engineering, magnet optics, diagnostics, mechanical fabrication and commissioning into a complete experimental machine.
That machine ultimately produced the first experimental demonstration of transverse-to-longitudinal emittance exchange, and Tim’s dissertation work was recognized with Rutgers University’s Richard J. Plano Dissertation Prize.
In that sense, the best way to describe Tim’s Ph.D. may be that it was less a conventional dissertation project than a seven-year apprenticeship in the full practice of experimental accelerator physics. He worked on two major accelerator projects, encountered the very real possibility that years of successful technical work might not become his thesis, started again, and ultimately finished by doing what experimental physicists aspire to do: design the apparatus, build it, understand it, make it work, and use it to demonstrate something that had never before been experimentally observed.
The Human Side of Fermilab
Perhaps the best part of pursuing a Ph.D. at Fermilab was not the machines, the physics, or even the experiments—it was the people. There was a remarkable collective sense of mission: scientists, engineers, technicians, students, and staff working together toward the shared goal of understanding the universe around us. The work could be extraordinarily demanding, but it was undertaken in an environment of collaboration, mutual support, and shared purpose. Long days in the lab, difficult technical problems, successes, failures, and discoveries forged relationships that extended far beyond any single experiment. Some of the most enduring products of those years were not made of niobium, stainless steel, or data, but the lifelong friendships formed along the way.
The End of an Era — September 2011
The shutdown of Fermilab’s Tevatron on September 30, 2011, brought an end not only to one of the great machines of particle physics, but also to the era of accelerator infrastructure that had supported smaller facilities around it. Among them was the A-Zero Photoinjector, where Tim conducted much of his graduate research.
A-Zero relied upon the Tevatron complex for an especially important resource: liquid helium. Its superconducting accelerator systems required cryogenic operation, and the relatively small amount of makeup helium needed by A-Zero was practical when it could be supplied as part of the enormous cryogenic enterprise already maintained for the Tevatron. Once the Tevatron shut down, maintaining that capability for a small experimental facility by itself was no longer economically viable. A-Zero therefore reached the end of its operating life along with the larger complex that had sustained it.
The moment carried particular poignancy for Tim’s Ph.D. advisor, Helen Edwards. Helen had been one of the central figures in creating and commissioning the superconducting Tevatron nearly three decades earlier, and on September 30 she was given the honor of terminating its final beam and powering down its magnets. At essentially the same moment, the A-Zero Photoinjector—another machine to which Helen had devoted an important chapter of her accelerator career—was also coming to an end. In a single day, Helen witnessed the closing of two machines that represented very different scales, but two deeply connected chapters, of her extraordinary life in accelerator physics.
