The Advanced Photon Source makes X-rays from electrons. It boils the electrons off a hot piece of metal, drives them to within about a meter per second of the speed of light, and keeps them circling in a ring 1.1 km around. Wherever their path bends they give off X-rays, and the beamlines around the ring put those to use. This guide follows the electrons from the gun to the ring and shows how the ring holds on to them. It describes the machine as it runs today.
Each section has a plain explanation and a figure you can adjust. The equations are folded away under the figures. Open any of them, or all of them with the button at the top, if you want the detail.
The Fill pattern menu at the top chooses how many bunches of electrons the ring holds. The figures and worked numbers in the sections on bunches and swap-out follow it. The values used throughout, with their sources, are in the table at the end.
Electrons are easy to come by. In any metal some of them are free to wander about, held in only by a barrier at the surface. Heat the metal and they jostle faster, until some have enough energy to get over the barrier and boil off. The hotter the metal, the more escape, and the number climbs very steeply with temperature. The piece of hot metal is called the cathode.
The APS gun has its cathode in the wall of a small copper cavity with a strong radio-frequency field inside. The field pulls the escaped electrons away and sends them on as a string of tightly spaced bunches. The gun fires thirty such bursts a second.
The linear accelerator, or linac, comes next. It is a long row of copper cavities with a radio wave traveling down the middle. Electrons that set off at the right moment ride near the crest of that wave like a surfer, and its electric field pushes them the whole way. They leave with an energy of 425 MeV.
At that energy an electron is already moving at 99.99993% of the speed of light. From here on, more energy hardly changes its speed. What it does is make the electron's path harder to bend, and that turns out to be the thing that matters.
What it saysOnly electrons with energy above W can leave, and the share of them that have it rises very steeply with temperature. A lower W helps just as steeply, which is why cathodes are made of tungsten treated with barium compounds and not of plain metal.
In numbersWith W = 2 eV, a typical value for such a cathode: about 2 amperes per square centimeter at 1,000 °C, and about four times as much for every 100 °C more. These are illustrative numbers, not those of the APS gun.
What it saysThe electron keeps pace with the wave, so it feels the same field all the way along. On the crest it gains the most. Off the crest it gains less, and a quarter of a wave away it gains nothing at all.
In numbersThe APS linac delivers 425 MeV. With the bunch 30° off the crest it would deliver 425 × cos 30° = 368 MeV.
What it saysOnce γ is large, the speed is so close to the speed of light that more energy barely changes it. What keeps growing is the electron's momentum, and momentum is what a magnet has to work against.
In numbersAt 425 MeV, γ = 832 and the electron is slower than light by about 216 m/s. At 6 GeV, γ = 11,742 and the gap is 1.1 m/s.
One burst from the linac holds about a nanocoulomb of charge, roughly six billion electrons. The storage ring can need a bunch with a dozen times that. So the bursts are first collected in a small ring called the particle accumulator ring. Each new burst is dropped in beside the electrons already circulating there, and they settle into a single bunch.
Electrons circling in a ring give off light, and the light carries away the sideways jitter they arrived with. So the bunch shrinks while it waits. In the last quarter of a second a second radio-frequency system squeezes it shorter still. Then the whole bunch is passed to the booster.
The booster is a ring about a third the size of the storage ring. It takes the bunch from 425 MeV to 6 GeV in a fraction of a second. As the electrons gain energy their path gets harder to bend, so the booster's magnets are strengthened in step to keep them on the same path. A ring that works this way is called a synchrotron.
For 324 bunches the ring needs about 2.5 nC in each fresh bunch, so the accumulator collects three bursts or so before passing the bunch on. Once a second, a finished bunch is ready at 6 GeV.
What it saysThe charge of a bunch is a head count. One burst from the linac is about 1 nC. The accumulator ring can collect up to twenty of them into a single bunch.
In numbersA fresh bunch for timing mode holds about 12 nC, which is 7.5×1010 electrons.
What it saysA magnet bends a fast electron into a curve whose radius grows with the electron's momentum. To hold the same curve as the energy climbs, the field has to climb in proportion. In the booster the field rises fourteen-fold while the bunch goes from 425 MeV to 6 GeV.
In numbersAt 6 GeV, Bρ = 20.0 T·m. A 0.5 T magnet bends the beam on a radius of 40 m.
The storage ring is where the electrons stay. It is 1,104 m around, and an electron circles it about 272,000 times a second. Nothing in the ring speeds the electrons up. Its job is to hold them on the same closed path for hours.
Three kinds of magnet do the holding. Bending magnets turn the beam, a little at each one, until the path closes on itself. Focusing magnets, called quadrupoles, act on electrons that stray from the ideal path and turn them back toward it. A third kind, called sextupoles, makes sure that electrons with a little more or a little less energy than the rest are focused just as well.
A quadrupole has a quirk. If it focuses the beam from side to side, it spreads it up and down, and the other way around. The cure is to alternate them. A focusing magnet followed by a defocusing one, at the right spacing, focuses in both directions overall, much as a pair of glass lenses can. The ring is a long chain of such pairs.
The ring is made of 40 sectors, each with the same set of magnets, joined by straight stretches. Thirty-five of the straights hold the undulators that make X-rays for the beamlines. The two NE-CAT undulators share the straight in sector 24.
What it saysThe field in a quadrupole is zero on the ideal path and grows with distance from it. An electron on the path is left alone. One that has strayed is turned back by an amount in proportion to how far it strayed, which is what a lens does to a ray of light. Up and down, the same magnet does the opposite and pushes strays further out.
In numbersFor illustration: a gradient of 80 T/m over 0.25 m at 6 GeV gives f = 20.0 / (80 × 0.25) = 1.0 m.
What it saysA row of lenses that alternately focus and defocus holds the beam only between two limits. Too weak, and the beam is barely held and grows wide. Too strong, and each lens over-corrects, the swings build up from one lens to the next, and the beam is lost. The figure shows both.
The electrons travel inside a metal pipe with almost all the air pumped out of it. They have to. In ordinary air an electron at this energy would hit a gas molecule and be knocked out of the beam within about a hundred meters, less than a tenth of one turn.
A stored electron covers about a billion kilometers every hour. To last, it must meet almost nothing on the way. The pressure in the pipe is kept near two billionths of a torr, hundreds of billions of times thinner than the air around us. That is a better vacuum than the one outside the Space Station.
Getting there is harder in this ring than in most. The pipe is narrow, about 22 mm across on the inside, because the magnets have to sit close to the beam to be strong enough. A long, narrow pipe is hard to pump out from its ends. So about half the pipe in each sector is lined with a thin metal film that traps gas molecules when they touch it, which turns the wall itself into a pump. Ion pumps along the ring do the rest.
The X-rays make it harder still. Wherever they strike the wall they heat it and knock gas loose from the metal. Water-cooled copper absorbers take most of the heat. The gas cures itself with time: as the beam runs, the X-rays scrub the walls clean and the vacuum keeps improving. The design called for two billionths of a torr at full current once the ring had stored 1,000 ampere-hours of beam.
At that pressure, gas removes electrons far more slowly than their collisions with each other do, as step 8 describes. The vacuum has done its job when it is no longer what limits the beam.
What it saysAn electron sweeps past molecules at the speed of light, and each one is a small chance of being lost. Halve the pressure and the beam lasts twice as long, as far as gas is concerned.
In numbersFor nitrogen-like gas σ is about 5×10−24 cm². At a billionth of a torr there are 32 million molecules in each cubic centimeter and the lifetime comes to about 57 hours. This is a rough estimate made for this guide. Hydrogen, which is most of what remains in a clean system, is much gentler.
For a beamline, what matters most about the electron beam is how small it is and how nearly parallel its electrons travel. One number, the emittance, measures both together. A small emittance means a small, bright source of X-rays.
What sets it is a tug of war. Each time an electron gives off an X-ray inside a bending magnet, it loses a little energy all at once. An electron with less energy is bent more sharply, so it finds itself on the wrong path for its new energy and starts to swing from side to side about the right one. Countless such jolts keep the beam stirred up. Against them, the steady loss and return of energy calms the swinging down. The beam settles at the width where the two balance.
The jolt is small if each bending magnet turns the beam only slightly, because then the paths for different energies have little room to move apart. So the way to a small beam is to turn each corner with more, gentler bends. The emittance falls as the cube of the number of bends.
Each sector of the APS ring turns its corner with seven bending magnets, where most earlier rings use two or three. The layout is called a multi-bend achromat. Multi-bend is the seven bends. Achromat is a word borrowed from lenses that bring every color to the same focus. Here it means that electrons of different energies, which travel on slightly different paths inside the sector, are back on the same path by the time they reach the straight at its end. The undulators sit in those straights, so the spread of energies in the beam does not make the X-ray source any wider.
The APS version is a hybrid. In two places in each sector the paths for different energies are deliberately let apart, by about a millimeter for an electron that is one percent off in energy. The sextupoles, which correct the focusing for electrons of the wrong energy, can only tell those electrons from the rest where their paths differ. Placing them at these two bumps lets them do their work with much weaker fields.
Two more refinements trim the emittance further. Four of the seven bends have a field that changes along their length, so that the hardest bending is done where the paths for different energies lie closest together. And six small magnets bend the beam slightly the wrong way. That sounds like a mistake and is not: they hold those paths closer together inside the main bends, and they strengthen the calming effect of the energy loss on the side-to-side motion. The result is an emittance of 42 picometers, and a beam at the undulators about 15 µm wide and 3 µm high.
The price is paid in room to move. With so much focusing between so many bends, electrons survive only within a couple of millimeters of the ideal path. That one fact decides how the ring has to be filled, as step 8 shows.
What it saysBending magnets create dispersion, because they bend a low-energy electron more than a high-energy one. Focusing magnets steer it. An achromat is a run of magnets that begins and ends with almost none.
In numbersThe APS model gives η = 90 mm at the bumps and 0.39 mm at the undulators. The electrons in the beam differ in energy by about 0.135%. That is 0.12 mm at the bumps and half a micron at the undulators, where the beam is 15 µm wide.
What it saysHalving the angle of each bend cuts the emittance eight times. Lowering the energy helps too. The figure uses this rule, pinned to the APS value at seven bends and 6 GeV. Real rings do better or worse than the simple rule. The APS does better, with its reverse bends and with bending magnets whose field changes along their length.
In numbersSeven bends at 6 GeV: 42 pm. The same rule with two bends in each sector at 7 GeV gives about 2,400 pm.
What it saysSize multiplied by angular spread is the emittance, and it is the same all around the ring. The focusing magnets only decide how it is shared between the two at each place.
In numbersAt an APS undulator, from the machine model: 40 pm with β = 5.3 m gives 14.5 µm and 2.7 µrad across. Up and down, 4 pm with β = 2.4 m gives 3.1 µm and 1.3 µrad.
The electrons give off X-rays all the way around, in every bending magnet and every undulator. On each turn an electron loses about 2.9 MeV in the bending magnets alone, one part in two thousand of its energy. Left alone it would be lost within a thousandth of a second.
The energy is paid back by radio-frequency cavities. These are metal chambers in which an electric field swings back and forth 352 million times a second, and an electron passing through at the right moment gets a push. The cavities can give 4.5 million volts per turn, which is more than is needed. The surplus is put to use.
The field is timed so that an electron on schedule arrives while the voltage is falling and gets back exactly what it lost. An electron with too much energy takes a slightly longer way around, arrives late, meets a lower voltage and gets less. One with too little arrives early and gets more. So each electron is steered back toward the right energy and the right timing, and rocks gently around both.
This is why the beam comes in bunches. Only electrons that arrive near the right moment are held. There are 1,296 such moments, called buckets, in each turn of the ring: one for every swing of the field.
What it saysThe loss climbs as the fourth power of the energy. That is why storage rings do not simply run at ever higher energy. Undulators add to the loss when their gaps are closed.
In numbersThe APS bending magnets take 2.94 MeV per turn at 6 GeV, as if the ring were bent on one radius of 39 m. At 200 mA that is 2.94 MV × 0.2 A = 590 kW of X-rays, before any undulator is counted.
What it saysThe on-time electron gets back exactly what it lost. There are two moments in each swing with the right voltage, one while it rises and one while it falls. Only the falling one is stable, because there a late electron gets less and an early one gets more.
In numbersV = 4.5 MV and U₀ = 2.94 MeV give sin φs = 0.65. The on-time electron arrives about 0.39 billionths of a second after the peak.
What it saysThe RF must swing a whole number of times per turn, so that a bunch meets the same voltage every time it comes around.
In numbersC = 1,103.6 m gives 3.681 µs per turn, or 271,647 turns a second. With h = 1,296 the RF frequency is 352 MHz and the buckets are 2.84 billionths of a second apart.
Not every bucket is filled. The choice of which ones to fill is called the fill pattern, and it is a compromise between two kinds of experiment. Most want the smallest, steadiest beam and do not care about timing. Some use the flashes of X-rays as a stopwatch, and want them strong and well separated.
With many bunches the charge is spread thin. Each bunch is small, its electrons disturb each other little, and the beam is at its smallest. With few bunches each one holds a great deal of charge, and the flashes are far apart.
At present the APS runs with two patterns. The normal one has 216 bunches, evenly spaced, and a current of 200 mA. Timing mode has 48 bunches, 77 billionths of a second apart, and a current of 150 mA. The ring was designed for patterns of up to 324 bunches. The menu at the top of this page switches between them.
With 216 bunches sharing 200 mA, each bunch holds 3.41 nC.
Each bunch is short: a few centimeters long, gone past in about a tenth of a billionth of a second. The ring has one extra cavity whose only job is to stretch the bunches to two to four times their natural length. In a longer bunch the electrons are further apart and collide with each other less often, and the beam lasts longer.
For a diffraction experiment at NE-CAT the pattern makes no difference. The detector adds up an enormous number of flashes in every image.
What it saysCurrent is charge passing a point each second. Every bunch passes once per turn, so the current is the total charge divided by the time for one turn.
In numbersFor 216 bunches at 200 mA: 3.41 nC.
The stored beam does not last. Electrons packed into a tiny bunch bump into one another, and now and then a collision throws two of them so far off in energy that both are lost. A few more are lost to stray gas atoms in the vacuum pipe. The smaller and denser the bunches, the faster it goes. Left alone, the current in the ring would fall by half in a few hours.
Many rings top themselves up by adding a few fresh electrons to each bunch now and then. The newcomers arrive a few millimeters to one side of the stored beam and take thousands of turns to settle in. The APS ring cannot do this. Its electrons survive only within a couple of millimeters of the ideal path, so there is no room at the side for newcomers.
So the APS swaps whole bunches. A fresh, full bunch from the booster is steered straight onto the ideal path, into the place of a worn one, and on the same turn the old bunch is kicked out into a block of metal that absorbs it. This is called swap-out injection, and the ring was designed around it.
The hard part is the kick. Bunches follow each other billionths of a second apart, and the kicker has to switch on, deflect one bunch and switch off again before the next one arrives. The APS kickers were designed to do it in about 15 billionths of a second. Shortly before a bunch is swapped out, another small kick makes it swell, so that its electrons are spread out when they hit the absorber and do not damage it.
With 324 bunches, a bunch is swapped about every 8 seconds.
For the beamlines the result is a current that never sags. It holds steady to within about a percent, hour after hour.
What it saysMost of the loss comes from electrons colliding with each other inside a bunch. It goes faster when the bunch holds more charge and when it is smaller, so the bright, dense bunches of this ring have short lives. Stretching the bunches makes them last longer.
In numbersProjected lifetimes at 200 mA: about 7.5 hours with 324 bunches and 3.5 hours with 48. These are design figures, not measurements.
What it saysBunches are replaced in turn, so each one waits while all the others are done. The more bunches there are, the more often a swap is needed, and the smaller the step each swap makes in the total current.
In numbersFor 324 bunches: about 8 s between swaps.
These are the values this guide uses, and where they come from. The guide How NE-CAT works picks up where this one stops, with what an undulator does to the beam and what a beamline does with the X-rays.
| Quantity | Value used in this guide |
|---|---|
| Electron energy in the storage ring | 6 GeV |
| Stored current | 200 mA, first reached in February 2025 |
| Length of the ring | 1,103.6 m, in 40 sectors, with 35 straights for undulators |
| Time for one turn | 3.681 µs, which is 271,647 turns a second |
| Bending magnets in each sector | 7, plus 6 reverse bends |
| Emittance | 42 pm by design. Measured: 44 ± 3 pm across and 3.3 ± 2 pm up and down |
| Beam size at an undulator (1σ) | 14.5 × 3.1 µm § |
| Spread of paths with energy (dispersion) | 90 mm at its largest, 0.39 mm at the undulators § |
| Vacuum | about 2 billionths of a torr at full current §. Pipe about 22 mm across inside |
| Energy lost per turn in the bending magnets | 2.94 MeV |
| RF system | 352 MHz, 1,296 buckets, 4.5 MV |
| Bunch-lengthening cavity | 1,408 MHz, superconducting. Stretches the bunches two to four times |
| Fill patterns in use, late 2026 | Normal mode: 216 bunches, evenly spaced, 200 mA. Timing mode: 48 bunches, 77 ns apart, 150 mA ¶ |
| Charge per bunch | 3.4 nC in normal mode, 11.5 nC in timing mode ‡ |
| Lifetime | Design figures at 200 mA: about 7.5 h for 324 bunches and 3.5 h for 48 §. The values this guide starts with for the two patterns in use are guesses † |
| Linac | 425 MeV, 30 bursts a second of about 1 nC |
| Accumulator ring | 425 MeV. Collects up to 20 bursts into one bunch of up to 20 nC, once a second. About 31 m around † |
| Booster | 425 MeV to 6 GeV, once a second. About 368 m around †, with a ramp of about a quarter of a second † |
| Swap-out kicker pulse | under 4.5 ns to rise, 5.9 ns flat, under 4.5 ns to fall § |
Sources. The APS storage ring parameters page (model values, August 2024). Conference papers on the upgraded ring and its injector: NAPAC 2025 MOXP02 (commissioning and measured emittance), IPAC 2021 MOXA02 (design overview), IPAC 2019 THYYPLM3 and a 2024 I.FAST workshop talk (linac, accumulator ring and booster), IPAC 2015 TUPJE067 (swap-out kicker), MEDSI 2018 TUPH04 and NAPAC 2019 TUYBB3 (vacuum system). APS News, February 2025 (200 mA).
¶ From NE-CAT, as the ring was running in late 2026.
† Not taken from those sources. The length of the accumulator ring is worked out from its 9.8 MHz RF system. The length of the booster and the duration of its ramp are approximate values that were not checked against a published source. The lifetime of the beam in gas is a rough estimate made for this guide. The beam lifetimes for the two patterns in use, the numbers for the cathode, and the pressures of the familiar places on the vacuum scale are round or typical values. Please correct any of these that are wrong.
‡ Calculated in this guide from the other rows.
§ Design or model values, not measurements of the ring as it runs. The fill patterns in use change from run to run, so check the APS operating schedule for the current one.
Last updated November 11, 2026. Release 1.2. What changed.
The NE-CAT beamlines are funded by the National Institute of General Medical Sciences from the National Institutes of Health (P30 GM124165).
© 2026 NE-CAT, Cornell University. Released under the MIT License.