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The Higgs boson is the most intriguing and unusual object yet discovered by fundamental science. There is no higher experimental priority for particle physics than building an electron–positron collider to produce it copiously and study it precisely.

Given the importance of energy efficiency and cost effectiveness in the current geopolitical context, this gives unique strategic importance to developing a humble technology called the klystron—a technology that will consume the majority of site power at every major electron–positron collider under consideration, but which has historically only achieved 60% energy efficiency.

The klystron was invented in 1937 by two American brothers, Russell and Sigurd Varian. The Varians wanted to improve aircraft radar systems. At the time, there was a growing need for better high-frequency amplification to detect objects at a distance using radar, a critical technology in the lead-up to World War II.

The Varian's RF source operated around 3.2 GHz, or a wavelength of about 9.4 cm, in the microwave region of the electromagnetic spectrum. At the time, this was an extraordinarily high frequency—conventional vacuum tubes struggled beyond 300 MHz. Microwave wavelengths promised better resolution, less noise, and the ability to penetrate rain and fog. Crucially, antennas could be small enough to fit on ships and planes. But the source was far too weak for radar.

The Varians' genius was to invent a way to amplify the electromagnetic signal by up to 30 dB, or a factor of 1,000. The U.S. and British military used the klystron for airborne radar, submarine detection of U-boats in the Atlantic and naval gun targeting beyond visual range. Radar helped win the Battle of Britain, the Battle of the Atlantic and Pacific naval battles, making surprise attacks harder by giving advance warning. Winston Churchill called radar "the secret weapon of WWII," and the klystron was one of its enabling technologies.

With its high gain and narrow bandwidth, the klystron was the first practical microwave amplifier and became foundational in radio-frequency (RF) technology. This was the first time anyone had efficiently amplified microwaves with stability and directionality. Klystrons have since been used in satellite communication, broadcasting and particle accelerators, where they power the resonant RF cavities that accelerate the beams. Klystrons are therefore ubiquitous in medical, industrial and research accelerators—and not least in the next generation of Higgs factories, which are central to the future of high-energy physics.

Klystrons and the Higgs

Hadron colliders like the LHC tend to be circular. Their fundamental energy limit is given by the maximum strength of the bending magnets and the circumference of the tunnel. A handful of RF cavities repeatedly accelerate beams of protons or ions after hundreds or thousands of bending magnets force the beams to loop back through them.

Thanks to their clean and precisely controllable collisions, all Higgs factories under consideration are electron–positron colliders. Electron–positron colliders can be either circular or linear in construction. The dynamics of circular electron–positron colliders are radically different as the particles are 2,000 times lighter than protons.

The strength required from the bending magnets is relatively low for any practical circumference, however, the energy of the particles must be continually replenished, as they radiate away energy in the bends through synchrotron radiation, requiring hundreds of RF cavities. RF cavities are equally important in the linear case. Here, all the energy must be imparted in a single pass, with each cavity accelerating the beam only once, requiring either hundreds or even thousands of RF cavities.

Either way, 50 to 60% of the total energy consumed by an electron-positron collider is used for RF acceleration, compared to a relatively small fraction in a hadron collider. Efficiently powering the RF cavities is of paramount importance to the energy efficiency and cost effectiveness of the facility as a whole. RF acceleration is therefore of far greater significance at electron–positron colliders than at hadron colliders.

From a pen to a mid-size car

RF cavities cannot simply be plugged into the wall. These finely tuned resonant structures must be excited by RF power—an alternating microwave electromagnetic field that is supplied through waveguides at the appropriate frequency. Due to the geometry of resonant cavities, this excites an on-axis oscillating electrical field. Particles that arrive when the electrical field has the right direction are accelerated. For this reason, particles in an accelerator travel in bunches separated by a long distance, during which the RF field is not optimized for acceleration.

Despite the development of modern solid-state amplifiers, the Varians' klystron is still the most practical technology to generate RF when the power required is in the MW level. They can be as small as a pen or as large and heavy as a mid-size car, depending on the frequency and power required. Linear colliders use higher frequency because they also come with higher gradients and make the linac shorter, whereas a circular collider does not need high gradients as the energy to be given each turn is smaller.

Klystrons fall under the general classification of vacuum tubes—fully enclosed miniature electron accelerators with their own source, accelerating path and "interaction region" where the RF field is produced. Their name is derived from the Greek verb describing the action of waves crashing against the seashore. In a klystron, RF power is generated when electrons crash against a decelerating electric field.

Every klystron contains at least two cavities: an input and an output. The input cavity is powered by a weak RF source that must be amplified. The output cavity generates the strongly amplified RF signal generated by the klystron. All this comes encapsulated in an ultra-high vacuum volume inside the field of a solenoid for focusing.

Inside the klystron, electrons leave a heated cathode and are accelerated by a high voltage applied between the cathode and the anode. As they are being pushed forward, a small input RF signal is applied to the input cavity, either accelerating or decelerating the electrons according to their time of arrival. After a long drift, late-emitted accelerated electrons catch up with early-emitted decelerated electrons, intersecting with those that did not see any net accelerating force. This is called velocity bunching.

A second, passive accelerating cavity is placed at the location where maximum bunching occurs. Though of a comparable design, this cavity behaves in an inverse fashion to those used in particle accelerators. Rather than converting the energy of an electromagnetic field into the kinetic energy of particles, the kinetic energy of particles is converted into RF electromagnetic waves. This process can be enhanced by the presence of other passive cavities in between the already mentioned two, as well as by several iterations of bunching and de-bunching before reaching the output cavity. Once decelerated, the spent beam finishes its life in a dump or a water-cooled collector.

Optimizing efficiency

Klystrons are ultimately RF amplifiers with a very high gain of the order of 30 to 60 dB and a very narrow bandwidth. They can be built at any frequency from a few hundred MHz to tens of GHz, but each operates within a very small range of frequencies called the bandwidth. After broadcasting became reliant on wider bandwidth vacuum tubes, their application in particle accelerators turned into a small market for high-power klystrons.

Most klystrons for science are manufactured by a handful of companies which offer a limited number of models that have been in operation for decades. Their frequency, power and duty cycle may not correspond to the specifications of a new accelerator being considered—and in most cases, little or no thought has been given to energy efficiency or carbon footprint.

When searching for suitable solutions for the next particle-physics collider, however, optimizing the energy efficiency of klystrons and other devices that will determine the final energy bill and CO₂ emissions is a task of the utmost importance. Therefore, nearly a decade ago, RF experts at CERN and the University of Lancaster began the High-Efficiency Klystron (HEK) project to maximize beam-to-RF efficiency: the fraction of the power contained in the klystron's electron beam that is converted into RF power by the output cavity.

The complexity of klystrons resides on the very nonlinear fields to which the electrons are subjected. In the cathode and the first stages of electrostatic acceleration, the collective effect of "space-charge" forces between the electrons determines the strongly nonlinear dynamics of the beam. The same is true when the bunching tightens along the tube, with mutual repulsion between the electrons preventing optimal bunching at the output cavity.

For this reason, designing klystrons is not susceptible to simple analytical calculations. Since 2017, CERN has developed a code called KlyC that simulates the beam along the klystron channel and optimizes parameters such as frequency and distance between cavities 100 to 1,000 times faster than commercial 3D codes. KlyC is available in the public domain and is being used by an ever-growing list of labs and industrial partners.

Perveance

The main characteristic of a klystron is an obscure magnitude inherited from electron-gun design called perveance. For small perveances, space-charge forces are small, due to either high energy or low intensity, making bunching easy. For large perveances, space-charge forces oppose bunching, lowering beam-to-RF efficiency. High-power klystrons require large currents and therefore high perveances. One way to produce highly efficient, high-power klystrons is therefore for multiple cathodes to generate multiple low-perveance electron beams in a "multi-beam" (MB) klystron.

Overall, there is an almost linear dependence between perveance and efficiency. Thanks to the efforts made in recent years, high-efficiency klystrons are now outperforming industrial klystrons by 10% in efficiency for all values of perveance, and approaching the ultimate theoretical limit.

One of the first designs to be brought to life was based on the E37113, a pulsed klystron with 6 MW peak power working in the X-band at 12 GHz, commercialized by CANON ETD. This klystron is currently used in the test facility at CERN for validating CLIC RF prototypes, which could greatly benefit from a larger power. As part of a collaboration with CERN, CANON ETD built a new tube, according to the design optimized at CERN, to reach a beam-to-RF efficiency of 57% instead of the original 42% (see "CLIC klystron" image and CERN Courier September/October 2022 p9).

As its interfaces with the high-voltage (HV) source and solenoid were kept identical, one can now benefit from 8 MW of RF power for the same energy consumption as before. As changes in the manufacturing of the tube channel are just a small fraction of the manufacture of the instrument, its price should not increase considerably, even if more accurate production methods are required.

In pursuit of power

Another successful example of re-designing a tube for high efficiency is the TH2167—the klystron behind the LHC, which is manufactured by Thales. Originally exhibiting a beam-to-RF efficiency of 60%, it was re-designed by the CERN team to gain 10% and reach 70% efficiency, while again using the same HV source and solenoid.

The tube prototype has been built and is currently at CERN, where it has demonstrated the capacity to generate 350 kW of RF power with the same input energy as previously required to produce 300 kW. This power will be decisive when dealing with the higher intensity beam expected after the LHC luminosity upgrade. And all this again for a price comparable to previous models.

The quest for the highest efficiency is not over yet. The CERN team is currently working on a design that could power the proposed Future Circular collider (FCC). Using about a hundred accelerating cavities, the electron and positron beams will need to be replenished with 100 MW of RF power, and energy efficiency is imperative.

Although the same tube in use for the LHC, now boosted to 70% efficiency, could be used to power the FCC, CERN is working towards a vacuum tube that could reach an efficiency more than 80%. A two-stage multi-beam klystron was initially designed that was capable of reaching 86% efficiency and generating 1 MW of continuous-wave power.

Motivated by recent changes in FCC parameters, we have rediscovered an old device called a tristron, which is not a conventional klystron but a "gridded tube" where the electron beam bunching mechanism is different. Tristons have a lower power gain but much greater flexibility. Simulations have confirmed that they can reach efficiencies as high as 90%.

This could be a disruptive technology with applications well beyond accelerators. Manufacturing a prototype is an excellent opportunity for knowledge transfer from fundamental research to industrial applications.