Physicists at the GSI Helmholtzzentrum für Schwerionenforschung in Germany have worked out how to build a compact drift tube linac without any magnets inside it. In a study published in EPJ Techniques and Instrumentation, Simon Lauber and colleagues present two beam dynamics layouts for an alternating phase focusing injector linac that would accelerate heavy ions from 300 keV per nucleon to 1400 keV per nucleon, feeding the proposed superconducting Helmholtz Linear Accelerator, or HELIAC. The trick is to let the accelerating electric field itself do the focusing, alternating the RF phase at successive gaps so the beam is squeezed transversely and longitudinally in turn.
Conventional drift tube linacs rely on magnetic quadrupole lenses embedded inside the drift tubes to keep the beam from blowing up transversely. Those internal magnets are expensive to install and maintain, they crowd the cavity, and they multiply the number of control parameters an operator must juggle. In an alternating phase focusing, or APF, cavity, no magnetic lenses sit inside the structure at all. Instead, positive synchronous phases provide transverse focusing while negative phases, traditionally used in linac layouts, deliver acceleration and longitudinal focusing. Applied in alternating sequence, the two signs focus the beam in all three room directions.
The principle is old but long underused. It was proposed independently by J. Adlam and M. Good in 1953 and by I. Fainberg in the Soviet Union in 1956, and the theoretical framework was elaborated by I. M. Kapchinsky in the following years. Yet the first operating APF linac was reported only in 2007, by Y. Iwata and co-workers at the Heavy Ion Medical Accelerator facility in Japan. The reason for the delay was computational: designing an APF cavity requires predicting the beam dynamics of a structure whose geometry changes gap by gap, a calculation that overwhelmed early computers. Modern software has removed that barrier.
The physics constraint that makes APF necessary is Gauss’s law. In charge-free space the electric field cannot focus a beam simultaneously in every direction, so sequential longitudinal and transverse electric focusing is mandatory. The designer’s core task is choosing a synchronous phase for each RF gap. Changing the synchronous phase between neighboring gaps changes the resonator geometry: the drift tube lengths shrink or grow according to the cell length formula, which alters the time a bunch takes to travel between gaps and thus shifts its arrival phase. Several iterations are needed to converge the voltage profile demanded by RF design with the phase profile demanded by beam dynamics, since the two are mutually dependent.
That convergence comes at a price. The voltage used in the beam dynamics calculation and the voltage actually achieved in the fabricated cavity must agree to within about two percent, a tight tolerance that must be built into the dynamic frequency tuning concept, because the moving tuning parts interfere directly with the electromagnetic field. To handle the non-linear transport, the team tracked each particle individually rather than using the averaged matrix approach common in linac design, wrapping the multi-particle tracking code DYNAMION with a dedicated optimization function. The objective function targeted minimum emittance growth together with high output energy, and the variables were the input Twiss parameters and the synchronous phase in every gap.
The first layout the team examined was a single cavity. Optimized for a transverse normalized input emittance of 0.8 mm mrad and 1.64 keV ns/u longitudinally, with a field gradient of 3 MV/m and a 10 mm aperture, the 3.4-meter structure showed no particle loss in simulations. The 90-percent effective emittance grew only about 10 percent transversely and 12 percent longitudinally, figures the authors describe as superb. But the total emittance growth, and with it the full beam size, proved unacceptable for continuous wave operation: even a few percent particle loss over decades of running could degrade machine performance at the target 1 mA average beam current. The single-cavity draft, produced in about two weeks of work, remains attractive for lower-current applications because its only control parameters are tank phase and voltage.
The final design therefore splits the acceleration into two separate interdigital H-mode cavities separated by an intertank equipped with an external quadrupole triplet. Cavity-1 lifts the beam to an intermediate energy of 700 keV/u over its first 1.3 meters; the triplet then refocuses the transversely divergent beam; and Cavity-2 carries it to the full 1400 keV/u. Because the triplet has already handled transverse focusing, the synchronous phase pattern in the second cavity leans toward acceleration rather than focusing. No rebuncher sits in the intertank, since Cavity-1 delivers output parameters that match the beam longitudinally into Cavity-2. The result is a channel with only about 5 percent transverse and 3 percent longitudinal 90-percent effective emittance growth, making it the preferred injector for the superconducting HELIAC.
The hybrid layout buys more than beam quality. The intertank region hosts phase probe sensors and beam position monitors, diagnostics that ease commissioning and routine operation and could not be installed in a single-cavity machine. The adjustable triplet also compensates for beam parameters that differ from the reference design, a real concern when the upstream electron cyclotron resonance ion source runs with very different ion species for material science and superheavy element research. The team weighed alternatives: three separately powered cavities were dismissed because two intertank sections would have bloated the length and many quadrupoles would have multiplied control parameters, while a single KONUS-style cavity with embedded lenses is sensitive to control fluctuations and costly to maintain.
The broader motivation is the hunt for superheavy elements. GSI, which discovered elements 107 through 112 using its UNILAC, now faces fusion probabilities so low that experiments stretch to weeks or months. Raising the average beam current shortens those campaigns, and for continuous wave heavy-ion beams superconducting machines are more economical than normal conducting ones. Since the UNILAC is being upgraded to deliver high peak-current beams at low duty cycle to FAIR, a dedicated new injector was needed. The APF approach also carries an economic argument: operation of APF linacs in general has been reported to reduce construction and operation costs by about 30 percent.
A working precedent exists at HIMAC in Japan, where a single-cavity APF linac accelerates carbon ions with a mass-to-charge ratio of 3 from 400 keV/u to 4 MeV/u in a 3.4-meter, 200 MHz structure with a 0.4 percent duty cycle. Its only control parameters are cavity phase and voltage, allowing rapid recommissioning that suits a medical injector. HELIAC’s design pushes harder, with a transported mass-to-charge ratio twice as high at A/z up to 6. The two-cavity APF channel, with its external quadrupole focusing, low parameter count, and integrated diagnostics, is the design the authors put forward as the acceleration unit for the superconducting Helmholtz Linear Accelerator’s injector.
Subject of Research: Alternating phase focusing beam dynamics designs for a heavy-ion drift tube linac injector
Article Title: Alternating phase focusing beam dynamics for drift tube linacs
Article References: Lauber, S., Barth, W., Basten, M., Dziuba, F. D., List, J., Miski-Oglu, M., Podlech, H., & Yaramyshev, S. (2024). Alternating phase focusing beam dynamics for drift tube linacs. EPJ Techniques and Instrumentation, 11(1), Article 5. https://doi.org/10.1140/epjti/s40485-024-00109-9
Image Credits: AI Generated
DOI: 10.1140/epjti/s40485-024-00109-9
Keywords: accelerator physics, drift tube linac, alternating phase focusing, heavy ions, HELIAC, GSI, beam dynamics, interdigital H-mode cavity, emittance growth, continuous wave, quadrupole triplet, superheavy elements
News Source: Denise Maddox. (October 29, 2026). Magnet-Free Accelerator Design Promises Compact, Efficient Heavy-Ion Beams. Scienmag.
