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USPAS Concepts:�RF Overview

Nicole Neveu, Sebastian Aderhold

Summer 2026

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Schedule

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The role of RF cavities in an accelerator

Transferring energy to the beam

Acceleration
Replenish lost beam energy due to synchrotron radiation
Maintain beam structure (collider and storage rings)
Diagnostics (deflecting cavities)

Three major design criteria

Want the cavity to store as much energy as practical
Want the cavity to store this energy as efficiently as possible
Want to transfer as much energy to the beam as possible

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Why RF?

DC electric fields limited by high-voltage breakdown (1MV/m in air, ~ one order of magnitude higher with insulating gases like SF₆)

Accelerating potential can only be used once
Cockcroft-Walton, Van de Graaff

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[CERN]

CERN 800kV Cockroft-Walton column,

used for pre-acceleration of protons

until replaced in 1993

Fermilab

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Why RF?

RF fields can be higher (up to 100s of MV/m, depending on frequency, pulse duration and surface conditions of the resonator)
RF accelerating structures can be traversed by the particles multiple times (circular accelerator) or arranged in series (linear accelerator)

Frequencies typically in the range from few 10 MHz to several GHz (based on application)

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[Rookie book p.4]

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From LC circuit to pillbox cavity

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Frequency is only dependent on radius, not cavity length

L: Inductance

C: Capacitance

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Cavity modes

Electromagnetic resonant modes of a cavity are solutions for Maxwell’s equations with the boundary conditions of the walls
Transverse Electric and Transverse Magnetic modes
Important mode for acceleration with cavities: TM₀₁₀(pill-box mode) has electric field on beam axis
Other modes for different applications (e.g. transverse deflecting cavities)

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Rookie Book, pg. 21

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Cavity modes

Modes are dependent on the geometry
Transverse Electric and Transverse Magnetic modes
Important mode for acceleration with cavities: TM₀₁₀(pill-box mode) has electric field on beam axis
Other modes for different applications (e.g. transverse deflecting cavities)

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https://indico.lightsource.ca/event/6/contributions/100/attachments/83/308/IAS-SRFI-Laxdal.pdf

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Higher Order Modes (HOM): beam induced

Higher Order Modes (HOMs) can come from the beam.
HOMs generated by the beam must be dampened to avoid instabilities.
Fundamental mode is used for acceleration, but HOMs exist and are excited.

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�

R. Wanzenberg DESY

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HOM Coupler

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HOM Coupler

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Drawings courtesy J. Maniscalco.

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From single cell to multi cell

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Electron acceleration in a 9-cell TESLA shape cavity

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Input RF power at 1.3 GHz

[Animation courtesy of S. Posen]

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Cavity figures of merit: Quality Factor Q

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With:

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Cavity figures of merit: Energy gain

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With:

Charge

Maximum Accelerating Voltage

Transit Time Factor

Longitudinal Focusing Term

Energy gain of a particle

What if the particle speed isn’t right?

What if the particle arrives at the wrong time?

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Cavity figures of merit: Energy gain

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*Let’s revisit this longitudinal figure…

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Cavity materials: Copper vs. Niobium

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Copper RF Cavity

Q₀ ~ 10⁴

Niobium SRF Cavity

Q₀ > 10¹⁰

At 20 MV, dissipated power in cavity walls is order of MW

(for cw, pulsed operation can be viable option)

At 20 MV, dissipated power in cavity walls is order of W

Cryogenic efficiency increases the wall power to order of kW

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Full Width Half Maximum and Quality Factor

Quality Factor Q

Measure for how well the resonator ’rings’, when excited once

A 440Hz tuning fork with a Q of 10E10 would ring for more than 260 days!

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By Arne Nordmann (norro) - Own illustration, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=3106631

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Off-frequency resonators

All cavities need to be driven at the same (nominal) frequency
An off-frequency cavity will need to be driven harder to achieve the same required accelerating voltage
More RF power is needed if the cavity is off the resonant frequency

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Tuner systems

Mechanical tuners

Adjust cavity length/shape to modify frequency
Typical elements are stepper motors (coarse) and piezo actuators (fine)
Tuning ranges up to several hundred kHz, precision down to few Hz

Temperature stabilization

Ferrite tuners

Coaxial RF transmission line coupled to the cavity, loaded with ferromagnetic material
Inductance can be changed by applying bias current

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Different cavity shapes: Low-beta cavities for FRIB

Different shapes are used for different applications

Acceleration vs deflection
Different particle velocities

Optimized for “low-speed” heavy ions

Quarter-wave resonator
Half-wave resonator

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[doi:10.18429/JACoW-SRF2019-THP061]

80 MHz

322 MHz

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Different cavity shapes: Elliptical cavities

Different shapes are used for different applications

Acceleration vs deflection
Different particle velocities

Optimized for electrons and “high(er)-speed” protons

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Different cavity shapes: Crab cavities for HiLumi-LHC

Different shapes are used for different applications

Acceleration vs deflection
Different particle velocities

Optimized to rotate or “crab” the beam

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[doi:10.18429/JACoW-SRF2017-THXA03]

DQW cavity with helium vessel and all couplers

[https://home.cern/crab-cavities-colliding-protons-head/]

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Different cavity shapes: Deflecting Cavities (XTCAV)

X-band Transverse Deflecting Mode Cavity (XTCAV)

Acceleration vs deflection
Different particle velocities
Operates at 11.424 GHz

Optimized to translate E/t into x/y dimension.

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Y. Ding, SLAC

https://www.nature.com/articles/ncomms4762

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RF systems: Low level RF

Creates the RF signal to be amplified by high power RF amplifiers

Can include feed forward and feedback systems for:

frequency
amplitude
phase

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[L. Doolittle]

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RF systems: High Power RF

Includes:

Amplification of LLRF signal

Klystrons
Tubes
Solid State Amplifiers

Transport

Waveguides (Rectangular or coaxial)

Coupling into accelerating structure

Fundamental Power Couplers

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Putting it together (LCLS-II as an example)

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[A. Benwell]

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Putting it together

Power consumption can be in the tens of MW per facility
Cost of RF cavities / cryomodules

~ 20% of total cost on billion-dollar scale projects like LCLS-II and PIP-II

Number of cavities per accelerator

Can range from single/few cavities in storage rings (e.g. 2 cavities in NSLS-II storage ring) to hundreds in linear accelerators (e.g. 800 cavities in EuXFEL accelerator)

Scales

3.9GHz LCLS-II cavity vs. CERN LEP 352 MHz copper cavity

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Questions?

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Standing wave vs. traveling wave

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Example of SRF cavity: everything it takes

Helium
Cooling
Cryostat
Cryoplant

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