PIP-II Dual Power Amplifier Cavities

• The paper details that PIP-II dual power amplifier cavities are enhanced Main Injector resonators, each using two 150kW tetrode chains to achieve ~240 kW per cavity for voltage upgrade.
• CST Microwave Studio simulations validate resonant frequency, Q-factor, and R/Q metrics while pinpointing high-field regions near beam-pipe corona rings that limit performance.
• The study distinguishes these dual-amplifier cavities from the one-amplifier-per-cavity design in the PIP-II linac, guiding future geometric modifications to mitigate breakdown risks.

“PIP-II dual power amplifier cavities” ordinarily denotes the Fermilab Main Injector accelerating cavities in their PIP-II-era configuration, in which each cavity is equipped with two power amplifiers to raise the available accelerating voltage for PIP-II operation. In the literature, this term does not describe the baseline superconducting cavities of the PIP-II linac itself: the linac RF architecture is organized around one amplifier per cavity, whereas the Main Injector study explicitly treats a dual-amplifier cavity configuration (Stevenson, 5 Aug 2025, Edelen et al., 2018).

1. Terminological scope and project setting

The term has a specific scope. In the Main Injector context, the dual power amplifier configuration is part of the RF upgrade path needed to support the PIP-II operating point. The Main Injector is the final synchrotron in the Fermilab chain, accelerating protons to 120 GeV before delivery to experiments, and its RF system is a direct determinant of longitudinal acceleration rate and therefore beam power. For the PIP-II upgrade, the Main Injector RF cavities are being equipped with two power amplifiers each, with the stated purpose of raising the total available accelerating voltage to the level required for PIP-II operation (Stevenson, 5 Aug 2025).

A recurring source of ambiguity is the relation between these Main Injector cavities and the PIP-II superconducting linac. The linac literature does not describe a dual-power-amplifier-per-cavity baseline. The 2018 PIP-II LLRF overview states that the superconducting half-wave resonators are powered individually by 7 kW solid state amplifiers, the 325 MHz superconducting spoke resonators are powered by 7 kW or 20 kW amplifiers depending on type, and the 650 MHz elliptical cavities are powered by 40 kW or 70 kW amplifiers depending on section. The only explicit multi-amplifier case in that overview is the normal-conducting RFQ, which is powered by two 75 kW solid state amplifiers (Edelen et al., 2018). The 2023 linac LLRF paper is consistent with this: it explicitly states, for example, that each SSR1 cavity is driven by a 7 kW solid-state amplifier, and it does not refer to any dual power amplifier cavity scheme in the superconducting linac (Varghese et al., 2023).

This distinction is significant because it separates two different RF problems. In the Main Injector, the dual-amplifier configuration is tied to cavity voltage headroom and breakdown limits. In the superconducting linac, the dominant documented problems are cavity field regulation, resonance control, beam loading compensation, and amplifier calibration, but within a one-amplifier-per-cavity architecture (Stevenson, 5 Aug 2025, Varghese et al., 2023).

2. Main Injector cavity architecture and dual-amplifier configuration

The Main Injector cavity is based on the original Main Ring design from the early 1970s and operates at approximately 53 MHz, tuned from 52.808 to 53.104 MHz during the ramp. Electromagnetically, it is a folded quarter-wave coaxial structure in which the body behaves as two back-to-back folded quarter-wave coaxial resonators. The principal conductors are the inner conductor, the intermediate cylinder, and the outer conductor. The intermediate region inside the intermediate cylinder is vacuum at approximately $5\times10^{-8}$ Torr, while the space outside it is at atmospheric pressure. The outer conductor is octagonal rather than circular, the intermediate cylinder and inner conductor are cylindrical, the intermediate cylinder has ceramic sections at both ends, and the inner conductor incorporates two accelerating gaps in the center of the structure (Stevenson, 5 Aug 2025).

In the PIP-II configuration, each cavity is driven by two independent tetrode-based power amplifier chains operating in push-pull. There are two tetrode power amplifiers per cavity, each designed for up to 150 kW output, physically mounted on the top of the cavity, with RF coupling provided by loops into the cavity volume. The loop coupling is such that the ratio of anode gap voltage in the amplifier to the accelerating gap voltage of the cavity is $1:12.1$. The study states that at nominal operation this corresponds to about 210 kV across the accelerating gaps (Stevenson, 5 Aug 2025).

Ferrite tuners provide frequency control. They are located on the lower $45^\circ$ faces of the octagonal outer conductor, two per cavity. Each tuner is a coaxial line filled with alternating copper and ferrite disks and has 10 turns of bus bar winding to provide a DC magnetic bias. Changing the bias current changes the ferrite permeability and thereby shifts the resonant frequency across the 52.8–53.1 MHz ramp (Stevenson, 5 Aug 2025).

At the system level, the PIP-II design point for the Main Injector requires a total accelerating voltage of $2.66\ \text{MV}$, with a total available RF voltage of 4.7 MV and a total operating voltage of 4.2 MV across all cavities. The PIP-II configuration uses two amplifiers per cavity, each nominally 150 kW, giving per-cavity apparent power of about 240 kW in the PIP-II operating scenario. The same study also frames the dual-amplifier configuration against a proposed future upgrade requiring $V_{\text{req,future}} = 5.54\ \text{MV}$, a total operating voltage of about 7.8 MV, and 8.9 MV total available, with the stated preference of delivering that higher voltage using the existing number of RF cavities because of cost, tunnel space, and civil construction constraints (Stevenson, 5 Aug 2025).

3. Electromagnetic parameters and CST model validation

The 2025 study develops a CST Microwave Studio model of the Main Injector cavity in its dual power amplifier configuration. The model was built from original Main Ring cavity drawings, with each component modeled and imported by drawing number, and the final geometry is described as a composite intended to reflect the common operating characteristics of the installed cavities. It includes the full body geometry, both power amplifier ports in representative form, both ferrite tuners with realistic ferrite material properties, the beam pipe, and the two accelerating gaps; higher-order mode dampers and some diagnosis hardware were not included (Stevenson, 5 Aug 2025).

Two solvers are used. The eigenmode solver is used to extract resonant frequencies, unloaded $Q$, $R/Q$, gap voltage, and the three-dimensional $\mathbf{E}$ and $\mathbf{H}$ field distributions for the fundamental accelerating mode. The frequency-domain solver is used mainly for S-parameter analysis, especially $S_{21}$, to validate tuning behavior and cavity frequency response with ferrite tuners. Weakly coupled coaxial probes are inserted on either side of the power amplifier ports, and frequency is swept from 40 MHz to 70 MHz for various ferrite bias currents (Stevenson, 5 Aug 2025).

The study reports the following benchmark values:

Parameter	Measured	Simulated
Resonant frequency with tuning	52.808–53.104 MHz	52.723–53.172 MHz
Quality factor with tuners	$1:12.1$0	$1:12.1$1
$1:12.1$2	$1:12.1$3	$1:12.1$4

These comparisons are used to justify the field analysis. The simulated tuning range is larger than the measured range, but the study characterizes it as still “well within reason.” The slight elevation of simulated $1:12.1$5 is attributed to the omission of HOM dampers and other attached hardware that lower the effective value in the real cavity (Stevenson, 5 Aug 2025).

Field normalization follows the conventional eigenmode convention of 1 J stored energy. Under that normalization, the fundamental mode gives a gap voltage of 278 kV. To translate the normalized fields to the operating condition used in the study, all field values are scaled by

$1:12.1$6

The relation

$1:12.1$7

is used to connect stored energy, gap voltage, and effective impedance (Stevenson, 5 Aug 2025).

4. High-field localization, sparking, and breakdown-limiting regions

The central technical result of the CST study is the localization of the highest electric fields in the cavity geometry. The paper identifies the highest electric fields on the corona rings around the ends of the beam pipes near the accelerating gaps, that is, on the inner conductor close to the region where the beam exits the beam pipe and crosses the gap. At the scaled operating condition of 240 kV gap voltage, the study reports

$1:12.1$8

for the gap field and

$1:12.1$9

for the peak surface field in the cavity (Stevenson, 5 Aug 2025).

This yields a field-enhancement factor of approximately

$45^\circ$0

showing that the cavity’s most stressed surfaces are not characterized by the average accelerating-gap field alone. The study notes that the simulated tetrode interior also shows very high fields, but explicitly treats those as artifacts of the tetrode representation rather than as realistic breakdown-risk regions. The breakdown concern is therefore localized to the cavity body, specifically the beam-pipe corona rings (Stevenson, 5 Aug 2025).

Operationally, this analysis is tied to an empirical problem: the cavities exhibit breakdown events when run at voltages higher than those required by the PIP-II project, and the precise physical location and geometric cause of those breakdowns is not known from hardware alone. The CST model is used to provide that localization. The study does not compute explicit breakdown thresholds through Kilpatrick-type criteria or through a detailed field-emission or multipacting model; instead it proceeds empirically, arguing from observed sparking above present operating limits and from the linear scaling of local peak fields with gap voltage (Stevenson, 5 Aug 2025).

This suggests that the dual-amplifier configuration is not itself the proximate cause of sparking. Rather, the dual-amplifier configuration provides the voltage and power capability needed for PIP-II operation, while the usable ceiling is set by geometric field enhancement in the cavity. A plausible implication is that higher-voltage operation beyond the PIP-II point depends less on adding amplifier capacity than on lowering the local enhancement factor at the corona rings (Stevenson, 5 Aug 2025).

5. Relation to the PIP-II linac LLRF architecture

The PIP-II linac LLRF literature is explicit that the superconducting linac is organized around one controlled RF load per cavity, not around dual amplifiers feeding one cavity. The 2018 overview states that the LLRF racks are organized into four-cavity stations; each station has two 8-channel down-converters, one 4-channel up-converter, two 2-cavity controller modules, one 4-cavity resonance controller module, and an LO/Clock distribution chassis. The signal path shown in the station schematic is singular on the drive side: controller, up-converter, SSA, and cavity, with forward and reflected signals taken from directional couplers (Edelen et al., 2018).

The same paper states that the PIP-II superconducting cavities are regulated individually to better than 0.01° in phase and 0.01% in amplitude, and that the principal challenge is resonance control, with total detuning during flat-top required to be less than 25 Hz in the presence of microphonics and Lorentz Force Detuning. None of that discussion introduces a dual-amplifier-per-cavity topology for the superconducting linac (Edelen et al., 2018).

The 2023 linac LLRF paper confirms the same architecture at larger system scale. The PIP-II linac has 125 RF cavities and uses two main controller families: low-latency I/Q control for the warm front-end and HWR cavities, and amplitude/phase control with SEL-based modes for the main SRF sections. The paper explicitly states that each SSR1 cavity is driven by a 7 kW solid-state amplifier, reports a single 40 kW SSA used to test HB650 cavities one at a time on the prototype stand, and states that it does not refer to any dual power amplifier or two-amplifiers-per-cavity configuration (Varghese et al., 2023).

A common misconception is therefore that “PIP-II dual power amplifier cavities” refers generically to PIP-II cavities. In the documented baseline, that is incorrect. The expression applies directly to the Main Injector cavities in the PIP-II-era upgrade study, while the superconducting linac retains a one-amplifier-per-cavity model (Stevenson, 5 Aug 2025, Varghese et al., 2023).

6. Control implications, non-linearity, and future design directions

Although the documented dual-amplifier cavity study is electromagnetic rather than LLRF-centered, later PIP-II control papers define several constraints that are directly relevant if dual-amplifier operation is treated as an RF-control problem. The 2025 SEL calibration paper shows that amplifier non-linearity can prevent stable operation if the mapping between DAC drive and forward power is assumed to be linear. For a 32 kW PIP-II HB650 solid-state amplifier, the authors replace a slope-only calibration with an affine model,

$45^\circ$1

and derive modified SEL limits that incorporate the offset. The paper states that without such compensation the cavity could not be driven in SELA and SELAP modes, whereas the affine calibration restored operability (Raman et al., 17 Oct 2025).

This suggests that any dual-amplifier cavity implementation requiring coherent RF addition would have to confront amplifier-to-amplifier non-linearity explicitly. A plausible implication is that per-amplifier calibration, or calibration of the combined effective actuator, would be necessary to prevent unequal sharing, erroneous loop gain, or premature saturation (Raman et al., 17 Oct 2025).

The 2025 PIP-II LLRF analysis paper, while not describing dual-amplifier-per-cavity hardware, also identifies beam loading and SEL saturation as the dominant control limits. It analyzes a single logical actuator per cavity and concludes that the existing $45^\circ$2 amplitude box inherited from LCLS-II is insufficient to cover PIP-II beam loading purely with feedback, recommending beam-loading feedforward and reduced latency. This suggests that adding a second amplifier does not by itself solve the fundamental control limitation; if two amplifiers were hardware-combined and presented to LLRF as a single effective SSA, the dominant constraints would remain loop delay, saturation limits, and calibration accuracy (Varghese et al., 23 Oct 2025).

On the hardware-design side, the CST study defines a concrete optimization program for extending cavity voltage beyond the PIP-II operating point. It states that future work will focus on lowering the peak electric fields by changing the geometrical properties of the beam pipe corona rings, using center frequency, $45^\circ$3, and $45^\circ$4 as metrics to monitor the success of each modification. The target is therefore not a wholesale change in resonator concept, but a geometry revision that preserves RF performance while reducing local surface overstress (Stevenson, 5 Aug 2025).

In that sense, the present understanding of PIP-II dual power amplifier cavities is twofold. As a realized system, they are Main Injector cavities equipped with two 150 kW tetrode amplifier chains per cavity to meet the PIP-II voltage requirement. As a research object, they are a breakdown-limited resonator geometry whose next development step is the reduction of the peak electric field at the beam-pipe corona rings, with CST simulation used as the principal tool for locating the limiting regions and guiding modification of the cavity geometry (Stevenson, 5 Aug 2025).