Conceptual design of a high reactive-power ferroelectric fast reactive tuner

We present a novel design of a ferroelectric fast reactive tuner (FE-FRT) capable of modulating mega-VAR reactive power on a submicrosecond timescale. The high reactive power capability of our design extends the range of applications of reactive tuners to numerous applications. We present a detailed analytical model of the performance of a megawatt-class reactive power device and benchmark it against finite-element method eigenmode and frequency domain electromagnetic simulations. We introduce new features, including an annulus design for the ferroelectric capacitors and capacitive window coupling to the cavity. We consider thermal design issues and nonlinear effects in the ferroelectric. The model covers several configurations, allowing control of the frequency of superconducting and normal-conducting cavities in a variety of applications and frequencies. We calculate that the FE-FRT designed should be capable of handling around 0.45 MVAR of reactive power with around 3 kW of resistive losses, providing a frequency tuning range of 8 kHz in an example of 400 MHz cavity geometry.

Figure 1

Circuit diagrams for three potential configurations of a tuner using ferroelectric loaded capacitors. The number of ferroelectric capacitors connected in series is $N_w$, set at four in this figure. Configuration (A) is a proportional, resonant, or nonresonant circuit. Configuration (B) employs a resonant circuit for increased reactance. Configuration (C) shows a resonant circuit for high-frequency applications and in addition a capacitive coupling to the transmission line through a window.

Figure 2

Detail of the model used to solve the impedance of the ferroelectric capacitor. Blue arrows represent the surface current flowing longitudinally on the surface of the spacers, encountering the capacitive gap, treated as a short section of a radial transmission line extending from $r_2$ to $r_1$. This transmission line comprises the two radial surfaces of the spacers and it is loaded by the ferroelectric wafer. The colored annulus of radius $r$ and width $dr$ is used in the integration.

Figure 3

Equivalent circuit diagram of a cavity with external capacitive coupling. The tuner’s impedance $Z$ is coupled to the cavity circuit, represented by $R_c-L_c-C_c$ through the coupling capacitor $k{C}_c$.

Figure 4

Model of a four-wafers ferroelectric tuner in configuration C. (A) Ferroelectric wafer. (B) Spacer. (C) Cooling line. (D) Series capacitor gap. (E) Dielectric window. (F) Inner conductor of transmission line. (G) Window support, part of the vacuum enclosure. The copper spacers between the wafers have channels for refrigerant flow. The refrigerant lines also connect the bias voltage but include rf isolation against shorting the rf voltage (not shown). The dielectric of the window capacitor is shown in blue. Yellow color represents copper parts.

Figure 5

Cutout view of the tuner of Fig. 4 with the full length of the transmission line. (I) Inner conductor of the transmission line. (II) Outer conductor of the transmission line. (III) Schematic of a possible dielectric support of the inner conductor. (IV) Ferroelectric stack. (V) Refrigerant line. (VI) Window. The inset figure shows the tuner connected to a cavity. The assembly shown is inside the vacuum vessel in the case of a superconducting cavity, or in air for a normal-conducting cavity. The internal volume of the transmission line and ferroelectric stack assembly is under vacuum in either case. Various engineering details are not shown due to the limited scope of this paper, such as heat sinks on the cavity’s coupler and rf and bias connections to the refrigerant lines.