Some vapor cell clocks require a microwave cavity to select the resonant mode of the microwave field. A standard cylindrical microwave cavity with TE_{011} mode is employed in a POP Rb clock (Godone et al. 2011), which has a typical volume of 100 mL. For such a cavity, the vapor cell is held in the core of the cylindrical cavity by long stems, which makes it difficult to stabilize the cell temperature via the heat conduction of the glass stems. Conversely, the magnetron cavity has a small size, and the resonant mode TE_{011}-like permits the magnetic component to be parallel to the quantization axis across the cavity. These characteristics enable the direct glue of the vapor cell on the metal cavity’s inner wall, which enhances the heat transfer between the vapor cell and heating oven. As shown in Fig. 1, a magnetron cavity includes two cylindrical shells, and the inner one is divided by several equally spaced slots. With the lumped elements equivalent model, the slots act as the capacitance *C* (Froncisz and Hyde 1982; Stefanucci et al. 2012):

$$C = \frac{\varepsilon wh}{tn}$$

(1)

where *ɛ* is the dielectric constant, and *w, h, t, n* are the thickness, height, width, and number of slots, respectively. Likewise, the metal electrodes act like the inductance *L*:

$$L = \frac{{\mu_{0} \pi r^{2} }}{h}$$

(2)

where *μ*_{0} is the permeability of vacuum and *r* is the radius of the inner shell. Considering the frequency shift generated by the outer shell and fringing fields, the resonant frequency *v* is given by

$$\nu = \frac{1}{2\pi r}\left( {\frac{nt}{{\pi w\varepsilon_{0} \mu_{0} }}} \right)^{1/2} \left( {1 + \frac{{r^{2} }}{{R^{2} - \left( {r + w} \right)^{2} }}} \right)^{1/2} \left( {\frac{1}{1 + 2.5(t/w)}} \right)^{1/2}$$

(3)

where *R* is the outer shield radius. Hence, the resonant frequency can be easily adjusted by changing the number *n*, thickness *t*, and width *w* of the slots.

As shown in Fig. 2a, we designed a copper magnetron-type cavity with four electrodes. It has an external diameter of 33 mm and a height of 35 mm; thus, its volume is approximately one third of the standard TE_{011} cavity. The microwave signal is transmitted with the antenna through a microwave cable and couples into the cavity. With the high frequency structure simulator (HFSS) software, Fig. 2b shows the numerical simulation of the magnetic field orientation inside the cavity. The magnetic lines are highly parallel to each other, indicating that the resonant mode is TE_{011}-like. Additionally, the measured Zeeman transition strengths between the hyperfine levels F = 1 and F = 2 of ^{87}Rb ground-state are shown in Fig. 2c, and the deduced field orientation factor is as high as 0.9 (Stefanucci et al. 2012). The loaded quality factor measured 120. Based on a research on a magnetron-type cavity with a loaded quality factor of 140 (Almat et al. 2020), we believe that the cavity-pulling effect caused by cavity temperature variations is negligible for such a cavity.

To characterize the performance of the proposed cavity, the clock signal is measured with a POP Rb clock. A contrast of Ramsey central fringe of 31% is obtained when the temperature of the vapor cell is set to 65 °C, as shown in Fig. 2d. The linewidth of the central fringe is 148 Hz, which is consistent with the theoretical value 1/(2T) (Ramsey time T = 3.5 ms). Additionally, the calculated shot noise limit of the package is 1.6 × 10^{−14}τ^{−1/2}, demonstrating no signal to noise ratio loss compared to previous works (Micalizio et al. 2012; Kang et al. 2015).

The primary reason for the high-temperature sensitivity is the collision shift between Rb atoms and buffer gases. An empirical second-order polynomial expression for this effect is (Vanier et al. 1982)

$$\Delta f = P_{t} (\delta^{{\prime }} \Delta T + \gamma^{{\prime }} \Delta T^{2} )$$

(4)

where *∆f* is the temperature-depended frequency shift, *P*_{t} is the total gas pressure, *δ*_{0} and *γ*_{0} are the linear and quadratic temperature coefficients, respectively, and *∆T* is the difference between the operating temperature and reference temperature. Here, we used a vapor cell of 20 mm length and 20 mm external diameter. It was filled with a mixture of Ar and N_{2} (P_{Ar}/P_{N2} = 1.6) with a total pressure of 25 Torr. The temperature coefficient is measured and shown in Fig. 3a. The result is well-fitted by the binomial fit. From Fig. 3a, we conclude that the relative frequency shift is at a negligible level of 10^{−12}/°C when setting the cavity temperature about 65 °C.

The geometric effect of the vapor cell also yields an enhanced temperature coefficient (ETC) (Calosso et al. 2012). As shown in Fig. 3b, a cell stem with 1% volume of the total is placed in the cavity. As the temperature fluctuation is small enough inside the cavity, it is unnecessary to stabilize the temperature of the stem independently. The temperature gradient produced by the heat conduction of glass is designed to avoid the Rb migration effect, and the ETC is theoretically estimated to be as small as 2 × 10^{−11}/°C in our case.