Fast DAQ system with image rejection for axion dark matter searches

Since no specific events that could be detected as trigger events exist in the case of axion haloscope experiments, the trigger was activated forcibly or, equivalently, the trigger condition was set to be satisfied in all events.

Standard (STD) and First In, First Out (FIFO) are the two major options for the acquisition modes of the digitizer. Both modes include processes for allocating the buffer on the digitizer memory, sampling, and transferring the data on the digitizer memory to the PC memory. The difference between the two modes is about when and how the data are written and transferred to the buffers.

The typical intermediate frequency (IF) of 10.7 MHz can be chosen at the heterodyne receiver for the CAPP-12TB experiment. With a sampling rate of 22.5 MSamples/s, the Nyquist frequency is 11.25 MHz which can result in a power spectrum span of 1.1 MHz with the IF as the central frequency. The span of 1.1 MHz is much wider than the relevant CAPP-12TB parameters, cavity bandwidths of $\sim$30 kHz and virialized axion [19] signal windows of $\sim$3 kHz, and thus meets the criteria of CAPP-12TB axion haloscope searches.

With a resolution bandwidth (RBW) of 20 Hz, data from this process can be used for nonvirialized axions [20] whose signal windows are at most 20 Hz as well as virialized axions mentioned above. This narrow RBW is also more effective for getting rid of IF and radio frequency (RF) interference as the narrow spikes in each power spectrum [21] of the virialized axion dark matter searches that is what we are primarily after.

We chose a dynamic range of $\pm$500 mV, which limits very high power electromagnetic interference backgrounds and provides a power resolution of about 0.5% with a 16-bit amplitude resolution of the digitizer and expected background power level of $\mathcal{O}(\mu$W). Table 1 lists the digitizer parameters used in this work.

The challenging part of our DAQ system using the fast digitizer is the post processing of the data, which includes unit conversion, online FFT, averaging, and writing the power spectra (ROOT [23] format in this work) to disk storage. The online FFT dominates the post processing time. In most cases axion haloscope experiments require data at different resonance frequencies, because the axion mass is unknown. Also for various reasons the data at each resonance frequency can be divided into several subsets at different timestamps. In such cases, the post process can be performed in parallel while the next data is sampled. Python’s multiprocessing module [24] was used to demonstrate such a scenario.

The essential parts of the post processing including writing to disk are defined separately, then integrated into a single function. The function is then called in a child process spawned by the main process at the end of the first DAQ cycle. The DAQ cycle ends as the child process starts, and the main process controls the digitizer to start a new DAQ cycle while the child process is running. After the new process ends the main process lets the child process join, then spawns more child processes for post processing the data from the new DAQ cycle. These procedures are repeated until the last DAQ cycle, and the main process ends before the post processing of data from the last DAQ cycle starts. For the detailed $\epsilon_{\rm DAQ}$ studies given in Sect. 4.3, the main process ends after the post processing of data from the last DAQ cycle ends.

In the child process, the data arrays are, at first, converted into a two dimensional array with each row containing a single spectrum. Then two child processes are again spawned, one for FFT and the other one for averaging the spectra and saving into a file. During the FFT process the data in each row are converted into voltage, and Fourier transformed. The output of the FFT is normalized and then converted into a single power spectrum. The power spectrum is finally put into a queue defined globally at the beginning of the main process. The other process receives the power spectra from the queue whenever it is filled, adds them together in a new buffer, divides it by the number of spectra after the last power spectrum is added, then saves it in the data file. Finally the two child processes merge with their parent processes, and again merge with the main process.

The main process waits until the child process from a previous DAQ cycle merges with its parents. This means the next DAQ cycle might be delayed if the total time necessary for the post process exceeds the DAQ cycle time segment explained below. The total time for post processing can be reduced in this case by employing several parallel jobs in multi-thread CPUs.

With multi-thread CPUs, each FFT process can be shortened by multi-threading, or the overall tasks can be divided and done by several threads in parallel. Considering the large number of iterations and the fairly short time for each iteration, the latter is in practice more efficient. Since the FFT processes are already being performed in parallel and automatically assigned to another thread, using more threads can be done simply by dividing the tasks equally and spawning more FFT processes for assigning the divided tasks. Figure 1 shows the schematic of our DAQ process described above.

Here we address how the DAQ cycle time segment was optimized with our DAQ PC which has a 16-thread CPU whose maximum clock speed is 5.3 GHz according to the manufacturer [25]. We found the optimum cycle time by varying the number of FFTs or, equivalently, the number of power spectra, per thread.

Figure 2 shows that a time ratio of FFT to DAQ cycle below 30% can be obtained by choosing the number of FFTs per thread to be greater or equal to 4. Our choice of the number of FFTs per thread was 8. From 128 FFTs (or power spectra) with 16 threads, therefore, our DAQ cycle time segment $\hat{t}_{\rm DAQ}$ was 6.4 s, corresponding to a data size of 288 MB for a single channel.

From the radiometer equation [27], the experimentally achieved SNR with an $\epsilon_{\rm SNR}$ of 100% [11] is

where $\sigma_{P_{n}}$ is the $P_{n}$ fluctuation, $t_{\rm DAQ}$ is the DAQ cycle time, and $N$ is the number of power spectra, which shows that the axion dark matter search sensitivity can be improved by increasing the DAQ cycle time or, equivalently, the number of power spectra, by increasing the number of DAQ cycles. Therefore, $t_{\rm DAQ}$ is equal to $n_{\rm iter}\hat{t}_{\rm DAQ}$ and our $\epsilon_{\rm DAQ}$ depends on $n_{\rm iter}$ with our DAQ algorithm explained above, where $n_{\rm iter}$ is the number of iterations for each resonant frequency scan. In our DAQ algorithm developed in this work, the first iteration time includes the digitizer starting ($t_{\rm digitizer~{}starting}$) and DAQ cycle, while the second includes the next DAQ cycle and online FFTs with ADC data from the first iteration, where online FFTs are executed in parallel with the current DAQ cycle. Subsequent iterations are identical to the second iteration, until the last iteration which is like the second one except for the additional online FFTs using ADC data from the iteration ($t_{\rm last~{}FFTs}$). Therefore, the DAQ efficiencies of the first and last iterations are lower because of the digitizer starting and the last online FFTs, respectively. The two inefficiency sources, however, become negligible as the $n_{\rm iter}$ increases. Even without the $n_{\rm iter}$ increasing, the inefficiency from the last online FFTs can be in practice ignored because the next resonant frequency scan can start right after the final iteration of data sampling, and the corresponding online FFTs can be finished during the cavity tuning and measurements before starting the new DAQ process.

The timestamp of the digitizer has limited usage, but turns out to be consistent with that of DAQ PC as shown in Fig. 3. This enables us to use handy timestamps from the PC.

With an $n_{\rm iter}$ of 10000 and the STD mode, Table 2 shows the $\epsilon_{\rm DAQ}$ depending on the conditions, and Fig. 4 shows the distribution of the timestamp differences between two consecutive iterations $\Delta t$. As mentioned above, $\epsilon_{\rm DAQ}$ with a large enough $n_{\rm iter}$ is independent of the two significantly inefficient iterations shown in Fig. 4.

Figure 5 shows the DAQ efficiency as a function of the number of iterations for both the STD and FIFO modes of the digitizer. The efficiencies are already higher than 98% and 99% after $\sim$200 iterations ($N$ of $\sim$26000) or $\sim$22 minutes for the STD and FIFO modes, respectively, and then converge to 98.4% and 99.7% with further iterations.

We checked whether the noise power fluctuations from our data with the DAQ process follow Eq. (4.1) using a 50 $\Omega$ termination input, where the fluctuations are the axion haloscope resolutions when they are measured through a full signal chain, i.e., a cavity, preamps, and digitizer or spectrum analyzer at the end. Figure 6 shows the noise power fluctuations depending on the number of power spectra, and they show good agreement with Eq. (4.1) as it should be, which is a fundamental requirement of the DAQ system for axion dark matter searches.

Table 3 shows the expected CAPP-12TB experimental parameters for the resonant frequency $\nu=$ 1 GHz, where the coupling strength $g_{a\gamma\gamma}$ corresponds to the DFSZ axion and $\beta$ denotes the cavity mode coupling to the load.

Given the experimental parameters listed in Table 3, Fig. 6 also shows the necessary number of power spectra to be sensitive to an SNR_achieved of 5 for the DFSZ axions, depending on the noise temperature. Accordingly, the DAQ efficiencies ignoring the last FFTs are higher than 99.2% with a noise temperature higher than 0.1 K in the FIFO mode. This noise power fluctuation study validates that the data from this DAQ process can be sensitive to the DFSZ axion even with a noise temperature of 1 K, if it goes with the CAPP-12TB experiment. Note that the statistics for this validation study was set to match the CAPP-12TB experiment, but the validation of our DAQ process can be extended easily to other experiments depending on the experimental parameters.