Quartz Resonator Instabilities Under Cryogenic Conditions

Maxim Goryachev, Serge Galliou, Philippe Abbé, Pierre-Yves Bourgeois, Serge Grop, and Benoît Dubois Abstract-The phase noise of a quartz crystal resonator working at liquid helium temperatures is studied. Measurement methods and the device environment are explained. The phase noise is measured for different resonance modes, excitation levels, amount of operating time, device orientations in relation to the cryocooler vibration axis, and temperatures. Stability limits of a frequency source based on such devices are evaluated in the present measurement conditions. The sources of phase flicker and white noises are identified. Finally, the results are compared with previous works.

I. I

S  the dawn of the cryogenic era in the 1950s, it has been widely known that quartz crystal BAW resonators exhibit very high quality factors at liquid helium temperatures [START_REF] Bömmel | Dislocations, relaxations and anelasticity of quartz crystal quartz[END_REF]- [START_REF] Smagin | Quartz crystal resonators with quality factors of about 120 • 10 6 at 2K[END_REF]. Impressed by these results, later researchers revived the idea of investigating BAW resonators at cryogenic temperatures, achieving even higher values [START_REF] Mossuz | Study and achievement of a quartz crystal oscillator at very low temperature[END_REF]- [START_REF] Habti | Low temperature limitation on the quality factor of quartz resonators[END_REF]. All these works are nonsystematic studies of some particular aspects of BAW device operation. For example, only some of the works note frequency-temperature resonator characteristics which are very important to device performance. Furthermore, no studies were done concerning resonator nonlinearities, different mode comparison, or analysis of loss phenomena. Some studies were partially related to quartz resonator proper phase noise at liquid helium temperatures [START_REF] Robichon | Frequency stability of quartz crystal at very low temperatures: Preliminary results[END_REF], [START_REF] Gagnepain | Relation between 1/f noise and Q-factor in quartz resonators at room and low temperatures, first theoretical interpretation[END_REF], [START_REF] Planat | 1/f noise in quartz crystal resonators in relation with acoustic losses and frequency dispersion[END_REF], but their results are questionable and are discussed in this work. The nonsystematic approach of these studies is a consequence of the many difficulties associated with cryogenic experiments. Indeed, the first investigations on the high quality factor resonators at cryogenic temperatures were made with bath cryostats. These systems have several disadvantages, such as difficulties of operation and experiment time limitations. In addition, experiment time limitations made long frequency stability measurements almost impossible. Recently, cryocoolers became widely available for liquid helium temperature experiments. These devices do not have any limitation on measurement time and they are rather simple in operation. These provided new opportunities to revive this area of research. The idea of practical use of cryogenic quartz resonators has become especially important in the light of quartz technology perspectives in general. Therefore, since 2007, some systematic researches in the field have been conducted at the Franche-Comté Electronique, Mécanique, Thermique et Optique-Sciences et Technologies (FEMTO-ST) Institute, Besançon, France. Thus, the different operation modes have been studied and compared, paying attention to frequency-temperature characteristics [START_REF] Galliou | Outstanding quality factors of bulk acoustic wave resonators at cryogenic temperature[END_REF], [START_REF] Galliou | Quartz crystal resonators exhibiting extremely high Q-factors at cryogenic temperatures[END_REF]. Based on measurement data, the loss phenomena in quartz resonators were analyzed [START_REF] Galliou | Losses in high quality quartz crystal resonators at cryogenic temperatures[END_REF]. Further, amplitude-frequency nonlinear effects, temperature sensitivity, LGT resonator investigation, and mode comparison [START_REF] Goryachev | Recent investigations on BAW resonators at cryogenic temperatures[END_REF] are also subjects of this research. The present work is a continuation of this global investigation. It concerns quartz resonator instabilities at cryogenic conditions.

The present research deals with quartz botier à vieillissement amélioré (BVA) resonators [START_REF] Besson | A new electrodeless resonator design[END_REF], because it has been already shown that electrodeless resonators exhibit higher quality factors than electrode-deposited resonators [START_REF] Suter | Acoustic loss phenomena in alpha quartz resonators over the 1.4-77K temperature range[END_REF]. More precisely, measurements are made with planoconvex SC-cut resonators [START_REF] Eernisse | Quartz resonator frequency shifts arising from electrode stress[END_REF] optimized to work on the 3rd overtone of the C-mode (5 MHz) at 80°C. At this temperature, the frequency-temperature characteristic of such a device exhibits a turn-over point. The devices are state-of-the-art commercial resonators provided by the BVA Industrie Company (Besançon, France).

The paper starts with the description of the cryogenic system and the main sources of environmental disturbance (Section II), and then passes to explanations of the phase noise measurement method in cryogenic conditions and preliminary results (Section III) for the open-loop case. Section IV considers resonator long-term instabilities measured in closed loop. Section V presents the resonator phase noise as a function of different parameters. In the final section, the obtained results are compared with some earlier works.

II. M S

In this work, a two-stage pulse-tube cryocooler (see Fig. 1) is used at the cryogenic system's core. The cryocooler is shielded with two protection screens: a vacuum chamber and an anti-radiation shield. The former prevents temperature losses resulting from heat conduction through air. The air pressure inside the chamber is about 10 -5 Pa. This shield is at room temperature and is made with a light-reflecting material. Both primary and secondary pumps are cut off from the chamber during the The authors are with the Time and Frequency Department of the Franche-Comté Electronique, Mécanique, Thermique et Optique-Sciences et Technologies (FEMTO-ST) Institute, Besançon, France (e-mail: maxim.goryachev@femto-st.fr). whole measurement time. The anti-radiation shield is attached to the first cryocooler stage and its temperature is about 50K. Its inner and outer surfaces are covered with a specially fabricated light-reflecting paper comprising several layers of metalized mylar sheeting to reduce radiation losses of the second stage.

Nominally, the cryocooler absorbs up to 1 W at its second stage at 4K. The second stage temperature can go down to almost 3K in the unloaded configuration. The thermal losses are mainly introduced with connecting cables needed for measurements and environmental control. The device under test (DUT) is attached to a temperature-controlled copper block.

The almost periodic temperature fluctuations of the cryocooler second stage resulting from the helium pulsation are about 0.3K. The power spectral density (PSD) of temperature fluctuations of the second stage in the steady state consists of an f -2 region for frequencies less than about 10 -2 Hz and an f 0 region for higher frequencies. In addition, a clear spurious frequency of 1.7 Hz and its harmonics are present as a result of temperature pulsations initiated by the pulse tube cycle.

To improve the thermal environment of the DUT, passive and active temperature stabilization methods are used. First, a thermal filter is introduced between the second stage and the copper block (see Fig. 1). The filter reduces the temperature pulsation down to 15mK, but increases the absolute temperature difference between both parts. This difference mainly depends on the number of cables connected to the DUT. Second, the active temperature regulation is implemented with a temperature controller (model 332, Lake Shore Cryotronics Inc., Westerville, OH), a Cernox temperature sensor (Lake Shore Cryotronics Inc.), and a 20-Ω heating resistor. The sensor and the actuator are installed inside the copper block under the filter. The control system eliminates the f -2 region in the temperature fluctuation spectrum (for frequencies higher than 10 -4 Hz) and reduces the temperature pulsation to 5mK. The power spectral densities of temperature fluctuations in both second stage (unregulated and non-filtrated part) and the DUT (after filtering with and without active regulation) is shown in Fig. 2.

Fig. 2 shows that the remaining noise resulting from temperature instabilities at the DUT level (with no thermal load or cables installed) is almost a white noise in the frequency range of 10 -3 to 10 0 Hz. Although it must be noted that the f -2 spectrum slope can still appear at this range of frequencies at the DUT level when measurements are performed during exponential transients in the whole thermo-mechanical system (cryogenerator, cables, DUT, etc.). This happens when the thermal load is high enough and the connection cables thermally relate regulated and unregulated parts of the system.

Another type of cryocooler environmental disturbance is vibration. According to the cryocooler specification, the permanent pulsation of helium inside the pulse-tube causes a DUT vibration with an amplitude A = 10 µm and a frequency f = 1.7 Hz. The spectrum of vertical DUT acceleration (Z-axis in Fig. 1) has been calculated, based on measurements made with a high-sensitivity piezoelectric accelerometer A/600 and a high-speed real-time system ADwin-Pro II (Jäger Computergesteuerte Messtechnik GmbH, Lorsch, Germany) with a custom-made low-noise charge amplifier. The DUT acceleration PSD along the vertical axis is shown in Fig. 3. In fact, the sensitivity of the accelerometer at cryogenic temperature is unknown, so the presented data lacks an accurately calibrated scale.

Nevertheless, the measurement suggests that the DUT is subject to f -1 instabilities in the frequency range of 10 -2 to 10 1 Hz resulting from external vibration in the vertical axis. It must be noted that no vibration compensation system is installed for the presented measurements.

III. O-L M

Usually, at room temperatures the phase noise of ultrastable quartz crystal resonators is measured with an inter- ferometric measurement system [START_REF] Rubiola | Flicker noise measurement of HF quartz resonators[END_REF]. Such a scheme is not possible for resonators working under cryogenic conditions because of a significant dispersion of resonator parameters at low temperatures. Thus, for example, two 5-MHz resonators (from the same batch) can exhibit a resonance frequency difference of 1.1 kHz, for the 5th overtone of the A-mode, at 4.2K. For 10-MHz resonators, this difference is about 500 Hz. This phenomenon is due to small differences in crystal blank orientations [START_REF] Gagnepain | Relation between 1/f noise and Q-factor in quartz resonators at room and low temperatures, first theoretical interpretation[END_REF]. This difference cannot be covered with trimming capacitors as in the case of room-temperature measurements. Therefore, to evaluate the resonator phase noise under cryocooler conditions, only a one-resonator scheme is available (see Fig. 4). Note that the synthesizer is an RF signal generator HP8665B (Agilent Technologies Inc., Santa Clara, CA). It is used to tune an excitation signal frequency to the resonance frequency.

Measurements are made step-by-step to identify and characterize all noise sources of the measurement system and to assure that the noise floor is lower than the measured noise. All the phase noise or frequency stability measurements are made with a phase noise test set (TSC5120A, Symmetricom Corp., San Jose, CA) which uses a cross correlation technique.

At the first step, the measurement noise floor is evaluated. To do so, the signal from a voltage-controlled oscillator (VCO) is split and used as the measured signal and as the reference of the phase noise test set. The result is shown in Fig. 5, curve (1).

Second, the phase noise of two amplifiers is measured by adding these devices into each branch of the system [see curve [START_REF] Mason | Use of internal friction measurements in determining the causes of frequency instabilities in mechanical vibrating frequency standards[END_REF] for the result].

Third, the cryogenic assembly, except for the resonator, is added to the measurement scheme. The cryogenic assembly includes the connectors, cables, and passive electronic components. At this step, the resonator is replaced with a resistance corresponding to its equivalent resistance at the cryogenic temperature. This measurement gives an estimation of the total noise floor of the cryogenic phase noise test bench. The result is presented in Fig. 5, curve [START_REF] Warner | Ultra-precise quartz crystal frequency standards[END_REF].

Fourth, the measurements are repeated the same scheme as in the third step, but with the crystal resonator inside its π-network. The frequency of the signal at the output of the synthesizer must be adjusted exactly to the resonant frequency of the crystal device at the working temperature. In Fig. 5, curve (4) shows the results of these measurements for the 5th overtone of the A-mode [START_REF] Goryachev | Recent investigations on BAW resonators at cryogenic temperatures[END_REF]. This mode has the highest value of quality factor (Q = 325 • 10 6 at 15.6 MHz) compared with that of the third and fifth overtones. Therefore, it is the best candidate for further closed-loop frequency measurements. In addition, the 5th overtone of the B mode (Q = 50.5 • 10 6 at 9.2 MHz) and the 3rd overtone of the A mode (Q = 114.6 • 10 6 at 9.4 MHz) are considered further.

The design of the cryogenic part of the measurement system implies several requirements. First, the resonator's loaded quality factor must be preserved. To do so, the load must be of the same order of magnitude as the resonator's motional resistance. Unfortunately, the equivalent motional resistance of the resonator at these modes and overtones is very low (approximately 3.5 Ω for the 5th overtone of the A-mode). Second, the influence of the connecting cables must be minimized. This also means that the loading resistances of the π-network must be minimized. Third, the resonator's nonlinear effects must be avoided to prevent the excess noise [START_REF] Gagnepain | Excess noise in quartz crystal resonators[END_REF]. Indeed, a quartz crystal resonator at the cryogenic temperature is subject to a strong amplitude-frequency effect [START_REF] Goryachev | Recent investigations on BAW resonators at cryogenic temperatures[END_REF]. This mainly results from high values of the Q-factor, because the frequency shift is proportional to the product of Q and the input signal power [START_REF] Bourquin | Amplitude frequency effect of SC-cut quartz trapped energy resonators[END_REF]. To limit this effect, the resonator active power must be kept low. This could be done by injecting lower-power signals or by increasing the resonator load. And, fourth, it is absolutely necessary that the π-network is able to provide at least +7 dBm at the output of the amplifiers, whose gain is limited. This could be achieved by increasing the level of the excitation signal or by increasing the resonator load. As can be seen, the four requirements are contradictory and difficult to fulfill simultaneously, so a trade-off must be achieved. This has been done by providing approximately 12% of the unloaded quality factor.

A crystal resonator can be differently installed inside the copper block of the cryogenerator. Various orientations of the crystal resonator in the copper block of the cryocooler second stage are possible. Indeed, the resonator plate can coincide with the X-Y plane or with the X-Z plane as shown in Fig. 1. All the measurements demonstrated in the present section are made with the crystal plate normal to the Z-axis.

The measurement system noise floor clearly consists of white and f -1 noises [Fig. 5, curve (1)]. It is lower than all measurements in the present work. The amplifier noise power spectral density also exhibits the same noise slopes [see curve [START_REF] Mason | Use of internal friction measurements in determining the causes of frequency instabilities in mechanical vibrating frequency standards[END_REF]]. Although these wide-band amplifiers are specified to be low-noise devices, their phase noise is relatively high. If one compares amplifier phase noise with that of the cryogenic assembly without the resonator [curve (3)], the random-walk phase noise appears for the low Fourier frequencies. Its origin is attributed to temperature fluctuations (it is known that temperature fluctuations are random walks whose spectral density is proportional to f -2 ) of the long cables used to connect both cryogenic and ambient temperature parts. As previously mentioned, these cables are not temperature regulated and connect ambient temperature devices (at about 295K) and the cryogenic circuit (at 4.1K), with an intermediate thermal connection at the first stage of the cryogenerator (at about 50K). This type of noise becomes important mostly in the case in which long thermal transients of the system are not over. This is explained in Section V.

When comparing measurements of the cryogenic part with and without the resonator [curves (4) and (3), respectively, in Fig. 5], two observations can be made. First, inside the resonator bandwidth (Fourier frequencies lower than 0.5 Hz), the VCO and synthesizer phase noises are compensated because both branches are similar, resulting from the fact that the resonator works as a flywheel. Therefore, in this first part of the spectrum, one obtains the sum of phase noises of the amplifiers, cables, and resonator. Because spectrum (4) in this region is considerably higher than spectrum (3) which does not contain the resonator phase noise, the difference can be attributed to the resonator phase noise. f -2 and f -1 slopes are present in this part of the PSD. Second, outside the resonator bandwidth, oscillator and synthesizer noises are no longer compensated, because in one of the branches the phase noise is filtered. In that case, the resulting phase noise includes noises from the amplifiers, cables, the oscillator, the synthesizer, and the resonator. In the region between 0.5 and 10 Hz, the resonator phase noise is dominant. An f -3 slope is clearly visible here. Between 10 and 200 Hz [zone (B) in Fig. 5], the synthesizer phase noise is the highest one (these values correspond to the synthesizer documentation). For Fourier frequencies higher than 200 Hz, the cryogenic assembly noise overlaps the others. Thus, between the lowest possible Fourier frequency and 10 Hz, one obtains the resonator phase noise. It must be noted that the presented measurements are completely realistic, because this phase noise is relatively high.

The measured quartz crystal resonator working at cryogenic conditions has a PSD consisting of f -2 , f -1 , and f -3 slopes. These results are similar to measurements made at room temperature [START_REF] Sthal | About quartz crystal resonator noise: Recent study[END_REF]. In fact, the resonator can be considered as a low-pass filter in the phase domain. Thus, the resonator filters its own phase noise, forming the f -1 slope inside its bandwidth and the f -3 slope outside; i.e., the output phase noise is the resonator flicker noise multiplied by a square of the resonator transfer function in the phase domain. The bandwidth of this filter corresponds to the corner frequency of the resonator phase noise PSD and is inversely proportional to the loaded quality factor. According to the measurement results, in the phase domain, the bandwidth of the resonator working at 15 597 319 Hz is about 0.5 Hz, giving a loaded quality factor of about Q l = 15.6 • 10 6 . In addition to stochastic instabilities of the resonator, deterministic fluctuations can be observed. These periodic fluctuations at 1.7 Hz and its integer multiples [see peaks (A) in Fig. 5] are due to the cryogenerator working cycle, which produces temperature changes and vibrations.

It is interesting to get an idea of the stability achievable by an oscillator built on such a resonator working at liquid-helium temperatures with the same loaded Qfactor used previously. It is still assumed that the resonator flicker noise dominates within the device bandwidth in comparison with the noise of sustaining electronics. Thus, the Allan deviation floor of such an oscillator can be estimated as

σ y h =2(2), 1 ln - (1)
where h -1 is the coefficient of the flicker power-law spectral density in terms of fractional frequency fluctuations (i.e., S y ( f ) = h -1 f -1 ) [START_REF] Rubiola | Phase Noise and Frequency Stability in Oscillators[END_REF]. For the resonator, the relationship between phase and frequency spectra in its bandwidth is

S f Q Sf Q f y ll ()= 1 2 ()= 1 2 2(). 22           ⋅           ⋅ φ L (2)
Thus, the power law coefficient h -1 can be estimated from the value of the f -1 asymptote line of L() f at f = 1 Hz from curve (4) in Fig. 5. At 1 Hz, this assymptote value is about -83 dB, giving h -1 = 1 • 10 -23 . Consequently, the Allan deviation floor of such an oscillator is σ y = 3.8 • 10 -12 . This value is more than 10 times higher than that of actual state-of-the-art quartz crystal oscillators working at ambient temperatures. The origins of such a high phase noise are unknown. Three possible reasons could be identified: 1) cryogenerator-induced vibration, 2) temperature instability, and 3) intrinsic resonator noise. These reasons are discussed in Section V.

IV. C-L M

Some more important information on the cryogenic resonator instabilities can also be deduced when the VCO (see Fig. 4) is locked on the cryogenic resonator frequency [START_REF] Goryachev | Recent investigations on BAW resonators at cryogenic temperatures[END_REF]. To do so, the output signals of both amplifiers are applied to a double balanced mixer for a downconversion to dc voltage. After low-frequency filtering, the dc signal is applied back to the VCO to lock the loop. It can be clearly shown that the Allan deviation curve of such a feedback system may be separated into three regions (see Fig. 6). The first region, for averaging times τ < 0.1 s, is determined mainly by short-term instabilities coming from the VCO electronics and the cryogenic assembly. The second region (0.1 < τ < 10 s) is due to noise sources of the loop elements. For the third region, τ > 10 s, the system Allan deviation level is proportional to the resonator noise and inversely proportional to its quality factor. By analyzing this last part, the resonator's long-term behavior can be estimated. This estimate is difficult to make using the open-loop approach.

Stability measurements shown in Fig. 6 are for the closed-loop system locked on the 5th overtone of the Amode. In these measurements, the frequency stability has been examined as a function of the amount of time of per-manent operation of the resonator inside the cryocooler. Therefore, Fig. 6 presents the Allan deviation measured during the first 12 hours [curve [START_REF] Mason | Use of internal friction measurements in determining the causes of frequency instabilities in mechanical vibrating frequency standards[END_REF]] and after at least 60 hours of permanent operation [curve [START_REF] Warner | Ultra-precise quartz crystal frequency standards[END_REF]]. Both results can be compared with the stand-alone oscillator stability [curve [START_REF] Bömmel | Dislocations, relaxations and anelasticity of quartz crystal quartz[END_REF]]. As expected, the closed-loop degrades the system frequency stability for small averaging times, τ, but improves it for large averaging times. For large τ, curve (3) exhibits the same slope as the stand-alone oscillator, i.e., τ +1/2 , which corresponds to the resonator f -2 phase noise (phase random-walk). This could be shown analytically using linearized models in the domain of signal phase fluctuations [START_REF] Rubiola | Phase Noise and Frequency Stability in Oscillators[END_REF]. On the other hand, after just 12 h of operation, the system shows a τ +1 law, i.e., a deterministic linear frequency drift. This drift probably results from a rapid aging of the resonator in the first hours after the cooling process, which changes its mechanical properties.

V. Q R P N  C T

Section III explained the measurement techniques and gave phase noise measurement results for one usable system configuration. In this section, these measurements are extended to different resonance modes, excitation levels, amount of cryogenerator operation time, and crystal orientations. The main difference in the measurement technique introduced in this section is that neither branch of the cryogenic part is designed to work in the closed-loop system. First, this implies that the system can work with a lower driving signal. Second, both branches are designed to be identical except for the resonator in one branch and a resistance in the other branch. This is done to minimize the influence of external disturbances on the cryogenic assembly and, thus, to minimize the measurement noise floor.

First, one compares the results of the phase noise measured for different operating modes and overtones. Three modes are of interest here because of their relatively large quality factors: the 5th overtone of the A-mode [curve [START_REF] Mason | Use of internal friction measurements in determining the causes of frequency instabilities in mechanical vibrating frequency standards[END_REF] in Fig. 7], the 3rd overtone of the A-mode [curve (3), Fig. 7], and the 5th overtone of the B-mode [curve (4), Fig. 7]. It is clear from the figure that all three modes have very similar phase noise spectra. However, an f -1 spectrum slope is almost absent for the 3rd overtone of the A-mode and the 5th overtone of the B-mode overtone. This may be a consequence of their high sensitivity to temperature fluctuations [START_REF] Goryachev | Recent investigations on BAW resonators at cryogenic temperatures[END_REF], and thus a rather high f -2 noise.

The next experiment compares phase noise spectra measured for the system with its resonator working at different excitation levels. Two measurements are made in this case. The first measurement is obtained with a level sufficient to provide +7 dBm at the inputs of the double balance mixer. Here, a +0.5 dBm level of the synthesizer output signal is used [see Fig. 8, curve [START_REF] Mason | Use of internal friction measurements in determining the causes of frequency instabilities in mechanical vibrating frequency standards[END_REF]]. Another experiment is done with a much lower level of the synthesizer signal, i.e., -4.5 dBm [see Fig. 8, curve (3)]. The main difference between the obtained results is seen in the region of high Fourier frequencies. As expected, the white noise of the experiment is significantly lower for the higher excitation level, resulting from a better signal-to-noise ratio. In all other ways, the results follow the same trend: no significant change is found for the crystal flicker noise.

Another experiment is made with the resonator working for different amounts of time in cryogenic conditions. As before, two cases are considered. The first measurement is made on the same day the cryocooler is turned on. This means that less than 12 hours elapsed between the time when the cryogenerator is turned on and the measurements. Nevertheless, the steady state seems to be reached according to the measured temperature. The second measurement is made after at least 24 h of cryogenerator permanent operation. The results are shown in Fig. 9 for the 5th overtone of the A-mode and in Fig. 10 for the 3rd overtone of the same mode.

As seen in Fig. 9, there is no clear difference between two measurements separated in time. Both spectra have similar patterns and almost the same level.

For the time-separated measurements made for the 3rd overtone of the A-mode (see Fig. 10), a difference can be observed for low Fourier frequencies. The first-day measurement has a very short region of f -1 slope, because the f -2 noise is relatively high. In contrast, the second day measurements [Fig. 10, curve (3)] have a much less important f -2 region. Because this type of noise depends on the temperature fluctuations and the temperature sensitivity of the mode, it can be concluded that the whole thermo-mechanical system (cryogenerator, cables, DUT, etc.) has some remaining temperature transient processes with time constants greater than 12 h. In the same time, flicker noises of all the modes and overtones do not change with the amount of time of cryogenerator operation. To separate the influences of temperature fluctuations from vibration-caused noise of the resonator, the phase noise is measured for two different crystal device orientations and different temperatures. Fig. 11 presents the resonator phase noise when the resonator disk is vertical (i.e., the resonator disk is normal to the y-axis, according to Fig. 1), whereas in Fig. 12 the resonator is horizontal (resonator disk normal to the Z-axis).

Taking into account the measured environmental disturbances (see Section II), comparison of Fig. 11 and 12 suggests the following conclusions:

1) temperature instabilities and vibrations are the main causes of the resonator phase noise when the cryocooler is operating; 2) as is the case at the usual temperatures, the resonator phase noise is shaped with a low-pass transfer function in the phase domain [START_REF] Sthal | About quartz crystal resonator noise: Recent study[END_REF], [START_REF] Rubiola | Phase Noise and Frequency Stability in Oscillators[END_REF], [START_REF] Rubiola | On the 1/f frequency noise in ultrastable quartz oscillators[END_REF] with f 0 and f -1 fluctuations at the input (see Fig. 13); 3) levels of f 0 and f -1 fluctuations depend on crystal orientation and temperature sensitivity at a given temperature; 4) vibrations of the crystal with a f -1 PSD result in a resonator f -1 phase noise (in other words, the resonator flicker phase noise is due to external vibrations); 5) the quartz crystal resonator is most sensitive to vibration when the main vibration axis is normal to the resonator plate (this is an obvious mechanism, in fact); 6) temperature instabilities of the crystal with a f 0 PSD result in a resonator f 0 phase noise; 7) temperature sensitivity of quartz crystal resonators decreases with temperature (this fact agrees with direct measurements of resonator characteristics [START_REF] Goryachev | Recent investigations on BAW resonators at cryogenic temperatures[END_REF]).

As a general conclusion to these points, it could be stated that the influence of the vibration on resonator parameters and noise can be reduced simply by choosing the proper angle of resonator orientation relative to the main (vertical) axis of vibration. Following the same procedure as in Section III, an oscillator frequency stability floor can be estimated. This time it is supposed that the f -1 -like resonator noise is hidden by its f 0 noise caused by temperature in the 5.3K measurement case [Fig. 11, curve [START_REF] Bömmel | Dislocations, relaxations and anelasticity of quartz crystal quartz[END_REF]]. The maximum level of such a noise would have a power spectral density of L() f ≈ -102 dBc/Hz in the worst case. This value gives an Allan deviation floor of the oscillator of σ y = 4.2 • 10 -13 for Q l = 15.6 • 10 6 . Even in this case, the oscillator frequency stability is not better than that of the state-of-the-art room-temperature quartz oscillators.

The measurement capability of the presented approach is limited by the test bench flicker noise [L() f = -110 dBc/ Hz at f = 1 Hz]. Therefore, the corresponding measurement noise floor of potential oscillators is also limited by σ y = 1.7 • 10 -13 for the same value of the loaded quality factor Q l = 15.6 • 10 6 .

VI. C W E W

Three works give values of the flicker noise for resonators operating in cryostats [START_REF] Robichon | Frequency stability of quartz crystal at very low temperatures: Preliminary results[END_REF], [START_REF] Gagnepain | Relation between 1/f noise and Q-factor in quartz resonators at room and low temperatures, first theoretical interpretation[END_REF], [START_REF] Planat | 1/f noise in quartz crystal resonators in relation with acoustic losses and frequency dispersion[END_REF]. Note that all three works present values of the fractional frequency fluctuations S y ( f ) for just one value of the Fourier frequency f = 1 Hz, and not over a wide Fourier frequency range, as in Figs. 78910. However, all authors attribute these single values to the resonator flicker noise without any discussion of the shape of the phase noise PSD. In fact, as it is seen from the experimental curves, this frequency always belongs to the f -3 spectrum region of the resonator noise. As can be seen, this situation is typical for cryogenic conditions because of the higher values of the quality factors and, thus, much lower resonator bandwidth. Therefore, for cryogenic conditions, the 1-Hz Fourier frequency is most likely situated outside the resonator bandwidth, and for the room temperature it is usually inside with present-day technology. This could lead to unjustified lower values of the resonator flicker noise. Moreover, depending on the quality of the temperature control (this is an issue for cryostats) and the actual resonator temperature sensitivity, this frequency range can lie within the f -2 phase noise slope, which is attributed to the random-walk temperature fluctuations. In this case, there is a risk of measuring only the temperature characteristics of the resonator-cryostat system, but not the resonator flicker noise.

Robichon et al. [START_REF] Robichon | Frequency stability of quartz crystal at very low temperatures: Preliminary results[END_REF] reports more than a one order of magnitude decrease in the phase noise for an AT-cut crystal, going from room temperature [S y (1 Hz) = 1.6 • 10 -24 ] to 4.2K [S y (1 Hz) = 1.4 • 10 -25 ]. The authors do not give any theoretical explanation for this phenomenon, stating only correlation with the increase of the unloaded Q.

Similar results are given by Gagnepain et al. [START_REF] Gagnepain | Relation between 1/f noise and Q-factor in quartz resonators at room and low temperatures, first theoretical interpretation[END_REF]. This work attempts to relate the resonator 1/f noise and the quantum 1/Q 4 law [START_REF] Handel | Quantum approach to 1/f noise[END_REF], [START_REF] Handel | Nature of 1/f frequency fluctuation in quartz crystal resonators[END_REF], which is itself questionable [START_REF] Dutta | Low-frequency fluctuations in solids: 1/f noise[END_REF], [START_REF] Kiss | An exact proof of the invalidity of 'Handel's quantum 1/f noise model', based on quantum electrodynamics[END_REF], [START_REF] Th | Objections to Handel's quantum theory of 1/f-noise[END_REF]. The authors admit the deviation of the measurement results from the theoretical law and make a guess that this fact is attributed to the presence of different loss phenomena and the dependence of the resonator parameters on temperature.

The work of Planat and Gagnepain [START_REF] Planat | 1/f noise in quartz crystal resonators in relation with acoustic losses and frequency dispersion[END_REF] presents the dependence of the resonator fractional frequency fluctuations S y at 1 Hz on the temperature between 4K and 30K. The work reports the strong correlation between acoustic wave attenuation around a phonon-phonon relaxation peak (20K) and the 1/f noise. In fact, the results clearly show the absence of a connection between measured noise and the Q -4 law. The phase noise at 1 Hz from the carrier exhibits a considerable increase for temperatures below 7K. As previously mentioned, this may be attributed to difficulties with temperature regulation at very low temperatures. According to this work, S y at 1 Hz equals about 1.5 • 10 -20 for the same type of 5-MHz AT-cut resonators. Thus, this result is almost 5 orders of magnitude higher than that shown in [START_REF] Robichon | Frequency stability of quartz crystal at very low temperatures: Preliminary results[END_REF], [START_REF] Gagnepain | Relation between 1/f noise and Q-factor in quartz resonators at room and low temperatures, first theoretical interpretation[END_REF].

Therefore, the previous works do not give an irrefutable answer on the question of the nature and even the value of the resonator flicker noise at liquid helium temperatures.

VII. C

In this work, the resonator phase noise at cryogenic conditions is studied as a function of different parameters. The origins of the excess noise are determined. It is shown that vibration-caused noise could be significantly reduced by an appropriate choice of the device orientation in relation to the cryogenerator's vibration axes. Therefore, temperature instabilities remain the main source of the device phase noise. Estimations suggest that an oscillator based on such resonators working in such conditions can-not outperform state-of the-art room-temperature quartz oscillators. Because it was found that the main limitations result from temperature instabilities, two solutions could be proposed. First, the temperature control can be improved. The second solution is to find a crystal cut with a turn-over point in the temperature-frequency characteristic for liquid helium temperatures because the existence of such cuts is not known. Though FC-cut resonators [START_REF] Suter | Acoustic loss phenomena in alpha quartz resonators over the 1.4-77K temperature range[END_REF], [START_REF] Robichon | Frequency stability of quartz crystal at very low temperatures: Preliminary results[END_REF] already exhibit a turn-over point, its parameters are not satisfactory for temperature compensation (it has a narrow parabolic shape rather than the desired cubic behavior). To find a satisfactory cut, the parameters of quartz at deep cryogenic temperatures must be derived. The identification of the flicker noise source can be a clue to the same problem at room temperature. A Special thanks are given to the staff of the Time and Frequency Department of FEMTO-ST Institute, Besançon, France, for their help and fruitful discussions. R

Fig. 1 .

 1 Fig. 1. Cryogenic system.

Fig. 2 .

 2 Fig. 2. Power spectral density of temperature fluctuations: (1) at the cryocooler second stage, (2) at the device under test (DUT) level with the active temperature control, (3) at the DUT level without the temperature control.

Fig. 3 .

 3 Fig. 3. Device under test (DUT) acceleration spectrum (vertical axis only): (1) DUT acceleration at 7K (not calibrated), (2) charge amplifier noise floor.

Fig. 4 .

 4 Fig. 4. Open-loop measurement scheme for cryogenic resonator instabilities.

Fig. 5 .

 5 Fig. 5. Phase noise spectra of different measurement experiments: (1) measurement system noise floor, (2) amplifier phase noise, (3) phase noise of the cryogenic assembly without the resonator, (4) phase noise of the cryogenic part with the resonator. (A) deterministic instabilities caused by the cryogenerator (1.7 Hz and its harmonics), (B) synthesizer phase noise.

Fig. 6 .

 6 Fig. 6. Allan deviation of the closed-loop frequency stabilization system locked on the A-mode of 5th overtone measured (2) within the first 12 hours of resonator operation inside the cryocooler, (3) measured after at least 60 hours of resonator permanent operation in cryogenic environment, and compared with the stand-alone oscillator (1), i.e., the voltagecontrolled oscillator.

Fig. 7 .

 7 Fig. 7. Phase noise power spectral densities: (1) measurement phase noise floor, (2) cryogenic part phase noise for the 5th overtone of the Amode, (3) cryogenic part phase noise for the 3rd overtone of the A-mode, (4) cryogenic part phase noise for the 5th overtone of the B-mode.

Fig. 8 .

 8 Fig. 8. Phase noise power spectral densities: (1) measurement phase noise floor, (2) cryogenic part phase noise for the 5th overtone of the Amode with -4.5 dBm synthesizer output signal, (3) cryogenic part phase noise for the 5th overtone of the A-mode with +0.5 dBm synthesizer output signal.

Fig. 9 .

 9 Fig. 9. Phase noise power spectral densities: (1) measurement phase noise floor, (2) cryogenic part phase noise for the A-mode 5th overtone measured within the first 12 h of cryogenerator operation, (3) cryogenic part phase noise for the A-mode 5th overtone after at least 24 h of cryogenerator operation.

Fig. 10 .

 10 Fig. 10. Phase noise power spectral densities: (1) measurement phase noise floor, (2) cryogenic part phase noise for the 3rd overtone the Amode measured within the first 12 h of cryogenerator operation, (3) cryogenic part phase noise for the 3rd overtone of the A-mode after at least 24 h of cryogenerator operation.

Fig. 11 .

 11 Fig. 11. Phase noise power spectral densities of the resonator (the 5th overtone of the A mode) installed vertically at different operating temperatures: (1) 5.3K, (2) 6K, (3) 7K, (4) 8K, (5) 9K.

Fig. 12 .

 12 Fig. 12. Phase noise power spectral densities of the resonator (the 5th overtone of the A mode) installed horizontally: (1) 5.3K, (2) 6K, (3) 7K, (4) 8K.

Fig. 13 .

 13 Fig. 13. Model of the resonator phase noise at cryogenic temperatures. τ is the resonator relaxation time τ = 2Q l /ω 0 . ϕ inp (t) and ϕ out (t) are the input and output phase fluctuations, respectively.


Alain Bauer

Wells

The Revenge of the Germs

Keywords: Crisis Management, Governance, Germs, COVID, Security

In 1898, H.G

----------------------------------In 1898, H.G. Wells published the War of the Worlds, a novel in which he imagined the first victorious invasion, then the final destruction of extraterrestrial forces, militarily and technologically superior, by means of a terrible weapon, but familiar to Earthlings: unidentified microbes suddenly annihilated the Martians.

On October 30, 1938, the eve of Halloween in the United States, the radio version of the story by the young Orson Welles, for which he was famous, became a national hoax and a model for the manipulation of people by the mass media.

Today, we are faced with a dramatic event that is an inverted mirror image of that classic of anticipation, a dramatic event that is no less a part of science, but not a part of fiction. For the first time in the history of humanity, a total crisis has struck the world as a whole.

The radical novelty of this crisis lies in the fact that it brings together these two dimensions and that, in order to understand it, it is necessary to grasp these two key concepts in a panoramic way.

At the beginning of the nineteenth century, looking at the Napoleonic adventure and extrapolating from it, Carl Von Clausewitz forged the idea of "Total" war to designate an extreme type of conflict where a belligerent mobilizes all its resources to annihilate an adversary who is himself ready to eradicate it, as the two world wars would become a terrible demonstration of. At the end of the twentieth century, Harvard professor Theodore Levitt popularized the concept of "globalization" to characterize the interactive integration of individuals, corporations, governments, and businesses into a single world economy that gradually shaped a single global village. Both expressions have remained. At the beginning of 2020, they collided and now, under the effect of a hitherto unknown acceleration, take on a completely different meaning.

Total, global: such is the unprecedented crisis that is hitting all the faces of the Earth entirely and simultaneously. This crisis is neither military nor economic, neither industrial nor financial, neither social nor political. It is all of these things at the same time. It is first and foremost a health and medical crisis. Above all, it is both individual and collective. We are all experiencing it, everywhere and at the same time, in all its aspects: personal, family, business, national, and international. This crisis overwhelms our consensual amnesias. The pandemic of 1918, known as the "Spanish flu" or "Annamitis fever"-although it seems to have originated in Kansas-caused more deaths than the Great War, but its memory was drowned in that of the hell in the trenches. The stock market crashes of 1929 or 2008 showed the chaos that the race to financialization could lead to, but once contained, they faded from our memory to take the rank of accidents that had been controlled.

Why our astonishment at the appearance of the coronavirus? Because we chose oblivion. Because we did not take the time to prepare. However, apart from the Spanish flu of 1918, since the Russian flu of 1889, the Asian flu of 1956, the Hong Kong flu of 1968, or the H1N1 of 2009, we have not lacked alerts or high quality scientific studies to alarm us. Without success.

Even more serious, since Charles Delorme, the French physician of kings who invented the beak mask in 1619 to fight the plague, but who struggled to convince the authorities to adopt it, or the Hungarian doctor Ignace Semmelweis, who explained in 1850 to medical luminaries in Vienna the hygienic imperative of washing hands to counter contagion (but who was the laughing stock of these mandarins), we have regressed rather than evolved. It took Louis Pasteur for things to finally change. At least, a little. Then we unlearned the basic principles. Very quickly we thought we were invincible and dreamed of immortality. We imagined a "transhuman" whose microchip had just fried for lack of available oxygen.

Fascinated by the conquest of space, we forgot the power, resilience, and resistance of microbes-those microorganisms invisible to the naked eye, vibrios, bacteria, parasites, and viruses that are considered to be the first forms of life that appeared on Earth more than three billion years ago, that survive by invading a host cell that they then cannibalize, that have far preceded the human species and pose a recurrent threat to it in the form of epidemics and pandemics.

The scholarly community has not escaped this syndrome. It has been divided both internationally and nationally, although partial consensus has emerged as the epidemic has developed. Like many of us, scientists have found themselves judging that "incredible" and "unthinkable" rhyme with "impossible." The West had already made a similar mistake by brushing aside, before the 2001 attacks, the nuisance capacity of al-Qaida and others.

This crisis thus has an anthropological part to it, as it makes us brutally rediscover the vulnerability of our condition. This crisis is also economic, because it consists simultaneously of a crisis of supply and a crisis of demand within a system that is more globalized than ever before, and it clearly poses a risk of a long and dangerous recession on many levels. Finally, this crisis is political, because it affects all institutions and powers, whether local or central, governmental or continental, state or international, indiscriminately. We must, unfortunately, add to the above in the case of many countries, particularly France: • a crisis in health organization that reveals a fundamental error of considering public health as a cost and not as an investment; • an industrial crisis that, although long-standing, is immediately worsening and whose shock wave will be felt for a long time; • a structural crisis affecting the service sector, which is resisting as best it can as the pandemic "domestic front" that is disrupting every distribution circuit and supply chain, is revealed;

• an administrative crisis that amplifies the endless errors of the state bodies, which produce the best and are capable of the worst (for example, the Regional Health Agency of the Grand Est deems it normal to propose massive job cuts for care workers at the height of the epidemic!); • a military crisis that, as in 1918, but in limited theatres and often in the context of external operations, exposes the troops involved to an invisible and uncon-trollable danger; • a security crisis that leaves the police and gendarmes destitute, while their missions are redirected essentially toward the supervision of the population.

Unfortunately, this list is not exhaustive.

Unpredictable, incoherent, inexperienced: such were the views of most governments and few will emerge unscathed from their generally chaotic manage-ment of the event. Some chose the Azincourt option and remained stunned by an event that surprised and overwhelmed them. Others took the Maginot option and believed either in the practice of limited containment or in the desirability of herd immunity. Finally, a few have chosen the Waterloo option, which inevitably sees the operations carried out against the odds ending badly, without taking into account the extent of the risks incurred by the populations: England, the United States, and Brazil are now paying a high price for this.

General MacArthur said that "the battles lost can be summed up in two words: too late." In the face of an exceptional crisis, humility should not prevent lucidity. If we had all been affected in the same way, we would have had to believe in fatality. But, before our eyes, one country effectively used preventive and proactive methods (Taiwan), while two others used more or less decisive techniques (South Korea and China)-and this in very different social and political configurations.

Hitting the world as a whole, the crisis has shaken all international bodies, the WHO in the first place and all continental organizations, including the Euro-pean Union, and has exacerbated all geopolitical tensions, starting with the fun-damental opposition between China and the United States. It has thus shown, as never before, how inextricable the links between foreign and domestic policy are now within each state and between all states.

From January 2020, in Wuhan where it all began, a city that is a symbol in the imagination of the Middle Kingdom, the posture of Mayor Zhou Xianwang, candidate for the highest offices within the Communist Party, weighs heavily in the initial concealment of information. In Beijing, the event was used to hasten the purging of the security apparatus by arresting Sun Lijun, the last survivor of the so-called Shanghai team affiliated with former President Jiang Zemin, on cor-ruption charges.

Meanwhile, the international press is having fun and is mainly interested in the folkloric city market of Wuhan where pangolins and bats are traded.

The existence of a P4 laboratory, not far from the market, is revealed to the general public in April 2020. Largely built by France, this institute is dedicated to the study of "class 4 pathogenic" microorganisms, which are highly dangerous and lack a vaccine or treatment. Like its forty or so counterparts around the world, it requires maximum safety conditions. Have they been met? This question will al-low for guesses and accusations to be made.

A cradle on the other side of the world

Wuhan, the capital of Hubei province, has often taken a decisive place at the heart of Chinese history. Cradle of the revolt against the Qing, the uprising in Wuchang (Wuhan district) on October 10, 1911 heralded the fall of the empire and the end of five thousand years of dynastic power. Since then, the "double ten" (tenth day of the tenth month) has been celebrated as a national holiday, but the central government also views the city with suspicion as "indicative of the signs from heaven to the Emperor."

On June 11, 1938, the Japanese imperial army attacked the provincial capital to meet strong resistance and suffer its first defeat. The fighting lasted four months. Wuhan will remain like Verdun or the Chinese Stalingrad.

In 1967, China is in the midst of a Cultural Revolution. Once again, Wuhan stands out for the army uprisings and bloody confrontations it experiences. Mao is forced to travel to the area in order to restore order to the disorder he has caused. The Wuhan incident will remain a turning point in the "red" chronicle.

Extremely annoyed by the sale of a P4 laboratory to China at France's ini-tiative, the United States has kept a close eye on the project. Following an authorized visit by US diplomats in 2018, an alert note on security failures was sent to Washington. It fueled the

A secret laboratory

Founded in 1956 and qualified as an institute of microbiology between 1962 and 1978, the Wuhan Institute of Virology is a research center administered by the Academy of Sciences. Located in Jiangxia district, it has been home to China's first P4 laboratory since 2015.

An anti-seismic bunker of 3000 square meters spread over four levels, the enormous Fort Knox-type building stands in the Zhengdian industrial zone, some 30 kilometers south of Wuhan. But this clever undertaking is also the result of a diplomatic agreement.

In 2003, China was confronted with the severe acute respiratory syndrome (SARS) pandemic, an infectious disease caused by a coronavirus, SARS-CoV, and transmitted from animals to humans. President Hu Jintao then asked France, which had lent him P3 mobile laboratories, to help him build an inte-grated P3 and a P4.

In his book France-China, les liaisons dangereuses, Antoine Izambard recalls the background to this negotiation: "The powerful Chinese Academy of Sci-ences, the equivalent of the CNRS (and in particular the main shareholder of the world leader in computer sales, the Chinese giant Lenovo), announced in Paris that it wished to acquire a high biological safety laboratory. The request has received a very mixed reception [...] If France is helping China to build a P4 laboratory, how can it be sure that the technology it is going to transfer will not be diverted by Beijing to develop bacteriological weapons?"This fear is "supported by the suspicions of the French intelligence services about the existence of a Chinese o.ensive biological programme."

The Assembly of 100, the scientific and collegiate body of the Institut Pasteur, signifies its disapproval, which the Prime Minister, Jean-Pierre Raffarin, ex-pressed after discussing the project with Professor Chen Zhu, who was trained in Paris and is close to President Jiang Zemin. The agreement was signed in 2004 by Foreign Minister Michel Barnier. It provided for a bilateral monitor-ing committee chaired by Professor Alain Mérieux, who would eventually leave it in 2015: in the meantime, China has not invited any of the fifty French scientists supposedly involved in the laboratory's work.

Started in 2011 and inaugurated in 2017, the P4 is not yet certified by the WHO at the beginning of 2020. feud between the two contemporary giants. There is no shortage of accidents in laboratories. Including on the North American continent. Could Wuhan's P3 or P4 have leaked the coronavirus? Worse yet: could it have been the result of intentional manufacture with lethal intent? Quickly, the conspiratorial hypotheses come to confront the scientific theses. With very few exceptions, the "signature" of human intervention is not identified in any of the virus's sequences. But Dr. Jean Claude Perez, a former collaborator of Professor Montagnier's, suggests a different voice regarding a potential sequence anomaly in RaTGT3 (the original strain).

While the possibility of an accidental escape of the coronavirus remains widely considered, no one can commit beyond this conjuncture at the time of writing.

While the two great powers vying for world leadership have a new oppor-tunity to confront each other, observers are pointing out that China's ecological novelty and America's organic disorder are now, for the first time, taking their place as a matter of course in the eyes of world opinion.

In the decade following the attacks of September 11, 2001, the anthrax ba-cillus, responsible for anthrax, entered the terrorist arsenal and was sent for examination in unsecured shipments to more than two hundred research cen-ters around the world, which were responsible for the contamination of at least an equal number of scientists.

In November 2014, an investigation by the British Health and Safety Executive revealed that, over the previous five years, the total number of incidents in the various high-risk laboratories had been close to one hundred.

In February 2019, Lynn Klotz of the Center for Arms Control and Non-Proliferation published a report to this effect. Between 2009 and 2015, she count-ed 749 such incidents, of which 594 were due to human error, mostly in the United States, but also in the Netherlands. The National Institutes of Health (NIH or the coordination of the American Institutes of Health), for its part, acknowledges 128 incidents over the period from 2004 to 2017, while its coun-terpart, the Centers for Disease Control and Prevention (CDC), attests to four major accidents involving the Ebola or Marburg viruses in various P4s.

In June 2019, the main military laboratory of this kind in the United States, USAMRIID in Fort Detrick, was shut down urgently for "security breaches." This is not, however, a cause for celebration in France, which is also being hit hard by the revealing dimension of the crisis. The national triptych "Negation, Minoration, Ejection" (in everyday French: "ce n'est pas vrai," then "ce n'est pas grave," and finally "ce n'est pas de ma faute") will serve as an excuse. There is no point in going back here on the "masquerade" of the tricks and turns of a Health Minister who, dreaming of becoming another Simone Veil, took the risk of being caricatured as a new Doctor Garretta! In France's chaotic management of the ep-idemic, total containment, which is nonetheless one of the conceivable and effective weapons, ultimately appeared to be the fruit of unpreparedness, denial, and scarcity, even though the previous pandemic had been perfectly anticipated.

Between 2007 and 2012, following the outbreak of the H1N1 virus, the state had indeed built a remarkable system against pandemics-a system that, fortunately, was not needed at that time. With the same determination, the state then deconstructed its tool in the belief that what had not happened would never hap pen. It was as if, every year, people asked for their're insurance or health insurance premiums to be reimbursed because they did not have to use it.

Very often, what seems new appears mostly as what we had lost sight of. Administrative amnesias also have a lasting impact on crisis management. As Michel Rocard was fond of reminding us: "When it comes to major bureaucratic disasters, we have to rely much more on bullshit than on conspiracy. The former is within everyone's reach, and therefore widespread, while the latter requires a great deal of intelligence and organization, and proves to be much rarer than one might think."

In matters of police, defense, justice, and health, the political choices of recent years have been dictated above all by accountants. Obviously, public money must be well managed-indeed, the French demand it. But is it so badly man-aged in Germany, which seems to have far more equipped emergency beds than in France, both in absolute number and in proportion? Or is it so badly managed in Taiwan, an isolated and "encircled" country, but with a recognized dynamism, which has perfectly mastered the pandemic?

Contrary to what is too often thought, rigor is not austerity, and investment is often a useful expense, much more than a risky cost. The creation of speculative bubbles is generally more the result of an accounting entry, fair value, than a phenomenon of pure capitalism.

The management of chaos is a difficult art, and one cannot systematically make current leaders bear the consequences of old decisions, going back a decade, sometimes two, but also of a structuring culture that would like, against any politi-cal decision, that an invisible hand, sitting at the Treasury, remain the only regalian tool that must always rule everything. If rigor is a value that a taxpayer cannot ignore, it alone cannot prevent the beautiful risk of investment, nor can it reverse priorities by forgetting the value of the human being.

It is all well and good to salute and consecrate the "heroes" of everyday life, but we cannot ignore the degraded conditions in which their heroism had to express itself, nor the fact that this outburst is due above all to the incredible agility of the national D system. In any event, it should never be forgotten that it was the very people that the administration wanted to sacrifice who saved the hospital system through their dedication, will, creativity, risk-taking, and dedication. Like the policemen (too many, too well paid, not working enough), the cashiers (to be eliminated to make way for machines), the bakers and pharmacists (remnants of the ancient world good for museums), not to mention the teachers (necessarily shirkers), in short, all contact professions that have also become contact profes-sions, allowing the country to hold on despite everything.

In addition, it is hard scientists, social scientists, and also elected representatives, especially parliamentarians, who have patiently prevented, informed, and sometimes prepared the French people by fighting against the inertia and sufficiency of a restive administration.

The state has often shown that it knows how to be a true strategist, but also that it regularly needs to be confirmed in its choices by confrontation with reality. Everyone can see that we are going through this ordeal painfully. Today we are paying dearly for our lack of prevention tools. As always, we are paying dearly for our lack of prevention tools. As in criminal or terrorist matters, the lesson is a cruel one. Let us make sure it will not have been in vain. Let us take advantage of this opportunity to prepare for the aftermath by giving a clear, coherent, simple, and direct public speech. Now is the time to face the crisis. After the obligation of confinement, what is at stake is the pedagogy of deconfinement. The most studied and most accepted models throughout the world outline the contours of this process.

The following sketch emerges:

• The peak of the pandemic is followed by a plateau period that is essentially the result of the effects of successful containment. The flow of hospitalized patients is reduced, but the stock remains at a high level. When the decrease in the number of severe cases reaches a significant level, it is necessary to set up a tool for chronological (return to the point where it all began), geographical (on the basis of coherent territories of a manageable size), virological, and even, if possible, serological (but only with tests that make it possible to identify those who are relatively immune, those who are asymptomatic, those who have recovered, and those who are still vulnerable) deconfinement.

• Once these tests have been carried out on the largest possible part of the population concerned in a delimited territory, a progressive deconfinement is possible on the condition that masks and protective gestures (known as barriers) are consistently worn over the long term, that reception in public and commercial spaces is reorganized, and that the occupancy rate in public transport and col lective and convivial places is reduced.

• All this will take place while awaiting the hypothetical arrival of a treatment and a vaccine and therefore getting used to a pandemic that lasts and survives for a long time.

These measures will also have a positive impact on seasonal influenza, which could finally be considered to be a serious and dangerous disease that must be fought against, causing thousands of deaths every year in general indifference.

Hence the urgent need to rediscover what the ethics of responsibility means. The virus does not spread by itself: it is individuals who spread it. It is therefore up to us to make a conscious choice. Either encourage the epidemic, washing our hands of it in the manner of Pontius Pilate and thus leaving the other to die, or fight the epidemic by washing our hands in order to protect the other. In other words, in practice, organize resistance, systematize precautions, and move to targeted confinement and generalized testing in order to ensure together the protection of all by all.

Breaking the chains of transmission is the only real way out of the health crisis. Aftershocks, which are very likely to occur as long as a large part of the population remains vulnerable, will undoubtedly require localized reconfinements of lesser intensity. The pandemic wave will thus be replaced by a multiplication of clusters, or targeted and sporadic "outbreaks," which will be easier to control if several conditions are met. It is here, as long as they are available and accessible, that proper virological tests (i.e., PCR) will find their place, in particular to identify asymptomatic carriers. Above all, however, a successful exit from the crisis will require citizens to comply with barrier measures, to accept tracing and, if necessary, the isolation of contact cases, and the prudent conduct of each individual guaranteeing the informed preservation of all. This is what used to be known as civic-mindedness. In other words, nothing decisive will happen without a broad collective commitment to promote and establish the new culture of living together without contaminating others.

A new way of living together will have to be organized outside the stable, the constant, the consistent, the orderly, the determinable.

A new way of living together will have to be established on the basis of the observation, without discussion, that the initial delay in the face of the health crisis, in addition to its human, economic, and social cost, will not have been made up in the time announced by the political authorities. And this same power will have lost a large part of its authority as crisis manager, even though it had managed to preserve it during the wave of terrorist attacks.

A new living together will be heckled, will take on the face of dynamic chaos, and will force citizens and their organizations to move away from orderly and counted certainties to reinvent themselves.

A renewed living together will exist, like after all wars, as this conflict has been dubbed, even though it has no visible enemy.

Unfortunately, bad governance, lack of courage or credibility, may create side effects creating waves after waves, or sometimes peaks after peaks, until somebody finally create confidence with the people and enhance a real strategy using the Taiwan democratic model. The total and global crisis that we are experiencing can become the lever for the indispensable redefinition of liberalism in each of its terms. It has everything to be the major element of a better balance between shareholders and employees, sustainable capitalists and financial speculators, investors and profiteers. It is capable of bringing about long-term rebalancing in favor of increased protection of the planet, active relocation of strategic industries, and reinforced regulation of the financial markets.

The sudden shift from skepticism to panic that many leaders around the world have experienced and shown is now in danger of taking everything in its path, where as the main thing now is the battle that must be won. We must take advantage of this tragic moment to restore meaning to the most important investment: the investment we must make for life.


Alain Bauer

Christophe Soullez

2019: Homicide Big Comeback in France

Keywords: France, Homicide, Violence, Statistics

The annual number of homicides is one of the main statistics for criminologically characterizing a territory, be it a city, a region or a country. It can be used to conduct situational analyses of the recent past or, if looking at a longer time period or comparing jurisdictions, it can be compared to the number of people living in a jurisdiction. This gives the reference indicator for the level of violence, the homicide rate. The balance sheet published at the beginning of 2020 by the Ministry of the Interior nevertheless confirms this deterioration with an increase in the number of homicide victims (including assault and battery followed by death) of 12.4% in one year, thus beating the tragic record of 1983 (3,562 acts against 3,183) and becoming the worst result since 1972 in gross numbers and the third in relation to the population with a rate of 5.32 per 100,000 inhabitants against 5.68 in 1983 and 5.42 in 1986. In any case, a profound return of physical violence seems to be taking place, particularly in the West. It is being ignored, whether voluntarily or involuntarily, or underestimated. Its causes are undoubtedly multiple, but the increase in the number of victims cannot be underestimated for much longer.

The annual number of homicides is one of the main statistics for criminologically characterizing a territory, be it a city, a region or a country. It can be used to conduct situational analyses of the recent past or, if looking at a longer time period, or comparing jurisdictions, it can be compared to the number of people living in a jurisdiction. This gives the reference indicator for the level of violence, the homicide rate. It is generally expressed per 100,000 inhabitants.

The annual number of homicides is usually part of the statistics available promptly after the end of each year. Indeed, checks carried out in the course of the year make it possible to have almost exhaustive information on the victims of homicides from the previous year at the beginning of January. In some territories, the annual homicide toll is thus commented on very early on. This is the case, for example, in the major cities of the United States, where the 2019 homicide figures were the subject of press articles, sometimes as early as December 31st. We were thus able to find out about the trends observed, whether there were declines in cities such as Chicago, New York (except for homicides), or Los Angeles, or peaks in other cities such as Baltimore and Philadelphia.

But, while we are rightly moved by the increase of mass murders and the homicide rate in the United States (about 5 per 100,000), and even more so in countries such as Mexico (about 20 per 100,000), or Brazil (about 30 per 100,000), an inconspicuous but increasingly accentuated trend is affecting France and is raising its rate from the low point reached in 2014 (close to 1 per 100,000).

The most shocking part of this trend, the "feminicides" (formerly uxoricides), is rightly shocking. But this situation seems to hide an even more disturbing one: that the overall numbers of homicides and attempts (failed homicides) has increased.

A detailed analysis of the police homicide count tool (Etat 4001) since 1972 shows identified cycles and a clear deterioration in an accelerating phase.

In order to get closer to the truth (the homicides taken into account by the police are not the same as those recorded by other services such as Health or Justice), we considered that the error variable was stable over the period, as the Ministry of the Interior's measurement tool had not been structurally modified (it should be noted, however, that attempted homicides are only clearly identified from 1987 onwards).

Moreover, since 2015, following a report by the National Observatory of Delinquency and Penal Responses (ONDRP) on the double counting of certain homicides, the Ministerial Statistical Service of Internal Security (SSMSI) has been making corrections that make the tool more unstable than usual, even though this is often for a technically justified cause. Thus, from 1994 to 2014, the National Observatory of Delinquency and Penal Responses (ONDRP) had described a phenomenon of continuous decline in the homicide rate, the main component of a Western movement called crime drop in Anglo-Saxon countries.

In an article published in December 2015, it was reported that between 1994 and 2014, the homicide rate had fallen by almost 60% in metropolitan France.

In November 2018, in the newspaper Libération, Cédric Mathiot, a journalist who pioneered fact checking in France, looked into the subject, following a question asked via the Checknews website by Cyril Rizk, former head of the ONDRP. In the article entitled "Homicides: Beauvau is afraid of his number" we learned that if we confine ourselves to "only homicides (excluding intentional assault and battery followed by death, which the interior ministry counts) in metropolitan France" their 12-month level was "clearly on the rise, breaking the trend of decline and then stagnation observed for nearly 15 years." Cyril Rizk then offered an explanation: the attacks "have changed the nature of homicidal violence committed in France. They have also changed the way the issue of violence is addressed in public debate. The fight against terrorism has become the number one security issue, relegating everyday security problems to the background. Monthly figures from the police and gendarmerie now suggest that something may have slipped through the cracks.

In other words, no one would have seen anything. The interior ministry had been contacted several times but had not replied, first questioning the figures provided and then saying that it wanted to "get to the bottom of this" before commenting on them.

However, according to provisional official data published on 7 January 2020, there has been an 8.5% increase over one year in metropolitan France, i.e. 76 more victims between 2018 (894) and 2019 (970). However, the provisional data should still be treated with caution. The provisional figure for 2017 had been revised from 896 to 825, while the 2018 figure had been revised from 894 to 845. The final fig2019: Homicide Big Comeback in France 5 ures for 2015 and 2016, 872 and 892 victims respectively, have the particularity of including the mass crimes resulting from the attacks of 13 November 2015 and 14 July 2016.

We are therefore faced with the strong possibility that the final figure for homicides in 2019 could exceed 900, which would make it a deadlier year than the years when the Bataclan attacks or the killing of the Promenade des Anglais in Nice occured, albeit without any major attack.

But there is also a clear trend towards homicide (homicides, attempts and intentional assault and battery resulting in death) which reverses a long process of decline in ultimate violence. Indeed, if all homicides and attempted homicides are taken together, the summary table shows a situation that slowly deteriorated between 1972 and 1983 (from 2,093 to 3,183 incidents, i.e. an overall increase of 52 per cent).

There are considerable differences in the settlement of accounts: 69 in 1972, 105 in 1973, 85 in 1974, then after a certain stability, 184 in 1983). The same is true for children, with a high level in 1972 (140), a rapid decrease (44 in 1978) and a sharp increase in 1982 (109). From 1987 onwards, erratic movements can be observed (sharp fall in 1987: 2,496 victims including 59 children) followed by a sharp rise in 1988 (2,835 including 101 children). The level of homicide will remain high with a good year in 1994 for minors (only 13 victims).

It was not until 2009 that the threshold of 2,000 victims was broken at the bottom (1,767 incidents). This level will rise again in 2011 and accelerate sharply in 2015 (2,805 victims following the attacks of 13 November), and will continue until 2018 with 3,168 recorded incidents (the highest level in 35 years and the second worst record in modern homicide statistics), including 84 settlements of accounts (the highest level in 10 years) and 67 minor victims.

The balance sheet published at the beginning of 2020 by the statistical service of the Ministry of the Interior nevertheless confirms this deterioration with an increase in the number of homicide victims (including assault and battery followed by death) of 12.4% in one year, thus beating the tragic record of 1983 (3,562 acts against 3,183) and becoming the worst result since 1972 in gross numbers and the third in relation to the population with a rate of 5.32 per 100,000 inhabitants against 5.68 in 1983 and 5.42 in 1986. The data will have to be adjusted in the coming weeks, but the characteristics of the phenomenon will also have to be clarified: methods of operation (firearms, knives or other weapons), profiles of victims and perpetrators, and the places where crimes are committed.

In any case, a profound return of physical violence seems to be taking place, particularly in the West. It is being ignored, whether voluntarily or involuntarily, or underestimated. Its causes are undoubtedly multiple, but the increase in the number of victims cannot be underestimated for much longer.

For, behind this violence of everyday life, masked by attacks or mass murder, there is a global social process of questioning a founding achievement of what makes civilization what it is: the right to live. For women, minors ... and men, the violence that is coming back seems to be overwhelming the whole society, and not only in the streets ...


Alain Bauer

Espionage Makes a Big Comeback

Keywords: Spy, Espionage, Le Carre, GRU, Five Eyes

In the space of a few weeks, an attempt in Great Britain to eliminate a Russian GRU traitor who had defected to the West, reports of former French foreign intelligence agents spying for China, and the comic real-life episode of the faked assassination of a Russian journalist who had fled to Kiev, staged by Ukrainian secret services, have brought memories of twentieth-century spy stories back into our minds.

The adventures of James Bond and those written by John Le Carré have recently made a triumphant return to our screens in real life.

In the space of a few weeks, an attempt in Great Britain to eliminate a Russian GRU traitor who had defected to the West, reports of former French foreign intelligence agents spying for China, and the comic real-life episode of the faked assassination of a Russian journalist who had fled to Kiev, staged by Ukrainian secret services, have brought memories of twentieth-century spy stories back into our minds.

Since the Snowden affair, the public has gradually gained the impression that cyber-breaches have supplanted the previous generation of espionage and that the outdated techniques used by Le Carré's Smiley have been filed away in the post-war nostalgia archive.

It was thought that war could be waged remotely by videogame controller and we found that it still led to the same cortege of mutilated corpses and barbaric destruction of cities and civilizations. This belief also applied to what was, in German, previously called "the profession of the nobles."

Of course, everyone remembers that there used to be spies and people who were spied upon. Could it be that states only have old enemies, adversaries and rivals who could become enemies once more? General de Gaulle summarized this perspective very astutely when he said: "States do not have friends, only interests."

If we look at the matter more closely and extricate ourselves from the stereotypical emotions of continuous alternative disinformation, we can identify some fundamental points:

• All the major powers eliminate their spies. Generally they do this from a legal perspective, and occasionally in a more definitive way. According to the top historians in the field, France has never shied away from doing this. Recently, a former president, who should not have said what a book revealed, told journalists he had given instructions for the targeted killing of jihadists (a revelation that is more complicated to justify in a country that has fortunately removed the death penalty). Great Britain, the United States, Russia, China .... The Soviet Union even introduced a specialist service (SMERSH) in 1943 whose primary activity was to eliminate traitors, deserters, spies and, above Espionage Makes a Big Comeback 105 all, political opponents of Stalin. All states, or almost all, can take drastic and definitive measures, especially when a traitor flees his or her country ...

• All the major powers engage in espionage, whether proactively, as a precaution, or "just in case." Even close allies like the United States and Israel have experienced a major crisis with the Pollard affair, which drew large-scale media coverage and is not such an isolated case as may have been believed. The Snowden revelations showed the capacity of the United States to take action, particularly but not exclusively in economic and industrial terms, and not just against France, the ugly duckling of the Atlantic Alliance, but also by targeting its close friends. This includes fellow members of the "Five Eyes" alliance (Australia, Canada, Great Britain and New Zealand), which has shared intelligence tools since 1941.

• As for the farce in Ukraine, it would be no more than a comical footnote if the operation had not, at the same time as saving a potential target, cast permanent doubt on all operations that might occur. This "fake" attack has provided the conditions of justification for all alternative realities in the future, and is more than could have been hoped for by those who may have had an interest in eliminating the journalist. But journalists are dying, not only those on assignment in combat zones, but also those who are being targeted directly and personally. More than 1,000 have died over the last fifteen years according to Reporters Without Borders. This has happened in the East, in South America, in Africa, in Asia-and also in the heart of Europe, recently in Malta and Slovakia.

Intelligence is built around a number of crafts (gathering, analysis, intervention) and a number of cultures (espionage, counter-espionage, anti-terrorism). While wars between states have for a long time primarily been waged based on traditional frameworks, asymmetric wars, guerilla activities and infra-state terrorism have brought about fundamental change.

The revolution in terrorism that ISIS has succeeded in establishing has disrupted the usual rules: the range of terrorist profiles is now so diverse that typical profiles no longer exist, operating procedures are now so varied that there are no longer any signature methods, and the mechanisms for making demands are now so opportunistic that it is hard to know what to believe any more.

Accelerating its return to analysis, anti-terrorism has incorporated key methods that are now making it possible to rebalance operations, particularly at the French General Directorate for Internal Security (DGSE). However, the emergence of complex and multiple forms of terrorism that are hybrid and evolving has not replaced traditional problems. It has only added new tasks and risks to those already in existence.

Something that deserves attention is the recent media coverage of files dating back several decades, following the decision taken by the head of the DGSE in April 2017 to judicialize internal mechanisms. This is due less to the decision being a move that allows these mechanisms to catch up with common law, and more down to the fact that this information was leaked just before Macron's visit to China. Was it a personal message to the head of the armed forces to show more prudence in antiterrorist security cooperation? Could it have been a diplomatic message aimed at China? Or was it a message reminding the government of its responsibility not to neglect the implications of counter-espionage? We will need to wait for a few months or maybe even years to get to the root of the matter and its sudden raised profile. Three cultures. Three crafts. Civil and military services, at home and abroad, that are better coordinated and better suited to sharing what needs to be brought together without putting sources in danger: this is the balance of development that it befits the state to implement. After this crucial rebalancing, it will be necessary to find ways of developing preventative and proactive tools. Consequently, France's Intelligence Academy-which is judiciously placed under the authority of the National Centre for Counter Terrorism and its academic partners-will need to be given the means to become a true school of intelligence capable of dealing with identified and existing threats.