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We are developing a single-ion optical clock based on a surface-electrode (SE) trap that we will operate with $^{171}$Yb$^+$ ions on the electric quadrupole transition at 435.5 nm. We present heating rate measurements performed with a prototype SE trap. We also introduce a new, micro-fabricated SE trapping chip using silicon on insulator technology. Electric tests were performed under ultra-high vacuum using a testing chip, including breakdown voltages measurements and flashover detection. We present suitable trapping parameters for this chip, as well as a road-map for improving its design., Comment: 10 pages, 6 figures

We report on the development of a sub-kelvin, single-crystal silicon Fabry-Perot cavity. Operating such a cavity below 1~K should reduce the thermal noise limit of the cavity, and by this way address the current limitations of ultrastable lasers. To further decrease mechanical losses, mirrors with silicon substrates and crystalline coatings are optically contacted to the spacer, resulting in a room-temperature finesse of 220,000. To operate our cavity at sub-kelvin temperatures, we use a dilution refrigerator able to reach temperatures down to 10 mK. We have designed a mechanical mount to house our cavity in such a cryostat, with optimized heat transfer that will decrease the cooldown time for temperatures below 1~K. The estimated thermal noise is projected to be $\sim 7{\times}10^{-19}$ at 100~mK. However, silicon cavities with crystalline mirror coatings at cryogenic temperatures have shown birefringence correlated frequency fluctuations as well as unknown additional noise mechanisms \cite{yu2023, kedar2023}. We have measured a room-temperature TEM$_{00}$ birefringent mode splitting of about 250 kHz. Understanding and measuring these noise mechanisms will be a key to attaining fractional frequency stabilities beyond state-of-the-art., Comment: 9 pages, 5 figures

We present the characterization of a prototype surface-electrode (SE) trap as a first step towards the realization of a compact, single-ion optical clock based on Yb$^+$. The use of a SE trap will be a key factor to benefit from clean-room fabrication techniques and technological advances made in the field of quantum information processing. We succesfully demonstrated trapping at a 500 $\mu$m electrodes distance and characterized our trap in terms of lifetime and heating rate. This is to our knowledge the highest distance achieved for heating rates measurements in SE traps. This simple 5-wire design realized with simple materials yields a heating rate of $\mathbf{8\times 10^3}$ phonons/s. We provide an analysis of the performances of this prototype trap for optical frequency metrology., Comment: 7 pages, 3 figures

The stabilization of lasers on ultra-stable optical cavities by the Pound-Drever-Hall (PDH) technique is a widely used method. The PDH method relies on the phase-modulation of the laser, which is usually performed by an electro-optic modulator (EOM). When approaching the $10^{-16}$ level, this technology requires an active control of the residual amplitude modulation (RAM) generated by the EOM in order to bring the frequency stability of the laser down to the thermal noise limit of the ultra-stable cavity. In this article, we report on the development of an active system of RAM reduction based on a free space EOM, which is used to perform PDH-stabilization of a laser on a cryogenic silicon cavity. A RAM stability of $1.4 \times 10^{-7}$ is obtained by employing a digital servo that stabilizes the EOM DC electric field, the crystal temperature and the laser power. Considering an ultra-stable cavity with a finesse of $2.5\times 10^5$, this RAM level would contribute to the fractional frequency instability at the level of about $5\times 10^{-19}$, well below the state of the art thermal noise limit of a few $ 10^{-17}$., Comment: 6 pages, 4 figures

Progress made in optical references, including ultra-stable Fabry-Perot cavities, optical frequency combs and optical atomic clocks, have driven the need for ultra-stable optical fiber networks. Telecom-wavelength ultra-pure optical signal transport has been demonstrated on distances ranging from the laboratory scale to the continental scale. In this manuscript, we present a Doppler-cancellation setup based on a digital phase-locked loop for ultra-stable optical signal dissemination over fiber. The optical phase stabilization setup is based on a usual heterodyne Michelson-interferometer setup, while the Software Defined Radio (SDR) implementation of the phase-locked loop is based on a compact commercial board embedding a field programmable gate array, analog-to-digital and digital-to-analog converters. Using three different configurations including an undersampling method, we demonstrate a 20 m long fiber link with residual fractional frequency instability as low as $10^{-18}$ at 1000 s, and an optical phase noise of $-70$ dBc/Hz at 1 Hz with a telecom frequency carrier., Comment: 11 pages, 6 figures

We present a first experimental characterization of our ultra-compact, ultra-stable laser. The heart of the apparatus is an original Fabry-Perot cavity with a 25 mm length and a pyramidal geometry, equipped with highly-reflective crystalline coatings. The cavity, along with its vacuum chamber and optical setup, fits inside a 30 L volume. We have measured the cavity thermal and vibration sensitivities, and present a first estimation of the cavity fractional frequency instability at $\sigma_y(1\rm{s})=7.5{\times}10^{-15}$., Comment: 4 pages, 5 figures

The ytterbium atom is widely used in the fields of atomic physics, cavity quantum electrodynamics, quantum information processing and optical frequency standards. There is however a strong dispersion among the reported values of the ${}^1{\rm S}_0 \rightarrow {}^1{\rm P}_1$ transition frequency. In this article, we present two independent measurements of the absolute frequency of this transition performed with two different wavemeters using atomic fluorescence spectroscopy. The cancellation of Doppler shifts is obtained by fine tuning the angle between the probe laser and the atomic beam. The resulting $^{174}\mathrm{Yb}$ isotope transition frequency is estimated to be $\,751\,526\,537\pm27$ MHz., Comment: 9 pages, 4 figure

We examine the role of stratification in determining the scale for turbulent anelastic convection. Motivated by the range of scales observed in convection at the solar photosphere, we perform local numerical simulations of convection for a range of density contrasts in large domains. We analyse both the Eulerian and Lagrangian statistics of the convection and demonstrate that increasing the stratification shifts the scale of the most energetic structures in the flow to smaller scales; furthermore, the relative amplitude of vertical to horizontal flows in the convection decreases with increasing stratification. We discuss the implications of our results to the issue of solar mesogranulation., Comment: Submitted to ApJ

Optical frequency division of an ultrastable laser to the microwave frequency range by an optical frequency comb has allowed the generation of microwave signals with unprecedently high spectral purity and stability. However, the generated microwave signal will suffer from a very low power level if no external optical frequency comb repetition rate multiplication device is used. This paper reports theoretical and experimental studies on the beneficial use of the Vernier effect together with the spectral selective filtering in a double directional coupler add-drop optical fibre ring resonator to increase the comb repetition rate and generate high power microwaves. The studies are focused on two selective filtering aspects: the high rejection of undesirable optical modes of the frequency comb and the transmission of the desirable modes with the lowest possible loss. Moreover, the conservation of the frequency comb stability and linewidth at the resonator output is particularly considered. Accordingly, a fibre ring resonator is designed, fabricated, and characterized, and a technique to stabilize the resonator's resonance comb is proposed. A significant power gain is achieved for the photonically generated beat note at 10 GHz. Routes to highly improve the performances of such proof-of-concept device are also discussed., Comment: 16 Pages, 13 Figures

We report on the characterization, including residual phase noise and fractional frequency instability, of fiber-coupled PPLN non-linear crystals. These components are devoted to frequency doubling 871 nm light from an extended-cavity diode laser to produce a 435.5 nm beam, corresponding to the ytterbium ion electric quadrupole clock transition. We measure doubling efficiencies of up to 117.5 %/W. Using a Mach-Zehnder interferometer and an original noise rejection technique, the residual phase noise of the doublers is estimated to be lower than ${\rm -35\, dBrad^2/Hz}$ at 1 Hz, making these modules compatible with up-to-date optical clocks and ultra-stable cavities. The influence of external parameters such as pump laser frequency and intensity is investigated, showing that they do not limit the stability of the frequency-doubled signal. Our results demonstrate that such compact, fiber-coupled modules are suitable for use in ultra-low phase noise metrological experiments, including transportable optical atomic clocks., Comment: 4 pages, 3 figures

We numerically compute the flow induced in a spherical shell by fixing the outer sphere and rotating the inner one. The aspect ratio $\epsilon=(r_o-r_i)/r_i$ is set at 0.04 and 0.02, and in each case the Reynolds number measuring the inner sphere's rotation rate is increased to $\sim10\%$ beyond the first bifurcation from the basic state flow. For $\epsilon =0.04$ the initial bifurcations are the same as in previous numerical work at $\epsilon=0.154$, and result in steady one- and two-vortex states. Further bifurcations yield travelling wave solutions similar to previous analytic results valid in the $\epsilon\to0$ limit. For $\epsilon=0.02$ the steady one-vortex state no longer exists, and the first bifurcation is directly to these travelling wave solutions, consisting of pulse trains of Taylor vortices travelling toward the equator from both hemispheres, and annihilating there in distinct phase-slip events. We explore these time-dependent solutions in detail, and find that they can be both equatorially symmetric and asymmetric, as well as periodic or quasi-periodic in time., Comment: 7 pages, 5 figures. Submitted to Physica D

We present the design of a compact optical clock based on the $^2S_{1/2} \rightarrow ^2D_{3/2}$ 435.5 nm transition in $^{171}$Yb$^+$. The ion trap will be based on a micro-fabricated circuit, with surface electrodes generating a trapping potential to localize a single Yb ion a few hundred $\mu$m from the electrodes. We present our trap design as well as simulations of the resulting trapping pseudo-potential. We also present a compact, multi-channel wavelength meter that will permit the frequency stabilization of the cooling, repumping and clear-out lasers at 369.5 nm, 935.2 nm and 638.6 nm needed to cool the ion. We use this wavelength meter to characterize and stabilize the frequency of extended cavity diode lasers at 369.5 nm and 638.6 nm., Comment: 7 pages, 5 figures. Proc. of the 8th FSM 2015, Potsdam, Germany. To be published in IOP Journal of Physics: Conference Series

Interferometric wavelength meters have attained frequency resolutions down to the MHz range. In particular, Fizeau interferometers, which have no moving parts, are becoming a popular tool for laser characterization and stabilization. In this article, we characterize such a wavelength meter using an ultra-stable laser in terms of relative frequency instability $\sigma_y(\tau)$ and demonstrate that it can achieve a short-term instability $\sigma_y(1 s) \approx 2{\times}10^{-10}$ and a frequency drift of order $10$ MHz/day. We use this apparatus to demonstrate frequency control of a near-infrared laser, where a frequency instability below $3{\times}10^{-10}$ from 1 s to 2000 s is achieved. Such performance is for example adequate for ions trapping and atoms cooling experiments., Comment: 5 pages, 4 figures

We present the characterisation of three Cryogenic Sapphire Oscillators using the three-corner-hat method. Easily implemented with commercial components and instruments, this method reveals itself very useful to analyse the frequency stability limitations of these state-of-the-art ultra-stable oscillators. The best unit presents a fractional frequency stability better than 5e-16 at 1 s and below 2e-16 for integration times less than 5,000s., Comment: 7 pages, 8 figures

We consider the nonaxisymmetric modes of instability present in Taylor-Couette flow under the application of helical magnetic fields, mainly for magnetic Prandtl numbers close to the inductionless limit, and conduct a full examination of marginal stability in the resulting parameter space. We allow for the azimuthal magnetic field to be generated by a combination of currents in the inner cylinder and fluid itself, and introduce a parameter governing the relation between the strength of these currents. A set of governing eigenvalue equations for the nonaxisymmetric modes of instability are derived and solved by spectral collocation with Chebyshev polynomials over the relevant parameter space, with the resulting instabilities examined in detail. We find that by altering the azimuthal magnetic field profiles the azimuthal magnetorotational instability, nonaxisymmetric helical magnetorotational instability, and Tayler instability yield interesting dynamics, such as different preferred mode types, and modes with azimuthal wave number $m>1$. Finally, a comparison is given to the recent WKB analysis performed by Kirillov $et$ $al$. [Kirillov, Stefani, and Fukumoto, J. Fluid Mech. 760, 591 (2014)] and its validity in the linear regime., Comment: 11 pages, 11 figures

In this paper, we present a very simple design based on commercial devices for the all-optical generation of ultra-low phase noise microwave signals. A commercial, fibered femtosecond laser is locked to a laser that is stabilized to a commercial ULE Fabry-Perot cavity. The 10 GHz microwave signal extracted from the femtosecond laser output exhibits a single sideband phase noise $\mathcal{L}(f)=-104 \ \mathrm{dBc}/\mathrm{Hz}$ at 1 Hz Fourier frequency, at the level of the best value obtained with such "microwave photonics" laboratory experiments \cite{Fortier2011}. Close-to-the-carrier ultra-low phase noise microwave signals will now be available in laboratories outside the frequency metrology field, opening up new possibilities in various domains., Comment: 8 pages, 3 figures. To be published in Applied Optics, early posting version available at http://www.opticsinfobase.org/ao/upcoming_pdf.cfm?id=231146

Here, we study the paramagnetic ions behavior in presence of a strong microwave electromagnetic field sustained inside a cryogenic sapphire whispering gallery mode resonator. The high frequency measurement resolution that can be now achieved by comparing two CSOs permit for the first time to observe clearly the non-linearity of the resonator power sensitivity. These observations that in turn allow us to optimize the CSO operation, are well explained by the Electron Spin Resonance (ESR) saturation of the paramagnetic impurities contained in the sapphire crystal., Comment: 8 pages, 9 figures

Motivated by consideration of the solar tachocline, we derive, via an asymptotic procedure, a new set of equations incorporating velocity shear and magnetic buoyancy into the Boussinesq approximation. We demonstrate, by increasing the magnetic field scale height, how these equations are linked to the magneto-Boussinesq equations of Spiegel and Weiss (1982)., Comment: 14 pages, 0 figures. Accepted for publication in Geophysical and Astrophysical Fluid Dynamics

To create a stable signal from a cryogenic sapphire maser frequency standard, the frequency-temperature dependence of the supporting Whispering Gallery mode must be annulled. We report the ability to control this dependence by manipulating the paramagnetic susceptibility of Fe3+ ions in the sapphire lattice. We show that the maser signal depends on other Whispering Gallery modes tuned to the pump signal near 31 GHz, and the annulment point can be controlled to exist between 5 to 10 K depending on the Fe3+ ion concentration and the frequency of the pump. This level of control has not been achieved previously, and will allow improvements in the stability of such devices., Comment: 17 pages, 10 figures

The molecular structure of a 3d 5 configuration ion in a trigonal ligand field is theoretically established on the basis of the 252\times252 complete energy matrice. The optical absorption and the electron paramagnetic resonance spectra of the Fe3+ ion in the sapphire crystal ({\alpha}-Al2 O3) have been studied by diagonalizing the complete energy matrice. The calculated results are in very good agreement with previous experimental observations. The strength of the transition probabilities between pairs of the energy levels have been calculated to determine the possibility to achieve a population inversion in the ground state by applying optical pumping to the crystal. Preliminary results based on the computed transition parameters and on the maser rate equations model show that a 31 GHz maser signal can be effectively generated depending on the cryogenic resonator design.

We report what we believe to be the lowest phase noise optical-to-microwave frequency division using fiber-based femtosecond optical frequency combs: a residual phase noise of -120dBc/Hz at 1 Hz offset from a 11.55GHz carrier frequency. We furthermore report a detailed investigation into the fundamental noise sources which afflicts the division process itself. Two frequency combs with quasi-identical configurations are referenced to a common ultrastable cavity laser source. To identify each of the limiting effects we implement an ultra-low noise carrier-suppression measurement system, which circumvents the detection and amplification noise of more conventional techniques. This technique now allows the suppression of these unwanted sources of noise to very low levels. In the Fourier frequency range of ~200 Hz to 100 kHz, a fed-forward technique based on a voltage-controlled phase shifter delivers a further noise reduction of 10 dB. For lower Fourier frequencies, optical power stabilization is implemented in order to reduce the relative intensity noise which causes unwanted phase noise through power to phase conversion in the detector. We implement and compare two possible control schemes based on an acousto-optical modulator and comb pump current. We also present wideband measurements on the relative intensity noise of the fiber comb., Comment: 16 pages, 10 figures accepted in

This article reports on the long-term frequency stabilty characterisation of a new type of cryogenic sapphire oscillator using an autonomous pulse-tube cryocooler as its cold source. This new design enables a relative frequency stability of better than 4.5e-15 over one day of integration. This represents to our knowledge the best long-term frequency stability ever obtained with a signal source based on a macroscopic resonator., Comment: 9 pages, 5 figures

The zero-field Fe3+:sapphire whispering-gallery-mode maser oscillator exhibits several alluring features: Its output is many orders of magnitude brighter than that of an active hydrogen maser and thus far less degraded by spontaneous-emission (Schawlow-Townes) and/or receiving-amplifier noise. Its oscillator loop is confined to a piece of mono-crystalline rock bolted into a metal can. Its quiet amplification combined with high resonator Q provide the ingredients for exceptionally low phase noise. We here concentrate on novelties addressing the fundamental conundrums and technical challenges that impede progress. (1) Roasting: The "mase-ability" of sapphire depends significantly on the chemical conditions under which it is grown and heat-treated. We provide some fresh details and nuances here. (2) Simplification: This paper obviates the need for a Ka-band synthesizer: it describes how a 31.3 GHz loop oscillator, operating on the preferred WG pump mode, incorporating Pound locking, was built from low-cost components. (3) "Dark Matter": A Siegman-level analysis of the experimental data determines the substitutional concentration of Fe3+ in HEMEX to be less than a part per billion prior to roasting and up to a few hundred ppb afterwards. Chemical assays, using different techniques (incl. glow discharge mass spectra spectroscopy and neutron activation analysis) consistently indicate, however, that HEMEX contains iron at concentrations of a few parts per million. Drawing from several forgotten-about/under-appreciated papers, this substantial discrepancy is addressed. (4) Excitons: Towards providing a new means of controlling the Fe3+:sapph. system, a cryogenic sapphire ring was illuminated, whilst masing, with UV light at wavelengths corresponding to known electronic and charge-transfer (thus valence-altering) transitions. Preliminary experiments are reported., Comment: pdf only; submitted to the proceedings of the 24th European Frequency and Time Forum, 13-15th April, 2010

We use two fiber-based femtosecond frequency combs and a low-noise carrier suppression phase detection system to characterize the optical to microwave synchronization achievable with such frequency divider systems. By applying specific noise reduction strategies, a residual phase noise as low as -120 dBc/Hz at 1 Hz offset frequency from a 11.55 GHz carrier is measured. The fractional frequency instability from a single optical-to-frequency divider is 1.1E-16 at 1 s averaging down to below 2E-19 after only 1000 s. The corresponding rms time deviation is lower than 100 attoseconds up to 1000 s averaging duration., Comment: 4 pages, 3 figures

This article reports the design, the breadboarding and the validation of an ultra-stable Cryogenic Sapphire Oscillator operated in an autonomous cryocooler. The objective of this project was to demonstrate the feasibility of a frequency stability of 3x10-15 between 1 s and 1,000 s for the European Space Agency deep space stations. This represents the lowest fractional frequency instability ever achieved with cryocoolers. The preliminary results presented in this paper validate the design we adopted for the sapphire resonator, the cold source and the oscillator loop., Comment: 13 pages, 10 figures

In this letter, we report on all-optical fiber approach to the generation of ultra-low noise microwave signals. We make use of two erbium fiber mode-locked lasers phase locked to a common ultra-stable laser source to generate an 11.55 GHz signal with an unprecedented relative phase noise of -111 dBc/Hz at 1 Hz from the carrier.The residual frequency instability of the microwave signals derived from the two optical frequency combs is below 2.3 10^(-16) at 1s and about 4 10^(-19) at 6.5 10^(4)s (in 5 Hz bandwidth, three days continuous operation)., Comment: 12 pages, 3 figures

We report observations of the gyrotropic change in magnetic susceptibility of the Fe$^{3+}$ electron paramagnetic resonance at 12.037GHz (between spin states $|1/2>$ and $|3/2>$) in sapphire with respect to applied magnetic field. Measurements were made by observing the response of the high-Q Whispering Gallery doublet (WGH$_{\pm17,0,0}$) in a Hemex sapphire resonator cooled to 5 K. The doublets initially existed as standing waves at zero field and were transformed to traveling waves due to the gyrotropic response., Comment: Accepted for publication in Phys. Rev. B

We report observations of the Schawlow-Townes noise limit in a cryogenic sapphire secondary frequency standard. The effect causes a fundamental limit to the frequency stability, and was measured through the novel excitation of a bimodal maser oscillation of a Whispering Gallery doublet at $12.04 GHz$. The beat frequency of $10 kHz$ between the oscillations enabled a sensitive probe for this measurement of fractional frequency instability of $10^{-14}\tau^{-1/2}$ with only 0.5 $pW$ of output power., Comment: Published in PRL 100, 233901 (2008)

Motivated by the problem of the formation of active regions from a deep-seated solar magnetic field, we consider the nonlinear three-dimensional evolution of magnetic buoyancy instabilities resulting from a smoothly stratified horizontal magnetic field. By exploring the case for which the instability is continuously driven we have identified a new mechanism for the formation of concentrations of magnetic flux., Comment: Published in ApJL. Version with colour figures

We report the first observation of above-threshold maser oscillation in a whispering-gallery(WG)-mode resonator, whose quasi-transverse-magnetic, 17th azimuthal-order WG mode, at a frequency of approx. 12.038 GHz, with a loaded Q of several hundred million, is supported on a cylinder of mono-crystalline sapphire. An electron spin resonance (ESR) associated with Fe3+ ions, that are substitutively included within the sapphire at a concentration of a few parts per billion, coincides in frequency with that of the (considerably narrower) WG mode. By applying a c.w. `pump' to the resonator at a frequency of approx. 31.34 GHz, with no applied d.c. magnetic field, the WG (`signal') mode is energized through a three-level maser scheme. Preliminary measurements demonstrate a frequency stability (Allan deviation) of a few times 1e-14 for sampling intervals up to 100 s., Comment: REVTeX v.4, 3 pages, with a separate .bbl file and 3 .eps figures

This chapter details 2020 global patterns in select observed oceanic physical, chemical, and biological variables relative to long-term climatologies, their differences between 2020 and 2019, and puts 2020 observations in the context of the historical record. In this overview we address a few of the highlights, first in haiku, then paragraph form: La Niña arrives, shifts winds, rain, heat, salt, carbon: Pacific—beyond. Compiled by NOAA’s National Centers for Environmental Information, "State of the Climate in 2020" is based on contributions from scientists from around the world. It provides a detailed update on global climate indicators, notable weather events, and other data collected by environmental monitoring stations and instruments located on land, water, ice, and in space. The full report is available from: https://doi.org/10.1175/2021BAMSStateoftheClimate.1.

We derive new stability criteria for purely MHD instabilities in rotating jets, in the framework of the ballooning ordering expansion. Quite unexpectedly, they involve a term which is linear in the magnetic shear. This implies that cylindrical configurations can be destabilized by a negative magnetic shear as well as by a favorable equilibrium pressure gradient, in distinction with the predictions of Suydam's stability criterion, which suggests on the contrary that the shear is always stabilizing. We have used these criteria to establish sufficient conditions for instability. In particular, the magnetic shear can always destabilize jets with vanishing current density on the axis, a feature which is generically found in jets which are launched from an accretion disk. We also show that standard nonrotating jet models (where the toroidal field dominates the poloidal one), which are known to be unstable, are not stabilized by rotation, unless the plasma $\beta$ parameter and the strength of the rotation forces are both close to the limit allowed by the condition of radial equilibrium. The new magnetic shear-driven instability found in this paper, as well as the more conventional pressure-driven instability, might provide us with a potential energy source for the particle acceleration mechanisms underlying the high energy emission which takes place in the interior of AGN jets., Comment: 12 pages, 2 figures; accepted for publication in Astronomy and Astrophysics

Gamma-Ray Bursts are good candidates of the ``bottom up'' scenario for the generation of the UHE Cosmic Rays. In the most discussed model of GRBs, namely the ``fireball'' model, a highly relativistic shock forms and seems capable of accelerating the cosmic rays up to the EeV range. However, only the first Fermi cycle produces a large energy gain to particles coming from the external medium. Thus, a complementary acceleration is proposed, downstream of the external shock, in the relativistic plasma of the GRBs, where crossings of relativistic fronts are likely to occur. Both forward and backward fronts are necessary for the internal Fermi acceleration to work and the physical process that generates them is presented. We found that there exists a relevant physical process similar to Brillouin backscattering that redistributes the incoming energy in the plasma shell. This redistribution occurs through the generation of sound waves that heat the plasma shell and also through the generation of both forward and backward relativistic Alfven fronts that accelerate cosmic rays by the Fermi process. We show that this ensemble of processes is able to account for the generation of UHE cosmic rays. There are two opportunities for these combined processes, first during the ``primary'' Gamma-Ray Burst where baryons are entrained by the relativistic pair wind, second during the predeceleration and deceleration stages when the fireball interacts with the interstellar medium. However, because of the synchrotron losses, only the second stage can produce the UHE cosmic rays., Comment: 8 pages, 3 figures; accepted for publication in Astronomy and Astrophysics