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The step-edge type high temperature superconductor (HTS) radio frequency (rf) superconducting quantum interference devices (SQUIDs) were fabricated from YBa2Cu3O7−δ thin films with a field sensitivity of 66 fT/Hz1/2. Even though the sensitivity of the rf SQUID sensor used in the experiments was degraded to 77 fT/Hz1/2 in the magnetic shielded room (MSR), the performance of the rf SQUID sensor was good enough for the ultra-low field (ULF) nuclear magnetic resonance (NMR) experiments at a measurement field of 61.5 μT. With the help of a strictly controlled fast switching circuit and a coupled LC circuit which acted as flux transformer, the signal-to-noise ratio (SNR) of the rf SQUID-based ULF NMR system with different operating points was measured. The optimum SNR was 40 dB which increased significantly by coupling an input coil closely beneath the rf SQUID sensor. The extracted 1/T1 value for pure water sample at 23 ∘C showed the rf SQUID based ULF NMR was an effective system for ULF NMR researches. All above, the direct coupled method and the control circuit show a great potential in the future rf SQUID-based ULF NMR &MRI system.

The BiFeO3/YBCO heterostructures were fabricated on (001)-oriented SrTiO3 substrates by pulsed laser deposition. The superconducting transition temperature of YBCO was found to decline with increasing the c-axis parameter. The microstructure and dislocations in BiFeO3/YBCO heterostructure were detected by transmission electron microscopy (TEM) proving the epitaxial growth of BiFeO3/YBCO heterostructures on SrTiO3. The edge dislocation with a Burgers vector [100] was observed in BiFeO3, which contributed to the relaxation of BiFeO3. The results of magnetization hysteresis cycles indicated that the saturation magnetization increased from 14 emu/cm3 of BiFeO3/SrTiO3 to 42 emu/cm3 of BiFeO3/YBCO/SrTiO3. The second phase Fe2O3 on the surface of BiFeO3 was found to be α-Fe2O3 with weak magnetization at room temperature. Therefore, the increased magnetization could be accounted for by the induced ferromagnetism at the interface of BiFeO3/YBCO.

We report on improvements of mode-locked soliton pulse energy and peak power in a thulium-doped fiber laser. At the pump power of 370 mW, conventional soliton can be first generated using nonlinear polarization rotation technology. By increasing the pump power to 550 mW and appropriately adjusting cavity polarization state, the conventional soliton pulse can be converted into the Gaussian pulse. Due to dispersion management, excess accumulation of nonlinear phase shifts in the cavity can be avoided. In this case, the pulse energy and peak power can be increased from 77 pJ to 1.38 nJ and from 106.9 W to 2.67 kW, respectively. These improvements indicate that the Gaussian pulse operation can effectively enhance the pulse energy and peak power of the thulium-doped fiber laser.

We propose and demonstrate a high repetition-rate passively mode-locking Tm-doped fiber laser. Mode-locking operation is achieved by using a conventional nonlinear polarization rotation (NPR) structure. Fundamental frequency soliton laser is obtained with the repetition-rate of 5.05 MHz and the pulse width of 54.7 ps. 3-dB bandwidth and signal and noise ratio (SNR) are 3.1 nm and 53.03 dB, respectively. In order to improve repetition-rate of the mode-locking pulse, a narrow band filter is adopted. In this case, maximum repetition-rate of the output pulse can be up to 7.75 GHz (1534 orders). Pulse width and 3-dB bandwidth of mode-locking laser are compressed to 67.2 ps and 0.2 nm, respectively, and SNR is 19.71 dB. In addition, the laser center wavelength can be tuned from 1882 nm to 1925 nm by adjusting the filter.

We report on the experimental observations of stable single soliton and soliton molecules in an anomalous-dispersion thulium-doped passively mode-locked fiber laser by using the nonlinear polarization rotation technology. The stable single soliton operation can convert to the soliton pair operation by cautiously adjusting the PCs, at the pump power of 350 mW. It is experimentally demonstrated that the formation of stationary soliton pairs is related to the interaction between solitons and dispersive waves. By appropriately adjusting the cavity parameters, more complex soliton molecules composed of three, four, and five bound solitons can be observed. Meanwhile, we experimentally analyze complex nonlinear dynamics of soliton molecules around 2- ${\mu }\text{m}$ .

We propose and demonstrate a multi-wavelength actively mode-locked fiber laser around $2.07~\mu \text{m}$ . A holmium-doped fiber is used as the gain medium which is pumped by a 1.93- $\mu \text{m}$ fiber laser. The multi-wavelength laser is achieved by employing a fiber Lyot filter in cavity, and actively mode-locking is achieved by driving a sinusoidal radio frequency signal on the electro-optic modulator. Stable actively mode-locked pulses can be obtained with up to 10.078-GHz repetition rate. The shortest measured pulse width is 16 ps. The wavelength channels can be accurately tuned under a fixed pump power by adjusting the polarization controllers and the BIAS voltage. Up to 27 channels can be obtained under a stable mode-locked operation. However, the increase of output channels leads to a significant increase in the threshold, and the maximum output channels have a strong dependence on the repetition rate.

Low-temperature sintering to fabricate MgB2 is considered a promising method because it reduces the formation of MgO and reduces the grain size, thereby increasing the critical current density. Chemical doping, ball milling of precursor and modifying the Mg source in precursor for low-temperature sintering have all been carefully investigated. However, the threshold of sintering temperature have been kept near 500 °C. A new in-situ method to low-temperature sintering using Mg(BH4)2 as a precursor is presented in this paper. Mg(BH4)2 decomposes into highly reactive nanoscale Mg and B in a molar ratio of 1:2 without impurities. In this method, only 2 h of sintering at 400 °C is required to completely react Mg with B to produce MgB2, and after 54 h sintering, the sample has comparable J C to the normal MgB2 from solid-state reaction method sintered at 800 °C. The sample sintered at 500 °C give better J C than normal MgB2 under both high and low magnetic field.

We propose and demonstrate the operation of Q-switched mode-locked square-wave pulses in a thulium-holmium co-doped fiber laser. By using a nonlinear amplifying loop mirror, continuous square-wave dissipative soliton resonance pulse is obtained with 4.4 MHz repetition rate. With the increasing pump power, square-wave pulse duration can be broadened from 1.7 ns to 3.2 ns. On such basis Q-switched mode-locked operation is achieved by properly setting the pump power and the polarization controllers. The internal mode-locked pulses in Q-switched envelope still keep square-wave type. The Q-switched repetition rate can be varied from 41.6 kHz to 74 kHz by increasing pump power. The corresponding average single-pulse energy increases from 2.67 nJ to 5.2 nJ. The average peak power is also improved from 0.6 W to 1.1 W when continuous square-wave operation is changed into Q-switched mode-locked operation. It indicates that Q-switched mode-locked operation is an effective method to increase the square-wave pulse energy and peak power.

BiFeO3 (BFO)/YBCO heterostructures are fabricated on (001)-oriented SrTiO3 substrates. The transport properties of BFO/YBCO heterostructures with Au and YBCO top electrode are investigated. The Au/BFO/YBCO heterostructures show obvious rectification effect. The current through Au/BFO/YBCO heterostructures at positive bias is mainly bulk-limited space-charge-limited current (SCLC) at temperatures from 15 K to 280 K. As the applied voltage on Au electrode is negative, Au/BFO/YBCO heterostructures satisfy the interface-limited Schottky emission at temperatures from 220 K to 300 K, instead of interface-limited Fowler-Nordheim tunneling at temperatures from 15 K to 80 K. The leakage current density is reduced by two orders of magnitude through substituting the Au electrode by YBCO electrode. The transport mechanism in YBCO/BFO/YBCO heterostructures also changes to SCLC. The different leakage mechanisms result from the reduced oxygen vacancies because the fabrication of YBCO layer increased oxygen concentration in BFO films.

200 nm Ni film is coated on 25 μm thick Mo foil, and graphene is grown on the Ni–Mo system by CVD method. After the annealing process of CVD, the Ni/Mo bilayer transforms into Ni–Mo alloy, then we have successfully fabricated MgB 2 films on graphene/Ni–Mo alloy system via the hybrid physical–chemical vapor deposition (HPCVD) technique. The transition temperature T c onset is 38.25 K with a corresponding transition width of 0.75 K. The average thickness of MgB 2 films is 200 nm (25% concentration B 2 H 6 ). The critical current density derives from the magnetization measurement at 5 K is, j c (5 K, 0 T) = 9.6 × 10 6 A/cm 2 . We can easily deposite MgB 2 on graphene/Ni–Mo alloy system with a lower B 2 H 6 concentration and less gas flow, which lays a good foundation for depositing MgB 2 thick films. The graphene in this system is multilayer and with defects, it may act like an intermediary film for the growth of MgB 2 , or a carbon-doping source.

Using pulsed laser deposition, the (0 0 1)-oriented YBa 2 Cu 3 O 7− δ (YBCO) films were epitaxially grown on BiFeO 3 (BFO) films on SrTiO 3 substrates. The YBCO/BFO heterostructure retained the ferroelectricity of BFO layer and the superconductivity of the YBCO layer. A ferroelectric hysteresis loop was observed in the BFO layer and the remnant polarization was approximately 4.6 μC/cm 2 . The fabrication of YBCO layer resulted in a c -axis decrease of BFO layer, which affected its ferroelectric properties. Especially, as increasing the thickness of BFO film, the superconducting transition width of YBCO film increased. And the c -axis of YBCO film tended towards stability at 11.7 A which ensured that all the samples were superconductive. The YBCO/BFO heterostructure could be used to fabricate YBCO Josephson junctions and the YBCO and BFO multilayers.

The experiment for preparing MgB 2 thin films by electron beam (e-beam) annealing of Mg–B multilayer is reported. The annealing process lasts less than 1 s, which effectively suppresses the volatility of Mg as well as the reaction of Mg and oxygen. The influence of annealing parameters on the film quality including exposure time, accelerating voltage and beam current is investigated. It is found that e-beam with lower accelerating voltage can acquire MgB 2 film with smaller annealing energy density. Also, double e-beam scan annealing process helps to obtain more uniform MgB 2 thin films than the single scan. This rapid annealing method synthesizes MgB 2 thin films with critical temperature T c of 35 K and critical current density J c at 15 K of 7.6 × 10 6 A cm −2 .

We experimentally studied a passive mode-locked square-wave fiber laser with net-normal dispersion by using a nonlinear amplifying loop mirror. The output pulse width of the square-wave pulse (SWP) can be extended with the increasing of the pump power as well as single pulse energy. The SWP can be amplified without shape distortion when the mode-locked laser is injected into an erbium-ytterbium codoped fiber amplifier. Then, by inputting the amplified SWPs into a single mode fiber (SMF), a supercontinuum (SC) can be observed with the spectral range of about 1550 to 1850 nm. Broader and flatter SC with the 20-dB spectral range of about 1550 to 1950 nm can also be generated using a segment of dispersion-shifted fiber instead of SMF.

The crystal structure stability as well as electric conductance of (Sr/Ca)2CuO2Cl2 compound with K2NiF4 structure was investigated up to 31 GPa using diamond anvil technique. It seems that (Sr/Ca)2CuO2Cl2 is quite stable under pressure but with obvious anisotropic compressibility. The equation of state (EOS) obtained shows relative large bulk modulus.

We theoretically investigate the spontaneous magnetization in double-junction and multi-junction π rings when the junctions' superconducting critical currents are not equal. The analytical solutions for the relations between the total magnetic flux Φ and the external magnetic flux Φx, the free energy f and the circulating current i, and the spontaneous magnetization conditions of the double-junction π rings are deduced. For the multi-junction π rings consisting of more than two junctions, mathematical computation is needed to analyse the Φ–Φx and f–i relations. In the conditions where the absolute critical current value of each junction is equal and there are hystereses on the Φ–Φx characteristic curve, the system has spontaneous magnetization solutions. However, the non-spontaneous magnetization state with zero circulating current is a metastable state with local minimum free energy; therefore, the multi-junction π ring system probably would not spontaneously magnetize.

MgB 2 thin films were prepared by ex - situ annealing of Mg/B multilayers. Different precursor, substrate and annealing condition were investigated. After annealed in a flow of Mg vapor with reducing hydrogen ambient for 1–4 min, high quality 20 nm-thick c-oriented MgB 2 thin films with T c onset = 35.6 K and critical current density J C = 2 × 10 6 A cm −2 at 30 K were obtained. The mean roughness of the 20 nm-thick film was 2.68 nm.

We attempt to make MgB2 thin films by using a pulsed-laser-deposition (PLD) and a magnetron sputtering method. We have deposited metal magnesium and boron on various substrates under different vacuum conditions. The PLD method has been employed to fabricate layers of magnesium and boron sandwiches under room temperature and the multi-layer system was then annealed in-situ under different temperatures. We also attempted to co-deposit magnesium and boron under high vacuum (5 × 10−5 Pa) on heated substrates with PLD. We have successfully grown superconducting MgB2 thin films on an STO (100) substrate by magnetron sputtering. The onset transition temperature was 37 K and zero resistance temperature was 34 K.

We report on the research work at Peking University on optimizing high-temperature superconductor (HTS) rf superconducting quantum interference device (SQUID) systems and applying them in geophysical survey and magnetocardiography (MCG). Emphasis is placed on the design of comb-shape resonators for HTS rf SQUID systems and the experimental results of two applications: transient electromagnetics and MCG. The magnetic-field sensitivity of HTS magnetometers is now adequate for MCG applications. However, in order to be commercially used, the system still needs some improvements: development of suitable gradiometers and multi-channel systems.

We report on well characterized a -axis trilayers made of NdBa 2 Cu 3 O 7− δ and PrBa 2 (Cu,Co) 3 O 7− δ films with smooth surface morphology and high crystallinity. The thin films were grown on (100) SrTiO 3 substrates by rf+dc hybrid sputtering. X-ray diffraction and Rutherford backscattering spectrometry analyses provided evidence of well-equilibrated and relaxed crystal. Planar junctions were fabricated from these a -axis oriented NdBa 2 Cu 3 O 7− δ /PrBa 2 (Cu,Co) 3 O 7− δ /NdBa 2 Cu 3 O 7− δ trilayers. The current–voltage characteristics exhibited Josephson current. Well developed Shapiro steps for 7–20 GHz microwave irradiation were observed. The dependence of the maximum amplitude of the Josephson current under applied magnetic field made evident spatial variations of the critical current over the PrBa 2 (Cu,Co) 3 O 7− δ barrier layer. The current–voltage characteristics were qualitatively consistent with the resistively-shunted-junction model.

Y 1 Ba 2 Cu 3 O x films, ranging in thickness from 0.9 to 10 μm, were grown on MgO(100) substrates by liquid phase epitaxy. These films were characterized structurally and electrically. From θ−2σ and ƒ scan X-ray diffraction, and Rutherford backscattering spectrometry measurements, it was found that the films were c -axis oriented and had good in-plane alignment, showing that good epitaxial growth was achieved. The T c,end values in a 20 mm long and 15 mm wide Y 1 Ba 2 Cu 3 O x film exceeded 90 K. The T c and resistivity values did not become degraded after patterning into a strip. Although J c values decreased with increasing film thickness, even a 7 μm-thick film showed a J c value of 9.3 × 10 5 A/cm 2 at 77 K. These data are comparable to those reported for Y 1 Ba 2 Cu 3 O x films prepared on CeO 2 /YSZ(100) by pulse laser deposition, and thought to be due to the c -axis orientation and good in-plane alignment of the liquid phase epitaxially grown thick films.

We have characterized oxide superconductor single crystal substrates for thin film processing, called ‘homoepitaxial growth’, which were fabricated from single crystals of YBa2Cu3O7 δ and 123-structure related materials such as YBa2 (Cu1 x Znx)3O7 δ and Pr1 + x Ba2 xCu3O7 δ grown by the pulling method. Those substrates have good crystallinity with a Zmin value of approximately 2%, evaluated by Rutherford backscattering spectrometry and good surface morphology with unit-cell steps observed by atomic force microscopy. Therefore, those substrates are necessary for completing fine processing, 123-structure pseudo-homoepitaxial growth, for device applications.

We have performed ion channeling characterizations on the (001) and (100) surfaces of YBa2Cu3O7−x single crystals, using 950 keV He+ ions at temperatures ranging from 20 to 780 °C. In oxygen pressures below 5×10−5 Torr, we directly observed the surface changes as the sample temperature was increased, and found that the compositional and structural changes occurred from around 400 °C. At higher oxygen pressures, we heated the crystals and performed channeling analysis before and after the heating. We found that the YBa2Cu3O7−x crystal surfaces were stable at temperatures up to 780 °C in the oxygen pressure range of 1 mTorr–1 Torr. Beyond this range, the surfaces deteriorated at high temperatures.

High‐quality single phase Nd1+xBa2−xCu3O7−d thin films have been fabricated on SrTiO3 substrates by the laser ablation method. The resistivity of the deposited films are usually lower than that of the YBCO film. The Tc(onset) and Tc(R=0) in the optimized thin films are as high as 91 and 88 K, respectively. The crystallinity of our films are higher than the best YBCO films ever reported. The rocking curve FWHM of the (005) peaks in our thin films is typically 0.05°, which is superior to the best reported YBCO films.

We report the fabrication and properties of heterostructures formed by the BiFeO3 (BFO) ferroelectric and YBa2Cu3Ox (YBCO) superconductor. Four measurement configurations on BFO/YBCO heterojunctions are proposed and showed different I-V characteristics. Moreover, one type of BFO/YBCO heterostructures which had the strongest rectification effect at 15K, showed the abnormal rectification effect dependent on temperature. The rectifying effect enhanced with decreasing temperature below the superconducting transition temperature of YBCO. YBCO electrode played an important role in increasing the rectifying parameter because of the high density of states for quasi-particles in YBCO in the superconducting state.

The proximity effect in multilayer structures with dirty two band superconductors and ferromagnets is investigated here. With a homogeneous exchange field and interband scattering in the ferromagnetic layer, the condensate functions that penetrate the ferromagnet are coupled up. This coupling effect is intensively suppressed by the exchange field and modulated by the diffusion coefficients of the two bands. Such coupling also affects the superconductor where the condensate functions of the two bands are also coupled up through the proximity effect. An inhomogeneous exchange field raises the damped oscillation of the condensate functions as the spatial distance from the interface increases. There is a 0−π phase shift when the ferromagnetic layer thickness varies beyond the ferromagnetic coherence length.

a-Axis oriented NdBa2Cu3O7-δ/PrBa2(Cu,Co)3O7-δ/ NdBa2Cu3O7-δtrilayers were prepared on (100) SrTiO3substrates. The trilayers were sputtered using a DC-95MHz hybrid plasma. The I-V characteristics of the trilayers were analyzed as a function of PrBa2(Cu,Co)3O7-δthickness (25–100 nm). In the case of the 50 nm thick PrBa2(Cu,Co)3O7-δlayer, the I-V characteristics show clear Shapiro steps corresponding to 7–20 GHz microwave irradiation. The Fraunhofer pattern was also observed for applied magnetic fields up to 1.00x10–3T.

Homoepitaxial NdBa2Cu3O7-y (NBCO) thin films have been prepared on NBCO (001) substrates in a cold wall lateral flow reactor by metalorganic chemical vapor deposition. It was observed by atomic force microscopy that one-unit-cell-high step structure or grains grew on as-polished substrate according to each growth condition. We found that zigzag steps appear when the initial steps on the as-polished substrate run off the [100] and [010] directions.

We successfully created a smooth surface on liquid phase epitaxially (LPE) grown YiBa2Cu3O7-δ (YBCO) films by employing a mechanical polishing process. We used an alumina powder with an average grain diameter of 0.03µm which was dispersed in oil for mechanical polishing, which made it possible to avoid a degradation of the Tc value for YBCO. While the as-grown surface of LPE-YBCO films contains various pyramidal structures with heights of about 400nm, the polished surface has only a roughness of 2 to 3nm as measured by a step profiler. A χmin value of 2.6% according to Rutherford backscattering spectrometry suggests that the damage after mechanical polishing is negligible. After annealing in O2 gas at 1 atm, the polished YBCO films transformed from tetragonal to orthorhombic phase and had a Tc value of about 91K.

The a-axis oriented PrBa2Cu3O7-δ. films and PrBa2Cu3O7-δ. /NdBa2Cu3O72δ/PrBa2Cu3O7-δ multilayers were deposited on (001) YBa2Cu3O7-δ and (001) NdBa2Cu3O7-δ single-crystal substrates using a DC-95MHZ hybrid plasma sputtering method to form ramp-edge SNS junctions with a ground plane. We found that both the PrBa2aCu3O7-δ film and the multilayer showed less precipitates on the surface of (001) NdBa2Cu3O7-δ substrate than that of (001) YBa2Cu3O7-δ substrate by atomic force microscopy measurements. Futhermore, the multilayers deposited on (001) YBa2Cu3O7-δ substrate and (001) NdBa 2Cu3O7-δ substrate had precipitates on the surface, while that deposited on the multilayered SrTiO7-δ substrate, PrBa2Cu3O7-δ/ NdBa2Cu3O7-δ/ SrTiO3, for reference had no precipitates. An electric resistance of the PrBa2Cu3O7-δ film on (001) YBa2Cu3O7-δ substrate was measured by a standard four-probe method. The electric resistance vs temperature curve suggested the tendency of becoming superconductivity below 13 K.

We have investigated the surfaces of YBa2Cu3O7-δ and NdBa2Cu3O7-δ single crystals using 950keV He+ Rutherford backscattering spectrometry and the ion channeling technique. The surface stability at temperatures up to 780°C was examined as a function of oxygen pressure. We found that the YBa2Cu3O7-δ and the NdBa2Cu3O7-δ crystal surfaces were stable at high temperatures in a limited O2 pressure between 1mTorr and 1Torr. Beyond this range, the YBa2Cu3O7-δ surfaces deteriorated significantly at high temperatures, while the NdBa2Cu3O7-δ surfaces only showed a slight degradation. These results revealed that the crystalline surface of NdBa2Cu3O7-δ remains stable at high temperatures in a larger O2 pressure range than that of YBa2Cu3O7-δ.

We have investigated the surface of high quality YBa2Cu2Ox single crystal substrates, fabricated from YBa2Cu3Ox single crystals grown by the crystal pulling method, for homoepitaxy. They have good crystallinity with χmin of under 2% evaluated by Rutherford backscattering spectrometry and good surface morphology with unit-cell steps observed by atomic force microscopy. Furthermore, we also discuss the initial stage of homoepitaxial growth by using metalorganic chemical vapor deposition method and YBa2Cu3Ox single crystal substrates as mentioned above.

The technique of electron beam annealing for fabricating MgB2 thin films has been explored. MgB2 thin films were prepared by e-beam evaporation of M?B precursor films on 6H?SiC (0001) substrates followed by ex?situ electron beam annealing without any extra Mg vapor or argon gas protection. The very short annealing duration, about 1?s, effectively prevented volatilization and oxidation of Mg and decomposition of MgB2. In comparison with the MgB2 thin films grown by other techniques, our films show medium qualities including a superconducting transition temperature of Tconset ~ 35.3?K, a transition width ?Tc ~ 0.2?K, and a critical current density of Jc(5?K, 0?T) ~ 3.2 ? 106?A?cm ? 2. Such an electron beam annealing technique has potential for the fabrication of large-scale MgB2 thin films as well as MgB2 wires and tapes.

We have investigated the (001) and (100) surfaces of YBa 2 Cu 3 O 7−x single crystals as a function of temperature and oxygen partial pressure, using the channeling technique of 950keV He + ions. The compositional and structural changes of the samples surfaces were directly observed in the temperature range of 20∼780°C. The changes were found to be dependent on the oxygen pressure. The YBa 2 Cu 3 O 7−x crystal surfaces were stable at temperatures up to 780°C in the oxygen pressure range of 1mTorr∼1Torr. Beyond this range, the surfaces deteriorated at high temperatures.

We have evaluated the properties of YBa2Cu3O x (001) single-crystal substrates with areas as large as 10×10 mm. They have good crystallinity with a χ min value of 1.8% determined by Rutherford backscattering spectrometry, grains with areas as large as 5×5 mm confirmed by X-ray topography, and excellent surface morphology with unit-cell steps which were observed by atomic force microscopy. However, approximately one unit-cell-thick degraded layer on the surface, which was observed by angle-resolved X-ray photoelectron spectroscopy, presents problems which must be resolved. These analyses indicate that YBa2Cu3O x single crystal grown by the pulling method is a promising substrate material for homoepitaxial growth.

The interaction of a low energy O+ ion beam on cuprate oxide, superconducting thin film surfaces was investigated in Ultra High Vacuum. Following the process by Reflection High Energy Electron Diffraction and Rutherford Backscattering and Ion Channeling we found that the O+ ion beam can change the surface structure, forming a different compound, and disordering the films, down to a depth of 300 Å. Using an Atomic Force Microscope we found that this process smoothes the surface of the films, with a rate that was found to be an exponential function of the ion energy, with a threshold energy of 50 eV.