Given the high energy density of gasoline, the exploration of alternative media to store the energy of powering a car, such as hydrogen or battery, is strongly limited by the energy density of the alternative medium. The same mass of lithium-ion storage, for example, would result in a car with only 2% the range of its gasoline counterpart. If sacrificing the range is undesirable, much more storage volume is necessary. Alternative options are discussed for energy storage to increase energy density and decrease charging time, such as supercapacitors.[9][10][11][12]

High-pressure tanks weigh much more than the hydrogen they can hold. The hydrogen may be around 5.7% of the total mass,[22] giving just 6.8 MJ per kg total mass for the LHV.

It should be noted that all the intersections of each two lines are nearly overlapped and are close to 70%, which means the dependence of the collimation effect on the laser power can be reversed. Furthermore, the transverse temperature seems independent of the laser power at this point. Fortunately, the optical loss of windows and mirrors is unlikely to cause such a poor symmetry ratio. Nevertheless, the calculation results indicate that the collimation will be more sensitive to the symmetry when the collimation laser power is higher.

A method called optical molasses finally becomes widely adopted in the atomic collimation, which can eliminate the compromise between the light intensity limit and the collimation efficiency19. The classical optical molasses took advantage of the laser-radiation pressure. It was improved later with the Lin⊥Lin configuration, which includes two counter-propagating light waves with orthogonal linear polarizations. This special light field, in which the light-shifted energies oscillate in space with a period of \(\lambda /2\), forces atoms to be more likely at the uphill state than the downhill state. The atoms lose energy when propagating through the light field and “climbing” the potential hill. An alternative approach is to use the \({\sigma }^{+}-{\sigma }^{-}\) configuration. In this case the two counter-propagating waves are absorbed with different efficiencies, which gives rise to unbalanced radiation pressures. These two cooling methods can reach the level of sub-Doppler temperatures20.

Collimatedbeammeaning

The first term of equation (8) is the negative-frequency component, while the second one is the positive-frequency component

The density of thermal energy contained in the core of a light-water reactor (pressurized water reactor (PWR) or boiling water reactor (BWR)) of typically 1 GWe (1,000 MW electrical corresponding to ≈3,000 MW thermal) is in the range of 10 to 100 MW of thermal energy per cubic meter of cooling water depending on the location considered in the system (the core itself (≈30 m3), the reactor pressure vessel (≈50 m3), or the whole primary circuit (≈300 m3)). This represents a considerable density of energy that requires a continuous water flow at high velocity at all times in order to remove heat from the core, even after an emergency shutdown of the reactor.

The M2 of multimode beams can vary greatly from around 3-4 for a multimode laser diode to greater than 20 for certain types of high powered lasers. Figure 5.

Collimating lens

We use the initial state to build an atomic beam model and program a random number generator which is used in emulational sampling of the original atomic factors. Then the force of the collimation laser is calculated. In this section, only the DC force is taken into consideration, and the effects of the Sisyphus cooling and the polarization gradient cooling (PGC) will be discussed in the next section.

Energy density differs from energy conversion efficiency (net output per input) or embodied energy (the energy output costs to provide, as harvesting, refining, distributing, and dealing with pollution all use energy). Large scale, intensive energy use impacts and is impacted by climate, waste storage, and environmental consequences.

\({{\boldsymbol{\varepsilon }}}_{x}\) and \({{\boldsymbol{\varepsilon }}}_{y}\) are unit vectors whose directions are horizontal and vertical, respectively. The z axis is along the direction of laser lights. There are gradients of ellipticity when one moves along Oz. For the 1S0–1P1 transition in 171Yb (I = 1/2) shown inFig. 7, this kind of gradients can form a sub-Doppler cooling, which is usually called the Sisyphus cooling. And it can cool the atoms by dissipating the kinetic energy of atoms when atoms transit from one sublevel of the ground state to the excited state and go back to another ground sublevel in a finite time \({\tau }_{p}\). In addition, the detuning should be negative and the PGC is more powerful when the velocity of atoms is lower than the capture velocity \({\upsilon }_{c}\) which is related to the laser power. If the linearly polarized laser beams are contaminated by circular polarizations, the effect of PGC may be influenced and this is of interest to us.

There are different types of energy stored, corresponding to a particular type of reaction. In order of the typical magnitude of the energy stored, examples of reactions are: nuclear, chemical (including electrochemical), electrical, pressure, material deformation or in electromagnetic fields. Nuclear reactions take place in stars and nuclear power plants, both of which derive energy from the binding energy of nuclei. Chemical reactions are used by organisms to derive energy from food and by automobiles from the combustion of gasoline. Liquid hydrocarbons (fuels such as gasoline, diesel and kerosene) are today the densest way known to economically store and transport chemical energy at a large scale (1 kg of diesel fuel burns with the oxygen contained in ≈15 kg of air). Burning local biomass fuels supplies household energy needs (cooking fires, oil lamps, etc.) worldwide. Electrochemical reactions are used by devices such as laptop computers and mobile phones to release energy from batteries.

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The atomic beam collimation by laser cooling is used to decrease the divergence angle and increase the beam flux density in the preparation of cold atoms or the atomic lithography technology3,24. The polarization purity may be more meaningful when the critical velocity range is broadened or the atomic initial velocity distribution is more concentrated. But in our discussion, it is only a less important factor.

Silicone immersion oil is used for deep observations of live specimens. Silicone oil (ne≒1.40) closely matches the refractive index of cells (ne≒1.38) thereby ...

where \({P}_{+}\) is the power in the input direction and \({P}_{-}\) is the reflected one. The ratio of \({P}_{-}/{P}_{+}={\gamma }_{m}{\gamma }_{2}^{2}\) is defined as the symmetry ratio. We study the dependence of the transverse temperature on the symmetry ratio for various laser powers, as shown in Fig. 6. In addition, other simulation parameters are set to be optimal values.

Akamatsu, D. et al. Frequency ratio measurement of 171Yb and 87Sr optical lattice clocks. Opt. Express 22, 7898–7905 (2014).

Nuclear fuels typically have volumetric energy densities at least tens of thousands of times higher than chemical fuels. A 1 inch tall uranium fuel pellet is equivalent to about 1 ton of coal, 120 gallons of crude oil, or 17,000 cubic feet of natural gas.[15] In light-water reactors, 1 kg of natural uranium – following a corresponding enrichment and used for power generation– is equivalent to the energy content of nearly 10,000 kg of mineral oil or 14,000 kg of coal.[16] Comparatively, coal, gas, and petroleum are the current primary energy sources in the U.S.[17] but have a much lower energy density.

The optimum detuning is around −10 MHz for different laser powers, as shown in Fig. 4. It is interesting to see the curves become flatter near the optimum detuning when the laser power is increased. The optimal detuning ranges, where the difference between the transverse equivalent temperature and the lowest is below 5 mK, are listed in Table 2.

Dalibard, J. & Cohen-Tannoudji, C. Laser cooling below the Doppler limit by polarization gradients: simple theoretical models. J. Opt. Soc. Am. B 6, 2023–2045 (1989).

Energy per unit volume has the same physical units as pressure, and in many situations is synonymous. For example, the energy density of a magnetic field may be expressed as and behaves like a physical pressure. The energy required to compress a gas to a certain volume may be determined by multiplying the difference between the gas pressure and the external pressure by the change in volume. A pressure gradient describes the potential to perform work on the surroundings by converting internal energy to work until equilibrium is reached.

The criterion we use to measure the laser collimation effect is the equivalent transverse temperature in the atomic beam. The temperature depends on the average atomic kinetic energy \(\bar{E}\) in the following way: \(T=2\bar{E}/{k}_{B}\), where \({k}_{B}\) is the Boltzmann constant.

Electric and magnetic fields can store energy and its density relates to the strength of the fields within a given volume. This (volumetric) energy density is given by

Dependence of the transverse temperature of the atomic beam on the polarization purity of the laser beam. Each point is averaged over 10 calculations to reduce the uncertainty. The blue squares correspond to results with a 673 K oven temperature. The red circles indicate the results with a lower oven temperature of 523 K. The orange shaded areas are the root mean square of the 10 times simulation results.

The oven temperature has evident influence on the initial transverse temperature. But the tendencies of the curves are similar, as shown in Fig. 5. The curves level off when the power is greater than 20 mW. If the polarizations of the counter-propagating laser beams are both linear and parallel, the red detuned standing wave will reduce the collimation effect.

The density values for chemical fuels do not include the weight of the oxygen required for combustion. The atomic weights of carbon and oxygen are similar, while hydrogen is much lighter. Figures are presented in this way for those fuels where in practice air would only be drawn in locally to the burner. This explains the apparently lower energy density of materials that contain their own oxidizer (such as gunpowder and TNT), where the mass of the oxidizer in effect adds weight, and absorbs some of the energy of combustion to dissociate and liberate oxygen to continue the reaction. This also explains some apparent anomalies, such as the energy density of a sandwich appearing to be higher than that of a stick of dynamite.

The DC force is an atomic velocity dependent function23, so we use the Runge-Kutta method to solve the atomic trajectories and velocities in the laser field. Figure 1 shows the atomic position distribution in the cross section. We can see the difference between collimation OFF in Fig. 1(a) and ON in Fig. 1(b). When the cooling lasers take effect in the collimation, the atomic beam diameter decreases, which essentially is the desired effect. However, the atomic beam is not concentrated enough with the default collimation factors listed in Table 1, so further analysis and optimization are necessary.

Lu, S. T., Chen, Y., Wu, X. H., Wang, Z. D. & Li, Y. Three-dimensional sulfur/graphene multifunctional hybrid sponges for lithium-sulfur batteries with large areal mass loading. Sci. Rep. 4, 4629 (2014).

For a set of ideal conditions of orthogonal linear polarizations and equal amplitudes of both counter-propagating laser beams, one can write

How to make a collimatedbeam

For energy storage, the energy density relates the stored energy to the volume of the storage equipment, e.g. the fuel tank. The higher the energy density of the fuel, the more energy may be stored or transported for the same amount of volume. The energy of a fuel per unit mass is called its specific energy.

In physics, energy density is the quotient between the amount of energy stored in a given system or contained in a given region of space and the volume of the system or region considered. Often only the useful or extractable energy is measured. It is sometimes confused with stored energy per unit mass, which is called specific energy or gravimetric energy density.

where D is the electric displacement field and H is the magnetizing field. In the case of absence of magnetic fields, by exploiting Fröhlich's relationships it is also possible to extend these equations to anisotropic and nonlinear dielectrics, as well as to calculate the correlated Helmholtz free energy and entropy densities.[18]

This work is supported by the National Key Basic Research and Development Program of China (Grant No. 2016YFA0302103), the National High Technology Research and Development Program of China (Grant No. 2014AA123401), the National Natural Science Foundation of China (Grant No. 11134003), and Shanghai Excellent Academic Leaders Program of China (Grant No. 12XD1402400).

The incapacity to cool the cores of three BWRs at Fukushima after the 2011 tsunami and the resulting loss of external electrical power and cold source caused the meltdown of the three cores in only a few hours, even though the three reactors were correctly shut down just after the Tōhoku earthquake. This extremely high power density distinguishes nuclear power plants (NPP's) from any thermal power plants (burning coal, fuel or gas) or any chemical plants and explains the large redundancy required to permanently control the neutron reactivity and to remove the residual heat from the core of NPP's.

Laserbeam collimation

The greatest energy source by far is matter itself, according to the mass-energy equivalence. This energy is described by E = mc2, where c is the speed of light. In terms of density, m = ρV, where ρ is the mass per unit volume, V is the volume of the mass itself. This energy can be released by the processes of nuclear fission (~0.1%), nuclear fusion (~1%), or the annihilation of some or all of the matter in the volume V by matter-antimatter collisions (100%).[citation needed]

The calculation delivers the information that the transverse temperature becomes more sensitive to the detuning at low laser powers. It is well understood because the cooling force becomes saturated at high laser intensity. Additionally, the laser power has little influence on the optimum detuning.

McGowan, R. W., Giltner, D. M. & Lee, S. A. Light force cooling, focusing, and nanometer-scale deposition of aluminum atoms. Opt. Lett. 20, 2535–2537 (1995).

The dependence of the transverse temperature on the laser detuning. The black squares indicate the simulation results with 40 mW laser power. The red circles are the results in 20 mW and the green triangles are the results in 10 mW. The laser power is mean to the sum of the 2-D collimation lasers.

If the laser polarizations form a complete Lin⊥Lin configuration, the optical pumping time \({\tau }_{p}\), which characterize the mean time that an atom takes to be transferred by a fluorescence cycle from one sublevel to another, is given by

The simulations with the ideal conditions help us find the optimum parameters and a narrow experimental optimizing range. But some non-ideal factors in the real experimental conditions may limit the collimation effect. We study the influence of intensity imbalance and polarization impurity of the lasers in order to provide the critical values of imperfect conditions.

Balykin, V. I., Letokhov, V. S., Minogin, V. G., Rozhdestvensky, Y. V. & Sidorov, A. I. Radiative collimation of atomic beams through two-dimensional cooling of atoms by laser-radiation pressure. J. Opt. Soc. Am. B 2, 1776–1783 (1985).

When a pulsed laser impacts a surface, the radiant exposure, i.e. the energy deposited per unit of surface, may also be called energy density or fluence.[19]

by JD Evans · 1992 · Cited by 4 — Formulas for the time dependant focal length and temperature rise of the window are developed using the thin lens equation. These formulas are expressed in ...

Joffe, M. A., Ketterle, W., Martin, A. & Prichard, D. E. Transverse cooling and deflection of an atomic beam inside a Zeeman slower. J. Opt. Soc. Am. B 10, 2257–2262 (1993).

Li, S., Zhou, M. & Xu, X. Analysis of atomic beam collimation by laser cooling. Sci Rep 8, 9971 (2018). https://doi.org/10.1038/s41598-018-28218-y

The position distribution of the atomic beam obtained from the MCL simulation. The deceleration length is 30 mm and there are 10,000 emulational atoms. Other parameters are set to be default.

Balykin, V. I., Letokhov, V. S. & Mishin, V. I. Cooling of sodium atoms by resonant laser emission. Zh. Eksp. Teor. Fiz. 78, 1376–1385(1980) [Soc. Phys. JETP 51, 692–696 (1980)].

First of all, we define the ideal conditions that remain constant in each simulation. Then, the method we choose for collimating the atomic beam is Doppler cooling (DC), and the dominant cooling force is the radiative force. Besides, the interaction between atoms is not taken into account. The classic setup of the 1-D atomic beam collimation consists of two symmetric lasers that are entirely identical in their characteristics, such as the laser power, the detuning, and the spot size in this part of the paper. In order to collimate the atomic beam in two dimensions, two sets of 1-D setups are required. One is employed in the horizontal collimation and the other one is used for the vertical collimation. Table 1 lists the default simulation values of the factors that have a significant influence on the initial conditions of the system.

Equation (17) is used to calculate the trajectory of atoms in the laser field, and the MCL simulation result can show the dependence of the transverse temperature of the atomic beam on the polarization purity.

Bjorkholm, J. E., Freeman, R. R., Ashkin, A. & Pearson, D. B. Observation of focusing of neutral atoms by the dipole forces of resonance-radiation pressure. Phys. Rev. Lett. 41, 1361–1364 (1978).

Allen is a brand of hand tools, most widely recognized for its wrenches, known generically as "Allen wrenches". As a brand, it is owned by Apex Tool Group.

The collimation area, which is associated with the light spot size, has an important implication for the cooling time. The laser with a larger spot size can collimate more atoms within a longer time. However, the cost is the decrease in the light intensity. In the following we search for an optimal range of the spot size.

In general an engine will generate less kinetic energy due to inefficiencies and thermodynamic considerations—hence the specific fuel consumption of an engine will always be greater than its rate of production of the kinetic energy of motion.

9 jobs · Assistant EHS Officer · Supplier Quality Assistant Engineer · Accountant/Assistant Accountant · QA Technician · Optometrist (Bukit Indah) · OPTOMETRIST.

Collimating lens vs focusing lens

The dependence of the transverse temperature on the symmetry ratio. The green dashed line shows the transverse temperature without laser cooling. The solid lines represent the dependences of transverse temperatures on symmetry ratio at different collimation light powers. The inset shows an enlarged view with the symmetry ratio ranging from 50% to 80%.

The adjacent figure shows the gravimetric and volumetric energy density of some fuels and storage technologies (modified from the Gasoline article). Some values may not be precise because of isomers or other irregularities. The heating values of the fuel describe their specific energies more comprehensively.

Influence of the oven spout diameter and the light spot width on the atomic beam collimation. The width at which the laser has the best collimation effect is marked by the red dots, and the yellow short dashed line is the linear fitting for the guide to eyes.

It is always necessary to calculate the collimation efficiency whether one designs the cold-atom systems or optimizes the experiments. Although the theoretical model of the optical molasses for the atomic cooling has been widely studied and accepted, the collimation process seems more complex. Direct calculation of the collimation efficiency is very difficult and not suitable for systems with multiple stochastic processes2. The existing research in the field of the 2-D atomic beam collimation is not yet complete. For example, the cooling forces are regarded as damping forces and are characterized as near-linear with the velocity of the atoms3. In fact, the transverse velocity of an atomic beam depends on the oven temperature and the structure of the pre-collimator, which may lead to a deviation from the linear approximation. The Sisyphus effect is taken into consideration, while the effect of the polarization purity is not. Some researches discuss the influence of the imbalanced light intensity, but further quantitative study is necessary because the intensity imbalance is unavoidable in an experiment19.

where E is the electric field, B is the magnetic field, and ε and µ are the permittivity and permeability of the surroundings respectively. The solution will be (in SI units) in joules per cubic metre.

Both the cooling laser detuning and the Doppler shift caused by the velocity of atoms contribute to the spontaneous force. In this section, the size of laser beam is 3 × 30 mm2 and the oven temperature is 673 K. We simulate the dependences of the transverse temperature on laser detuning for different laser powers. The laser beams are frequency shifted slightly below the atomic resonance. The red detuning is necessary to ensure the forces are opposite between the counter-propagating laser beams. However, if the detuning is too large, the cooling force will be decreased because the probability of spontaneous radiation becomes small. So there should be an optimum detuning.

The simulation conditions are optimized, and the number of the simulation atoms is \(4\times {10}^{4}\). We notice that the capture velocity in DC should match the distribution of the non-collimation atomic transverse velocity. As a result, the atomic transverse velocity distribution is rearranged and most atoms are collimated by the DC force. However, the critical range of the Sisyphus force is much narrower. So it only interacts with a small part of the atomic beam and decelerate it. That is why the transverse temperature hardly changed with polarization purity.

S.L. wrote the simulation program and analysed the data. M.Z. supplied guidance in laser cooling model. X.Y.X. supervised the simulation and analysis. All the authors did participate to manuscript writing.

McClelland, J. J., Scholten, R. E., Palm, E. C. & Celotta, R. J. Laser-focused atomic deposition. Science 262, 877–880 (1993).

By calculating the distribution of the atomic divergence angle, we find that almost all the atoms which shoot out with a large critical divergence angle \({\theta }_{i}\) cannot reach the collimation field, thus being dissipated. To reduce the spout wastage to 2.5%, a pre-collimator with \({\theta }_{0}\) < 15 mrad should be designed. For gaseous ytterbium, the thermal motion level depends on the temperature. The velocity of Yb atoms in the oven obeys the Maxwell-Boltzmann distribution, while the velocity of atoms that spout out of the oven nozzle becomes the modified Maxwell-Boltzmann distribution. When the laser intensity and detuning are set, the damping ratio \(\beta \) is obtained. It should be mentioned that the laser power stands for the power in one dimension, so the total power is doubled.

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As expected, the collimation effect by laser cooling is sensitive to the symmetry ratio. The intersections of the dashed line and solid lines indicate the critical values of symmetry ratio, below which the laser may heat or push away the atoms and the collimation gets weakened. Table 3 shows the critical values at different laser powers.

Ushijima, I., Takamoto, M., Das, M., Ohkubo, T. & Katori, H. Cryogenic optical lattice clocks. Nat. Photon. 9, 185–189 (2015).

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

Balykin, V. I., Letokhov, V. S. & Sidorov, A. I. Radiative collimation of an atomic beam by two-dimensional cooling by a laser beam. JETP Lett. 40, 1026–1029 (1984) [Pis’ma Zh. Eksp. Teor. Fiz. 40, 251–253 (1984)].

OD is referring to the density or darkness of the film after exposure (and processing). More photons hitting the film creates a darker region ( ...

The transverse equivalent temperature of the atomic beam after being collimated by laser beams with different spot sizes. In this simulation, the efficient size range is marked with the dark blue colour. Even at the optimal size, the lowest equivalent temperature is still far above 0.7 mK, which is the Doppler cooling limit of the 399 nm transition in Yb.

RFLXF | Complete Reflex Advanced Materials Corp. stock news by MarketWatch. View real-time stock prices and stock quotes for a full financial overview.

We define the incident light power as \({P}_{i}\), and the reflected power as \({P}_{r}\). The transmissivity of two vacuum chamber windows are \({\gamma }_{1}\) and \({\gamma }_{2}\), respectively. The mirror loss is defined as \({\gamma }_{m}\). The reflected laser power can then be written as

The order of diffraction refers to the integer that represents the number of wavelengths by which light is out of phase when it passes through a diffraction ...

How to collimate a divergingbeamof light

In the context of magnetohydrodynamics, the physics of conductive fluids, the magnetic energy density behaves like an additional pressure that adds to the gas pressure of a plasma.

Unless otherwise stated, the values in the following table are lower heating values for perfect combustion, not counting oxidizer mass or volume. When used to produce electricity in a fuel cell or to do work, it is the Gibbs free energy of reaction (ΔG) that sets the theoretical upper limit. If the produced H2O is vapor, this is generally greater than the lower heat of combustion, whereas if the produced H2O is liquid, it is generally less than the higher heat of combustion. But in the most relevant case of hydrogen, ΔG is 113 MJ/kg if water vapor is produced, and 118 MJ/kg if liquid water is produced, both being less than the lower heat of combustion (120 MJ/kg).[20]

No single energy storage method boasts the best in specific power, specific energy, and energy density. Peukert's law describes how the amount of useful energy that can be obtained (for a lead-acid cell) depends on how quickly it is pulled out.

Collimator

In the real world this comes out to objects that are 250-300nm in size, if you are using a NA=1.4 objective lens (under optimal conditions). This means that you ...

In photography, the metering mode refers to the way in which a camera determines exposure. Cameras generally allow the user to select between spot, ...

Another sub-Doppler cooling method includes a pair of \({\sigma }^{+}\) and \({\sigma }^{-}\) polarized laser beams. In the Lin⊥Lin configuration, if the polarization of laser light is not pure, it becomes a combination of Lin⊥Lin and \({\sigma }^{+}-{\sigma }^{-}\) configurations. Nevertheless, DC still dominates the cooling process in the \({\sigma }^{+}-{\sigma }^{-}\) configuration, as \({J}_{g}=1/2\) for 171Yb.

The dependence of the transverse temperature on the total laser power. The blue triangles are the results at 873 K oven temperature. The black squares are at 573 K, and the red circles stand for results at 673 K. The inset shows the dependence of the transverse temperature on the power distribution with a total laser power of 40 mW at 673 K. The power distribution, with its value lying in the range of zero to unity, represents the power ratio between lasers in the vertical and horizontal dimensions.

Chen, Y. H., Tao, H. S., Yao, D. X. & Liu, W. M. Kondo metal and ferrimagnetic insulator on the triangular kagome lattice. Phys. Rev. Lett. 108, 246402 (2012).

Sukachev, D. D. et al. Collimation of a thulium atomic beam by two-dimensional optical molasses. Quantum Electron. 43, 374–378 (2013).

Then we decide to increase the number of captured atoms. If we increase the laser power, the collimation force will be changed as well, which will further complicate the discussion. So we reduce the oven temperature to 523 K that has a narrower velocity distribution and more atoms may be captured by the polarization gradient force. Finally, the influence of polarization is still too weak on the transverse temperature, but significant on the velocity distribution as shown in Fig. 9.

As shown in Fig. 8, we calculate the curve for the oven temperature at 673 K. The blue squares are the mean values of 10 MCL simulations, and the error bars are the statistic uncertainties. We cannot find an obvious influence of the polarization purity according to this curve. The reason that the sub-Doppler cooling is invalid may be because the capture velocity band is narrow. The laser power is 10 mW which corresponds to \({\upsilon }_{c}=0{\rm{.0436}}\,{\rm{m}}/{\rm{s}}\). Therefore, the transverse velocity of the atomic beam has been damped, and there are only a few atoms captured by the polarization gradient force.

Rathod, K. D., Singh, P. K. & Natarajan, V. Cold beam of isotopically pure Yb atoms by deflection using 1D-optical molasses. Pramana - J. Phys. 83, 387–393 (2014).

The oven temperature is set at 673 K, at which the most probable velocity of atoms is \({v}_{mp}=310\,{\rm{m}}/{\rm{s}}\). As seen in Fig. 2, the optimal light spot width is around 3 mm which is near the diameter of the oven spout. To confirm whether it is coincidental, we study the optimal light spot width with different spout diameters, as shown in Fig. 3. The linear fitting result shows that when the diameter of the oven spout is changed, the optimum light spot width changes linearly.

The mechanical energy storage capacity, or resilience, of a Hookean material when it is deformed to the point of failure can be computed by calculating tensile strength times the maximum elongation dividing by two. The maximum elongation of a Hookean material can be computed by dividing stiffness of that material by its ultimate tensile strength. The following table lists these values computed using the Young's modulus as measure of stiffness:

When discussing the chemical energy contained, there are different types which can be quantified depending on the intended purpose. One is the theoretical total amount of thermodynamic work that can be derived from a system, at a given temperature and pressure imposed by the surroundings, called exergy. Another is the theoretical amount of electrical energy that can be derived from reactants that are at room temperature and atmospheric pressure. This is given by the change in standard Gibbs free energy. But as a source of heat or for use in a heat engine, the relevant quantity is the change in standard enthalpy or the heat of combustion.

In cosmological and other contexts in general relativity, the energy densities considered relate to the elements of the stress-energy tensor and therefore do include the rest mass energy as well as energy densities associated with pressure.

Collimationradiology

Because antimatter-matter interactions result in complete conversion from the rest mass to radiant energy, the energy density of this reaction depends on the density of the matter and antimatter used. A neutron star would approximate the most dense system capable of matter-antimatter annihilation. A black hole, although denser than a neutron star, does not have an equivalent anti-particle form, but would offer the same 100% conversion rate of mass to energy in the form of Hawking radiation. Even in the case of relatively small black holes (smaller than astronomical objects) the power output would be tremendous.

The most widely used scheme of atomic beam collimation is still based on the optical molasses method3,4,14. Monte Carlo (MCL) simulation method which has been well-established is widely used in the field of cold atom physics18,21,22 and can be used for this research. We use MCL methods to simulate the process of collimating a thermal ytterbium (Yb) beam with the 2-D optical molasses. Firstly, the dependences of the collimation efficiency on power, frequency detuning, beam size of the laser and spout size of the oven in ideal conditions are studied. Then the influences of some non-ideal factors, especially for cases with an unsymmetrical laser intensity and an impure laser polarization are investigated quantitatively. We also compare the Lin⊥Lin and \({\sigma }^{+}-{\sigma }^{-}\) configurations, followed by a discussion of the dominating effects of the beam collimation. Finally, we draw some conclusions about the design and optimization of the 2-D atomic beam collimation.

The most effective ways of accessing this energy, aside from antimatter, are fusion and fission. Fusion is the process by which the sun produces energy which will be available for billions of years (in the form of sunlight and heat). However as of 2024, sustained fusion power production continues to be elusive. Power from fission in nuclear power plants (using uranium and thorium) will be available for at least many decades or even centuries because of the plentiful supply of the elements on earth,[13] though the full potential of this source can only be realized through breeder reactors, which are, apart from the BN-600 reactor, not yet used commercially.[14]

Peters, A., Chung, K. Y. & Chu, S. High-precision gravity measurements using atom interferometry. Metrologia 38, 25–61 (2001).

The collimation of a thermal atomic ytterbium beam utilizing a two-dimensional optical molasses is analysed by employing the Monte Carlo simulation. The dependencies of the collimation efficiency on power, frequency detuning and beam size of the laser are studied for various conditions, especially for the case of an imbalanced laser intensity and an impure laser polarization. The influences of these imperfect factors are discussed, and the lowest transverse temperature by the collimation in the experiment is evaluated.

Aspect, A., Dalibard, J., Heidmann, A., Salomon, C. & Cohen-Tannoudji, C. Cooling atoms with stimulated emission. Phys. Rev. Lett. 57, 1688–1691 (1986).

The MCL method is an effective way to simulate the atomic dynamics. In this work, we investigate the influence of the laser power and the detuning on the atomic beam collimation. The lowest transverse temperature is 3 mK and is considerably hotter than the Doppler limit of 0.7 mK. The main reason is that there is insufficient interaction time. This algorithm can be reliably upgraded from only utilizing generalizations of ideal conditions to specific cases with non-ideal conditions. Then, it is shown that the polarization is not a dominant factor with our parameters, but the symmetry of the laser intensity has a remarkable influence on the collimation. Finally, the critical value of the intensity symmetry ratio is presented and we search for an explanation for that the collimation is insensitive to the light polarization. However, even using the optimal parameters and the sub-Doppler cooling method, the collimation by laser cooling does not reach the desired efficiency. In case the laser power is limited or the experimental setup has to be compact, this collimation unit is not necessary. This work will give a guideline for pursuing a good collimation of atomic beam in experiments on the optical lattice clocks with two-valence electron atoms.

and it is proportional to the laser power. In addition, the calculation of equations (10–12) requires \(k\upsilon \ll {\rm{\Gamma }}\).

When the linear polarization light is mixed with a fraction of circular polarization part, the energy shift between two sublevels of the ground state will be decreased, which leads to a weak PGC. We define the polarization purity \({\kappa }_{p}\) as

A set of two counter-propagating laser beams are generally produced by one laser beam combined with a \(0^\circ \) high reflector. However, the power loss of the reflector and the vacuum chamber windows cannot be ignored in a real experiment. This effect leads to the inequality of the counter-propagating lasers’ power that may influence the collimation effect.

In the previous section, we find the saturation of the laser power. In order to make full use of the laser power, the analysis of the laser power optimization must be done at the optimum laser detuning −10 MHz.

The following unit conversions may be helpful when considering the data in the tables: 3.6 MJ = 1 kW⋅h ≈ 1.34 hp⋅h. Since 1 J = 10−6 MJ and 1 m3 = 103 L, divide joule/m3 by 109 to get MJ/L = GJ/m3. Divide MJ/L by 3.6 to get kW⋅h/L.

As is well known, the collimation of the atomic beam becomes an important stage in the experiments on atom optics1,2,3,4, such as atomic clocks5,6,7,8,9,10, atomic interferometers11,12, and atomic lithography13,14. Besides mechanical ways, numerous techniques of manipulating the position and velocity of atoms by using the laser light have been demonstrated for beam collimation. The first demonstration employed a red detuned light overlapped the atomic beam with a radial intensity gradient for generating the transverse dipole forces15. Apart from dipole forces, scattering forces can collimate the atomic beam as well. Atomic beam deceleration by laser-radiation pressure was first reported in ref.16. Later V. I. Balykin’s team demonstrated a radiative collimation experiment through two dimensional (2-D) cooling of atoms by laser-radiation pressure in an axisymmetric light field formed by a reflecting axicon17. A technique called atomic lens has appeared with the development of the laser cooling methods. It uses an intense standing wave formed by blue-detuned lasers and does not saturate at high intensity18. It is noted that, the radiative collimation only works well under low light intensity and the atomic lens methods are not suitable for experiments with limited laser power.

The solid curves are the probability densities as a function of the atomic transverse velocity acquired by the MCL simulation. The dashed lines are the damping forces in DC and PGC, respectively. The gray shaded area indicates the range of the capture velocity of the Sisyphus force.