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61-554: As electron kinetic energy and undulator parameters can be adapted as desired, free-electron lasers are tunable and can be built for a wider frequency range than any other type of laser, currently ranging in wavelength from microwaves , through terahertz radiation and infrared , to the visible spectrum , ultraviolet , and X-ray . The first free-electron laser was developed by John Madey in 1971 at Stanford University using technology developed by Hans Motz and his coworkers, who built an undulator at Stanford in 1953, using

122-401: A Lyot filter into the laser cavity, which is rotated to tune the laser. Other tuning techniques involve diffraction gratings, prisms, etalons, and combinations of these. Multiple-prism grating arrangements , in several configurations, as described by Duarte , are used in diode, dye, gas, and other tunable lasers. Lorentz factor The Lorentz factor or Lorentz term (also known as

183-553: A wiggler , because the Lorentz force of the field forces the electrons in the beam to wiggle transversely, traveling along a sinusoidal path about the axis of the undulator. The transverse acceleration of the electrons across this path results in the release of photons , which are monochromatic but still incoherent, because the electromagnetic waves from randomly distributed electrons interfere constructively and destructively in time. The resulting radiation power scales linearly with

244-490: A clear view, a resolution of 0.1–0.3 nm is required. The short pulse durations allow images of X-ray diffraction patterns to be recorded before the molecules are destroyed. The bright, fast X-rays were produced at the Linac Coherent Light Source at SLAC. As of 2014, LCLS was the world's most powerful X-ray FEL. Due to the increased repetition rates of the next-generation X-ray FEL sources, such as

305-421: A design energy by a particle accelerator , usually a linear particle accelerator . Then the beam passes through a periodic arrangement of magnets with alternating poles across the beam path, which creates a side to side magnetic field . The direction of the beam is called the longitudinal direction, while the direction across the beam path is called transverse. This array of magnets is called an undulator or

366-417: A distance equal to one radiation wavelength. This interaction drives all electrons to begin emitting coherent radiation. Emitted radiation can reinforce itself perfectly whereby wave crests and wave troughs are optimally superimposed on one another. This results in an exponential increase of emitted radiation power, leading to high beam intensities and laser-like properties. Examples of facilities operating on

427-546: A high-voltage supply. The electron beam must be maintained in a vacuum , which requires the use of numerous vacuum pumps along the beam path. While this equipment is bulky and expensive, free-electron lasers can achieve very high peak powers, and the tunability of FELs makes them highly desirable in many disciplines, including chemistry, structure determination of molecules in biology, medical diagnosis , and nondestructive testing . The Fritz Haber Institute in Berlin completed

488-400: A laser chip, so that the light emerges through the top of the device, rather than through the edge. As a result, VCSELs produce beams of a more circular nature than their cousins and beams that do not diverge as rapidly. As of December 2008 , there is no widely tunable VCSEL commercially available any more for DWDM -system application. It is claimed that the first infrared laser with

549-454: A light-beam-induced current (LBIC) experiment, from which the external quantum efficiency (EQE) of a device can be mapped. They can also be used for the characterisation of gold nanoparticles and single-walled carbon nanotube thermopiles , where a wide tunable range from 400 nm to 1,000 nm is essential. Tunable sources were recently used for the development of hyperspectral imaging for early detection of retinal diseases where

610-542: A mid-infrared and terahertz FEL in 2013. The lack of mirror materials that can reflect extreme ultraviolet and x-rays means that X-ray free electron lasers (XFEL) need to work without a resonant cavity . Consequently, in an X-ray FEL (XFEL) the beam is produced by a single pass of radiation through the undulator . This requires that there be enough amplification over a single pass to produce an appropriate beam. Hence, XFELs use long undulator sections that are tens or hundreds of meters long. This allows XFELs to produce

671-511: A much larger tunable range; by the use of vernier-tunable Bragg mirrors and a phase section, a single-mode output range of > 50 nm can be selected. Other technologies to achieve wide tuning ranges for DWDM -systems are: Rather than placing the resonator mirrors at the edges of the device, the mirrors in a VCSEL are located on the top and bottom of the semiconductor material. Somewhat confusingly, these mirrors are typically DBR devices. This arrangement causes light to "bounce" vertically in

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732-482: A person who is less than 37 years of age at the time of the FEL conference. Tunable laser A tunable laser is a laser whose wavelength of operation can be altered in a controlled manner. While all laser gain media allow small shifts in output wavelength, only a few types of lasers allow continuous tuning over a significant wavelength range. There are many types and categories of tunable lasers. They exist in

793-501: A seeding technique called "High-Gain Harmonic-Generation" that works to X-ray wavelength has been developed. The technique, which can be multiple-staged in an FEL to achieve increasingly shorter wavelengths, utilizes a longitudinal shift of the radiation relative to the electron bunch to avoid the reduced beam quality caused by a previous stage. This longitudinal staging along the beam is called "Fresh-Bunch". This technique

854-518: A tunability of more than one octave was a germanium crystal laser. The range of applications of tunable lasers is extremely wide. When coupled to the right filter, a tunable source can be tuned over a few hundreds of nanometers with a spectral resolution that can go from 4 nm to 0.3 nm, depending on the wavelength range. With a good enough isolation (>OD4), tunable sources can be used for basic absorption and photoluminescence studies. They can be used for solar cells characterisation in

915-399: A wide range of wavelengths, a small bandwidth, and outstanding isolation is needed to achieve efficient illumination of the entire retina . Tunable sources can be a powerful tool for reflection and transmission spectroscopy , photobiology , detector calibration, hyperspectral imaging, and steady-state pump probe experiments, to name only a few. The first true broadly tunable laser was

976-405: Is a list of formulae from Special relativity which use γ as a shorthand: Corollaries of the above transformations are the results: Applying conservation of momentum and energy leads to these results: In the table below, the left-hand column shows speeds as different fractions of the speed of light (i.e. in units of c ). The middle column shows the corresponding Lorentz factor, the final

1037-648: Is a special case of a binomial series . The approximation γ ≈ 1 + 1 2 β 2 {\textstyle \gamma \approx 1+{\frac {1}{2}}\beta ^{2}} may be used to calculate relativistic effects at low speeds. It holds to within 1% error for v  < 0.4  c ( v  < 120,000 km/s), and to within 0.1% error for v  < 0.22  c ( v  < 66,000 km/s). The truncated versions of this series also allow physicists to prove that special relativity reduces to Newtonian mechanics at low speeds. For example, in special relativity,

1098-495: Is clear that to pave the way towards single-particle X-ray FEL imaging at full repetition rates, several challenges have to be overcome before the next resolution revolution can be achieved. New biomarkers for metabolic diseases: taking advantage of the selectivity and sensitivity when combining infrared ion spectroscopy and mass spectrometry scientists can provide a structural fingerprint of small molecules in biological samples, like blood or urine. This new and unique methodology

1159-900: Is generally denoted γ (the Greek lowercase letter gamma ). Sometimes (especially in discussion of superluminal motion ) the factor is written as Γ (Greek uppercase-gamma) rather than γ . The Lorentz factor γ is defined as γ = 1 1 − v 2 c 2 = c 2 c 2 − v 2 = c c 2 − v 2 = 1 1 − β 2 = d t d τ , {\displaystyle \gamma ={\frac {1}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}={\sqrt {\frac {c^{2}}{c^{2}-v^{2}}}}={\frac {c}{\sqrt {c^{2}-v^{2}}}}={\frac {1}{\sqrt {1-\beta ^{2}}}}={\frac {dt}{d\tau }},} where: This

1220-466: Is generating exciting new possibilities to better understand metabolic diseases and develop novel diagnostic and therapeutic strategies. Research by Glenn Edwards and colleagues at Vanderbilt University 's FEL Center in 1994 found that soft tissues including skin, cornea , and brain tissue could be cut, or ablated , using infrared FEL wavelengths around 6.45 micrometres with minimal collateral damage to adjacent tissue. This led to surgeries on humans,

1281-443: Is invoked to explain the so-called "compactness" problem: absent this ultra-relativistic expansion, the ejecta would be optically thick to pair production at typical peak spectral energies of a few 100 keV, whereas the prompt emission is observed to be non-thermal. Muons , a subatomic particle, travel at a speed such that they have a relatively high Lorentz factor and therefore experience extreme time dilation . Since muons have

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1342-788: Is rarely used, although it does appear in the Maxwell–Jüttner distribution . Applying the definition of rapidity as the hyperbolic angle φ {\displaystyle \varphi } : tanh ⁡ φ = β {\displaystyle \tanh \varphi =\beta } also leads to γ (by use of hyperbolic identities ): γ = cosh ⁡ φ = 1 1 − tanh 2 ⁡ φ = 1 1 − β 2 . {\displaystyle \gamma =\cosh \varphi ={\frac {1}{\sqrt {1-\tanh ^{2}\varphi }}}={\frac {1}{\sqrt {1-\beta ^{2}}}}.} Using

1403-405: Is the elementary charge . Expressed in practical units, the dimensionless undulator parameter is K = 0.934 ⋅ B 0 [T] ⋅ λ u [cm] {\displaystyle K=0.934\cdot B_{0}\,{\text{[T]}}\cdot \lambda _{u}\,{\text{[cm]}}} . In most cases, the theory of classical electromagnetism adequately accounts for

1464-542: Is the most frequently used form in practice, though not the only one (see below for alternative forms). To complement the definition, some authors define the reciprocal α = 1 γ = 1 − v 2 c 2   = 1 − β 2 ; {\displaystyle \alpha ={\frac {1}{\gamma }}={\sqrt {1-{\frac {v^{2}}{c^{2}}}}}\ ={\sqrt {1-{\beta }^{2}}};} see velocity addition formula . Following

1525-487: Is the reciprocal. Values in bold are exact. There are other ways to write the factor. Above, velocity v was used, but related variables such as momentum and rapidity may also be convenient. Solving the previous relativistic momentum equation for γ leads to γ = 1 + ( p m 0 c ) 2 . {\displaystyle \gamma ={\sqrt {1+\left({\frac {p}{m_{0}c}}\right)^{2}}}\,.} This form

1586-438: Is the undulator wavelength (the spatial period of the magnetic field), γ {\displaystyle \gamma } is the relativistic Lorentz factor and the proportionality constant depends on the undulator geometry and is of the order of 1. This formula can be understood as a combination of two relativistic effects. Imagine you are sitting on an electron passing through the undulator. Due to Lorentz contraction

1647-457: Is truly monochromatic ; all lasers can emit light over some range of frequencies, known as the linewidth of the laser transition. In most lasers, this linewidth is quite narrow (for example, the 1,064 nm wavelength transition of a Nd:YAG laser has a linewidth of approximately 120 GHz, or 0.45 nm ). Tuning of the laser output across this range can be achieved by placing wavelength-selective optical elements (such as an etalon ) into

1708-484: The European XFEL , the expected number of diffraction patterns is also expected to increase by a substantial amount. The increase in the number of diffraction patterns will place a large strain on existing analysis methods. To combat this, several methods have been researched to sort the huge amount of data that typical X-ray FEL experiments will generate. While the various methods have been shown to be effective, it

1769-1102: The Maclaurin series : γ = 1 1 − β 2 = ∑ n = 0 ∞ β 2 n ∏ k = 1 n ( 2 k − 1 2 k ) = 1 + 1 2 β 2 + 3 8 β 4 + 5 16 β 6 + 35 128 β 8 + 63 256 β 10 + ⋯ , {\displaystyle {\begin{aligned}\gamma &={\dfrac {1}{\sqrt {1-\beta ^{2}}}}\\[1ex]&=\sum _{n=0}^{\infty }\beta ^{2n}\prod _{k=1}^{n}\left({\dfrac {2k-1}{2k}}\right)\\[1ex]&=1+{\tfrac {1}{2}}\beta ^{2}+{\tfrac {3}{8}}\beta ^{4}+{\tfrac {5}{16}}\beta ^{6}+{\tfrac {35}{128}}\beta ^{8}+{\tfrac {63}{256}}\beta ^{10}+\cdots ,\end{aligned}}} which

1830-451: The Office of Naval Research announced it had awarded Raytheon a contract to develop a 100 kW experimental FEL. On March 18, 2010 Boeing Directed Energy Systems announced the completion of an initial design for U.S. Naval use. A prototype FEL system was demonstrated, with a full-power prototype scheduled by 2018. The FEL prize is given to a person who has contributed significantly to

1891-434: The dye laser in 1966. Hänsch introduced the first narrow-linewidth tunable laser in 1972. Dye lasers and some vibronic solid-state lasers have extremely large bandwidths, allowing tuning over a range of tens to hundreds of nanometres. Titanium-doped sapphire is the most common tunable solid-state laser, capable of laser operation from 670 nm to 1,100 nm wavelengths. Typically these laser systems incorporate

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1952-553: The gamma factor ) is a dimensionless quantity expressing how much the measurements of time, length, and other physical properties change for an object while it moves. The expression appears in several equations in special relativity , and it arises in derivations of the Lorentz transformations . The name originates from its earlier appearance in Lorentzian electrodynamics – named after the Dutch physicist Hendrik Lorentz . It

2013-468: The temperature of the laser is changed, then the index change of the DBR structure causes a shift in its peak reflective wavelength and thus the wavelength of the laser. The tuning range of such lasers is typically a few nanometres, up to a maximum of approximately 6 nm, as the laser temperature is changed over ~50 K . As a rule of thumb, the wavelength is tuned by 0.08 nm/K for DFB lasers operating in

2074-421: The ultraviolet and blue through to green wavelengths. For some types of lasers, the laser's cavity length can be modified, and thus they can be continuously tuned over a significant wavelength range. Distributed feedback (DFB) semiconductor lasers and vertical-cavity surface-emitting lasers (VCSELs) use periodic distributed Bragg reflector (DBR) structures to form the mirrors of the optical cavity. If

2135-411: The wiggler magnetic configuration. Madey used a 43 MeV electron beam and 5 m long wiggler to amplify a signal. To create an FEL, an electron gun is used. A beam of electrons is generated by a short laser pulse illuminating a photocathode located inside a microwave cavity and accelerated to almost the speed of light in a device called a photoinjector . The beam is further accelerated to

2196-460: The 1,550 nm wavelength regime. Such lasers are commonly used in optical communications applications, such as DWDM -systems, to allow adjustment of the signal wavelength. To get wideband tuning using this technique, some such as Santur Corporation or Nippon Telegraph and Telephone (NTT Corporation) contain an array of such lasers on a single chip and concatenate the tuning ranges. Sample Grating Distributed Bragg Reflector lasers (SG-DBR) have

2257-470: The SASE FEL principle include the: In 2022, an upgrade to Stanford University ’s Linac Coherent Light Source (LCLS-II) used temperatures around −271 °C to produce 10 pulses/second of near light-speed electrons, using superconducting niobium cavities. One problem with SASE FELs is the lack of temporal coherence due to a noisy startup process. To avoid this, one can "seed" an FEL with a laser tuned to

2318-421: The added benefit of minimal collateral damage. A review of FELs for medical uses is given in the 1st edition of Tunable Laser Applications. Several small, clinical lasers tunable in the 6 to 7 micrometre range with pulse structure and energy to give minimal collateral damage in soft tissue have been created. At Vanderbilt, there exists a Raman shifted system pumped by an Alexandrite laser. Rox Anderson proposed

2379-434: The advancement of the field of free-electron lasers. In addition, it gives the international FEL community the opportunity to recognize its members for their outstanding achievements. The prize winners are announced at the FEL conference, which currently takes place every two years. The Young Scientist FEL Award (or "Young Investigator FEL Prize") is intended to honor outstanding contributions to FEL science and technology from

2440-400: The behavior of free electron lasers. For sufficiently short wavelengths, quantum effects of electron recoil and shot noise may have to be considered. Free-electron lasers require the use of an electron accelerator with its associated shielding, as accelerated electrons can be a radiation hazard if not properly contained. These accelerators are typically powered by klystrons , which require

2501-465: The brightest X-ray pulses of any human-made x-ray source. The intense pulses from the X-ray laser lies in the principle of self-amplified spontaneous emission (SASE), which leads to microbunching. Initially all electrons are distributed evenly and emit only incoherent spontaneous radiation. Through the interaction of this radiation and the electrons' oscillations , they drift into microbunches separated by

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2562-420: The bunched electrons is in phase, and the fields add together coherently . The radiation intensity grows, causing additional microbunching of the electrons, which continue to radiate in phase with each other. This process continues until the electrons are completely microbunched and the radiation reaches a saturated power several orders of magnitude higher than that of the undulator radiation. The wavelength of

2623-418: The first ever using a free-electron laser. Starting in 1999, Copeland and Konrad performed three surgeries in which they resected meningioma brain tumors . Beginning in 2000, Joos and Mawn performed five surgeries that cut a window in the sheath of the optic nerve , to test the efficacy for optic nerve sheath fenestration . These eight surgeries produced results consistent with the standard of care and with

2684-2261: The following two equations hold: p = γ m v , E = γ m c 2 . {\displaystyle {\begin{aligned}\mathbf {p} &=\gamma m\mathbf {v} ,\\E&=\gamma mc^{2}.\end{aligned}}} For γ ≈ 1 {\displaystyle \gamma \approx 1} and γ ≈ 1 + 1 2 β 2 {\textstyle \gamma \approx 1+{\frac {1}{2}}\beta ^{2}} , respectively, these reduce to their Newtonian equivalents: p = m v , E = m c 2 + 1 2 m v 2 . {\displaystyle {\begin{aligned}\mathbf {p} &=m\mathbf {v} ,\\E&=mc^{2}+{\tfrac {1}{2}}mv^{2}.\end{aligned}}} The Lorentz factor equation can also be inverted to yield β = 1 − 1 γ 2 . {\displaystyle \beta ={\sqrt {1-{\frac {1}{\gamma ^{2}}}}}.} This has an asymptotic form β = 1 − 1 2 γ − 2 − 1 8 γ − 4 − 1 16 γ − 6 − 5 128 γ − 8 + ⋯ . {\displaystyle \beta =1-{\tfrac {1}{2}}\gamma ^{-2}-{\tfrac {1}{8}}\gamma ^{-4}-{\tfrac {1}{16}}\gamma ^{-6}-{\tfrac {5}{128}}\gamma ^{-8}+\cdots \,.} The first two terms are occasionally used to quickly calculate velocities from large γ values. The approximation β ≈ 1 − 1 2 γ − 2 {\textstyle \beta \approx 1-{\frac {1}{2}}\gamma ^{-2}} holds to within 1% tolerance for γ > 2 , and to within 0.1% tolerance for γ > 3.5 . The standard model of long-duration gamma-ray bursts (GRBs) holds that these explosions are ultra-relativistic (initial γ greater than approximately 100), which

2745-404: The gain of the strongest transition is suppressed, such as by use of wavelength-selective dielectric mirrors . If a dispersive element, such as a prism , is introduced into the optical cavity, tilting the cavity's mirrors can cause tuning of the laser as it "hops" between different laser lines. Such schemes are common in argon - ion lasers , allowing tuning of the laser to a number of lines from

2806-454: The gas, liquid, and solid states. Among the types of tunable lasers are excimer lasers , gas lasers (such as CO 2 and He-Ne lasers), dye lasers (liquid and solid state), transition-metal solid-state lasers , semiconductor crystal and diode lasers , and free-electron lasers . Tunable lasers find applications in spectroscopy , photochemistry , atomic vapor laser isotope separation , and optical communications . No real laser

2867-636: The lack of conventional x-ray lasers. In late 2010, in Italy, the seeded-FEL source FERMI@Elettra started commissioning, at the Trieste Synchrotron Laboratory . FERMI@Elettra is a single-pass FEL user-facility covering the wavelength range from 100 nm (12 eV) to 10 nm (124 eV), located next to the third-generation synchrotron radiation facility ELETTRA in Trieste, Italy. In 2001, at Brookhaven national laboratory ,

2928-453: The laser's optical cavity , to provide selection of a particular longitudinal mode of the cavity. Most laser gain media have a number of transition wavelengths on which laser operation can be achieved. For example, as well as the principal 1,064 nm output line, Nd:YAG has weaker transitions at wavelengths of 1,052 nm, 1,074 nm, 1,112 nm, 1,319 nm, and a number of other lines. Usually, these lines do not operate unless

2989-405: The medical application of the free-electron laser in melting fats without harming the overlying skin. At infrared wavelengths , water in tissue was heated by the laser, but at wavelengths corresponding to 915, 1210 and 1720 nm , subsurface lipids were differentially heated more strongly than water. The possible applications of this selective photothermolysis (heating tissues using light) include

3050-445: The number of electrons. Mirrors at each end of the undulator create an optical cavity , causing the radiation to form standing waves , or alternately an external excitation laser is provided. The radiation becomes sufficiently strong that the transverse electric field of the radiation beam interacts with the transverse electron current created by the sinusoidal wiggling motion, causing some electrons to gain and others to lose energy to

3111-404: The optical field via the ponderomotive force . This energy modulation evolves into electron density (current) modulations with a period of one optical wavelength. The electrons are thus longitudinally clumped into microbunches , separated by one optical wavelength along the axis. Whereas an undulator alone would cause the electrons to radiate independently (incoherently), the radiation emitted by

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3172-845: The property of Lorentz transformation , it can be shown that rapidity is additive, a useful property that velocity does not have. Thus the rapidity parameter forms a one-parameter group , a foundation for physical models. The Bunney identity represents the Lorentz factor in terms of an infinite series of Bessel functions : ∑ m = 1 ∞ ( J m − 1 2 ( m β ) + J m + 1 2 ( m β ) ) = 1 1 − β 2 . {\displaystyle \sum _{m=1}^{\infty }\left(J_{m-1}^{2}(m\beta )+J_{m+1}^{2}(m\beta )\right)={\frac {1}{\sqrt {1-\beta ^{2}}}}.} The Lorentz factor has

3233-453: The radiation emitted can be readily tuned by adjusting the energy of the electron beam or the magnetic-field strength of the undulators. FELs are relativistic machines. The wavelength of the emitted radiation, λ r {\displaystyle \lambda _{r}} , is given by or when the wiggler strength parameter K , discussed below, is small where λ u {\displaystyle \lambda _{u}}

3294-435: The resonance of the FEL. Such a temporally coherent seed can be produced by more conventional means, such as by high harmonic generation (HHG) using an optical laser pulse. This results in coherent amplification of the input signal; in effect, the output laser quality is characterized by the seed. While HHG seeds are available at wavelengths down to the extreme ultraviolet, seeding is not feasible at x-ray wavelengths due to

3355-404: The second γ {\displaystyle \gamma } factor to the above formula. In an X-ray FEL the typical undulator wavelength of 1 cm is transformed to X-ray wavelengths on the order of 1 nm by γ {\displaystyle \gamma } ≈ 2000, i.e. the electrons have to travel with the speed of 0.9999998 c . K , a dimensionless parameter, defines

3416-517: The seeding limitation for x-ray wavelengths by self-seeding the laser with its own beam after being filtered through a diamond monochromator . The resulting intensity and monochromaticity of the beam were unprecedented and allowed new experiments to be conducted involving manipulating atoms and imaging molecules. Other labs around the world are incorporating the technique into their equipment. Researchers have explored X-ray free-electron lasers as an alternative to synchrotron light sources that have been

3477-618: The selective destruction of sebum lipids to treat acne , as well as targeting other lipids associated with cellulite and body fat as well as fatty plaques that form in arteries which can help treat atherosclerosis and heart disease . FEL technology is being evaluated by the US Navy as a candidate for an anti-aircraft and anti- missile directed-energy weapon . The Thomas Jefferson National Accelerator Facility 's FEL has demonstrated over 14 kW power output. Compact multi-megawatt class FEL weapons are undergoing research. On June 9, 2009

3538-414: The undulator is shortened by a γ {\displaystyle \gamma } factor and the electron experiences much shorter undulator wavelength λ u / γ {\displaystyle \lambda _{u}/\gamma } . However, the radiation emitted at this wavelength is observed in the laboratory frame of reference and the relativistic Doppler effect brings

3599-405: The wiggler strength as the relationship between the length of a period and the radius of bend, where ρ {\displaystyle \rho } is the bending radius, B 0 {\displaystyle B_{0}} is the applied magnetic field, m e {\displaystyle m_{e}} is the electron mass, and e {\displaystyle e}

3660-411: The workhorses of protein crystallography and cell biology . Exceptionally bright and fast X-rays can image proteins using x-ray crystallography . This technique allows first-time imaging of proteins that do not stack in a way that allows imaging by conventional techniques, 25% of the total number of proteins. Resolutions of 0.8 nm have been achieved with pulse durations of 30 femtoseconds . To get

3721-615: Was demonstrated at x-ray wavelength at Trieste Synchrotron Laboratory . A similar staging approach, named "Fresh-Slice", was demonstrated at the Paul Scherrer Institut , also at X-ray wavelengths. In the Fresh Slice the short X-ray pulse produced at the first stage is moved to a fresh part of the electron bunch by a transverse tilt of the bunch. In 2012, scientists working on the LCLS found an alternative solution to

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