M. V. Gorbunkov

Laser-electron generator for X-ray applications in science and technology

The possibility of the creation and the application prospects of the laser-electron X-ray generator based on Thomson scattering of laser radiation on a bunch of relativistic electrons are considered. Such a generator fills the existing gap between X-ray tubes and synchrotron radiation sources, which is several orders of magnitude in terms of the brightness, average intensity, size, and also in the construction and running costs.

Proposal of a compact repetitive dichromatic x-ray generator with millisecond duty cycle for medical applications

Many practical applications of x-rays lie in the important for the society fields of medical imaging, custom, transport inspection and security. Scientific applications besides of fundamental research include material sciences, biomicroscopy, and protein crystallography. Two types of x-ray sources dominate now: conventional tubes and electron accelerators equipped with insertion devices. The first are relatively cheap, robust, and compact but have low brightness and poorly controlled photon spectrum. The second generate low divergent beams with orders of magnitude higher brightness and well-controlled and tunable spectrum, but are very expensive and large in scale. So accelerator based x-ray sources are mainly still used for scientific applications and x-ray tubes - in commercial equipment. The latter motivated by the importance for the society made an impressive progress during last decades mostly due to the fast developments of radiation detectors, computers and software used for image acquisition and processing. At the same time many important problems cannot be solved without radical improvement of the parameters of the x-ray beam that in commercial devices is still provided by conventional x-ray tubes. Therefore there is a quest now for a compact and relatively cheap source to generate x-ray beam with parameters and controllability approaching synchrotron radiation. Rapid developments of lasers and particle accelerators resulted in implementation of laser plasma x-ray sources and free electron lasers for various experiments requiring high intensity, shrt duration and monochromatic x-ray radiation. Further progress towards practical application is expected from the combination of laser and particle accelerator in a single unit for efficient x-ray generation.

Design study of compact Laser-Electron X-ray Generator for material and life sciences applications

X-ray generators utilizing Thomson scattering fill in the gap that exists between conventional and synchrotron-based X-ray sources. They are expected to be more intensive than X-ray tubes and more compact, accessible and less expensive than synchrotrons. In this work, two operation modes of Thomson X-ray source (or laser-electron X-ray generator — LEXG) are documented: quasi continuous wave (QCW) and a pulsed one. They are considered for material sciences and medical applications that are currently implemented at Synchrotron Radiation (SR) facilities. The proposed system contains a ~ 50 MeV linac and a picosecond laser with an average power ~ few hundred Watts. The Thomson X-ray source is able to deliver up to 5 × 1011 photons in a millisecond flash and an average flux of 1012–1013 phot/sec. To achieve these parameters with existing optical and accelerator technology, the system must also contain a ring for storage of e-bunches for 103–105 revolutions and an optical circulator for storage of laser pulses for 102 passes. The XAFS spectroscopy, small animal angiography and human noninvasive coronary angiography are considered as possible applications of laser-electron X-ray generator.X-Ray generations utilizing Thomson scattering fill in the gap that exists between conventional and synchrotron-based X-ray sources. They are expected to be more intense than X-ray tubes and more compact, accessible and less expensive than synchrotron. In this work, two operation modes of Thomson X-ray source are documented: quasi CW(QCW) and a pulsed one are considered for material sciences and medical applications being implemented currently at Synchrotron Radiation (SR) facilities.

Submicrosecond regular and chaotic nonlinear dynamics in a pulsed picosecond Nd:YAG laser with millisecond pumping

We propose and study both numerically and experimentally a feedback-controlled laser system capable of generating regular bursts with a submicrosecond period. Bursting is obtained in a laser that is controlled by a combination of feedbacks in which the negative feedback loop action is delayed by one cavity round trip with respect to the positive one, and the period is adjusted by relative feedback sensitivity. The proper combination of feedbacks is realized in a Nd:YAG laser with millisecond pumping by means of a single optoelectronic negative feedback unit that utilizes the signal reflected from an intracavity Pockels cell polarizer. Regular bursting (microgroups of picosecond pulses) with controlled periods from 25 to 75 cavity round trips is obtained experimentally. The development of chaotic dynamics displayed by the system at a higher pumping level differs from the Feigenbaum scenario.

Relativistic Thomson scattering in compact linacs and storage rings: a route to quasi-monochromatic tunable laboratory-scale X-ray sources

Free electron lasers are expected to become brightest hard X-ray sources in the next decade. Meanwhile a quest still exists for moderately bright but lab scale X-ray sources to fill in the gap between conventional X-ray tubes and synchrotron radiation beamlines. Thomson scattering of picosecond laser pulses on electron bunches is considered as possible solution to this problem.

Self-stimulated emission of undulator radiation

We attract attention that interaction of particle in downstream undulator with its own wavelet emitted in upstream undulator could be as strong as with the frictional field in undulator itself. This phenomenon could be used for enhancement of signal from pickup undulators in optical stochastic cooling methods as well as for increase of damping. Particle passed an undulator emits undulator radiation wavelet (URW) which length is 1 uf06c M where M is the number of undulator periods, 1 uf06c – is the wavelength of first harmonic. In system of N identical undulators located along straight line the particle radiates train of wavelets with separation l; both l and 1 uf06c defined by Doppler effect, by angle uf071 between instant velocity and direction to observer, by distance between undulators 0 l , by period of undulator u uf06c and by relativistic factor 1 uf067 uf03euf03e . In straight forward direction 0 uf071 uf03d they are 2 0 / 2 l l uf067 uf03d , 2 1 / 2 u uf06c uf067 uf06c uf03d . Energy radiated by particle in system of N undulators is N times bigger than the one radiated in just one undulator. Spectrum of radiation emitted in arbitrary direction also changes: appears line-type spectrum. Integrated spectrum changes not much, see [1]. In this publication we suggest to increase the loss rate in system of N undulators by introduction of controlled delays in motion of particles relative to the URW between undulators, Fig.1. Figure 1: Scheme of installation. Delays chosen so that particle enters the following undulator together with the front edge of URW emitted in anterior undulators in decelerating phase. In this case the particle will experience deceleration in its self field generated by its instant motion in a field of undulator (friction force generated by spontantenous incoherent radiation) as well as in the field of URW from anterior undulators (induced radiation in field of co-propagating electromagnetic wave). Under such condition occurs superposition of wavelets which yield the electric field grows ~N so the energy emitted grows ~N 2 . To be effective and optimal, this system must use appropriate focusing elements such as lenses and/or focusing mirrors, see the scheme of installation on Figs. 1, 2. Mirrors and lenses must form crossover with the Rayleigh length of the order of the length of undulator 2 / u R M Z uf06c uf040 [2]. Figure 2: Equivalent optical scheme. The scheme of installation suggested could be used effectively in different methods of optical cooling (OC) of particles in damping rings [2]-[5]. So this installation can serve as effective pick-up undulator. According to OC principle the optical parametric amplifier(s), controllable screens [2] and kicker undulators could be located in the subsequent straight sections. We would like to remind here that for any method of Optical Stochastic Cooling it is important to inject in spectral bandwidth / ~1/ 2M uf06c uf06c uf044 and in angles ~ 1 / M uf071 uf067 uf044 as many photons as possible. This number does not depend on the length of undulator [2]. So usage of three pickup undulators is 3 times more effective in the emitted field strengths and 9 times more effective in the emitted energy, than just single pickup undulator and so on. It means that usage of three pickup undulators and singe kicker one in the schemes of OSC is 3 times more effective for damping time, than just single pickup and single kicker undulator. Usage of three pickup undulators and three kicker undulator is 9 times more effective, than just single pickup and single kicker undulator and so on. So the effectiveness of the pickup and kicker systems consisting of N undulators each is proportional to N 2 . We considered here the case when optical delays tuned so that wavelets emitted by particle are congruent and particle always stays in decelerating phase. To be so the beam delay system must be isochronous for all particles in the beam. There is a possibility for another scheme with self-stimulated undulator radiation. This scheme uses isochronous storage ring with undulator installed in one straight section. Mirrors installed at both sides of undulator set an optical cavity so that period of oscillation of wavelet in optical cavity coincides with period of revolution of particles in storage ring. In that case the wavelets will be accumulated in optical cavity superimposed one by another with the accuracy uf06c uf03cuf03c 1 . This scheme is typical for FEL, but the difference is that the storage ring is isochronous and that the motion of the wavelet and the bunch are synchronized one with another. In this case there is no coherence in radiation among different particles in the bunch (as the particles are not grouped in microbunches with longitudinal dimensions uf07cuf07c uf031 uf073 uf03cuf03c uf06c separated by distances which are integer of 1 uf06c ), but stimulated processes are going in their own fields of URWs emitted in undulator in earlier times. All properties of spontantenous incoherent radiation emitted by particles in this case are not changed, except intensity, which becomes higher now in Q times, where Q is the quality factor of optical cavity. If however, conditions of synchronicity are broken weakly so the wavelets emitted at each pass through undulator are shifted by 1 1 ~ M uf06c uf06c uf0b8 , then properties of radiation might be different now (intensity will drop, but monochromaticity will be enhanced). If isochronicity satisfied for particles in some narrow diapason of angles and energy, then this will narrow angular divergence and spectrum of undulator radiation at the exit of optical cavity. Strong dependence of intensity of undulator radiation on energy may change the cooling rate of particles in storage ring [6]. This phenomenon of self-stimulated emission in undulator can be used for tuning optical system of any optical stochastic cooling schemes. This correspond operation of system with optical amplifier turned off and the optical delay shifted by 2 / ~ uf06c with respect to the optimal cooling phase. So some tuning could be done without optical amplifier at all, if someone just registering intensity of forward radiation after kicker undulator. Then just by shifting optical delay back by half wavelength and tuning on optical amplifier, the system will be set to optimal phasing. We would like to mention that in parametric FEL with mirrors [7], [8] (stimulated superradiant emission in pre-bunched Free-Electron Laser) the process of radiation is similar to described in our paper. However there new portions of particles, bunched into small-size, passing through undulator with the same periodicity. This work was supported in part by RFBR under Grant No 09-02-00638a. References [1] E.G.Bessonov, “Undulators, Undulator Radiation, Free-Electron Lasers”, Proc. Lebedev Phys. Inst., Ser.214, 1993, p.3-119, Chief ed. N.G.Basov, Editor-in-chief P.A.Cherenkov; “Peculiarities of harmonic generation in a system of identical undulators”, Nucl. Instr. Meth. A 341 (1994), ABS 87 (http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6TJM-470F3WY-J01&_cdi=5314&_user=492137&_pii=0168900294904596&_orig=search&_coverDate=03 %2F01%2F1994&_sk=996589998&view=c&wchp=dGLbVzzzSkzV&md5=8309b9f8f17e8b2ad6263367db281526&ie=/sdarticle.pdf ). [2] E.G. Bessonov, M.V. Gorbunkov, A.A. Mikhailichenko, “Enhanced Optical Cooling System Test in a Muon Storage Ring”. Phys. Rev. ST Accel. Beams 11, 011302 (2008). [3] A.A. Mikhailichenko, M.S. Zolotorev,” Optical Stochastic Cooling”, Phys. Rev. Lett.71: 4146-4149, 1993. [4] A.A. Zholents, M.S. Zolotorev, W. Wan “Optical Stochastic Cooling of Muons”, Phys. Rev. ST Accel. Beams 4, 031001, (2001). [5] W.A. Franklin, “ Optical Stochastic Cooling Proof-of-Principle Experiment”, Proceedings of PAC07, p.1904-1906, 2007. [6] E.G. Bessonov, “The Evolution of the Phase Space Density of Particle Beams in External Felds”, Proceedings of COOL 2009, Lanzhou, China http://cool09.impcas.ac.cn/JACoW/papers/tua2mcio02.pdf, see also: arXiv:0808.2342v1; http://lanl.arxiv.org/abs/0808.2342; http://arxiv.org/ftp/arxiv/papers/0808/0808.2342.pdf . [7] V.I. Alexeev, E.G.Bessonov et al., “A Parametric Free-Electron Laser Based on the Microtron”, Nucl. Instr. Meth., 1989, A282, p.436-438; Brief reports on Physicas No 12 (1987), p. 43. [8] M.Arbel, A.Abramovich, A.L.Eichenbaum, A.Gover, H.Kleinman, Y.Pinhasi, I.M.Yakover Superradiant and Stimulated Superradiant Emission in Prebunched Free-Electron Maser”, PRL, v.86, No 12, 2001, p. 2561-2564.We raise attention to the fact that a particle in a downstream undulator interacting with its own wavelet emitted from an upstream undulator can be as strong as its direct interaction with the frictional field of undulator itself. This phenomenon could be used for the enhancement of the signal from pickup undulators in optical stochastic cooling as well as to decrease of the damping time of particles in storage rings.

Laser Physics Research Relevant to Laser-Electron X-Ray Generator

A prototype of laser unit for Laser Electron X-Ray Generator is constructed on the basis of the optoelectronic control. The laser system in which an optoelectronic negative feedback is realized by means of a signal reflected from an intracavity Pockels cell polarizer is proposed and tested. The design provides flexible control over pulse train time structure.

Enhanced Optical Cooling of ion beams for LHC

The possibility of enhanced optical cooling (EOC) of Lead ions in LHC is investigated. Non-exponential features of cooling and requirements to the ring lattice, optical, and laser systems are discussed. Comparison with optical stochastic cooling (OSC) is also represented.The possibility of the enhanced optical cooling (EOC) of Lead ions in LHC is investigated. Non-exponential feature of cooling and requirements to the ring lattice, optical and laser systems are discussed. Comparison with optical stochastic cooling (OSC) is represented. INTRODUCTION In original OSC with usage of quadrupole wiggler as a pickup [1], particles with small betatron amplitude do not make an input into signal generation (radiation), so they are not heating the beam. In contrast, in EOC method such selective action achieved by usage of movable screens. These screens located on image plane of optical system having radiating beam as source. Motion realized with the help of fast electro-optical elements driven by external voltage. As a result of this selection the ions with extreme deviations of dynamic variables keep the neighboring ions undisturbed in the first approximation. By this way the number of the particles in the bandwidth, which defines the damping time can be reduced drastically. Some detailed schemes of EOC were suggested in [2]–[4]. Below we consider EOC of fully stripped Lead ions in LHC as example. THE SCHEME OF COOLING The EOC method uses a pickup undulator and one or more kicker undulators installed in different straight sections of a storage ring. The distance determined by a betatron phase advance (2 1) p π − between the pickup and the first kicker undulator and π p′ 2 between each of the following kicker undulators; where p p ′ , = 1, 2, 3... Undulator Radiation Wavelets (URW), emitted by ions in the pickup undulator, transferred by optical system to the movable screen located on the image plane. Here the undesirable part of radiation, corresponding to small betatron amplitudes, is cut. Residual fraction or URW amplified in optical amplifier and pass together with the ions through the followed kicker undulators. THE RATE OF COOLING The change of the square of the amplitude of betatron oscillations of an ion, caused by sudden energy change E δ in a kicker undulator is determined in smooth approximation by 2 2 , 2 ( ) x k A x x x β η η δ δ δ = − + , (1) where ,k xβ is the ion deviation from it’s closed orbit in the kicker undulator; 2 ( / ) x x E E η δ η β δ − = is the change of it’s closed orbit position; x η is the dispersion function in the storage ring; β is the normalized velocity. In the approximation , | | 2 | | 2 k x x x A η β δ < < both the betatron amplitude and the position of the closed orbit will be decreased, if the values , 0 k xβ < , 0 xη δ < . It follows that to cool the ion beam the screen in the optical system must open the pass for URWs emitted by extreme ions entering the pickup undulator with higher energy and betatron deviations , 0 p xβ > from theirs orbits. After that the screen will open images of ions with lower and lower energies until the optical system must be switched off. Then the cooling process can be repeated. So the EOC is going simultaneously both in the longitudinal and transverse degrees of freedom. Optical lengths between pickup and kicker undulators should be picked up so that to inject ions in the kicker undulators at decelerating phases of their own URWs. The total energy of the undulator radiation (UR) emitted by a relativistic ion traversing an undulator with magnetic field B is given by 2 2 2 2 3 to t i u E r B L γ = , (2) where 2 B is an average square of magnetic field along the undulator period u λ ; 2 2 2 / i i r Z e M c = is the classical radius of the ion; e, i M are the electron charge and ion mass respectively; Z is the atomic number, u u L M λ = ; M is the number of undulator periods; γ is the relativistic factor. For a plane harmonic undulator 2 2 0 / 2 B B = , where B0 is the peak of the undulator field. For helical undulator 2 2 0 B B = . The spectrum of the first harmonic of the UR is 1 1 / ( ) dE d E f ξ ξ = , where 1 E = / tot E 2 (1 ) K + , K = 2 / u Ze B λ 2 2 i M c π , ( ) 3 (1 2 f ξ ξ ξ = − + 2 2 ), ξ ξ = 1,min 1 / λ λ , 1min 1 0 |θ λ λ = = , ( 0 1 ξ ≤ ≤ ), ( ) 1 f d ξ ξ = ∫ , 1 M >> , 2 2 2 1 (1 ) / 2 u K λ λ θ γ = + + is the wavelength of the first harmonic of the UR, θ γθ = ; θ , the axial angle. The number of the equivalent photons in the URW in the suitable for cooling frequency range ( / ) 1/ 2 c M ω ω Δ = and angular range 2 (1 ) / 2 K M θ Δ = + 2 2 1 1max / ph N E Z K ω πα = Δ = h , (3) where 2 1 1 ( / ) 3 / 2 (1 ) tot E dE d E M K ω ω Δ = Δ = + , 1max ω = 1min 2 / c π λ , 2 2 1min (1 ) / 2 u M L K γ λ = + . An aperture or filters must be used in the optical system to select a portion of _________________________________________________ *Supported by RFBR under grant No 05-02-17162 and by NSF. Corresponding author; bessonov@x4u.lebedev.ru Proceedings of EPAC 2006, Edinburgh, Scotland TUPLS001 01 Circular Colliders A14 Advanced Concepts 1483 URW in this frequency range for resonance interaction of ions with their URW’s in kicker undulators. Below we accept a Gaussian distribution for the URW, its Rayleigh length 2 1min 4 / /2 R w u Z L πσ λ = = , the rms waist size 1min /8 w u L σ λ π = . In this case the rms electric field strength w E of the wavelet in the kicker undulator 2 3 2 2 3/2 1 1min 2 / 8 / (1 ) w w i u E E r B L K σ λ π γ = Δ = + (4) The rate of the energy loss for ions in the amplified URW is loss w u m kick ampl P eZE L f N β α ⊥ = or 2 2 2 3/ 2 8 /(1 ) loss i kick ampl P eZr f N B K K π γ α = ⋅ + , (5) where γ β / K = ⊥ ; f is the revolution frequency; kick N is the number of kicker undulators; ampl α is the gain in optical amplifier. The damping time for the ion beam in the longitudinal degree of freedom is / E loss P τ σ = , (6) where E σ is the energy spread of the ion beam. According to (6), the damping time for EOC is proportional to the energy spread of the beam which is much less then the energy of ions included in similar expression for damping time controlled by Robinson’s damping criterion. Moreover, because of the nonexponential decay of both energy and angular spreads of the beam the degree of cooling of ion beams for EOC is much higher than 1/e reduction of these parameters. Note that the higher the dispersion function and the less the beta function at the location of the kicker undulator the higher the rate of damping of betatron oscillations. In this case energy jumps of ions lead to larger jumps of closed orbits and near the same jumps of betatron amplitudes. Zero dispersion function at the location of the pick-up undulator can be used to select ions on their amplitudes of betatron oscillations. STOCHASTIC PROCESSES IN THE EOC URW of one ion does not disturb trajectories of other ions if an average distance between ions in the longitudinal direction is more, than the URW’s length, ,1 UR M λ , and the transverse dimensions of the URW’s in kicker undulators are overlapped and higher then the transverse total (dispersion + betatron) dimensions of the being cooled ion beam. This case is named “single ion in the sample”. It corresponds to the beam current

Laser-Electron X-Ray Generator

The possibility of developing a laser-electron x-ray generator based on the Thomson scattering of laser radiation by relativistic electrons and prospects for its application are considered. In its specifications (brightness, average intensity, and dimensions), as well as its construction and operation cost, such a generator is intermediate between x-ray tubes and synchrotron sources. The configuration of channels and experimental stations intended for applications of an x-ray laser-electron generator in studies of the elemental composition and structure of materials is discussed.

Enhanced optical cooling of muon beams

The possibility of the Enhanced Optical Cooling (EOC) of muon beams in storage rings is investigated.