DE102016109171B4 - Device for amplifying micro-electron-packet instabilities - Google Patents

Abstract

A device (1) for amplifying micro-electron-packet instabilities, arranged along a first direction (X): a first arrangement of magnets (10) for beam focusing comprising a sequence of at least two multipoles arranged one behind the other along the first direction (X) Second or higher order (12), wherein the multipoles (12) have an alternating polarity and wherein the beam cross-section σ is within the range after the beam focusing, with λ = wavelength of the micro-electron packets and γ = relativistic factor and at least one second arrangement of magnets (40) for the implementation of energy modulation in density modulation comprising a sequence of a plurality of first polarity (22) groups (22) of different polarity dipoles (24) and a second order multipole (50) preceding the dipoles and wherein one incoming beta function in the second arrangement by at least a factor four is enlarged.

Description

The present invention relates to an apparatus for amplifying microelectron packet instabilities and to a synchrotron radiation source comprising such apparatus.

State of the art

A synchrotron radiation source consists of a high-frequency electron source in which separate electron packets of spatially and temporally co-moving electrons are generated, one or more high-frequency cavity resonators for acceleration, preferably separated by intermediate drift paths (field-free stretches) in which the electron packets collimated and brought to relativistic speeds, one or more undulators, in which the electron packets are forced on oscillating paths transversely to the direction of propagation and thereby excited to emit radiation.

Accelerator systems such as free-electron lasers (FELs) as synchrotron radiation sources produce intense coherent electromagnetic radiation with high brilliance. The technique is based on the generation, acceleration and deflection of electron beams, during the deflection of such an electron beam in an undulator the interaction between already emitted light and the electron beam is used to stimulated emission of coherent radiation.

Modern free-electron lasers are based on the targeted amplification of initial density fluctuations within the electron bunches generated by the radio frequency electron source. In these so-called SASE-FELs, where SASE stands for self-amplifying spontaneous emission (English: self-amplified spontaneous emission), it comes through the mutual interaction between the oscillating electron packet and the initial still spontaneous emission of light radiation generated by the electron packet in the undulator to one longitudinal fine structuring of the electron density. This self-assembly within the electron packet generates thin electron disks (so-called micro-electron packets, MEP) with a mutual distance corresponding to the wavelength of the responsible for the fine structuring radiation. As it continues to pass through the undulator, the micro-electron packets emit radiation at a wavelength corresponding to the undulator's resonant condition and thus its distance. This coherent emission leads to an additional amplification of the total radiated electromagnetic field.

A change in the radiated wavelength is preferably made via the energy of the electron packets or field strength of the undulators. In order to generate the shortest possible electromagnetic radiation into the X-ray range, extremely high charge densities or peak currents must be generated within the electron packets. For this purpose, so-called electron pack compressors, in which the electron packets are deflected dispersively in magnetic baffles, are used in particular.

The high intensity of the FELs is based on the high peak currents of the electron packets and is also desired for many applications. However, the high peak currents also cause an increase in the destructive space charge forces and non-linear dynamic effects within an electron packet. This in turn causes a deterioration of the beam quality, especially with respect to emittance (measure of bundling and cross-section of a particle beam) and energy distribution. In addition, the FEL becomes more susceptible to statistical and dynamic error sources.

Free-electron laser systems are known for space-charge-driven microelectron-packet instability (English: space-charge driven microbunching instability). This instability bundles the electrons into small groups even before they enter an undulator: micro-electron bunches. These micro-electron packets within an electron packet originate in the longitudinal space charge forces created by density fluctuations in the electron packet. These density fluctuations combine with the impedance of the electron packet, which is a consequence of the longitudinal electric field in the electron packet itself. This field causes a broadband modulation of the energy in the electron packet. This energy modulation in turn can be converted into density modulation by the longitudinal dispersion of the accelerator, with some of the original modulations amplified and others suppressed. As a result, in particular density fluctuations are intensified at certain wavelengths. The increased density fluctuations, in turn, cause stronger space charge forces that produce even more energy modulations and thus also the density fluctuations in those particular ones Amplify wavelengths further. This causes the space-charge driven microelectron packet instability.

As already mentioned, the micro-electron instability, also called "microbunching instability", is frequently observed in free-electron lasers and is undesirable there, since in the normal operation of a free-electron laser it leads to a significant deterioration of the quality of the radiated light and a reduction in the achievable stability leads.

This microelectron packet instability is in a simplified model, for example, in Essay 1 of EL Saldin et al. (Longitudinal space-consuming microbunching instability in the TESLA Test Facility linac; Nuclear Instruments and Methods in Physics Research A, 528, 2004, 355-359) and in the essay 2 of S. Heifets et al. (Coherent synchrotron radiation instability in a bunch compressor, Physical Review Special Topics - Accelerator and Beams, vol. 5, 2002, pp. 064401-1 - 10) described.

In the essay 3 of EA Schneidmiller and MV Yurkov (Using the longitudinal space charge instability for vacuum generation ultraviolet and x-ray radiation, Physical Review Special Topics - Accellerators and Beams Vol 13, 2010, pp. 110701-1 - 110701-9) It is proposed to increase the microelectron packet instabilities in order to use the density fluctuations thus generated to generate radiation in the wavelength range of the VUV and the X-ray radiation. For this purpose, a device is specified, which consists of a field-free distance (English also drift space) and a dispersive beam path, the transverse beam dimensions along the field-free Stecke simplified are assumed to be constant and the dispersive beam path from a so-called chicane (C-chicane or so-called "Dogleg") is formed. The latter has to effect an optimized pulse length compression, which can be represented by the element R _{56 of} the transfer matrix of the dispersive beam guidance path. This is based on an initial shot noise (corresponds to the initial density modulation, which is generated spontaneously and statisitcally in the electron source) in the electron packets. The theoretical starting point of the optimization is based on a one-dimensional (1D) model for the observation of the density fluctuations, as described in the article 1. The optimization of the field-free paths undertaken in article 1 means a minimization of the mean beta function, which is reflected in smaller transverse beam dimensions in the dispersive path. The beta function sets the beam cross-section σ in relation to the emittance ε, generally in accordance with β = σ ² / ε, with σ = maximum beam cross-section. In the realizations for the dispersive route (C-baffles, doglegs) selected in article 3, this leads to a limitation of the producible wavelengths downwards, ie to shorter wavelengths, because the combination of the required beta functions and the dispersive coupling of the longitudinal and transverse movement planes results it addresses the problem of "smearing" (superimposition) of the density fluctuations, which greatly negatively affects the effect of enhancing micro-electron-packet instabilities. Micro-electron packets with short wavelengths, for example in the EUV (extreme ultraviolet, here assumed in the range between 0.1 nm and 200 nm and thus also the XUV range mentioned range from 0.1 nm to 10 nm including) can not be generated directly as stated and explained in the essay 3 itself.

A longitudinal space charge amplifier (LSCA), as it also corresponds to that from article 3, is also in the article 4 of M. Dohlus et al. (Generation of attosecond soft x-ray pulses in a longitudinal space charge amplifier, Physical Review Special Topic Accelerators and Beams, Vol. 14, 2011, p. 090702-1 - 10) disclosed. This serves in addition to an X-ray free-electron laser for the generation of attosecond laser pulses. The LSCA is composed of a cascade of sequences of focussing channels which are alternated by baffling and ultimately lead to an undulator, followed by another focussing channel, a modulating undulator, a chicane and a final undulator. This arrangement makes it possible to set the length of a drift path, the beta function and the element r _{56 of} the transfer matrix, for a given wavelength, as also described in article 3.

The operation of a LSCA, as disclosed in the article 4, is described in the article 5 of A. Halavanau and E. Piot (Simulation of a cascade longitudinal space charge amplifier for coherent radiation generation, Nuclear Instruments and Methods in Physics Research A, Vol 819, 2016, pp. 144-153). examined by simulations. The concrete use of such a LSCA at the "Fermi National Accelerator Laboratory" is also described in article 6 by A. Halavanau and E. Piot (Simulation of cascaded longitudinal-space-charge-amplifier at the fermilab accelerator science & technology (fast) facility, Proceedings of FEL 2015, 37th International Free Electron Laser Conference, 23-28 August 2015, Daejeon, Korea, p. 707 -710) examined by means of simulations.

The actual use of an LSCA, as described in Articles 3 to 6, at the Next Linear Collider Test Accelerator (NLCTA) of the SLAC (Stanford Linear Accelerator Center) National Accelerator Laboratory will be reviewed in article 7 of A. Marinelli et al. (Generation of coherent broadband photon pulses with a cascaded longitudinal space charge amplifier, Physical Review Letters, Vol. 110, 2013, p. 264802-1 - 5) reported.

Disclosure of the invention

It is an object of the present invention to provide a device with which the space charge driven microelectron packet instability in the EUV (extreme ultraviolet, see above) wavelength range is caused in an accelerator system, so that coherent intense synchrotron radiation with wavelengths in the EUV range can be generated.

The invention proposes a device for amplifying space-charge-driven micro-electron-packet instabilities, which are along a first direction X , which corresponds to the beam direction, comprises the elements described below. A first arrangement of magnets, which are a sequence of at least two consecutive along the first direction X arranged multipoles second or higher order, with one multipole focusing and the other acts defocusing. The number of focusing and defocusing magnets can correspond, which, due to the symmetry given thereby, leads to a simplification of the execution. The arrangement of the multipoles is followed in the beam direction by a second arrangement of magnets, comprising a sequence of several, along the first direction X arranged groups of dipoles with different polarity and at least one multipole, at least second order, which precedes the dipoles in the beam direction. The first direction X , which corresponds to the beam direction, is determined by an originating from a main accelerator electron beam in their spatial position and the movement target.

The device according to the invention can also be referred to as a compact focusing and pulse shaping channel. The device drives the so-called space charge driven micro-electron-packet instability. With an undulator downstream of the device according to the invention, the generated light pulses have a very high spectral purity and are Fourier transformation limited.

This makes it possible, for example, to generate femtosecond coherent EUV pulses with repetition rates in the several 100 MHz to GHz range in a subsequent undulator. The device may also enhance space-charge driven micro-electron-beam instability in the infrared region. In addition, the spectral purity in the EUV regime for femtosecond pulses is higher in the present invention than in prior art free electron lasers.

While the first array of magnets transversally focuses the electron beams and thus enhances the energy modulation produced by the three-dimensional space charge fields within the electron packet, the second array of magnets serves to translate the energy modulations into density modulations and thus the creation of fine structures within the electron packets. The reaction is accomplished by multiple dipoles and at least one multipole, at least second order, preceding the dipoles. The device according to the invention is designed to drive the space-charge-driven microelectron packet instability in beams with low peak currents, thereby reducing the requirements for the accelerator system.

The beam parameters which the accelerator system must supply in order for the device according to the invention to reinforce space-charge-driven microelectron packet instabilities in the wavelength interval of the EUV to be functional and to interact constructively with a potentially subsequent in-vacuum undulator are listed in Table 1. The necessary values for the beam parameters can be achieved by appropriate adjustment of the electron source as well as the magnets of the beam guide and the accelerator cavities. Table 1 Average of electron packet length [μm] 1-10 Charge of electron packets [pC] 1 - 20 Beam cross section rms [μm] 1 - 20 Radiation energy [MeV] 40 - 1000 Standard deviation of local energy deviation [%] <0.002 Energy normalized emittance [mm mrad] 0.1-0.6 Beta function β _trans [m] 0.01 to 800

The embodiment of the device is based on the following theoretical considerations.

The consideration according to the invention not only of the longitudinal density fluctuations but also of the transverse density fluctuations shows that micro-electron packets with very short wavelengths can arise. This is due to the fact that for short wavelengths the influence of transverse density fluctuations increases. A consideration of not only the longitudinal density fluctuations but also the transversal corresponds to a 3D (three-dimensional) model. For longer wavelengths, a description will suffice with a 1D model, as is known in the art.

wie es aus dem Aufsatz 4 von D. Ratner et al. (Three Dimensional Analysis of Longitudinal Space Charge Microbunching Starting From Shot Noise, TUPPH041 Proceedings of FEL08, Gyeongju, Korea, 2008, S. 338-341) folgt, und wobei r = (x, y), k = 2π/λ_3D λ_3D: Wellenlänge im 3D Model, γ₀ = gemittelter relativistischer Faktor, ε₀ = elektrische Feldkonstante und K₀ die modifizierte Besselfunktion darstellt.The Fourier transform of the longitudinal electric field E _z (x, y, z) in the 3D model of a round-section electron cluster and N non-correlated electrons provides information about the wavelength-dependent impedance that causes the gain of the initial density modulation $${\tilde{e}}_k\left(r\right)=\frac{-ie\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="DE102016109171B4\_0017.png,DE102016109171B4\_0019.png"\; state="\{\{state\}\}">k</figure-callout>}}{2\mathrm{<figure-callout\; id="0"\; label="\pi \; \gamma "\; filenames="DE102016109171B4\_0016.png,DE102016109171B4\_0017.png"\; state="\{\{state\}\}">\pi \; </figure-callout>}{\gamma }_{}^{}{}_0^2{\mathrm{<figure-callout\; id="0"\; label="\epsilon "\; filenames="DE102016109171B4\_0016.png,DE102016109171B4\_0017.png"\; state="\{\{state\}\}">\epsilon </figure-callout>}}_0}{{\displaystyle {\Sigma }_j^{N}e}}^{-ik{z}_j}{K}_0\left(\frac{k|r-r_j|}{{\gamma }_0}\right)$$

as it is from the article 4 of D. Ratner et al. (Three Dimensional Analysis of Longitudinal Space Charge Microbunching Starting From Shot Noise, TUPPH041 Proceedings of FEL08, Gyeongju, Korea, 2008, pp. 338-341) follows, and where r = (x, y), k = 2π / λ _3D λ _3D : wavelength in the 3D model, γ ₀ = averaged relativistic factor, ε ₀ = electric field constant and K _{0 represents} the modified Bessel function.

wobei Ĩ(k) die Fourier-Transformierte des Stroms ist.The associated impedance per unit length Z (k) is then given by: $${\tilde{e}}_k=-Z\left(k\right)\tilde{I}\left(k\right)$$

where Ĩ (k) is the Fourier transform of the stream.

dass die Impedanz Z(k) im 1D-Modell invers proportional zur transversalen Strahlgröße und invers proportional zur Strahlenergie ist, während die Voraussagen des 3D-Modells einen konstanten Wert für die Impedanz in kurzen Wellenlängenbereichen ergeben. Das bedeutet, dass sobald man mit den Strahlparametern in den Bereich kommt, in dem das 3D-Modell gültig ist, Dichtemodulationen mit beliebig kurzen Modulationswellenlängen erzeugt werden können, unabhängig von der Energie und dem Strahlquerschnitt. Im Anwendungsbereich des 1D-Modells hingegen muss eine sehr hohe Spitzenstromstärke (ab ca. 1 kA) erzeugt werden, um Dichtemodulationen mit kurzen Wellenlängen (im EUV Bereich) zu erzeugen, da die Strahlenergien nicht beliebig hoch und die Strahlquerschnitte nicht beliebig klein gemacht werden können. Die Qualität des Elektronenstrahls beizubehalten bei gleichzeitiger Erhöhung der Spitzenströme in den Elektronenpaketen wie sie das 1D-Modell für EUV-Wellenlängen fordert, ist technisch aber auch physikalisch wegen stromabhängiger Wechselwirkungen des Strahls mit der Kammerwand nicht möglich.From this relationship, taking into account the 1D and 3D models, follows for small wavelengths (in the lower part of the ultra-ultraviolet) and looking at the mean of the ensemble $<{\tilde{e}}_k\left(r\right){\tilde{e}}_{k\text{'}}^{*}\left(r\right)>.$

that the impedance Z (k) in the 1D model is inversely proportional to the transverse beam size and inversely proportional to the beam energy, while the predictions of the 3D model give a constant value for the impedance in short wavelength ranges. This means that as soon as the beam parameters reach the area in which the 3D model is valid, density modulation with arbitrarily short modulation wavelengths can be generated, regardless of the energy and the beam cross section. In the field of application of the 1D model, on the other hand, a very high peak current intensity (from approx. 1 kA) must be generated in order to generate short-wave density modulation (in the EUV range), since the beam energies can not be arbitrarily high and the beam cross-sections can not be made arbitrarily small , Maintaining the quality of the electron beam while increasing the peak currents in the electron packets as required by the 1D model for EUV wavelengths is technically and physically impossible due to current-dependent interactions of the beam with the chamber wall.

mit Z₀ = 376,73 Ω (Wellenwiderstand des Vakuums), I₀ = Spitzenstrom des Elektronenpakets, I_A = 17 kA (Alfvén-Strom), L_d = Länge der Strecke in der die Raumladungskräfte die Energiemodulation bewirken, δ_E = lokale Energieverbreiterung und r₅₆ = longitudinale Dispersion (1. Ordnung), Element der Transfermatrix des Beschleunigerbereichs.The enhancement of density fluctuation in the 1D model as in article 5 of Huang et al. (Microbunching Instability Due to Bunch Compression, SLAC-PUB-11597, December 2005) described is given by: $$G\left(k\right)\approx \frac{I_0}{{\gamma }_0{I}_A}|k{r}_{56}{\displaystyle {\int }_0^{{\mathrm{<figure-callout\; id="4"\; label="L\; d"\; filenames="DE102016109171B4\_0017.png,DE102016109171B4\_0019.png"\; state="\{\{state\}\}">L\; </figure-callout>}}_d}\frac{4\pi Z\left(k.s\right)}{Z_0}ds|exp\left(-\frac{k^2{r}_{56}^2{\mathrm{<figure-callout\; id="2"\; label="\delta \; e"\; filenames="DE102016109171B4\_0017.png,DE102016109171B4\_0019.png"\; state="\{\{state\}\}">\delta \; </figure-callout>}}_e^{}}{2{\mathrm{<figure-callout\; id="0"\; label="\gamma "\; filenames="DE102016109171B4\_0016.png,DE102016109171B4\_0017.png"\; state="\{\{state\}\}">\gamma </figure-callout>}}_0^2}\right)}$$

with Z ₀ = 376.73 Ω (characteristic impedance of the vacuum), I ₀ = peak current of the electron packet, I _A = 17 kA (Alfvén current), L _d = length of the distance in which the space charge forces cause the energy modulation, δ _E = local energy broadening and r ₅₆ = longitudinal dispersion (1st order), element of the transfer matrix of the accelerator region.

In order to increase the gain, the exponential function in (3) must almost be 1. This is done by adjusting the longitudinal dispersion as a function of the wavelength range of the micro-electron packets and the local energy broadening. If the exponential function has a value close to 1 then optimizing the impedance can lead to further amplification. For a given longitudinal dispersion, only the impedance is adjusted accordingly.

im 3D Modell (nach Aufsatz 4): $$<{\left|b_c\left(k\right)\right|}^2>\approx \frac{4}{3N}{\left(\frac{I_0{r}_{56}{L}_d}{{\gamma }_0{I}_A{\sigma }_{tra}^2}\right)}^2\frac{exp\left(-\frac{k^2{r}_{56}^2{\delta }_E^2}{2{\gamma }_0^2}-\frac{k^2\left(R_2^2+{\theta }_y^2{r}_{34}^2\right){\sigma }_{tra\text{'}}^2}{2}\right)}{1+{\gamma }_0^2\left(R_1^2+{\theta }_y^2{r}_{33}^2\right)}$$

mit σ_tra und σ_tra' = transversale Größe und Divergenz des Ensembles, R₁ = r₅₁ + Θ_xr₁₁, R₂ = r₅₂ + Θ_xr₁₂ mit r_ij = Elemente der Transfermatrix des Beschleunigerbereichs.Considering the 3D model, the exponent of the exponential function in function (3) must be extended to take into account the effects resulting from the transverse dispersion. If one calculates the bunching factor for a given wavenumber k at small angles (Θ _x Θ _y ) relative to the longitudinal direction, one obtains for the mean of the ensemble $<{\tilde{e}}_k\left(r\right){\tilde{e}}_{k\text{'}}^{*}\left(r\right)>$

in the 3D model (after essay 4): $$<{\left|b_c\left(k\right)\right|}^2>\approx \frac{4}{3N}{\left(\frac{I_0{r}_{56}{L}_d}{{\gamma }_0{I}_A{\sigma }_{tra}^2}\right)}^2\frac{exp\left(-\frac{k^2{r}_{56}^2{\mathrm{<figure-callout\; id="2"\; label="\delta \; e"\; filenames="DE102016109171B4\_0017.png,DE102016109171B4\_0019.png"\; state="\{\{state\}\}">\delta \; </figure-callout>}}_e^{}}{2{\mathrm{<figure-callout\; id="0"\; label="\gamma "\; filenames="DE102016109171B4\_0016.png,DE102016109171B4\_0017.png"\; state="\{\{state\}\}">\gamma </figure-callout>}}_0^2}-\frac{k^2\left({\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="DE102016109171B4\_0017.png,DE102016109171B4\_0019.png"\; state="\{\{state\}\}">R</figure-callout>}}_2^2+{\theta }_y^2{r}_{34}^2\right){\sigma }_{tra\text{'}}^2}{2}\right)}{1+{\mathrm{<figure-callout\; id="0"\; label="\gamma "\; filenames="DE102016109171B4\_0016.png,DE102016109171B4\_0017.png"\; state="\{\{state\}\}">\gamma </figure-callout>}}_0^2\left({\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="DE102016109171B4\_0013.png,DE102016109171B4\_0015.png"\; state="\{\{state\}\}">R</figure-callout>}}_1^2+{\theta }_y^2{r}_{33}^2\right)}$$

with σ _tra and σ _{tra '} = transverse size and divergence of the ensemble, R ₁ = r ₅₁ + Θ _x r ₁₁ , R ₂ = r ₅₂ + Θ _x r ₁₂ with r _ij = elements of the transfer matrix of the accelerator region.

mit K = Undulatorparameter.The micro-electron packets obtained according to (4) generate a power in a short-period-length undulator according to: $$P_{cOH}\approx \frac{I_0^2}{4\pi {\sigma }_{tra}^2}\frac{{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="DE102016109171B4\_0017.png,DE102016109171B4\_0019.png"\; state="\{\{state\}\}">K</figure-callout>}}^2}{\mathrm{<figure-callout\; id="0"\; label="8th\; \gamma "\; filenames="DE102016109171B4\_0016.png,DE102016109171B4\_0017.png"\; state="\{\{state\}\}">8th\; </figure-callout>}{\gamma }_{}^{}{}_0^2}<{\left|b_c\left(k\right)\right|}^2>$$

with K = undulator parameters.

The above statements show that (in the normal case) the chromatic or aberration effects in the dispersive chicanes greatly reduce the amplification of space-charge-driven microelectron-packet instability, since the beam divergence is very large due to the deliberately minimized transverse beam cross-sections , From this it can be concluded that the space-charge-driven microelectron pact instability can only occur for longer wavelengths or only with the help of very high peak currents (several 1 kA) at shorter wavelengths.

If, on the other hand, one considers that a) the transverse beam cross sections in the baffles may be quite large, since the space charge driven energy modulation takes place beforehand in a dedicated transport path and b) according to the 3D model, the impedance for short wavelengths assumes a constant value irrespective of the beam cross section, a large beam cross section and correspondingly a small beam divergence for the chicane (in the device according to the invention) is selected and the magnetic structures of the chicane are designed accordingly. If one dedicates a dedicated first arrangement (transport path), which favors a space-charge-driven energy modulation to short wavelengths for the given beam parameters and a chicane according to the considerations described above, then moderate (in the range of approximately 100 A to 1 kA) to obtain significant short-wavelength micro-pact amplification to low (<100 A) peak currents. This significant amplification of the micro-electron pacts can result in an increase in the emitted coherent power in a modeled undulator. By exploiting the effect of space-charge driven micro-electron-packet instability, as described above, low peak currents of the electron packets at sufficiently high repetition rates result in a large synchrotron light output. The beam instabilities due to high (> 1 kA) peak currents of the electron packets are avoided, which ensures increased stability.

mit λ = Wellenlänge der Mikro-Elektronenpakete und γ = relativistischer Faktor.In the proposed device, energy modulation takes place during transport through the first array consisting of focusing and defocusing multipoles. This modulation can be described by the 3D model. The condition required in the region of the 3D model for the beam cross sections for target wavelengths in the range of 1 μm to 1 nm, with electron beam energies of 40 MeV to 1 GeV, is the following: $$1<\frac{2\pi \cdot {\sigma }_{tra}}{\gamma \cdot \lambda }\le 6\leftrightarrow \frac{\gamma \cdot \mathrm{<figure-callout\; id="2"\; label="\lambda "\; filenames="DE102016109171B4\_0017.png,DE102016109171B4\_0019.png"\; state="\{\{state\}\}">\lambda </figure-callout>}}{2\pi }<{\sigma }_{tra}\le \frac{6\cdot \gamma \cdot \mathrm{<figure-callout\; id="2"\; label="\lambda "\; filenames="DE102016109171B4\_0017.png,DE102016109171B4\_0019.png"\; state="\{\{state\}\}">\lambda </figure-callout>}}{2\pi }.$$

with λ = wavelength of the micro-electron packets and γ = relativistic factor.

gilt das 1D-Modell und für $\frac{2\pi \cdot {\sigma }_{tra}}{\gamma \cdot \lambda }>6$

nimmt die radiale Korrelation der Moden der Raumladungsfelder sehr stark ab. Damit der Anwendungsbereich des 3D Modells nicht verlassen wird, wird die longitudinale Strahldimension (Bereich des 3D Modells) entsprechend σ_z ≦ σ und σ = σ_tra gewählt, wobei letztere Relationen kleine Abweichungen erlauben. Damit ergeben sich für kleine Ladungen der Elektronenpakete, im Bereich von 1 pC bis 20 pC Spitzenströme deutlich kleiner als 1 kA, insbesondere kleiner 500 A. Die Umsetzung der Energiemodulation in eine räumliche Modulation (sogenannte Pulsformung, auch Bunching genannt) findet in der zweiten Anordnung statt. Hierbei wird die eingehende transversale Betafunktion β_trans , (siehe Tabelle 1) um einen Faktor mindestens größer 4 vergrößert. Die transversale Strahldivergenz nimmt entsprechend ab. Die Strahlquerschnitte in der zweiten Anordnung sind durch die Kombination einer großen (mindestens um einen Faktor 4 vergrößerten) Betafunktion und Dispersion wesentlich grösser als in der ersten Anordnung (Transportstrecke). Die Kopplung zwischen transversalen und longitudinalen Bewegungsebenen, gegeben durch die Elemente r₅₁ und r₅₂ (oder falls es sich um eine vertikale Schikane handelt r₅₃ und r₅₄ ) der Transfermatrix, wird für die Optimierung, relativ zum Strahlquerschnitt klein gehalten, d.h. mindestens eine Größenordnung kleiner als dieser. Dies wird durch mehrere kleine (kürzere und schwächere) Schikanen, die in Summe die gleiche longitudinale Dispersion wie eine große Schikane erzeugen, erzielt. Die kleinen Schikanen lenken jeweils abwechselnd in entgegengesetzte Richtungen ab, um die unerwünschten Effekte der kohärenten Synchrotronstrahlung (Coherent Synchrotron Radiation, CSR) in den Dipolen zu reduzierten. Die transversale Strahldimension wird durch vorgeschaltete, zur zweiten Anordnung gehörige einzelne Quadrupole oder andere Multipole kontrolliert. Während die longitudinale und transversale Strahldimensionen wie oben beschrieben in Abhängigkeit von der Zielwellenlänge und Strahlenergie gewählt werden, wird die longitudinale Dispersion so gewählt, dass einerseits der energieverbreitungsabhängige Term in der Exponentialfunktion der Gleichung (4) (Bunching-Formel) möglichst minimiert wird und anderseits die Amplitude des Bunching, (erster Faktor in Gleichung 4), maximiert wird. Dabei ist zu beachten, dass die Länge der ersten Anordnung (Transportstrecke) selbst eine longitudinale Dispersion, L_d/γ², (L_d = länge der Transportstrecke, y = relativistischer Faktor) erzeugt, die in die gesamtlongitudinale Dispersion eingeht.For $\frac{2\pi \cdot {\sigma }_{tra}}{\gamma \cdot \lambda }<1$

applies the 1D model and for $\frac{2\pi \cdot {\sigma }_{tra}}{\gamma \cdot \lambda }>6$

decreases the radial correlation of the modes of space charge fields very much. So that the scope of the 3D model is not left, the longitudinal beam dimension (area of the 3D model) is chosen according to σ _z ≦ σ and σ = σ _tra , the latter relations allowing small deviations. This results in small charges of the electron packets, in the range of 1 pC to 20 pC peak currents significantly smaller than 1 kA, especially less than 500 A. The implementation of energy modulation in a spatial modulation (so-called pulse shaping, also called bunching) takes place in the second arrangement instead of. Here, the incoming transversal beta function becomes β _trans , (see Table 1) increased by a factor of at least greater than 4. The transverse beam divergence decreases accordingly. The beam cross sections in the second arrangement are substantially larger by the combination of a large (at least a factor of 4) beta function and dispersion than in the first arrangement (transport path). The coupling between transverse and longitudinal planes of motion, given by the elements ₅₁ and ₅₂ (or if it is a vertical chicane r ₅₃ and ₅₄ ) of the transfer matrix is kept small for the optimization, relative to the beam cross-section, ie at least an order of magnitude smaller than this. This is achieved by several small (shorter and weaker) baffles, which together produce the same longitudinal dispersion as a large chicane. The small baffles alternately deflect in opposite directions to reduce the unwanted effects of Coherent Synchrotron Radiation (CSR) in the dipoles. The transverse beam dimension is controlled by upstream individual quadrupoles or other multipoles belonging to the second arrangement. While the longitudinal and transverse beam dimensions are chosen as described above as a function of the target wavelength and beam energy, the longitudinal dispersion is chosen so that, on the one hand, the energy dissipation-dependent term in the exponential function of equation (4) (Bunching formula) is minimized as far as possible Amplitude of the bunching, (first factor in equation 4) is maximized. It should be noted that the length of the first arrangement (transport path) itself produces a longitudinal dispersion, L _d / γ ² , (L _d = length of the transport path, y = relativistic factor), which is included in the Gesamtlongitudinale dispersion.

Preferably, the device further comprises two second arrangements following the first arrangement. In particular, a plurality of (> 2) second arrangements are arranged one behind the other. As a result, the dispersive beam path (the distance of the second arrangements or baffles) is extended (in L), which leads to a higher gain.

By dividing the pulse shaping into several dipole arrangements, the pulse shaping effect for the beam is further improved.

In one embodiment, two consecutive second arrays of magnets along the first direction X differ in that the polarities of the respective groups of dipoles along the first direction X are complementary to one another. This leads to efficient pulse shaping.

Furthermore, two consecutive second or higher order magnetic multiples along the first direction X may differ in that one multipole is focusing and the other is defocussing. This improves beam focusing.

Further, the apparatus may comprise a final first array of magnets comprising second or higher order multipoles for beam focusing.

In particular, the device is formed from a series (cascade) of at least two sequences, each sequence consisting of a first arrangement followed by second arrangements. The series, and thus also the device, is thereby completed by a first arrangement.

The multipoles used in accordance with the invention are preferably designed in the form of a ring with an opening for guiding the beam. The multipoles are more preferably quadrupoles formed from permanent magnets.

The second arrays of magnets may be C-baffles or zig-zag baffles combined with at least second-order multipoles, which are preferably quadrupoles.

In one embodiment, the multipoles are arranged equidistantly in a first arrangement of magnets.

The groups of dipoles in the second arrangements of magnets can also be arranged equidistant from one another.

According to the invention, a synchrotron radiation source is further provided, consisting of an electron beam source, a device for amplification of micro-electron-packet instabilities according to the invention, and an undulator.

In the present invention, micro-electron-packet instabilities are enhanced. The advantage of the invention is that the used amplification mechanism works much more robustly than in conventional free-electron lasers and even at low beam currents and energies intensive synchrotron radiation with short (EUV) wavelengths can be generated.

Embodiments of the invention

• 1 eine erfindungsgemäße Vorrichtung in einem ersten Ausführungsbeispiel,
• 2 die Struktur A aus zwei Quadrupolmagneten der 1,
• 3 eine erfindungsgemäße Vorrichtung in einem zweiten Ausführungsbeispiel,
• 4 Quadrupolgradienten in einem dritten Ausführungsbeispiel,
• 5 Quadrupolgradienten in einem vierten Ausführungsbeispiel,
• 6 Quadrupolgradienten in einem fünften Ausführungsbeispiel,
• 7 Verlauf der Betafunktion für das zweite Ausführungsbeispiel,
• 8 Verlauf der Strahlquerschnitte für das zweite Ausführungsbeispiel und
• 9 eine erfindungsgemäße Synchrotronstrahlungsquelle.

The above-described characteristics, features, and advantages of this invention, as well as the manner in which they will be achieved, will become clearer and more clearly understood in connection with the following description of the embodiments, which will be described in detail in conjunction with the drawings. Show it:

• 1 a device according to the invention in a first embodiment,
• 2 the structure A from two quadrupole magnets of the 1 .
• 3 a device according to the invention in a second embodiment,
• 4 Quadrupole gradients in a third embodiment,
• 5 Quadrupole gradients in a fourth embodiment,
• 6 Quadrupole gradients in a fifth embodiment,
• 7 Course of the beta function for the second embodiment,
• 8th Course of the beam cross sections for the second embodiment and
• 9 a synchrotron radiation source according to the invention.

Electrons are deflected and focused in accelerator systems with the aid of guide magnets. 1 shows a side view of a device according to the invention for the enhancement of space-charge driven micro-electron-packet instabilities in a first embodiment. The device 1 for amplifying micro-electron-packet instabilities, also called focusing channel, initially comprises a first arrangement of magnets 10 , The first arrangement of magnets 10 is used for beam focusing and comprises a sequence of at least two consecutive, along the first direction X arranged multipoles 12 second or higher order.

These at least two multipoles 12 are in the structure A summarized and in 2 shown separated from each other in a plan view. Each multipole 12 In the embodiment shown, but not limiting, is an annular quadrupole with an opening in the middle 18 acting as an electron channel 30 serves. A quadrupole magnet 12 has four poles 14 . 16 , two north and two south poles, with the poles of the same name facing each other diagonally. A quadrupole magnet 12 focuses the transverse dimension of a beam of charged particles in one plane while defocusing it in the other plane. The electron beam passes through the 1 from left to right in the electron channel 30 along the direction X , In other words, the first direction X the electron beam direction. The field course within the opening of the multipole 12 - 1 is due to the combination of the poles 14 and 16 determined fields determined. The multipole 12 - 1 focuses the electron beam in a horizontal plane and defocuses it in the vertical plane Level. In the second multipole 12 - 2 who in X Direction behind the first multipole 12 - 1 is arranged, are the poles 14 . 16 complementary to the poles 14 . 16 of the first multipole 12 - 1 educated. The multipole 12 - 2 defocuses the electron beam in a horizontal plane and focuses it in the vertical plane. This successive arranged complementary formation of the first arrangement is the compact beam focusing. Such a structure is z. B. a so-called FODO structure. It says " F "For horizontal focusing with simultaneous vertical defocusing," D "For vertical focusing with simultaneous horizontal defocusing and" O "For a neutral element. An FODO structure consists of an equidistant sequence of quadrupole magnets 12 with alternating polarity, so that a beam of charged particles is alternately focused and defocused as it traverses the structure in both transverse planes.

The quadrupoles are preferred 12 composed of permanent magnets and consist of NdFeB with a remanent field of z. B. 1.3 T. The first arrangement of magnets 10 is designed so that magnetization fields of 2 Tm ^-1 can be achieved. Field gradients between 300 and 800 Tm ^-1 are achievable. The opening 18 can z. B. have a diameter of only 6 mm, which is preferably between 5 and 10 mm. The quadrupole distances are preferably between 0.05 m and 0.15 m. The length of the focusing quadrupole may be equal to or different than the length of the defocusing quadrupole. The lengths are between 0.02 m and 0.1 m, preferably between 0.025 and 0.075 m.

To the first arrangement of magnets 10 closes a second array of magnets 40 on, coming from groups 22 of dipoles 24 exists with different polarity. A dipole magnet 24 consists of two different poles, north and south poles facing each other. The field of a dipole magnet 24 deflects a beam of charged particles by an angle that depends on the strength of the field and energy of the beam. The dipole magnets 24 consist according to the invention of permanent magnets. In addition, the second arrangement comprises magnets 40 a quadrupole 50 which precedes the dipoles. In 1 The dipoles of the second arrangement form an example of a so-called C-chicane 20 , A C-chicane deflects the beam from its axis and leads it on a path similar to a down-opened " C "Back to her. This arrangement can convert the energy modulation of a charged particle beam into a longitudinal modulation. A C chicane 20 consists of a first group 22 - 1 of dipoles 24 , here with exactly one dipole 24 , which deflects the electron beam to the right. The upper, first pole is a south pole 28 , the lower, second pole is a north pole 26 , The second group of dipoles 22 - 2 consists here by way of example of two left-deflecting dipoles 24 , but also only one dipole 24 include. The third group of dipoles 22 - 3 directs the beam in the electron channel 30 turn right again. Thus, the distraction runs in a left-opened " C ". This form of deflection gives the dipole arrangement 20 the name " C -Chicane". Considering only the upper row of poles, the poles would be in X Direction from the four poles "South-North-North-South". But you can also use zig-zag chicanes. A zigzag chicane consists of two groups of dipoles, with the poles of the first group of dipoles arranged complementary to the second group of dipoles. Each group of dipoles consists of two dipoles with poles arranged complementary to each other. For example, the top row of poles would be "(south-north) - (north-south)".

The dipole lengths can be between 0.01 m and 0.05 m. The dipole fields can be between 0.1 and 1 T, preferably between 0.4 and 0.7 T.

The total length of the device may vary between 1 m and 20 m, preferably between 5 and 15 m.

3 shows a device according to the invention in a second embodiment. Along the X Direction is first again a first arrangement of magnets 10 intended. This is followed by a second arrangement of magnets 40 , This is followed by further orders 40 from magnets on. In the embodiment shown are several, here eight second arrangements 40 arranged by magnets in a row. In the example, two are each along the first direction X successive second arrays of magnets 40 characterized in that the polarities of the corresponding groups 20 of dipoles 22 along the first direction X are complementary to each other. Includes a second arrangement of magnets 40 a C-chicane opened to the left 20 , contains the following second arrangement of magnets in the beam direction 40 a C-chicane opened to the right 20 , In addition, two magnetic multipoles succeeding one another along the beam direction preferably also differ 50 second or higher order in that a multipole 50 Focusing in one plane and the other defocusing is formed. In the embodiment shown, the focusing channel comprises 1 a final first arrangement of magnets 10 comprising multipoles 12 second or higher order for beam focusing.

Generally, there is a focus channel 1 preferably made of permanent magnets and is composed of three components: a) first arrangements of magnets 10 , z. B. FODO structures, b) second arrangements of magnets 40 , z. B. C-harassment 20 and individual quadrupole magnets 50 , In a focusing channel 1 follows a first arrangement of magnets 10 a sequence of second arrays of magnets 40 , each a single quadrupole magnet 50 and eg a C-chicane 20 include. The successive second arrays of magnets 40 divert the beam in opposite directions. A focusing channel 1 generally consists of several such arrangements of first arrays of magnets 10 and second arrays of magnets 40 , The number of arrangements required depends on the beam parameters and desired wavelengths. It is redefined for each application. This is done by adjusting the parameters introduced above and is to be checked by a simulation if necessary.

The number, dimensions and field strength of the quadrupole magnets 12 in the first arrangements of magnets 10 and the number of second arrays of magnets 40 and the dimension and field strength of the individual dipole magnets 24 and quadrupoles 50 are also parameters that are optimized depending on beam parameters and desired wavelengths according to the conditions introduced above.

In the first arrangements of magnets 10 a focusing channel 1 space-charge-driven microelectron packet instability generates a broadband energy modulation of the beam. This is from the second arrangement of magnets 40 converted into a spatial, longitudinal modulation (so-called microbunching). This has the consequence that a packet of charged particles is divided into many small packets, the beam is "microbuncht". This electron packet can then generate coherent radiation with wavelengths much shorter than the original packet.

The structure of the device may be modified to either enhance microbunching for beams with different beam parameters in the same wavelength range or to enhance microbunching in other wavelength ranges with the same beam parameters. For example, the strength of the dipole and quadrupole magnets can be changed to enhance microbunching in the same wavelength range for beams of different energies. It is also possible to change the number, lengths of dipole and quadrupole magnets, their field strength and spacings to enhance microbunching in the same wavelength range. Examples of adaptations of the device according to the invention are shown in the following figures.

4 Figure 4 shows calculated quadrupole gradients in a third embodiment corresponding to a series (cascade) of two sequences, each of which comprises a first arrangement following the eight second arrangements, and a final, first arrangement following the two sequences. The dipole gradients are not shown. In the embodiment, electron beams are focused at 600 MeV. The total length of the device is 15 m ( Z ). On a first arrangement of magnets 10 Eight second arrangements of magnets follow 40 , This is followed by a second, first arrangement of magnets 10 , and eight more second arrangement of magnets 40 and, finally, a third, first array of magnets 10 on. The length of the focusing / defocusing quadrupoles 12 is 0.05 m, the gradient is 400 T / m or -400 T / m and the opening 18 the quadrupole 12 has a diameter of 0.01 m. The distance between the quadrupoles 12 is 0.1 m. The second arrangements of magnets 40 each include a C chicane 20 with a dipole length of 0.03 m, a dipole field of 0.6 T, a length of the focusing / defocusing quadrupoles 50 of 0.05 m, a gradient of +/- 140 T / m and an opening of 0.01 m. The generated beam cross sections and beta functions for the first and second arrangements correspond to those of the 7 and 8th ,

5 Figure 4 shows calculated quadrupole gradients in a fourth embodiment corresponding to a series (cascade) of two sequences, each comprising a first array following the eight second arrays, and a final first array following the two sequences. The dipole gradients are not shown. In this embodiment, electron beams are focused at 400 MeV. The total length of the device is 12 m ( Z ). On a first arrangement of magnets 10 Eight second arrangements of magnets follow 40 , This is followed by a second, first arrangement of magnets 10 , and eight more second arrangements of magnets 40 and, finally, a third, first array of magnets 10 on. The length of the focusing quadrupole 12 is 0.025 m, the gradient is 711 T / m and the opening 18 the quadrupole 12 has a diameter of 0.008 m. The length of the defocusing quadrupole 12 is 0.025 m, the gradient is - 711 T / m and the opening 18 the quadrupole 12 has a diameter of 0.008 m. The distance between the quadrupoles 12 is 0.075 m. The second arrangements of magnets 40 each include a C chicane 20 with a dipole length of 0.015 m, a dipole field of 0.4 T, a length of the focusing / defocusing quadrupoles 50 of 0.025 m, a gradient of +/- 247 T / m and an opening of 0.008 m. The generated beam cross sections and beta functions for the first and second arrangements correspond to those of the 7 and 8th the size and the course after.

6 Figure 4 shows calculated quadrupole gradients in a fifth embodiment corresponding to a series (cascade) of two sequences, each comprising a first array following the eight second arrays, and a final first array following the two sequences. The dipole gradients are not shown. In the fifth embodiment, electron beams are focused at 900 MeV. The total length of the device is 15 m ( Z ). On a first arrangement of magnets 10 Eight second arrangements of magnets follow 40 , This is followed by a second, first arrangement of magnets 10 , and another eight second arrangement of magnets 40 and, finally, a third, first array of magnets 10 on. The length of the focusing / defocusing quadrupoles 12 in the first arrangements of magnets 10 is 0.05 m, the gradient is 600 T / m and the opening 18 the quadrupole 12 has a diameter of 0.01 m. The distance between the quadrupoles 12 is 0.1 m. The second arrangements of magnets 40 each consist of a C chicane 20 with a dipole length of 0.03 m, a dipole field of 0.9 T, a length of the focusing / defocusing quadrupoles 50 of 0.05 m, a gradient of +/- 210 T / m and an opening of 0.01 m. The generated beam cross sections and beta functions for the first and second arrangements correspond to those of the 7 and 8th ,

A representation of the course of the beta function and the beam cross sections along Z (total length of the device), which correspond to the 2nd, 3rd and 5th embodiment and the 4th of the size and the course after (other total length) are in 7 or. 8th shown.

In summary, the device according to the invention serves to selectively amplify micro-electron-packet instabilities in order to generate coherent synchrotron radiation in a subsequent short undulator. Due to the compact design of this device, the high demands on the electron beam quality for generating coherent synchrotron radiation, the wavelengths of the generated radiation, especially in the wavelength range starting with the infrared wavelength range over the range of EUV (extreme ultraviolet) of the spectrum to the spectrum of soft X-rays (XUV) are significantly reduced.

Thus, according to the invention, sections with short and extremely strong multipoles, preferably permanent quadrupole magnets, which are preferably arranged in a dense, so-called FODO structure with short dipole magnets as magnetic chicanes. The device is thus a compact focusing and pulse shaping channel.

The desired high mean synchrotron beam powers are produced by the high repetition rates. This allows the use of very small electron-packet charges in the range 1 to 20 pC, which in turn leads to a more stable operation of the accelerator system. The average (rms) length of the electron packets is in a range of 1 to 10 μm (which corresponds to 3 to 30 fs). In this case, transverse beam sizes between 5 and 200 microns can be achieved. Setting the parameters to these values also reduces the destructive effects of coherent synchrotron radiation in the baffles.

The beam cross section has a direct effect on the amplification of instabilities within an electron packet and should be kept as small as possible. Sufficiently small beam cross sections are realized by the focusing and defocusing components used in the focusing channel and arranged in a compact FODO structure.

The device for amplifying instabilities within an electron packet is thus formed from the combination of magnetic focusing and deflection magnets. As a focusing elements for maintaining or adjusting the beam cross-section standard quadrupoles can be used. The deflection magnets are used to adjust the longitudinal dispersion. It is possible to use standard dipoles, which are arranged, for example, as C-shaped baffles. The required length of the path for amplifying instabilities within an electron packet is dependent on the present beam parameters and is adapted thereto.

The amplification of the instabilities within an electron packet occurs from a density fluctuation of the electron beam and therefore has a statistical characteristic with high fluctuation values in the bundling factor. In a focusing channel, the essential parameters for adjusting the convergence factor are the energy of the electron beam and the charge of the electron packets.

Furthermore, according to the invention, a synchrotron radiation sources 100 consisting of a plant generating relativistic electron beams 110 (Accelerator), for example, a linear accelerator system consisting of an electron source and accelerator modules, a device according to the invention 1 to enhance space-charge driven microelectron packet instabilities and an undulator 120 arranged in particle beam direction one behind the other. This is in 9 shown. As an undulator 120 a standard undulator can be used.

While the invention has been further illustrated and described in detail by way of preferred embodiments, the invention is not limited by the disclosed examples, and other variations can be derived therefrom by those skilled in the art without departing from the scope of the invention.

LIST OF REFERENCE NUMBERS

1

Device for amplifying micro-electron-packet instabilities

10

First arrangement of magnets

12

Multipole at least second order

14

First groups of Poland

16

Second group of Poles

20

Arrangement of dipoles (baffles)

22

Groups of dipoles

24

dipole

26

First Pole (e.g., South Pole)

28

Second pole (e.g., North Pole)

30

electron channel

40

Second arrangement of magnets

50

At least second order multipole (in particular quadrupole)

100

synchrotron Radiation

110

Plant for the production of relativistic electron beams

120

undulator

Claims (13)

A device (1) for amplifying micro-electron-packet instabilities, arranged along a first direction (X): a first arrangement of magnets (10) for beam focusing comprising a sequence of at least two multipoles arranged one behind the other along the first direction (X) (12) second or higher order, wherein the multipoles (12) have an alternating polarity and wherein the beam cross section σ _tra after the beam focusing in the range $\frac{\gamma \cdot \lambda }{2\pi }<{\sigma }_{tra}\le \frac{6\cdot \gamma \cdot \lambda }{2\pi }$

with λ = wavelength of the micro-electron packets and γ = relativistic factor and at least one second arrangement of magnets (40) for implementing the energy modulation in density modulation comprising a sequence of a plurality of groups (22) arranged along the first direction (X) of FIG Dipoles (24) of different polarity and a multipole (50), at least second order, which precedes the dipoles and wherein an incoming beta function in the second arrangement is increased by at least a factor of four. Device after Claim 1 , characterized in that the device comprises at least one further second arrangement following the first second arrangement. Device after Claim 2 , characterized in that more than two second arrangements (40) are arranged one behind the other. Device after Claim 2 , or 3, characterized in that two consecutive second arrays of magnets (40) along the first direction (X) differ in that the polarities of the respective groups (22) of dipoles (24) along the first direction (X) are complementary to each other. Device according to one of Claims 2 to 4 , characterized in that two consecutive second or higher order magnetic multipoles (50) along the first direction (X) differ in that one multipole (50) is focused and the other defocusing. Device according to one of the preceding claims, characterized in that a first arrangement of magnets (10), comprising multipoles (12) of second or higher order for beam focusing, terminates the device. Device according to one of the preceding claims, characterized in that the device consists of a series of at least two sequences of first arrangements, followed by the second arrangements, the series being completed by a first arrangement. Device according to one of the preceding claims, characterized in that the multipoles (12, 50) are formed annularly with an opening for beam guidance. Device according to one of the preceding claims, characterized in that the multipoles (12, 50) are quadrupoles, which are formed from permanent magnets. Device according to one of the preceding claims, characterized in that the second arrangements of magnets (40) comprise C-baffles or zig-zag baffles. Device according to one of the preceding claims, characterized in that the multipoles (12) are arranged equidistantly in a first arrangement of magnets (10). Device according to one of the preceding claims, characterized in that the groups (22) of dipoles (24) in the second arrangements of magnets (40) are arranged equidistant from each other. A synchrotron radiation source (100) comprising an accelerator system (110), a device (1) for amplifying microelectron packet instabilities according to any one of the preceding claims, and an undulator (120).

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