Particle Beam Diagnostics and Control

Particle beam diagnostics and control

G. Kube

Deutsches Elektronen-Synchrotron DESY Notkestraße 85, 22607 Hamburg, Germany

Summary. — Beam diagnostics and instrumentation are an essential part of any kind of accelerator. There is a large variety of parameters to be measured for observation of particle beams with the precision required to tune, operate and improve the machine. Depending on the type of accelerator, for the same parameter the working principle of a monitor may strongly diﬀer, and related to it also the requirements for accuracy. This report will mainly focus on electron beam diagnostic monitors presently in use at 4th generation light sources (single-pass Free Electron Lasers), and present the state-of-the-art diagnostic systems and concepts.

1. – Introduction

Nowadays particle accelerators play an important role in a wide number of fields where a primary or secondary beam from an accelerator can be used for industrial or medical applications or for basic and applied research. The interaction of such beam with matter is exploited in order to analyze physical, chemical or biological samples, for a modification of physical, chemical or biological sample properties, or for fundamental research in basic subatomic physics. In order to cover such a wide range of applications different accelerator types are required. Cyclotrons are often used to produce medical isotopes for positron emission to-

⃝c SocietàItaliana di Fisica 1 2 G. Kube mography (PET) and single photon emission computed tomography (SPECT). For electron radiotherapy mainly linear accelerators (linacs) are in operation, while cyclotrons or synchrotrons are additionally used for proton therapy. Third generation synchrotron light sources are electron synchrotrons, while the new fourth generation light sources (free electron lasers) operating at short wavelengths are electron linac based accelerators. Neutrino beams for elementary particle physics are produced with large proton synchrotrons, and in linear or circular colliders different species of particles are brought into collision. As seen from this short compilation there exists a large number of accelerator types with different properties, and as consequence the demands on beam diagnostics and instrumentation varies depending on machine type and application. Being aware that such a wide field will not be summarized in a comprehensive way within a few pages, this report concentrates on the description of instrumentation and diagnostic concepts presently in use at 4th generation light sources, i.e. electron linac driven single-pass Free Electron Lasers (FELs). Examples from the VUV-FEL FLASH at DESY [1, 2] and the European XFEL (E-XFEL) [3, 4], currently under construction at DESY, will be given. Monitor concepts applied for particle beam diagnostics rely typically on one of the following physical processes: (i) influence of the particle electromagnetic field, (ii) Coulomb interaction of charged particles penetrating matter, (iii) nuclear or elementary particle physics interactions, and (iv) interactions of particles with photon beams. However, there are fundamental differences in signal generation and underlying physical processes applied for beam instrumentation between an electron machine and a hadron machine. In some cases this requires completely different monitor concepts even for the measurement of the same beam parameter. Therefore the emphasis in the following sections will be on diagnostics for single–pass FELs. The reader interested in general aspect of particle beam diagnostics will be referred to specific textbooks or lecture notes as in refs. [5, 6, 7, 8, 9] and the proceedings from the DIPAC and BIW conference series. Moreover, a detailed description of the sophisticated underlying monitor concepts is out of the focus of this report, only short summaries of the monitor working principles will be given together with references to the appropriate literature. This report is organized as follows: in the next section a short introduction to the instrumentation for beam current measurements will be given. Section 3 presents a brief overview over the instrumentation for beam position monitoring, while section 4 deals with transverse phase space diagnostics (i.e. emittance and transverse profile measurements). The last section is dedicated to beam instrumentation for the longitudinal phase space, i.e. bunch length diagnostics together with energy and energy spread monitors. In addition, a short introduction to timings systems at FELs will be given.

2. – Beam charge measurements

One of the most important accelerator parameters is the electric beam current resp. the beam charge. There exist different methods to measure this value, which can roughly Particle beam diagnostics and control 3 be classified in two categories, intercepting and non–intercepting measurements. In the following a short description of the most common monitor concepts which are in use at linacs (AC measurements) will be given: the Faraday cup, the wall current monitor, the Alternating Current Transformer or Toroid, and as recent development the cavity–based dark current monitor. For more details the interested reader is referred to the tutorials about beam current measurements [10, 11, 12] and the recently published overview article [13]. . 2 1. Intercepting measurements.– Intercepting measurements are usually destructive to the beam. The generated monitor signal results from the absorption of a significant amount of the particle beam energy. Faraday cups are widely used, especially for the commissioning phase of a linear accelerator and as reference for cross-calibrations. In order to measure the beam charge, a cup made of conducting material is inserted in the beam path which is isolated from the beam pipe ground potential. When the beam hits the cup the charges are collected and integrated, delivering a signal which is proportional to the primary beam intensity. In case of lepton beams radiative losses may form an electromagnetic shower which has to be completely absorbed inside the cup material. To keep the monitor dimensions at reasonable values, Faraday cups are typically deployed at low particle beam energies, i.e. short behind the gun in a linac. Moreover, due to the heat–load problems they are usually used only for low current measurements down to the pA region. In ref. [14] the cup design for an electron beam up to 300 MeV is described. . 2 2. Non–intercepting measurements.– Non–intercepting measurements use the electric or magnetic field coupling of the beam to the measuring instrument to determine the beam charge by typically integrating the beam current or Wall Image Current (WIC) coupled inductively or capacitively to the measurement device. The electric field of an ultra relativistic particle moving inside the vacuum chamber is effectively canceled outside the conducting chamber by the WIC induced at the inner chamber diameter, while the magnetic part of the particle’s field gets strongly attenuated in the non–magnetic chamber material. As consequence a high–resolution measuring device can only be installed either in the vacuum chamber (as it is the case e.g. for beam position monitors), or outside the chamber if an alternative path for the WIC is provided. The latter method is widely used for beam charge measurements and realized such that a ceramic ring is soldered at both ends to the beam pipe to form a non–conducting gap through which the particle’s field leaks out of the vacuum chamber. A Wall Current Monitor (WCM) is a device with rather high bandwidth up to 5 GHz and a lower cut–off frequency below hundreds of kHz which is sometimes also used for longitudinal bunch profile measurements, especially in hadron accelerators with bunch lengths in the nanosecond region. Here the non–conducting gap is bridged by a resistive network across the gap. The WCM acts as a current divider, providing separate paths for the high–frequency WIC component (through the load resistor) and the low–frequency one. The WCM lower cut–off frequency is proportional to the impedance ratio of the high–frequency and the low–frequency paths [13]. However, a WCM is prone to noise 4 G. Kube because leakage currents may flow directly through the resistors, and therefore a very good shielding is required. In addition, higher order modes (HOMs) leaking out of the gap have to be absorbed by ferrites. In case of high intensity beams care has to be taken that the heat generation due to HOM absorption in the ferrites is effectively dissipated. In an Alternating Current Transformers or Toroid the beam couples inductively to the measurement device. A particle bunch crossing the (ceramic) gap in the vacuum chamber induces a magnetic flux in a high permeability toroid surrounding the gap, i.e. it acts as a primary single turn winding in a classical transformer. The flux induces a secondary current in the transformer secondary windings. This current is a measure for the bunch current and can be detected as a voltage drop across a resistor. The bandwidth of a toroid ranges from a few Hz up to a GHz. The low–frequency cut–off is given by the winding inductance, the high–frequency cut–off by the capacitive coupling between the windings, stray and eddy currents, the energy loss in the core material, and the loss of permeability with high frequency [13]. Cavity monitors are also well suited for beam intensity monitoring. Here the amplitude of the monopole mode TM010 is a measure for the bunch current. Recently design and test of a monitor (originally designed as dark current monitor for the E-XFEL) with a sensitivity sufficient to resolve few-pC bunches was reported [15].

3. – Beam position monitors

Beam position monitors (BPMs) are the diagnostic devices which are most frequently used at nearly all types of accelerators like linacs, cyclotrons, synchrotrons operating with lepton, hadron or heavy–ion beams. They are essential during the phase of beam commissioning, for accelerator fault finding and trouble shooting, machine optics measurements, and accelerator optimization to achieve and keep the ultimate beam quality. A series of BPMs is distributed along the accelerator to monitor the beam center of mass position at the distinct locations and derive position information in both transverse orbit planes. Each BPM consists of a pickup coupling the particle electromagnetic field to a measurement device. In contrast to the beam intensity monitors the pickups are installed inside the vacuum chamber, usually consisting of two or four symmetrically arranged electrodes. The signals induced at the pickups are then transferred via UHV feedthroughs to the outside of the vacuum chamber, followed by a readout electronics system for signal conditioning and processing. In the following standard pickup types are shortly described which are common at most accelerators. They can roughly be diveded in two groups: broadband BPM pickups and narrowband resp. resonant pickups. Comprehensive review articles can be found e.g. in refs. [16, 17, 18, 19, 20] and in ref. [21]. The reader interested in readout electronic systems is referred to the review article ref. [22] or to ref. [23]. . 3 1. Broadband BPM pickups.– In case of a broadband BPM pickup the monitor sensitivity is independent on the frequency. Broadband pickups usually operate in terms Particle beam diagnostics and control 5 of the image current model [21]. The pickup type mainly in use is the so called button BPM which provides a capacitive or electrostatic coupling. The small button size (typical button diameters 5 - 20 mm) and the short vacuum feedthrough allows for a compact installation at a comparable low price, thus explaining the proliferation of this pickup type. The pickup transfer impedance has a typical high–pass characteristics with a cut–off frequency ωcut defined by the pickup capacity and the matching impedance. For frequencies ω ≪ ωcut the voltage drop measured across a matched resistor is proportional to the time derivative of the beam current. In order to increase the signal strength the first idea would be to increase the pickup area, thus increasing the induced charge. However, if the bunch length is in the order of the pickup size a signal deformation occurs due to the final propagation time. Therefore the button size should be smaller than the bunch length which results in a very low signal strength for short bunches. In this case stripline BPMs are well suited because the signal propagation is considered in the design as it is the case for transmission–lines in microwave engineering [20]. In addition, the azimuthal coverage of the stripline can be larger than that of a button pickup, thus yielding an increased signal strength. A stripline pickup consists of an electrode with length L of several cm, forming a transmission line between the electrode and the vacuum chamber wall. A signal is created by the beam at each end of the line depending on the characteristic impedance Zstrip of the electrode, which is often chosen to be 50 Ω. Depending on the termination R of the downstream port the signal there is canceled (R = Zstrip) or appears partially (R ≠ Zstrip). A complete cancellation at the downstream port happens only if the speed of the beam is equal to the speed of the signal in the transmission line which is almost true for β ≈ 1. At the upstream port it is always possible to extract the induced signal and the reflected inverted one separated in time by ∆t = 2L/c (for β = 1). The transfer impedance of a stripline BPM is composed of a series of maxima fmax = c/4L · (2n − 1) with n = 1, 2,... Therefore, for a given acceleration frequency facc the length L should be chosen to work close to such a maximum. . 3 2. Resonant BPM pickups.– In order to fulfill the high position resolution requirements of a linac–based FEL (E–XFEL: in the undulator section a single–shot accuracy of ≤ 1µm, bunch train averaged 0.1µm) an increase in the BPM signal strength is required. However, the standard BPM scheme relies on subtracting the signals from individual pickup electrodes to extract a position information, i.e. the signal power of the position information is typically much smaller than the signal power from an individual electrode. To avoid this reduction of information it is desirable to generate a beam signal right from the beginning which is proportional to the beam position. These demands can be fulfilled by excitation of resonator modes within a cavity, i.e. the resonator can be utilized as passive, beam driven cavity BPM. The cavity BPM is usually based on a pillbox resonator, and because the short bunch lengths of a linac deliver a wide frequency spectrum several resonator modes are excited resonating at slightly different frequencies. Position information is gained by detecting via pin antennas the TM110 dipole mode 6 G. Kube which has a node at the cavity center and whose excitation amplitude depends linearly on the beam displacement. Care has to be taken that no signal leakage of the slightly frequency–shifted monopole mode TM010 in the dipole mode signal occurs, which can be suppressed by an appropriate design of an outcoupling waveguide. For the position determination the amplitude of the dipole mode and its phase have to be processed; the magnitude represents the value of beam displacement and the sign is reconstructed from the phase which is defined with respect to the phase of the monopole mode. Therefore the TM010 mode has to be processed additionally which is usually performed via a reference cavity. The best resolution achieved so far with a cavity BPM was 8.72 nm [26], but the projected design resolution of this monitor amounted 2 nm. More information about cavity BPMs in general can be found e.g. in refs. [24, 25].

4. – Diagnostics for the transverse phase space

Particle beam properties in the transverse phase space are characterized by the transverse beam emittance which is one of the accelerator key parameters: for a synchrotron light source of 3rd or 4th generation the brilliance deﬁning the accelerator performance scales inversely proportional to the transverse emittances, and a similar situation occurs for the luminosity of a particle collider. The transverse emittances are the projected phase space areas, and according to Liouville’s theorem they are conserved in linear beam optics. In accelerator physics the transverse phase space variables are chosen to ′ be the beam position x and the beam angular divergence x = ∆px/p. The transverse emittance is either described in the form of an ellipse equation via the Courant–Snyder or Twiss parameters as

(1) ε = γx2 + 2αxx′ + βx′2 , or alternatively according to ref. [27] there exist a statistical deﬁnition

∫ ∞ √ + dxx2ρ(x) 2 ′2 − ′ 2 2 −∞∫ (2) εrms = < x >< x > < xx > with < x >= +∞ ,... −∞ dxρ(x) which is widely used at linacs because of the quite general applicability. The latter equation is based on the characterization of the beam charge distribution ρ(x) by its 2nd statistical moments, and it was assumend that all first moments vanish (which can be achieved in any case by a variable substitution because the first moments describe a static offset). More details about the general beam emittance concept can be found in each textbook about accelerator physics, or e.g. in refs. [28, 29]. Unfortunately the emittance itself is not directly accessible for beam diagnostics, the measurable quantities are the projections onto both axes: a beam profile or a beam divergence. Usual beam emittance measurements rely on the analysis of beam profiles, therefore after the description of general emittance diagnostic principles a short review about beam profile measurement schemes at linacs will be given. Particle beam diagnostics and control 7

It is important to note that all measurement techniques presented in this section refer to measurements of the projected emittance. However, an FEL relies on a resonant energy exchange between the electron beam and the emitted photon field, and the FEL working principle requires that the electron is slipping back in phase with respect to the photon field by one radiation wavelength each undulator period. Therefore the FEL is integrating over the slippage length, and it is not only the projected but also the slice emittance which is of interest. A method to determine the slice emittance will be presented in the next section in context with longitudinal phase space diagnostics. There exist two general schemes for (projected) emittance diagnostics which can roughly be classified in beam matrix based schemes exploiting the transfer properties of the beam matrix resp. the Twiss parameters, or a mapping of the phase space where a small phase space element (beamlet) is separated e.g. by a slit, and the beamlet propagation along a drift space converts the angle information in a position information. Both schemes will be shortly described in the following subsections. For more details about transverse emittance diagnostics the reader is referred to the review article ref. [30]. . 4 1. Beam matrix based schemes.– For simplicity the case of uncoupled motion is considered, i.e. the motion in horizontal, vertical (and longitudinal) plane is uncoupled and the following considerations are restricted to a 2 dimensional sub–space, here the horizontal phase space. The beam matrix can be expressed either in terms of the Twiss parameters or, based on the statistical approach, in terms of the moments of the beam distribution as ( ) ( ) β −α < x2 > < xx′ > (3) Σ = ε = beam −α γ < xx′ > < x′2 > √ √ √ 2 with σ = Σ11 = εβ = < x > the rms beam size, i.e. the parameter which can be measured for beam diagnostic purposes. The beam emittance is connected to the beam matrix via √ √ | | − 2 (4) ε = det Σbeam = Σ11Σ22 Σ12 in accordance to eqs.(1,2). While the single–particle transformation of the phase space coordinates (x,x’) from an initial to a final location in the accelerator lattice is represented by the so-called transport or R–matrix ( ) ( )( ) x R R x (5) = 11 12 , x′ R R x′ f 21 22 i the transformation of an initial beam matrix to the final observation point is performed according to

f i T (6) Σbeam = R Σbeam R . 8 G. Kube

For beam diagnostic measurements only the beam matrix element Σ11 is directly accessible and corresponds to the square of the beam size. The remaining matrix elements required for an emittance determination according to eq.(4), Σ12 = Σ21 and Σ22, have to be determined otherwise. Exploiting the transformation properties of the beam matrix eq.(6) the element Σ11 (being the observable) is transformed as follows:

f 2 i i 2 i 2 (7) Σ11 = R11Σ11 + 2R11R12Σ12 + R12Σ12 = σf .

From Eq.(7) an emittance measurement scheme can be deduced. A reference location in the accelerator (indicated by index i) is assumed. By measuring a beam profile σf under a slightly different situation (index f), a connection between the original and the final state can be established according to eq.(7). In an accelerator this change in state can be achieved in a pre–defined way, i.e. the matrix elements of the R–matrix are known a priori. Then eq.(7) represents an equation with 3 unknown parameters: the beam matrix elements at the reference point, while all other parameters are known either by f measurement (Σ11) or a priori (R-matrix elements). To determine the 3 unknown beam matrix elements at the reference location a minimum of 3 beam size measurements under different situations (index f) is required. With knowledge of the beam matrix elements at the reference point the emittance at the reference point can be deduced according to eq.(4), but supposing linear beam optics the emittance itself is a global parameter and does not depend on the location in the accelerator. Usually there are two possibilities to establish a slightly different situation for a beam profile measurement. The first method relies on a profile measurement with a single profile monitor in the accelerator, but a change in the beam optics (i.e. the elements of the R matrix) between monitor and reference point. This is the basis of the quadrupole scan method where the focussing strength of a quadrupole in front of the monitor is varied, and the beam size is measured as function of the focussing strength. In the second method the beam optics is kept fix but the beam size is measured at different locations in the accelerator with different profile monitors. This is the basis of the muli– profile monitor method. It is common for both emittance schemes that the number of profile measurements is chosen to be larger than the minimum number of 3, and the data are subjected to a least–square analysis. However, it is obvious that the number of available data points from a quadrupole scan is munch larger than from the multi– profile measurement because the space for profile monitors in an accelerator is limited. In addition, both methods are invasive and cannot be used parasitically. . 4 2. Phase space mapping based schemes.– Beam matrix based emittance diagnostics relies on the assumption of undisturbed phase space evolution. However, especially at low particle beam energies this assumption can be violated because space charge effects may affect the phase space evolution in a non–linear way. To reduce the space charge influence it is common to subdivide the beam into small samples (beamlets) which are emittance dominated and not any more space charge dominated, and to investigate the phase space evolution of each beamlet separately. Particle beam diagnostics and control 9

The subdivison of the beam into beamlets is performed by a small slit which cut out a small vertical slice in the beam phase space: all beam particles are absorbed in the slit material (typically tungsten or tantalum) except the ones crossing the slit opening. This beamlet is propagating along a drift space, so converting the angle information into a position information which is finally detected with a profile monitor. By scanning the slit position through the beam the transverse phase space is scanned and can be reconstructed to deliver the beam emittance. In ref. [31] the emittance reconstruction procedure is described in detail. Instead of a time consuming scanning of the slit in the space coordinate, the absorber can be designed such that it contains a mult–slit arrangement. The advantage of a multi–slit device is the capability to perform single–shot emittance measurements in one transverse plane, i.e. it allows to study shot-to-shot emittance fluctuations. An example for such kind of design together with operational results is described e.g. in refs. [32, 33]. To extend this method to single–shot capability in both planes the design is extended to a pepper–pot which consists of a matrix of holes in an absorber plate. Typically only a tiny fraction of the beam crosses the holes (about 1%), the rest of the beam particles is absorbed in the plate. Therefore heat load considerations are an important task in the design phase, and a high sensitivity detection system is required. In ref. [34] some useful hints concerning pepper–pot emittance analysis are given. While multi–slit and pepper–pot emittance monitors have the advantage of a single– shot capability, their range of application is restricted to the region of low particle energies, at least for lepton beams. In order to work properly only particles crossing the slit resp. the holes should contribute to the profile measurement, the rest of the beam particles should be completely absorbed. In order to absorb high energetic electrons a very thick absorber is required, but in this case particle scattered inside the slits or holes deteriorate the profile measurement. Therefore, this kind of emittance monitor is typically used up to electron beam energies of about 100 MeV. However, in ref. [35] emittance diagnostics with a pepper–pot for 508 MeV electrons is reported. All emittance diagnostic techniques presented so far rely on measurements of the beam profile. Therefore in the following subsection various techniques to determine beam profiles will be shortly reviewed. . 4 3. Beam profile measurements.– It is common to all beam profile monitors that a secondary signal is created with an intensity that is proportional to the charge density of the particle beam. This secondary signal can be generated in an interaction of the beam with matter (e.g. wire scanners, scintillation screens), with photons (e.g. laser wire scanner), or by separating the particle electromagnetic field from the beam particles (e.g. transition radiation or synchrotron radiation monitors). The secondary signal can be either a flux of charged particles (secondary electrons) or of electromagnetic radiation (visible light or γ–radiation), and in the detection scheme spatial resolution can be achieved via scanning a target or detector, or by spatial resolving detectors. Wire scanners deliver a very direct and reliable measurement with an achievable resolution down to 1 µm. The operation principle is such that a thin wire (material C, 10 G. Kube

W, Be, ... and wire size down to a few microns) is scanned across the beam, and the signal from the beam–wire interaction is detected as function of the wire position. For intense and high brilliant beams a fast scan speed of 5–20 m/s is required in order to minimize the emittance blow–up and to reduce the heat load on the wire. The secondary signal from the beam–wire interaction consists either from scattered beam particles and/or bremsstrahlung which is measured outside the vacuum chamber by a fast scintillation counter. Alternatively the secondary electron emission (SEM) signal from the beam–wire interaction can be used. The latter method is often applied for low energy beams where the scattered particles cannot penetrate the vacuum chamber and the bremsstrahlung intensity is to low. However, in this case one has to be careful, because if the wire temperature exceeds the thermionic threshold thermal electrons may superimpose the SEM signal. Wire scanners have the drawback that they deliver projected beam profiles and not the full 2D information. In some setups a third wire mounted under 45◦ with respect to the other 2 wires is used to have an estimate about the coupling between both transverse planes. An example for such a setup is described in ref. [36]. Instead of scanning a wire across a beam a grid of wires can be installed. Such a device is called a harp because of the appearance. Due to the minimum achievable distance between the individual wires in the order of a few 100 µm, a harp is suited to measure beam profiles in the order of a few mm and therefore is mainly used at hadron linacs. The operational principle of a laser wire scanner is very similar to the one of a conventional wire scanner with the exception that a laser beam is scanned across the particle beam, and the secondary signal consists of forward-scattered Compton–γ’s, see e.g. ref. [37]. In principle a resolution down to 1 µm can be achieved, limited by the minimum laser spot size at the interaction point which can be realized. The advantage of a laser wire scanner is that it is an almost non–invasive measurement technique which can in principle operate parasitically, and that the heat load problem in conventional wires can be avoided, but again the monitor delivers only projected beam profiles but not the full 2D information. So far only a few laser wire scanners are installed at accelerators, but they operate more like an experimental system than a beam monitor for daily use. Taking advantage of the rapid development and the huge market for commercial available optical sensors, in the past years optical measuring techniques took on greater significance. Nowadays area scan CCD or CMOS sensors are widely used in beam diagnostics because they provide the full 2D information about the transverse particle beam distribution, allowing in principle to investigate shot-to-shot profile fluctuations at mod- erate repetition rates. To apply optical measuring techniques the information about the particle beam charge distribution has to be converted in an optical intensity distribution which can be recorded by a standard area scan detector. In the selection of this conversion process, care has to be taken that (i) any resolution broadening introduced by the basic underlying physical process has to be small (i.e. the Point Spread Func- tion PSF of the physical process corresponding to the single particle resolution function should not dominate the total spatial resolution), and that (ii) the conversion process should be linear to avoid any deformation of the intensity distribution. There exist two principle possibilities for this conversion process, either to exploit the interaction of the Particle beam diagnostics and control 11 beam particles with matter (used e.g. for scintillation screens or residual gas luminescent monitors), or the particle electromagnetic field has to be separated from the beam to be detected in the far field as radiation. Optical beam profile monitors probing the particle electromagnetic field are widely used, therefore the process of radiation generation will be shortly explained in the following. Considering an ultra–relativistic electron with an electric field which is relativistic contracted (i.e. mainly transversal). The degree of contraction is described by the field 2 opening angle 1/γ with γ = E/m0c the Lorentz factor. In the limiting case γ → ∞ the field would be completely transversal and correspond to a plane wave (classical description of a photon). This situation occurs either by considering a particle with zero rest mass (i.e. a photon), or in the limiting case if the beam energy is increased into the relativistic regime. Due to the similarity between a real photon and the field of an ultra–relativistic particle, the action of this particle is described by so called virtual photons. However, to measure radiation in the far field the virtual photon field bound to the beam particle has to be separated from the particle. In case of a circular accelerator this is achieved by a force acting on the charged particle which is caused by the magnetic field of accelerator (bending) magnets, and the resulting radiation is called synchrotron radiation. However, synchrotron radiation based profile monitors are out of focus of this paper, they are reviewed e.g. in ref. [38]. In case of a linear accelerator there is (per definition) no particle bending, but the separation can be achieved by acting on the virtual photons itself via structures that diffract the particle electromagnetic field away from the particle. For better understanding the analogy between real and virtual photons can be exploited. Real photons can be refracted resp. reflected at a surface, the same holds for virtual photons. In this case the radiation is named Forward/Backward Transition Radiation. In classical optics the effect of edge diffraction is known, in the case of virtual photons the radiation effect is called Diffraction Radiation. Real photons can be diffracted at a grating, the same hold for virtual photons and the effect is called Smith–Purcell Radiation. Finally, high–energetic real photons (X–rays) are diffracted at a 3D structure of a crystal, and if a charged particle beam traverses such crystal Parametric–X Radiation is emitted. It is common to all these radiation phenomena depending on the diffraction of virtual photons that the radiation angular distribution has an on–axis minimum which reflects the property of the incoming virtual photon field and therefore is a fundamental one. Optical Transition Radiation (OTR) monitors are widely used for profile measurements at linacs. The radiation is emitted when a charged particle beam crosses the the boundary between two media with different optical properties, here a thin reflecting screen (e.g. a silicon wafer covered with a thin layer of aluminum or silver) and vacuum. For beam diagnostic purposes the visible part of the radiation is used and an observation geometry in backward direction is mainly chosen which corresponds to the reflection of virtual photons at the screen which acts as mirror. The screen has an inclination angle of 45◦ with respect to the beam axis, and observation is performed under 90◦. In a typical monitor setup the beam is imaged via OTR using standard lens optics, and the recorded intensity profile is a measure of the particle beam spot. The principle achiev- 12 G. Kube able resolution of an OTR monitor is given by δr = 1.12 Mλ/θm with λ the wavelength of observation, θm the lens acceptance angle, and M the magnification of the optical system (see e.g. ref. [39]). The best resolution achieved so far amounted 1 µm. With this monitor a vertical beam size of about 5 µm was measured at the accelerator test facility ATF at KEK (Japan) [40]. Advantages of OTR are the instantaneous emission process enabling fast single shot measurements, and the good linearity (neglecting coherent effects). Disadvantages are that the process of radiation generation is invasive, i.e. a screen has to be inserted in the beam path, and that the radiation intensity is much lower in comparison to scintillation screens. Therefore for low–energetic electron beams luminescent screen monitors are used instead of OTR screens. For high intensity or high brilliant electron beams and OTR monitors the interaction of the beam with the screen material may lead to a screen degradation or even a damage. In these cases the applicability of OTR monitors is usually restricted to single or few bunch operation, and permanent beam observation is not possible. In order to overcome this drawback Optical Diffraction Radiation (ODR) monitors might be a suitable alternative. Diffraction radiation is emitted when a charged particle passes through an aperture on a boundary of two media with different optical properties, usually through a thin slit is a screen. The radiation is generated in an interaction of the particle electromagnetic field with the screen, taking advantage that the field has a certain transverse extension characterized by the impact parameter h = λγ/2π with λ the wavelength of observation and γ the Lorentz factor. If the beam is imaged via ODR as it was the case with OTR, the result would be an illuminated slit image but no beam profile. In order to extract information about the beam profile the visibility of the interference fringes of the angular distribution is exploited. So far ODR based diagnostics is still in an experimental stage, results of an ODR experiment performed at FLASH are described e.g. in ref. [41]. In the meantime the experiment was extended to perform ODR interferometry generated at two slits to increase the sensitivity on the beam parameters [42]. Recently the experience from modern linac based light sources showed that profile diagnostics based on the detection of radiation originating from the particle electromagnetic field might fail because of coherence effects in the emission process. Cause of this coherent emission is the Microbunching Instability, i.e. some unstable micro structures in the electron bunch that compromise the use of this kind of monitors as reliable diagnostic tool. Coherent OTR (COTR) was observed e.g. at the Linac Coherent Light Source LCLS in Stanford (USA) and at the free–electron laser FLASH at DESY in Hamburg (Germany). In ref. [43] the present knowledge about COTR observations is summarized. As consequence for the new 4th generation light sources new reliable tools for transverse beam profile measurements are discussed. One option would be to use transition radiation (TR) profile diagnostics at higher photon energies where coherence effects should be absent. In ref. [44] a test experiment is described dedicated to the investigation of the TR intensity in the EUV region. A further option currently under discussion is to use Luminescent Screens. In a luminescent screen the energy from the beam particles deposited in the screen material is converted into atomic excitations which are followed by radiative relaxations. The Particle beam diagnostics and control 13 light intensity of these optical transitions is a measure for the particle beam profile. In contrast to OTR the scintillation light is emitted isotropically, i.e. there is no restriction on the observation geometry and screen and camera can be placed under arbitrary angles with respect to each other. Inorganic scintillators are of special interest for electron beam diagnostics because of their good radiation resistance, high stopping power for high light yield, and short decay times of the excited atomic levels. The application of scintillation screens for particle beam diagnostics was recently reviewed in ref. [45], and ref. [46] describes the results of a study about the achieveable spatial resolution for profile measurements with different scintillator materials and micro–focussed ultra–relativistic electron beams. According to this study LYSO:Ce and BGO scintillators could be a suitable screen material for electron beam diagnostics. Moreover it was demonstrated that the observation geometry strongly affects the achievable resolution and therefore has to be considered carefully. Furthermore care has to be taken that additionally OTR is produced at the boundary between screen and vacuum which might be reflected from the screen surface to the camera. Usually the intensity of this OTR contribution is to neglect, but in the case of COTR emission it may even compromise the use of scintillating screen monitors as shown in ref. [47]. As it was demonstrated there exist to possibilities to suppress the COTR contribution: (i) a temporal suppression by using a fast gated camera, and (ii) a spatial one by tilting away the screen surface from the camera. While the first method was already tested successfully the possibility of spatial suppression is presently under investigation.

5. – Diagnostics for the longitudinal phase space

As it was the case for the transverse phase spaces, the longitudinal beam properties are characterized by the longitudinal emittance. In case of the longitudinal phase space the phase space variables are the phase deviation ϕ (measured with respect to the synchronous particle), and the momentum deviation δ = ∆p/p. In case of ultra–relativistic particles as it is usually the case for electrons, the momentum deviation can be identified with the energy deviation, i.e. δ = ∆E/E. Considering a particle bunch rather than a single particle, the rms values are taken to characterize√ the particle ensemble. The 2 characteristic values are then√ the phase spread σϕ = < ϕ > and the energy resp. 2 momentum spread σδ = < δ >. In beam diagnostics the phase spread is a rather cumbersome parameter because it is not directly accessible. Instead of the bunch length σz is usually taken which is related to the phase spread according to σz = c/ωRF · σϕ. The formalism for the treatment of the longitudinal phase space is rather similar to the one for the transverse phase spaces, i.e. the beam matrix is constructed according to eq.(3) simply by replacing x by ϕ and x’ by δ, and the emittance is deduced from the beam matrix by eq.(4). Because of the similarity between longitudinal and transverse phase space, in principle similar techniques for emittance diagnostics could be applied: instead of a quadrupole scan with transverse profile monitor a longitudinal focussing device with bunch length monitor could be used. Such longitudinal focussing device exist and is called buncher, however a buncher works effectively only at low particle beam 14 G. Kube energies (short behind the gun) and is used mainly at hadron accelerators. Instead of measuring directly the longitudinal emittance, usually their projections onto the phase space axes are investigated, i.e. the bunch length and the energy spread. Together with diagnostic schemes for both of these parameters, in the following particle beam energy measurements and timing and synchronization issues are briefly presented. . 5 1. Bunch length measurements.– Depending on the type of accelerator the length of a bunch is spread from the nanosecond region (hadron storage ring) over the picosecond region (lepton storage ring) to the range of several femtoseconds (linac driven FEL with bunch compression). To cover such a wide range a number of different techniques are applied which can briefly be classified in (i) electromagnetic monitors, (ii) optical methods, (iii) methods based on the bunch frequency spectrum, (iv) laser based monitors, and (v) monitors based on RF cavity manipulation. Due to the bandwidth limitation of electromagnetic monitors typically in the range of several GHz, these techniques are mainly applied at hadron accelerators and will not be considered in the following. Optical Methods are widely applied because standard instrumentation is available, typically also for reasonable costs. There exist some sophisticated schemes like non– linear mixing [48] or the analysis of the shot noise spectrum [49] which will not be discussed in the following. The device which is mainly in use at various accelerators is the Streak Camera (SC). In a SC visible light generated in an instantaneous process from the beam (synchrotron radiation, OTR, Cherenkov radiation, ...) hits a photo cathode where the light pulses are converted into a number of electrons proportional to the incident intensity distribution. The photo electrons are then accelerated along a streak tube and transversely swept by deflecting plates so that the incident time distribution is converted in a spatial distribution on a Micro Channel Plate (MCP). The photo-electrons amplified by the MCP are impinging on a phosphor screen where they are reconverted in visible light which is detected with a scientific grade CCD detector. A SC is a powerful tool commercially available to study bunch lengths and longitudinal beam dynamics. However, with a resolution limit of about 200 fs [50] it is not sufficient to resolve beam profiles from fully compressed beams of a FEL. According to ref. [51] there are 3 factors limiting the time resolution: (i) the initial velocity distribution of the photo electrons from the photo cathode (see also ref. [52]), the temporal spread occuring in the deflection field, and (iii) the time spread because of space charge effects inside the streak camera. Therefore a SC should be operated with a narrow–bandwidth interference filter in front of the camera and at a low incoming intensity level which can be adjusted by the entrance slit in front of the SC system. Furthermore, in order to achieve a resolution of about 200 ps a reflective light collecting optical system should be used because dispersion effects in the lenses spoil the time resolution. To overcome the resolution limit imposed by a streak camera different diagnostics schemes can be applied, e.g. based on the detection of the bunch frequency spectrum: as shorter the bunch length, as broader the frequency spectrum of the electron bunch. Therefore the bandwidth of the radiation produced from a Gaussian bunch may extend to the THz region for ultra short bunch lengths. One option to measure the bunch length Particle beam diagnostics and control 15 via the frequency spectrum is to use an RF pickup as described in ref. [53]. However, methods widely applied in particle beam diagnostics are based on Coherent Radiation Diagnostics (CRD) [54]. Radiation is emitted coherently if the wavelength is in the order of the bunch length, i.e. information about bunch length and shape is encoded in the emission spectrum which is exploited in CRD. In case of coherent emission the spectral intensity is strongly amplified which can be expressed in the following form: ( ) ∫ dU dU ( ) ∞ (8) = N + N(N − 1)|F (λ)|2 with F (λ) = dz S(z) e−2πiz/λ . dλ dλ 1 −∞

Here (dU/dλ)1 is the single particle emission spectrum, N the number of particles in the bunch, and F (λ) the bunch form factor which is related to the normalized bunch profile S(z) via a Fourier transform. According to eq.(8), from a measurement of the spectral intensity and with knowledge of the single electron spectrum together with the bunch charge, the form factor can be determined. Inverting the Fourier transform results in the reconstructed bunch profile S(z). The situation is more complex because it is the magnitude |F (λ)| of the form factor which is determined rather than the complex form factor itself. Reconstruction is possible only if both amplitude and phase are available. Although a strict solution of this phase–reconstruction problem is not possible, a so– called minimal phase can be constructed with the Kramers–Kronig relation which gives a handle to solve this problem satisfactory. A detailed treatment of this problem can be found e.g. in ref. [55]. In principle any kind of coherent radiation can be used as a radiation source. Measurements were performed with coherent synchrotron radiation, transition radiation, and diffraction radiation. The resolution of CRD is limited to about 100 fs, mainly caused because of uncertainties in the spectral reconstruction. Drawback of CRD is that the radiation sources are polychromatic, i.e. a spectrometer is required for the spectral decomposition which is usually a scanning device and does not allow single–shot measurements. In this context the development of multi–stage spectrometers (see e.g. ref. [56]) might be an interesting alternative, or the application of Smith–Purcell radiation [57] because the radiation source is dispersive by itself. To achieve better resolution laser–based methods can be applied. The laser can be used either by directly scanning the particle beam profile (laser wire scanner, see ref. [58]), or by probing the action of the particle electromagnetic field (similar as an electromagnetic pickup does, but with much higher bandwidth providing better resolution). The latter scheme is exploited in Electro–Optical (EO) techniques. EO detection schemes can be applied for ultra–relativistic electrons where the particle Coulomb field is purely transversal, i.e. the field strength of the non–propagating particle field is a measure of the longitudinal bunch profile. If the bunch passes close to an electro–optical crystal (ZnTe or GaP), its Coulomb field induces a change in the crystal refractive index (so called Pockels effect). The information about the longitudinal profile is therefore encoded in an refractive index change which can be converted into an intensity variation by means of a laser together with polarizers. In the simplest scheme of EO sampling a polarized laser beam is scanned along the bunch, and the change in intensity is recorded as function of 16 G. Kube the time delay. There exist more sophisticated schemes with even the capability of single shot resolution like spectrally [59], temporally [60], or spatially [61] resolved detection. Principle resolution limits of EO bunch lengths measurements are crystal phonon resonances, dispersion in the crystal leading to a gradual distortion and lengthening of the THz pulses, and a laser pulse broadening which can be neglected for crystal thicknesses smaller than 200 µm. The shortest bunch length resolved so far was about 60 fs with temporally resolved EO detection, being close to the principle limit of a GaP crystal. Detailed information about EO techniques and measurements performed at FLASH can be found in ref. [62]. The most state-of-the-art instrument for bunch length measurements and even more is a Transverse Deflecting Structure (TDS). A TDS is an iris loaded RF waveguide structure designed to provide hybrid deflecting modes (HEM11), a linear combination of TM11 and TE11 dipole modes resulting in a transverse force that acts on the synchronously moving relativistic particle bunch. They exist as traveling wave structures [63, 64] or as standing wave structures [65], and their working principle resembles that of an intra beam streak camera: a single bunch inside the bunch train, traversing the structure at an appropriate RF phase experiences a vertical kick which depends linearly on time and vanishes in the bunch center. Due to the vertical deflection, the vertical position of the electrons inside this bunch are linearly correlated to their longitudinal coordinates. Usually a fast horizontal kicker deflects the bunch onto an off–axis screen. The spot at the screen in vertical direction is a measure of the longitudinal bunch profile. The resolution limit of a TDS is determined by √ E/e ε (9) σres = · √ V02πfRF cos ψ βtds sin ∆ϕ with E the beam energy, V0 the deflecting voltage (should be high for good resolution), fRF the TDS RF frequency (should be high), ψ the phase between bunch centroid and RF wave (should be operated at zero–crossing), ε the transverse beam emittance, βtds the β function at the location of the TDS (should be as large as possible for most effective kick), and ∆ϕ the phase advance between TDS and location of the screen (should amount 90◦ or 270◦). At FLASH a traveling wave–type vertical deflecting S–band (2.865 GHz) RF structure is operated [66]. For the E–XFEL several TDS setups are planned with a resolution of about 10 fs/sin ∆ϕ [67]. Besides the excellent time resolution, the advantage of operating a TDS is to have the possibility to measure additional beam parameters in a time resolved way which are not accessible with any other diagnostic instrument. For example, the streaked image onto the screen in horizontal direction contains information about the horizontal beam size, but now for each longitudinal position inside the bunch. If a quadrupole scan is performed with one of the upstream quadrupoles in front of the structure, the horizontal beam size in each slice is determined as function of the quadrupole settings, and this technique gives access to the horizontal slice emittance [68]. The quadrupole scanning gives rise to a rotation of the beam in the transverse phase space. Applying tomographic Particle beam diagnostics and control 17 reconstruction schemes (see e.g. ref. [69]) it is even possible to reconstruct the complete phase space information in one transverse plane [70]. In addition, with a screen located in a horizontally dispersive section behind the deflecting structure it is possible to measure directly the longitudinal phase space distribution, i.e. to have access also to the energy spread [71]. . 5 2. Energy spread.– The energy spread is a phase space variable of the longitudinal phase space. However, the dispersion in an accelerator results in a coupling between the transverse (i.e. usually the horizontal one) and the longitudinal phase space. Therefore measurements of the energy spread can be performed either with longitudinal or with transverse phase space diagnostics schemes. Longitudinal schemes are widely used at circular accelerators where the rms energy spread linearly depends on the bunch length. By changing the synchrotron frequency via the accelerator RF and measuring the bunch length with a streak camera the energy spread can be deduced, see e.g. ref. [72]. Measuring the impact of the energy spread in the transverse phase space is simply achieved by a transverse profile measurement. Taking the closed orbit contribution of an off–momentum particle into account in the displacement of a particle from the ideal trajectory, the rms beam size is affected by an additional contribution: √ ( ) σ 2 (10) σ = εβ + η δ x E with η the dispersion. According to eq.(10) a direct way to measure the energy spread in a linac is a proper selection of the transverse profile monitor location in the accelerator where the beam spot size is fully determined by the dispersion contribution. With knowledge of η the energy spread can easily be deduced. An example of such kind of measurement is described in ref. [73]. A completely different and non–invasive detection scheme of the energy spread is described in ref. [74]. In this Beam Energy Spread Monitor (BESM) the multipole moments induced by the passage of a charged particle beam in the multi–stripline electrodes (here: 8 units) of an electromagnetic pickup are exploited. The induced quadrupole moments contain information about the beam size which depends on the energy spread according to eq.(10). Finally the time resolved energy spread can be measured with a TDS if the screen is located in a horizontally dispersive section behind the deflecting structure as described in the previous subsection. . 5 3. Beam energy.– The precise knowledge of the beam energy is of vital interest for the experiments performed at an accelerator. For high energy physics experiments the accuracy in the particle beam energy determines the accuracy in the location of particle resonances and their widths, while for synchrotron light sources the energy is important to characterize the parameters of the insertion devices. Moreover, for the operation of an accelerator it is important to know the absolute beam energy to precisely 18 G. Kube understand the particle beam optics. Ref. [75] gives an overview over different methods to determine the beam energy. According to this reference the different schemes for energy determination can roughly be classified in (i) measurements via dipole spectrometers, (ii) measurements via particle or nuclear physics processes, (iii) photon based methods, (iv) energy measurements from the central frequency, (v) energy losses due to synchrotron radiation, and (vi) resonant depolarization. While the highest accuracy is achieved with the last method (∆E/E ≈ 10−5 − 10−6) it is only applicable for circular accelerators. The measurement schemes in use at linacs are either dipole spectrometers or photon based methods, and in the following these techniques will be briefly discussed. The principle of a Dipole Spectrometer relies on the fact that a dipole transforms a momentum resp. momentum spread into a position resp. position spread. The deflection angle is proportional to the integral over the magnetic field∫ seen by the particle, −1 and inversely proportional to the particle momentum: θ = p0 dsB. The detection scheme relies on spatial resolving detectors, i.e. BPMs or screens. For high resolution measurements one has to take into account that the beam position in dispersive direction behind the dipole not only depends on the position x0 in front of the dipole, but also on the angular divergence x’0. Therefore at least 2 position sensitive monitors in front of the dipole are required for a simultaneous measurement of x0 and x’0. To define both parameters very precisely in case of large emittance beams an entrance slit in front of the spectrometer is recommended. An example for a spectrometer setup is the LEP spectrometer [76]: with 1 µm position accuracy and a field stability of ∆B/B ≈ 10−5, an energy resolution of about ∆E/E ≈ 10−4 could be achieved. A photon originating from or interacting with the particle beam carries information about the beam energy which is encoded in either the photon spectrum or the angular distribution. Therefore Photon based Methods rely on the measurement of photon properties to draw conclusions about the beam energy. In a circular accelerator for example synchrotron radiation (SR) is emitted with a spectrum that strongly depends on the beam energy. From a measurement of the high energetic part of the SR photon spectrum it was possible to determine the beam energy to a level of about 10−3 [77]. In a linac the angular distribution of OTR can be exploited. Due to the fact that the angular distribution possesses characteristic maxima at angles 1/γ with γ the Lorentz factor, from such a measurement the beam energy can be derived. Instead of using photons emitted from the beam, laser photons can be backscattered at the particle beam (Comp- ton backscattering). From the determination of the maximum energy of the scattered Compton photons the beam energy could be determined to a level of ∆E/E ≈ 10−4 [78]. . 5 4. Beam synchronous timing.– A beam synchronous timing system (BST) has to fulfill the following tasks: it has to generate and remotely distribute a phase reference, (ii) it has to trigger fast and slow sub–systems, and it needs an interface to the control system. Usually it is based on the following building blocks: (i) the reference or master oscillator which defines the phase reference for all sub–systems, (ii) the master time– base or event system generating e.g. trigger and bunch clock signals and delivering experiment triggers, (iii) the distribution system (either coaxial cables or fiber optics) Particle beam diagnostics and control 19 to the various sub–systems, and (iv) the control system interface. Typically there exist two different timing levels in an accelerator environment, a fast timing which is at the level of individual bunches and a slower one being at the level of a revolution clock in a circular accelerator resp. on the level of bunch train repetition rate in a linac. A general review about accelerator timing systems, based on the experience of 3rd generation light sources, can be found in ref. [79]. The new 4th generation light sources however are capable to generate light pulses even with a duration below 10 fs, and even shorter pulse durations are envisioned. In order to take full advantage of these short light pulses, synchronization schemes on a sub–10 fs scale or even below together with precise measurements and control of the electron bunch arrival time are required. The required precision which is ideally a small fraction of the photon pulse duration can only be achieved with laser–based synchronization schemes. In the following a brief overview over the optical synchronization schemes together with the sub–systems in use at modern high–gain FELs will be given. The general concept of an optical synchronization system consists of a laser as timing reference (master oscillator), a distribution unit to split the timing reference signals, and actively length stabilized fiber–links that transport the reference signals to the different remote locations. There are two general concepts to encode the timing information and perform link stabilization, either to use a cw laser and maintain a constant number of optical wavelength over the fiber length [80], or to encode the timing information in the highly accurate repetition rate of a master laser oscillator (MLO) and maintain a constant repetition rate of forward and reflected pulses over the fiber length. The latter method which is in use at FLASH and has be designated for the E-XFEL will be presented in the following. It has the advantage that due to the short laser pulses, non–linear optical methods can be applied to measure timing changes of the optical pulse train. The MLO is an erbium fiber laser operating in the soliton regime and producing a train of sub-100 fs long laser pulses at a repetition rate of 216.7 MHz (sixth sub– harmonic of the accelerator RF frequency of 1.3 GHz) at a central wavelength of 1500 nm. In this wavelength range, many fiber–optic components are available developed for the telecommunication industry, and broadband transmission in dispersion compensated optical fibers is possible. The fiber laser provides excellent stability on short time scales, but in order to compensate for long time drifts (length change of the laser resonator due to thermal expansion or contraction, microphonics) the laser frequency is locked to a long–term stable RF oscillator [81]. However, the existing self–built laser system has been replaced recently by a commercial available SESAM (semiconductor saturable absorber mirror)–based erbium laser [82]. For the distribution of the MLO time reference signals to the different sub–systems over length scales of 400 m (FLASH) up to 3.5 km (E-XFEL) via optical fiber links, active stabilization is required in order to compensate for optical length changes of the fiber, e.g. due to changes in the environment temperature. The measurement of the optical length is performed such that the MLO pulses are transmitted through a dispersion compensated optical fiber, partly reflected at a Faraday rotating mirror, and then sent back to the MLO through the same fiber. There they are combined with the laser pulses coming 20 G. Kube directly from the laser in a balanced optical cross–correlator [83]. The temporal overlap between both pulse trains is measured with sub-fs resolution and length changes are compensated with a feedback loop acting on a piezo fiber stretcher (fine compensation) and an optical delay stage (coarse compensation) [81]. In order to measure the electron bunch arrival time with respect to the time reference signal, a Bunch Arrival Time Monitor (BAM) has been developed [84]. It consists of a commercial available Mach–Zehnder–type electro–optical modulator (EOM) which is driven by the transient voltage signal from a broadband electromagnetic pickup. The arrival time of the reference laser pulse is adjusted such that it coincides with the zero– crossing of the pickup for nominal bunch arrival time. Variations in the electron bunch arrival time result in a variation of the modulation voltage experienced by the reference laser pulse, and by detecting the amplitude of the pulse the arrival time can be derived. The resolution of a BAM installed in FLASH was determined to be 3-5 fs for optimized settings. Based on precise arrival–time information provided by the BAMs even a bunch arrival time feedback has been implemented at FLASH which improved the arrival–time stability from around 180 fs to 25 fs [85]. ∗ ∗ ∗

Many thanks to my DESY colleagues C. Behrens, H. Delsim-Hashemi, D. Lipka, D. Nölle,H. Schlarb, B. Steffen, M. Yan, and K. Wittenburg for their stimulating discussions and their help in the preparation of this lecture, and also to H. Braun (PSI), M. Ferianis (Synchrotrone Trieste), P. Forck (GSI), M. Minty (BNL), A.-S. Müller(KIT), U. Raich (CERN), and V. Schlott (PSI) for their lectures about different task in the field of particle beam diagnostics which I could use as illustrative material.

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