The axial electric field of Alvarez drift tube linacs (DTLs) is known to be susceptible to variations due to static and dynamic effects like manufacturing tolerances and beam loading. Post-couplers are used to stabilize the accelerating fields of DTLs against tuning errors. Tilt sensitivity and its slope have been introduced as measures for the stability right from the invention of post-couplers but since then the actual stabilization has mostly been done by tedious iteration. In the present article, the local tilt-sensitivity slope ${\mathrm{TS}}_n^{\prime }$ is established as the principal measure for stabilization instead of tilt sensitivity or some visual slope, and its significance is developed on the basis of an equivalent-circuit diagram of the DTL. Experimental and 3D simulation results are used to analyze its behavior and to define a technique for stabilization that allows finding the best post-coupler settings with just four tilt-sensitivity measurements. CERN’s Linac4 DTL Tank 2 and Tank 3 have been stabilized successfully using this technique. The final tilt-sensitivity error has been reduced from $\pm 100\%/\mathrm{MHz}$ down to $\pm 3\%/\mathrm{MHz}$ for Tank 2 and down to $\pm 1\%$/MHz for Tank 3. Finally, an accurate procedure for tuning the structure using slug tuners is discussed.

Beam coupling impedance is a fundamental parameter to characterize the electromagnetic interaction of a particle beam with the surrounding environment. Synchrotron machine performances are critically affected by instabilities and collective effects triggered by beam coupling impedance. In particular, transverse beam coupling impedance is expected to impact beam dynamics of the CERN Proton Synchrotron (PS), since a significant increase in beam intensity is foreseen within the framework of the LHC Injectors Upgrade (LIU) project. In this paper we describe the study of the transverse beam coupling impedance of the PS, taking into account the main sources of geometrical impedance and the contribution of indirect space charge at different energies. The total machine impedance budget, determined from beam-based dedicated machine measurement sessions, is also discussed and compared with the theoretical model.

Beam emittance has particular importance in particle physics, because it provides information about the quality of the particle beam. There are many techniques for measuring the beam emittance, such as that proposed by Miller et al. [Report No. SLAC-PUB-3186, (A) (1983)]. This technique is based on determining the emittance by measuring the second-order moment of the beam using quadrupole pickups consisting of four symmetrical electrodes placed around the beam pipe at 90° intervals, respectively. Based on Miller’s approach, two signal processing methods are generally used to get the quadrupole moment of the beam, namely the difference over sum and the log ratio [, IEEE Nuclear Science Symposium Conference Record, N24-404, 2007, pp. 1675–1678] methods. However, these traditional methods provide results with a good accuracy only for a well centered beam. The method presented in this paper, which starts with Miller’s approach, considerably reduces the impact of the dipole signal on the quadrupole moment measurement for both small and large values of the beam position. Furthermore, a methodology for the numerical determination of the sensitivity of quadrupole pickups will be presented.

Runaway electrons play an important role in the avalanche formation in nanosecond- and subnanosecond- pulse discharges. In this paper, characteristics of a supershort avalanche electron beam (SAEB) generated at the subnanosecond and nanosecond breakdown in sulfur hexafluoride (${\mathrm{SF}}_6$) in an inhomogeneous electric field were studied. One pulser operated at negative polarity with voltage pulse amplitude of $\sim 130\mathrm{kV}$ and rise time of 0.3 ns. The other pulser operated at negative polarity with voltage pulse amplitude of 70 kV and rise time of $\sim 1.6\mathrm{ns}$. SAEB parameters in ${\mathrm{SF}}_6$ are compared with those obtained in krypton (Kr), nitrogen (${\mathrm{N}}_2$), air, and mixtures of ${\mathrm{SF}}_6$ with krypton or nitrogen. Experimental results showed that SAEB currents appeared during the rise-time of the voltage pulse for both pulsers. Moreover, amplitudes of the SAEB current in ${\mathrm{SF}}_6$ and Kr approximately ranged from several to tens of milliamps at atmospheric pressure, which were smaller than those in ${\mathrm{N}}_2$ and air (ranging from hundreds of milliamps to several amperes). Furthermore, the concentration of ${\mathrm{SF}}_6$ additive could significantly reduce the SAEB current in ${\mathrm{N}}_2\text{−}{\mathrm{SF}}_6$ mixture, but it slightly affected the SAEB current in $\mathrm{Kr}\text{−}{\mathrm{SF}}_6$ mixture because of the atomic/molecular ionization cross section of the gas had a much greater impact on the SAEB current rather than the electronegativity.

We report the design, fabrication, and high gradient testing of a 17.1 GHz photonic band-gap (PBG) accelerator structure. Photonic band-gap (PBG) structures are promising candidates for electron accelerators capable of high-gradient operation because they have the inherent damping of high order modes required to avoid beam breakup instabilities. The 17.1 GHz PBG structure tested was a single cell structure composed of a triangular array of round copper rods of radius 1.45 mm spaced by 8.05 mm. The test assembly consisted of the test PBG cell located between conventional (pillbox) input and output cells, with input power of up to 4 MW from a klystron supplied via a ${\mathrm{TM}}_{01}$ mode launcher. Breakdown at high gradient was observed by diagnostics including reflected power, downstream and upstream current monitors and visible light emission. The testing procedure was first benchmarked with a conventional disc-loaded waveguide structure, which reached a gradient of $87\mathrm{MV}/\mathrm{m}$ at a breakdown probability of $1.19\times {10}^{-1}$ per pulse per meter. The PBG structure was tested with 100 ns pulses at gradient levels of less than $90\mathrm{MV}/\mathrm{m}$ in order to limit the surface temperature rise to 120 K. The PBG structure reached up to $89\mathrm{MV}/\mathrm{m}$ at a breakdown probability of $1.09\times {10}^{-1}$ per pulse per meter. These test results show that a PBG structure can simultaneously operate at high gradients and low breakdown probability, while also providing wakefield damping.

The linear-transformer-driver (LTD) is a recently developed pulsed-power technology that shows great promise for a number of applications. These include a $Z$-pinch-driven fission-fusion-hybrid reactor that is being developed by the Chinese Academy of Engineering Physics. In support of the reactor development effort, we are planning to build an LTD-based accelerator that is optimized for driving wire-array $Z$-pinch loads. The accelerator comprises six modules in parallel, each of which has eight series 0.8-MA LTD cavities in a voltage-adder configuration. Vacuum transmission lines are used from the interior of the adder to the central vacuum chamber where the load is placed. Thus the traditional stack-flashover problem is eliminated. The machine is 3.2 m tall and 12 m in outer diameter including supports. A prototype cavity was built and tested for more than 6000 shots intermittently at a repetition rate of 0.1 Hz. A novel trigger, in which only one input trigger pulse is needed by utilizing an internal trigger brick, was developed and successfully verified in these shots. A full circuit modeling was conducted for the accelerator. The simulation result shows that a current pulse rising to 5.2 MA in 91 ns (10%–90%) can be delivered to the wire-array load, which is 1.5 cm in height, 1.2 cm in initial radius, and 1 mg in mass. The maximum implosion velocity of the load is $32\mathrm{cm}/\mu \mathrm{s}$ when compressed to 0.1 of the initial radius. The maximum kinetic energy is 78 kJ, which is 11.7% of the electric energy stored in the capacitors. This accelerator is supposed to enable a radiation energy efficiency of 20%–30%, providing a high efficient facility for research on the fast $Z$ pinch and technologies for repetition-rate-operated accelerators.

Minimizing the dilution of the electron beam emittance is crucial for the performance of accelerators, in particular for free electron laser facilities, where the length of the machine and the efficiency of the lasing process depend on it. Measurements performed at the SwissFEL Injector Test Facility revealed an increase in slice emittance after compressing the bunch even for moderate compression factors. The phenomenon was experimentally studied by characterizing the dependence of the effect on beam and machine parameters relevant for the bunch compression. The reproduction of these measurements in simulation required the use of a 3D beam dynamics model along the bunch compressor that includes coherent synchrotron radiation. Our investigations identified transverse effects, such as coherent synchrotron radiation and transverse space charge as the sources of the observed emittance dilution, excluding other effects, such as chromatic effects on single slices or spurious dispersion. We also present studies, both experimental and simulation based, on the effect of the optics mismatch of the slices on the variation of the slice emittance along the bunch. After a corresponding reoptimization of the beam optics in the test facility we reached slice emittances below 200 nm for the central slices along the longitudinal dimension with a moderate increase up to 300 nm in the head and tail for a compression factor of 7.5 and a bunch charge of 200 pC, equivalent to a final current of 150 A, at about 230 MeV energy.

The Iranian Light Source Facility (ILSF) is a new 3 GeV synchrotron radiation laboratory which is in the design stage. The ILSF storage ring (SR) is based on a Five-Bend Achromat (5BA) lattice providing an ultra-low beam emittance of 0.48 nm rad. The ring is comprised of 100 pure dipole magnets, 320 quadrupoles, and 320 sextupoles with additional coils for dipole and skew quadrupole correctors. In this paper, we present some design features of the SR magnets and discuss the detailed physical design of these electromagnets. The related electrical and cooling calculations and mechanical design issues have been investigated as well.

The phase retrieval problem occurs in a number of areas in physics and is the subject of continuing investigation. The one-dimensional case, e.g., the reconstruction of the temporal profile of a charged particle bunch, is particularly challenging and important for particle accelerators. Accurate knowledge of the longitudinal (time) profile of the bunch is important in the context of linear colliders, wakefield accelerators and for the next generation of light sources, including x-ray SASE FELs. Frequently applied methods, e.g., minimal phase retrieval or other iterative algorithms, are reliable if the Blaschke phase contribution is negligible. This, however, is neither known a priori nor can it be assumed to apply to an arbitrary bunch profile. We present a novel approach which gives reproducible, most-probable and stable reconstructions for bunch profiles (both artificial and experimental) that would otherwise remain unresolved by the existing techniques.

A simplified numerical model has been developed to simulate nonlinear superconducting radiofrequency (SRF) losses on Nb surfaces. This study focuses exclusively on excessive surface resistance ($R_s$) losses due to the microscopic topographical magnetic field enhancements. When the enhanced local surface magnetic field exceeds the superconducting critical transition magnetic field $H_c$, small volumes of surface material may become normal conducting and increase the effective surface resistance without inducing a quench. We seek to build an improved quantitative characterization of this qualitative model. Using topographic data from typical buffered chemical polish (BCP)- and electropolish (EP)-treated fine grain niobium, we have estimated the resulting field-dependent losses and extrapolated this model to the implications for cavity performance. The model predictions correspond well to the characteristic BCP versus EP high field $Q_0$ performance differences for fine grain niobium. We describe the algorithm of the model, its limitations, and the effects of this nonlinear loss contribution on SRF cavity performance.

Effects of nonlinearity in Thomson scattering of a high intensity laser pulse from electrons are analyzed. Analytic expressions for laser pulse shaping in frequency (chirping) are obtained which control spectrum broadening for high laser pulse intensities. These analytic solutions allow prediction of the spectral form and required laser parameters to avoid broadening. Results of analytical and numerical calculations agree well. The control over the scattered radiation bandwidth allows narrow bandwidth sources to be produced using high scattering intensities, which in turn greatly improves scattering yield for future x- and gamma-ray sources.

A method is described to solve the Poisson problem for a three dimensional source distribution that is periodic into one direction. Perpendicular to the direction of periodicity a free space (or open) boundary condition is realized. In beam physics, this approach allows us to calculate the space charge field of a continualized charged particle distribution with periodic pattern. The method is based on a particle-mesh approach with equidistant grid and fast convolution with a Green’s function. The periodic approach uses only one period of the source distribution, but a periodic extension of the Green’s function. The approach is numerically efficient and allows the investigation of periodic- and pseudoperiodic structures with period lengths that are small compared to the source dimensions, for instance of laser modulated beams or of the evolution of micro bunch structures. Applications for laser modulated beams are given.

A high luminosity muon collider requires single, intense, muon bunches with small emittances: just one of each sign. An efficient front end and a cooling channel have been designed and simulated within the collaboration of the Muon Accelerator Program. The muons are first bunched and phase rotated into 21 bunches, and then cooled in six dimensions. When they are cool enough, they are merged into single bunches: one of each sign. The bunch merging scheme has been outlined with preliminary simulations in previous studies. In this paper we present a comprehensive design with its end-to-end simulation. The 21 bunches are first merged in longitudinal phase space into seven bunches. These are directed into seven “trombone” paths with different lengths, to bring them to the same time, and then merged transversely in a collecting “funnel” into the required single larger bunches. Detailed numerical simulations show that the 6D emittance of the resulting bunch reaches the parameters needed for high acceptance into the downstream cooling channel.

Accelerating gradients in excess of $100\mathrm{MV}/\mathrm{m}$, at very low breakdown rates, have been successfully achieved in numerous prototype CLIC accelerating structures. The conditioning and operational histories of several structures, tested at KEK and CERN, have been compared and there is clear evidence that the conditioning progresses with the number of rf pulses and not with the number of breakdowns. This observation opens the possibility that the optimum conditioning strategy, which minimizes the total number of breakdowns the structure is subject to without increasing conditioning time, may be to never exceed the breakdown rate target for operation. The result is also likely to have a strong impact on efforts to understand the physical mechanism underlying conditioning and may lead to preparation procedures which reduce conditioning time.

We have recently performed experiments to test the effectiveness of three ion-clearing strategies in the Cornell high intensity photoinjector: DC clearing electrodes, bunch gaps, and beam shaking. The photoinjector reaches a new regime of linac beam parameters where high continuous wave beam currents lead to ion trapping. Therefore ion mitigation strategies must be evaluated for this machine and other similar future high current linacs. We have developed several techniques to directly measure the residual trapped ions. Our two primary indicators of successful clearing are the amount of ion current removed by a DC clearing electrode, and the absence of bremsstrahlung radiation generated by beam-ion interactions. Measurements were taken for an electron beam with an energy of 5 MeV and continuous wave beam currents in the range of 1–20 mA. Several theoretical models have been developed to explain our data. Using them, we are able to estimate the clearing electrode voltage required for maximum ion clearing, the creation and clearing rates of the ions while employing bunch gaps, and the sinusoidal shaking frequency necessary for clearing via beam shaking. In all cases, we achieve a maximum ion clearing of at least 70% or higher, and in some cases our data is consistent with full ion clearing.

The frequency domain performance of a stripline beam position monitor depends largely on the longitudinal shape of its electrode. Some shapes other than a conventional rectangle have been proposed and tested. To attain a good impedance matching along the electrode, they need to be precisely bent down toward their downstream in proportion to their width. This is a considerable task, and a failure to comply with it will result in a large distortion of the frequency-domain transfer function from the ideal one due to unwanted signal reflections. In this report, we first propose a triangle electrode for easy fabrication and setup: it only requires that a triangularly cut flat electrode will be placed in a chamber while being obliquely inclined toward the downstream port. Theoretical and simulation results show that the simple triangle electrode has a remarkably flatter frequency response than the rectangle one. The frequency response, in particular at high frequencies, can be further improved by attaching an “apron” plate, perpendicular to the upstream edge of the electrode. The overshooting of the frequency response at low frequency can be eliminated by replacing the straight sidelines of the triangle by three-point polylines (with a result that the triangle is transformed to a concave pentagon). The concave pentagon electrode needs to be bent only once at the middle point of the polylines for a good impedance matching and thus its fabrication and setup remain to be easy. Rf measurements for the various electrode shapes have been carried out. We found that the concave pentagon electrode achieves a wide and flat frequency response up to about 4 GHz for the J-PARC Main Ring (MR).

In this paper we discuss the ultrashort pulse high gradient inverse free electron laser accelerator experiment carried out at the Lawrence Livermore National Laboratory which demonstrated gradients exceeding $200\mathrm{MV}/\mathrm{m}$ using a 4 TW 100 fs long 800 nm $\mathrm{Ti}:\mathrm{Sa}$ laser pulse. Due to the short laser and electron pulse lengths, synchronization was determined to be one of the main challenges in this experiment. This made necessary the implementation of a single-shot, nondestructive, electro-optic sampling based diagnostics to enable time-stamping of each laser accelerator shot with $<100\mathrm{fs}$ accuracy. The results of this experiment are expected to pave the way towards the development of future GeV-class IFEL accelerators.

A new two-dimensional beam-tracking simulation code for electron injectors using a bulk-to-point calculation technique for space charge fields was developed. The calculated space charge fields are produced not by a point charge but by a hollow cylinder that has a volume. Each tracked electron is a point charge. This bulk-to-point calculation technique for space charge fields is based on that used in the multiple beam envelope equations, which were developed by the author. The multiple beam envelope equations are a set of differential equations for investigating the beam dynamics of electron injectors and can be used to calculate bunched beam dynamics with high accuracy. However, there is one limitation. The bunched beam is assumed to be an ensemble of several segmentation pieces in both the transverse and longitudinal directions. In this bunch model, each longitudinal segmentation slice in a bunch must not warp; consequently, the accuracy of the calculated emittance is reduced in the case of a highly charged beam for calculations of a typical rf gun injector system. This limitation is related to the calculation model of longitudinal space charge fields. In the newly developed beam-tracking simulation code, the space charge field calculation scheme is upgraded and the limitation has been overcome. Therefore, the applicable range is extended while maintaining the high accuracy of emittance calculations. Simultaneously, the calculation time is markedly shortened because the emittance dependence on the segmentation number is extremely weak. In this paper, several examples of beam dynamics that cannot be calculated accurately using the multiple beam envelope equations are demonstrated using the new beam-tracking simulation code. The accuracy of the calculated emittance is also discussed.

In this paper we present undulator magnet tapering methods for obtaining high efficiency and multiterawatt peak powers in x-ray free electron lasers (XFELs), a key requirement for enabling 3D atomic resolution single molecule imaging and nonlinear x-ray science. The peak power and efficiency of tapered XFELs is sensitive to time dependent effects, like synchrotron sideband growth. To analyze this dependence in detail we perform a comparative numerical optimization for the undulator magnetic field tapering profile including and intentionally disabling these effects. We show that the solution for the magnetic field taper profile obtained from time independent optimization does not yield the highest extraction efficiency when time dependent effects are included. Our comparative optimization is performed for a novel undulator designed specifically to obtain TW power x-ray pulses in the shortest distance: superconducting, helical, with short period and built-in strong focusing. This design reduces the length of the breaks between modules, decreasing diffraction effects, and allows using a stronger transverse electron focusing. Both effects reduce the gain length and the overall undulator length. We determine that after a fully time dependent optimization of a 100 m long Linac coherent light source-like XFEL we can obtain a maximum efficiency of 7%, corresponding to 3.7 TW peak radiation power. Possible methods to suppress the synchrotron sidebands, and further enhance the FEL peak power, up to about 6 TW by increasing the seed power and reducing the electron beam energy spread, are also discussed.