Transverse mode-coupling instability (TMCI) is known to limit bunch intensity. Since space charge (SC) changes the spectra of the collective modes, it affects the TMCI threshold as well. In agreement with results of M. Blaskiewicz and V. Balbekov, we found that, when the wake is negative or it essentially negative, the instability threshold increases as fast as the space charge tune shift when the latter is large enough. In contrast, for oscillating wakes, when the oscillations are sufficiently pronounced, the threshold dependence on SC is non-monotonic; at sufficiently high SC tune shift the threshold goes inversely proportional to that.
Transverse mode coupling instability of a bunch with space charge is considered in frameworks of the boxcar model. Presented results demonstrate a monotonous growth of the TMCI threshold at increasing space charge tune shift, and do not support the supposition that the monotony can be violated at a higher SC.
Transverse mode-coupling instability (TMCI) is known to limit bunch intensity. Since space charge (SC) changes coherent spectra, it affects the TMCI threshold. Generally, there are only two types of TMCI with respect to SC: the vanishing type and the strong space charge (SSC) type. For the former, the threshold value of the wake tune shift is asymptotically proportional to the SC tune shift, as it was first observed twenty years ago by M. Blaskiewicz for exponential wakes. For the latter, the threshold value of the wake tune shift is asymptotically inversely proportional to the SC, as it was s…
Transverse mode coupling instability of a bunch with space charge and wake field is considered within the frameworks of the boxcar model. Eigenfunctions of the bunch without wake are used as a basis for the solution of the equations with the wake field included. A dispersion equation for constant wake is presented in the form of an infinite continued fraction and also as the recursive relation with an arbitrary number of the basis functions. Realistic wake fields are considered as well including resistive wall, square, and oscillating wakes. It is shown that the TMCI threshold of the negative …
Transverse mode coupling instability of bunched beam is investigated in the paper at different form of the bunches with space charge included. Equation of transverse motion of the bunch in parabolic potential well of synchrotron oscillations is derived and analysed. The bunch of constant density (flat bunch) is examined in detail to make comparison with the square well model. It is shown that both models result in very close instability thresholds of the flat bunch. Then different form bunches are investigated in the parabolic potential well. It is shown that decrease of the bunch r.m.s length…
Transverse mode-coupling instability (TMCI) with a high-frequency resonator wake is examined by the Nested Head-Tail Vlasov solver (NHT), where a Gaussian bunch in a parabolic potential (GP model) is represented by concentric rings in the longitudinal phase space. It is shown that multiple mode couplings and decouplings make impossible an unambiguous definition of the threshold, unless Landau damping is taken into account. To address this problem, instead of a single instability threshold, an interval of thresholds is suggested, bounded by the low and high intensity ones. For the broadband imp…
For a single hadron bunch in a circular accelerator at zero chromaticity, without multi-turn wakes and without electron clouds and other beams, only one transverse collective instability is possible, the mode-coupling instability, or TMCI. For sufficiently strong space charge (SC), the instability threshold of the wake-driven coherent tune shift normally increases linearly with the SC tune shift, as independently concluded by several authors using different methods. This stability condition has, however, a very strange feature: at strong SC, it is totally insensitive to the number of particles…
The transverse instability of a bunch in a circular accelerator is elaborated in this paper. A new tree-modes model is proposed and developed to describe the most unstable modes of the bunch. This simple and flexible model includes chromaticity and space charge, and can be used with any bunch and wake forms. The dispersion equation for the bunch eigentunes is obtained in form of a third-order algebraic equation. The known head-tail and TMCI modes appear as the limiting cases which are distinctly bounded at zero chromaticity only. It is shown that the instability parameters depend only slightly…
For booster synchrotrons, like the SIS at GSI, space charge is one of the main intensity limitations. At injection energy the space charge induced tune spreads in booster synchrotrons are large, reaching up to 0.5 and the ramping times are typically short. We study the effect of several localized electron lenses distributed equally around the circumference in order to compensate for the transverse space charge force.
The University of Maryland Electron Ring (UMER) has operated traditionally in the regime of strong space-charge dominated beam transport, but small-current beams are desirable to significantly reduce the direct (incoherent) space-charge tune shift as well as the tune depression. This regime is of interest to model space-charge effects in large proton and ion rings similar to those used in nuclear physics and spallation neutron sources, and also for nonlinear dynamics studies of lattices inspired on the Integrable Optics Test Accelerator (IOTA). We review the definition of space-charge intensit…
The space charge forces are those generated directly by the charge distribution, with the inclusion of the image charges and currents due to the interaction of the beam with a perfectly conducting smooth pipe. Space charge forces are responsible for several unwanted phenomena related to beam dynamics, such as energy loss, shift of the synchronous phase and frequency, shift of the betatron frequencies, and instabilities. We will discuss in this lecture the main feature of space charge effects in high-energy storage rings as well as in low-energy linacs and transport lines.
The role and mitigation of space charge effects are important aspects of the beam physics research to be performed at the Integrable Optics Test Accelerator (IOTA) at Fermilab. The impact of nonlinear integrability (partial and complete) on space charge driven incoherent and coherent resonances will be a new feature of this accelerator and has the potential to influence the design of future low energy proton synchrotrons. In this report we model transverse space charge effects using the PIC code pyORBIT. First we benchmark the single particle tracking results against MADX with checks on symple…
The nonlinear space-charge effects in a high intensity or high brightness accelerator can have a significant impact on the beam properties through the accelerator. These effects are included in the accelerator design via self-consistent multi-particle tracking simulations. In order to study the sensitivity of the final beam's properties with respect to the accelerator design parameters, one has to carry out the time-consuming space-charge simulation multiple times. In this paper, we propose a differentiable self-consistent space-charge simulation model that enables the study of the beam sensit…
Symplectic tracking is important in accelerator beam dynamics simulation. So far, to the best of our knowledge, there is no self-consistent symplectic space-charge tracking model available in the accelerator community. In this paper, we present a two-dimensional and a three-dimensional symplectic multi-particle spectral model for space-charge tracking simulation. This model includes both the effect from external fields and the effect of self-consistent space-charge fields using a split-operator method. Such a model preserves the phase space structure and shows much less numerical emittance gro…
Transverse mode coupling instability of a bunch with space charge and wake field is considered in frameworks of the boxcar model. Eigenfunctions of the bunch without wake are used as the basis for solution of the equations with the wake field included. Dispersion equation for the bunch eigentunes is obtained in the form of an infinite continued fraction. It is shown that influence of space charge on the instability essentially depends on the wake sign. In particular, threshold of the negative wake increases in absolute value until the space charge tune shift is rather small, and goes to zero a…
Space-charge effects belong to the category of the most long-standing issues in beam physics, and even today, after several decades of very active exploration and development of counter-measures, they still pose the most profound limitations on performance of high intensity proton accelerators. We briefly consider past experience in active compensation of these effects and present in detail the progress towards experimental studies of novel schemes of space-charge compensation at the Fermilab's IOTA ring.
Longitudinally hollow bunches provide one means to mitigate the impact of transverse space charge. The hollow distributions are created via dipolar parametric excitation during acceleration in CERN's Proton Synchrotron Booster. We present simulation work and beam measurements. Particular emphasis is given to the alleviation of space charge effects on the long injection plateau of the downstream Proton Synchrotron machine, which is the main goal of this study.
Particle tracking simulations with space charge effects are very important for high-intensity proton rings. Since they include not only Hamilton mechanics of a single particle but constructing charge densities and solving Poisson equations to obtain the electromagnetic field due to the space charge, they are extremely time-consuming. We have newly developed a particle tracking simulation code that can be used in Graphics Processing Units (GPU). GPUs have strong capacities of parallel processing so that the calculation of single-particle mechanics can be done very fast by complete parallelizati…
The space charge limit (SCL) of emission from photocathodes sets an upper limit on the performance of both high- and low-field electron guns. Generally, one is forced to strike a compromise between the space charge limit and the cathode's intrinsic emittance (I. Bazarov et al., Phys. Rev. Lett., 102,104801(2009)). However, it is possible to nearly eliminate the SCL due to the image charge by engineering the topography of the cathode's surface. A cathode with a surface plasma frequency below the frequency spectrum of the accelerating electrons will greatly reduce the bunch's image charge or pol…
Transverse mode coupling instability of a single bunch caused by oscillating wake field is considered in the paper. The instability threshold is found at different frequencies of the wake with space charge tune shift taken into account. The wake phase advance in the bunch length from 0 up to $4π$ is investigated. It is shown that the space charge can push the instability threshold up or down dependent on the phase advance. Transition region is investigated thoroughly, and simple asymptotic formulas for the threshold are represented.
Space charge is typically one of the performance limitations for the operation of high intensity and high brightness beams in circular accelerators. In the Proton Synchrotron (PS) at CERN, losses are observed for vertical tunes above $Q_y=6.25$, especially for beams with large space charge tune shift. The work presented here shows that this behaviour is associated to structure resonances excited by space charge due to the highly symmetric accelerator lattice of the PS, typical for first generation alternating gradient synchrotrons. Experimental studies demonstrate the dependency of the losses …
We theoretically investigate the use of the intense transverse field created by a relativistic electron bunch to drive strong-field processes. Such bunches can be easily implemented from beam shaping in existing electron accelerators. We focus on the process of strong-field driven high harmonic generation and calculate the single-atom dipole response to the space-charge field of relativistic tilted electron beam. We compare the emitted radiation spectrum of the space-charge field to that of a few-cycle laser pulse and show that the space-charge field creates a spectrum which extends much furth…
In Cartesian coordinate system, the fields generated by a point charge moving parallel to the axis of a rectangular vacuum chamber can be formulated in terms of eigenfunctions of the rectangular waveguide using the mode expansion method. In combination with the conventional impedance theory, the Green-function forms of the wake functions and impedance for space-charge effects can be obtained, and are found to be functions of the positions of both the source and test particles. Using the Green's functions calculated for a point charge, the wake fields and impedance of a beam with various distri…
Space-charge-induced emittance growth is a big con-cern for designing low energy and high intensity linacs. The Equipartitioning Principle was introduced to mini-mize space-charge-induced emittance growth by remov-ing free energy between the transverse and longitudinal degrees of freedom. In this study, a different design guide-line is being proposed. It suggests to hold the ratio of longitudinal emittance to transverse emittance around one and take advantage of low emittance transfer for minimizing emittance growth. Using a high intensity RFQ accelerator as an example, a comparison between th…
Effects producing gain dilution in Free Electron Laser devices are well documented. We develop here a unified point of view allowing the introduction of space charge effects, along with the gain deterioration due to inhomogeneous broadening contributions and discuss the relevant interplay. We outline future developments and comment on the possibility of including in the formalism effects of quantum mechanical nature.
First, this chapter introduces the expressions for the electric and magnetic space-charge internal fields and forces induced by high-intensity beams. Then, the root-mean-square equation with space charge is derived and discussed. In the third section, the one-dimensional Child-Langmuir law, which gives the maximum current density that can be extracted from an ion source, is exposed. Space-charge compensation can occur in the low-energy beam transport lines (located after the ion source). This phenomenon, which counteracts the spacecharge defocusing effect, is explained and its main parameters …
Longitudinal space charge (LSC) effects are generally considered harmful in free-electron lasers as they can seed unfavorable energy modulations that can result in density modulations with associated emittance dilution. It was pointed out, however, that such "micro-bunching instabilities" could be potentially useful to support the generation of broadband coherent radiation. Therefore there has been an increasing interest in devising accelerator beam lines capable of controlling LSC induced density modulations. In the present paper we augment these previous investigations by combining a grid-le…
We developed a model to calculate the stability of Gaussian beam distributions with non-linear space-charge forces in the presence of random and skew-quadrupole errors. The effect of the space-charge force on the beam matrix is calculated analytically including full cross-plane coupling in 4D phase space, which allows us to perform fast parameter studies. For stability analysis, we find the fixed points of the beam including the space-charge forces and construct a Jacobi-matrix by slightly perturbing the periodic solution. The stability of envelope oscillations is inferred by eigenvalue analys…
When a resistive feedback and single-bunch wake act together, it is known that some head-tail modes may become unstable even without space charge. This feedback-wake instability, FWI, modified by space charge to a certain degree, is shown to have a special single-maximum increasing- dropping pattern with respect to the gain. Also, at sufficiently large Coulomb and wake fields, as well as the feedback gain, a new type of transverse mode-coupling instability is shown to take place, 3FMCI, when head-to-tail amplified positive modes couple and the growth rate saturates with the gain.
Laser accelerators can provide proton beams with unique qualities, such as micron size, picosecond pulse duration and high peak current, and have been demonstrated for various applications and for scientific research purposes. The effect of the space charge force in high peak current beams is strong and raises challenges for application after beam transportation. We performed two-dimensional particle-in-cell simulations and studied the influence of electrons that have velocities close to that of the protons after laser acceleration. We employed ellipsoid models with different charge distributi…
We simulate numerically the classical charge dynamics in a microscopic, planar, vacuum diode with a finite emitter area and a finite number of electrons in the gap. We assume electrons are emitted under space-charge limited conditions with a fixed potential applied to the diode. The Coulomb interaction between all electrons is included using the method of molecular dynamics. We compare our results to the conventional two-dimensional Child-Langmuir and explain how it is limited in applicability for sub-micron diameter emitters. Finally, we offer some simple relations for understanding space-cha…
Electromagnetic fields induced by the space charge in relativistic beams play an important role in Accelerator Physics. They lead to emittance growth, slice energy change, and the microbunching instability. Typically, these effects are modeled numerically since simple description exists only in the limits of large- or small-scale current variations. In this paper we consider an axially symmetric charged beam inside a round pipe and find the solution of the space charge problem that is valid in the full range of current variations. We express the solution for the field components in terms of Gr…
We develop a universal framework which allows quickly solve a wide class of problems for longitudinal space charge effects in beams and plasmas in cylindrical geometry. We introduce the longitudinal dielectric permittivity for the beam of charged particles, which describes its collective space charge response. The analyis yields an effective plasma frequency, which depends on the transverse geometry of the system. This dielectric permittivity mirrors the dielectric permittivity of plasma and matches the one dimensional (1D) expression once the transverse size of the beam is large. Several part…
In this paper, we discuss effects of space charge fields on imaging performance in a single shot time-resolved electron microscope (TEM). Using a Green's function perturbation method, we derive analytical estimates for the effects of space charge nonlinearity on the image formation process and the associated aberration coefficients. The dependence of these coefficients on the initial beam phase space distribution is elucidated. The results are validated by particle tracking simulations and provide fundamental scaling laws for the trade-off between temporal and spatial resolution in single-shot…
