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Register a new userSpace charge fields in azimuthally symmetric beams: integrated Greens function approach
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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 Greens functions, which are fully determined by just a single function. We then find that this function is an on-axis potential from a charged disk in a round pipe, with transverse charge density $rho_perp(r)$, and it has a compact analytical expression. We finally provide an integrated Greens function based approach for efficient numerical evaluation in the case when the transverse charge density stays the same along the beam.
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We present an ab initio theory of core- and valence resonant inelastic x-ray scattering (RIXS) based on a real-space multiple scattering Greens function formalism and a quasi-boson model Hamiltonian. Simplifying assumptions are made which lead to an approximation of the RIXS spectrum in terms of a convolution of an effective x-ray absorption signal with the x-ray emission signal. Additional many body corrections are incorporated in terms of an effective energy dependent spectral function. Example calculations of RIXS are found to give qualitative agreement with experimental data. Our approach also yields simulations of lifetime-broadening suppressed XAS, as observed in high energy resolutionfluorescence detection experiment (HERFD). Finally possible improvements to our approach are briefly discussed.
Transverse beam stability is strongly affected by the beam space charge. Usually it is analyzed with the rigid-beam model. However this model is only valid when a bare (not affected by the space charge) tune spread is small compared to the space charge tune shift. This condition specifies a relatively small area of parameters which, however, is the most interesting for practical applications. The Landau damping rate and the beam Schottky spectra are computed assuming that validity condition is satisfied. The results are applied to a round Gaussian beam. The stability thresholds are described by simple fits for the cases of chromatic and octupole tune spreads.
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. Thus, were it correct, such a beam with sufficiently strong SC, being stable at some intensity, would remain stable at higher intensity, regardless of how much higher! This paper suggests a resolution of this conundrum: while SC suppresses TMCI, it introduces head-to-tail convective amplifications, which could make the beam even less stable than without SC, even if all the coherent tunes are real, i.e. all the modes are stable in the conventional {it absolute} meaning of the word. This is done using an effective new method of analysis of the beams transverse spectrum for arbitrary space charge and wake fields. Two new types of beam instabilities are introduced: the {it saturating convective instability}, SCI, and the {it absolute-convective instability}, ACI.
Progress on the Intensity Frontier of high energy physics critically depends on record high intensity charged particles accelerators. Beams in such machines become operationally limited by coherent beam instabilities, particularly enhanced in the regime of strong space charge (SC). Usual methods to control the instabilities, such as octupole magnets, beam feedback dampers and employment of chromatic effects, become less effective and insufficient. In [1] it was proposed to employ electron lenses for introduction of sufficient spread in particle oscillation frequencies needed for beam stabilization and in [2] it was shown that electron lenses are uniquely effective for Landau damping of transverse beam instabilities in high energy particle accelerators and their employment does not compromise incoherent (single particle) stability, dynamic aperture and the beam lifetime. Here we consider an important issue of effectiveness of the Landau damping with electron lenses in space-charge dominated beams and demonstrate that the desired stability can be assured with proper choice of the electron beam parameters and current distributions.
Longitudinal collective modes of a bunched beam with a repulsive inductive impedance (the space charge below transition or the chamber inductance above it) are analytically described by means of reduction of the linearized Vlasov equation to a parameter-less integral equation. For any multipolarity, the discrete part of the spectrum is found to consist of infinite number of modes with real tunes, which limit point is the incoherent zero-amplitude frequency. In other words, notwithstanding the RF bucket nonlinearity and potential well distortion, the Landau damping is lost. Hence, even a tiny coupled-bunch interaction makes the beam unstable; such growth rates for all the modes are analytically obtained for arbitrary multipolarity. In practice, however, the finite threshold of this loss of Landau damping is set either by the high-frequency impedance roll-off or intrabeam scattering. Above the threshold, growth of the leading collective mode should result in persistent nonlinear oscillations.
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