Related papers: A first taste of nonlinear beam dynamics
This paper gives a very brief summary of longitudinal beam dynamics for both linear and circular accelerators. After discussing synchronism conditions in linacs, it focuses on particle motion in synchrotrons. It summarizes the equations of…
In this paper, we apply approximate entropy (ApEn) analysis to the nonlinear beam dynamics in circular accelerators. Due to the presence of strong nonlinear magnets, chaos of beam motion gradually increases with amplitude. Such chaos can be…
We study the dynamics and the optimization of the shock deceleration supported by a payload when its airborne carrier impacts the ground. We build a nonlinear elastic model for a container prototype and an elastic suspension system for the…
We perform a numerical analysis of the effects of a nonlinear perturbation on the quantum dynamics of two models describing non-interacting cold atoms in a standing wave of light with a periodical modulated amplitude $A(t)$. One model is…
The subject of this introductory course is transverse dynamics of charged particle beams in linear approximation. Starting with a discussion of the most important types of magnets and defining their multipole strengths, the linearized…
Kinetic approaches provide an effective description of the process of particle acceleration at shock fronts and allow to take into account the dynamical reaction of the accelerated particles as well as the amplification of the turbulent…
We present a theoretical investigation of the chromatic dynamics of the witness beam within a plasma based accelerator. We derive the single particle motion of an electron in an ion column within a nonlinear, blowout wake including…
Nonlinear spin systems exhibit rich and exotic dynamical phenomena, offering promising applications ranging from spin masers and time crystals to precision measurement. Recent theoretical work [T. Wang et al., Commun. Phys. 8, 41 (2025)]…
Using photoemission intensities and a detection system employed by many groups in the electron spectroscopy community as an example, we have quantitatively characterized and corrected detector non-linearity effects over the full dynamic…
When the pressure of particles accelerated at shock waves is no longer negligible compared to the kinetic pressure of the gas, the linear theory of diffusive shock acceleration breaks down. This is expected in particular when the shock…
Neutral particles can be guided and focussed using electric field gradients that focus in one transverse direction and defocus in the other, alternating between the two directions. Such a guide is suitable for transporting particles that…
The oscillatory response of nonlinear systems exhibits characteristic phenomena such as multistability, discontinuous jumps and hysteresis. These can be utilized in applications leading, e.g., to precise frequency measurement, mixing,…
What prevents us from building super-high intensity accelerators? The answer is case-specific, but it often points to one of the following phenomena: machine resonances, various tune shifts (and spreads), and instabilities. These three…
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…
We show that the NLS systems with multiplicative noise, nonlinear damping and nonlocal dispersion exhibit a variety of interesting effects which may be useful for modelling the dynamical behavior of one- and two-dimensional molecular…
As the motions of nonconservative autonomous systems are typically not periodic, the definition of nonlinear modes as periodic motions cannot be applied in the classical sense. In this paper, it is proposed 'make the motions periodic' by…
Current physics models used to interpret experimental measurements of particle beams require either simplifying assumptions to be made in order to ensure analytical tractability, or black box optimization methods to perform model based…
In recent years, intense efforts have been devoted to studying how nonlinear effects can be used to shape the transverse beam distribution by means of an adiabatic crossing of nonlinear resonances. By this approach, it is possible to split…
Dynamical systems describe the changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for…
The performance and safe operation of a particle accelerator is closely connected to the transverse emittance of the beams it produces. For this reason many techniques have been developed over the years for monitoring the transverse…