Related papers: Stability of non-linear integrable accelerator
Modulation instability in a nonlinear optical waveguide array with alternating positive and negative refractive indices is investigated analytically. Particular solutions of a system of coupled nonlinear equations are found. These solutions…
Rayleigh-Taylor (RT) instability occurs in a variety of scenario as a consequence of fluids of different densities pushing against the density gradient. For example, it is expected to occur in the ion acceleration of solid density targets…
The ion-hose (or fast-ion) instability sets limits on the allowable vacuum in a long-pulse, high current accelerator. Beam-induced ionization of the background gas leads to the formation of an ion channel which couples to the transverse…
A method is presented to analyze the stability of feedback systems with neural network controllers. Two stability theorems are given to prove asymptotic stability and to compute an ellipsoidal inner-approximation to the region of attraction…
This paper analyzes a $\theta$-method and 3-point time filter. This approach adds one additional line of code to the existing source code of $\theta$-method. We prove the method's $0$-stability, accuracy, and $A$-stability for both constant…
This paper presents a robust non-linear state estimator for autonomous surface vehicles, where the movement is restricted to the horizontal plane. It is assumed that only the vehicle position and orientation can be measured, being the…
This paper considers the problem of robust stability for a class of uncertain nonlinear quantum systems subject to unknown perturbations in the system Hamiltonian. The case of a nominal linear quantum system is considered with non-quadratic…
We report on a test of Lorentz invariance performed by comparing the resonance frequencies of one stationary optical resonator and one continuously rotating on a precision air bearing turntable. Special attention is paid to the control of…
This paper considers the problem of nonlinear attitude estimation for a rigid body system using intermittent and multi-rate inertial vector measurements as well as continuous (high-rate) angular velocity measurements. Two types of hybrid…
Recently it has been shown that the unique locally perimeter minimizing partitioning of the plane into three regions, where one region has finite area and the other two have infinite measure, is given by the so-called standard lens…
We are commissioning a 2.5-MeV proton beam for the Integrable Optics Test Accelerator at Fermilab, allowing experiments in the strong space-charge regime with incoherent betatron tune shifts nearing 0.5. Accurate modelling of space-charge…
The Integrable Optics Test Accelerator at Fermilab will explore beam dynamics in a ring with intense space-charge using 2.5 MeV proton beams with an incoherent tune shift approaching -0.5. We will use this machine to explore the interplay…
The modulational instability of broadband optical pulses in a four-state atomic system is investigated. In particular, starting from a recently derived generalized nonlinear Schr\"odinger equation, a wave-kinetic equation is derived. A…
We demonstrate an all-optical bump-on-tail instability by considering the nonlinear interaction of two partially-coherent spatial beams. For weak wave coupling, we observe momentum transfer with no variation in intensity. For strong wave…
The large gradients of plasma-wakefield accelerators promise to shorten accelerators and reduce their financial and environmental costs. For such accelerators, a key challenge is the transport of beams with high divergence and energy…
Based on the technique of the discrete one-turn transfer maps, the problem of linear coupling between horizontal and vertical betatron oscillations in an accelerator has been treated exactly and entirely in explicit form. The stability…
The effect of the beam-beam interactions on the stability of impedance mode is discussed. The detuning is evaluated by the means of single particle tracking in arbitrarily complex collision configurations, including lattice non-linearities,…
A prototype of ion beam transport module has been developed at the Institut Pluridisciplinaire Hubert Curien (IPHC) and used as a test bed to investigate key issues related to the efficient transport of ion beams. This includes the…
Modern and future particle accelerators employ increasingly higher intensity and brighter beams of charged particles and become operationally limited by coherent beam instabilities. Usual methods to control the instabilities, such as…
The stability radius for finitely many interconnected linear exponentially stable well-posed systems with respect to static perturbations is studied. If the output space of each system is finite-dimensional, then a lower bound for the…