Particle-beam-driven plasma wakefield acceleration (PWFA) enables various novel high-gradient techniques for powering future compact light-source and high-energy physics applications. Here, a driving particle bunch excites a wakefield response in a plasma medium, which may rapidly accelerate a trailing witness beam. In this Letter, we present the measurement of ratios of acceleration of the witness bunch to deceleration of the driver bunch, the so-called transformer ratio, significantly exceeding the fundamental theoretical and thus far experimental limit of 2 in a PWFA. An electron bunch with ramped current profile was utilized to accelerate a witness bunch with a transformer ratio of 4.6_{-0.7}^{+2.2} in a plasma with length ∼10  cm, also demonstrating stable transport of driver bunches with lengths on the order of the plasma wavelength.

Tipping elements occur in various systems such as in socio-economics, ecology and the climate system. In many cases, the individual tipping elements are not independent of each other, but they interact across scales in time and space. To model systems of interacting tipping elements, we here introduce the PyCascades open source software package for studying interacting tipping elements (10.5281/zenodo.4153102). PyCascades is an object-oriented and easily extendable package written in the programming language Python. It allows for investigating under which conditions potentially dangerous cascades can emerge between interacting dynamical systems, with a focus on tipping elements. With PyCascades it is possible to use different types of tipping elements such as double-fold and Hopf types and interactions between them. PyCascades can be applied to arbitrary complex network structures and has recently been extended to stochastic dynamical systems. This paper provides an overview of the functionality of PyCascades by introducing the basic concepts and the methodology behind it. In the end, three examples are discussed, showing three different applications of the software package. First, the moisture recycling network of the Amazon rainforest is investigated. Second, a model of interacting Earth system tipping elements is discussed. And third, the PyCascades modelling framework is applied to a global trade network.