Adiabatic Trapping Research Articles

Exploring the potential of resonance islands and bent crystals for a slow extraction from circular hadron accelerators

New developments in accelerator physics have broadened the set of available techniques for manipulating charged-particle beams. Adiabatic trapping and transport of a beam in resonance islands has been studied and successfully implemented at the CERN Proton Synchrotron to perform multiturn extraction. Bent crystals have been successfully installed in the CERN Large Hadron Collider, improving the cleaning performance of the collimation system, and at the CERN Super Proton Synchrotron for reducing losses at the extraction septum in the case of slow extraction. In this Letter, we discuss the potential of the combined use of resonance islands and bent crystals to devise a technique to perform slow extraction in circular hadron accelerators. The proposed approach is promising, particularly for applications with high-intensity beams, as it could dramatically reduce the losses on the extraction devices. Published by the American Physical Society 2024

Effect of adiabatic trapping of electrons on the nonlinear evolution of ion temperature gradient driven drift mode in a dispersive plasma

We have theoretically investigated the effect of adiabatic trapping of electrons on ion temperature gradient (ITG) driven nonlinear drift mode in a warm and dispersive electron-ion plasma. For this purpose, we have incorporated the gradients in the background plasma density, ion temperature and ambient magnetic field and derived two different nonlinear partial differential equations (NLPDEs). One of them contains only fractional nonlinearity while the other one incorporates the effect of both quadratic and fractional nonlinearities. We have obtained the exact solutions of these NLPDEs by using the functional variable method. We have used the graphical analysis to carry out the parametric study of the obtained solutions for the Tokamak plasma parameters. We have shown that the amplitude and the width of these nonlinear structures depend on the plasma parameters like T e , T i and η i . This work may be helpful to understand the effect of electron trapping on the low frequency drift type modes in laboratory and space plasmas.

Analysis of double-resonance crossing in adiabatic trapping phenomena for quasi-integrable area-preserving maps with time-dependent exciters.

In this paper we analyze the adiabatic crossing of a resonance for Hamiltonian systems when a double-resonance condition is satisfied by the linear frequency at an elliptic fixed point. We discuss in detail the phase-space structure on a class of Hamiltonians and area-preserving maps with an elliptic fixed point in the presence of a time-dependent exciter. Various regimes have been identified and carefully studied. This study extends results obtained recently for the trapping and transport phenomena for periodically perturbed Hamiltonian systems, and it could have relevant applications in the adiabatic beam splitting in accelerator physics.

Damped quantum drift Zakharov-Kuznetsov equation for a dissipative inhomogeneous partially degenerate plasma with quantizing magnetic field

Damped quantum drift Zakharov-Kuznetsov (DQDZK) equation is investigated in two dimensions for a spatially inhomogeneous and dissipative plasma with adiabatic electron trapping in the presence of quantizing magnetic field and partial degeneracy. Linear and nonlinear analysis is presented in detail. For the 2D case, it is observed that the angular frequency of linear drift ion acoustic wave (DIAW) exhibits a cut-off point that gets modified by Landau quantization and partial degeneracy of the trapped electrons. It is observed that the inclusion of ion-neutral collisions leads to the formation of DQDZK equation for the system under consideration. The DQDZK is solved analytically using the hyperbolic tangent method and a decaying solitary wave solution is obtained. It is shown that the effects of quantizing magnetic field, partial degeneracy, and obliqueness significantly modify the properties of the nonlinear drift ion acoustic structures. The results presented here can be gainfully employed to understand the linear and nonlinear wave propagation in dense degenerate plasmas present in astrophysical compact objects like white dwarfs and neutron stars.

Spin-dependent properties of optical modes guided by adiabatic trapping potentials in photonic Dirac metasurfaces.

The Dirac-like dispersion in photonic systems makes it possible to mimic the dispersion of relativistic spin-1/2 particles, which led to the development of the concept of photonic topological insulators. Despite recent demonstrations of various topological photonic phases, the full potential offered by Dirac photonic systems, specifically their ability to emulate the spin degree of freedom-referred to as pseudo-spin-beyond topological boundary modes has remained underexplored. Here we demonstrate that photonic Dirac metasurfaces with smooth one-dimensional trapping gauge potentials serve as effective waveguides with modes carrying pseudo-spin. We show that spatially varying gauge potentials act unevenly on the two pseudo-spins due to their different field distributions, which enables control of guided modes by their spin, a property that is unattainable with conventional optical waveguides. Silicon nanophotonic metasurfaces are used to experimentally confirm the properties of these guided modes and reveal their distinct spin-dependent radiative character; modes of opposite pseudo-spin exhibit disparate radiative lifetimes and couple differently to incident light. The spin-dependent field distributions and radiative lifetimes of their guided modes indicate that photonic Dirac metasurfaces could be used for spin-multiplexing, controlling the characteristics of optical guided modes, and tuning light-matter interactions with photonic pseudo-spins.

Localized Dust Acoustic Solitons in Electron-Depleted Dusty Plasmas With κ-Gurevich Distributed Ions

A first theoretical attempt is made to investigate the adiabatically trapped suprathermal ions effect on dust acoustic (DA) solitons in electron-depleted dusty plasmas. Our investigation is motivated by space and laboratory plasma observations of plasmas containing suprathermal particles, resulting from long-tailed distributions, combined with trapped particles in a finite region of phase space. For this goal, the 1-D <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\kappa $ </tex-math></inline-formula> -Gurevich distribution, which describes the adiabatic trapping of suprathermal ions, is constructed, and the associated density expression is derived. The reductive perturbation method (RPM) has been adopted to establish a modified Kortweg-de-Vries (mK-dV)-like equation, and analyze its comportment. The numerical investigation revealed that the main properties (phase velocity, amplitude, and width) of small DA solitons are significantly affected by adiabatically trapped suprathermal ions. In particular, we have found that as the suprathermality of the ions increases, the DA soliton amplitude decreases while its width increases. The significant changes induced by the presence of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\kappa $ </tex-math></inline-formula> -Gurevich distributed ions on the transported energy and electrical field of DA solitons are also analyzed. We have shown that when the ions evolve far from their Maxwellian trapping (i.e., as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\kappa $ </tex-math></inline-formula> decreases), the DA soliton energy quantity (bipolar electric field) associated with electronically depleted dusty plasma becomes smaller (stronger). The results of the present study provide new insight into established findings on this issue.

Analysis of adiabatic trapping phenomena for quasi-integrable area-preserving maps in the presence of time-dependent exciters.

In this paper, results concerning the phenomenon of adiabatic trapping into resonance for a class of quasi-integrable maps and Hamiltonians with a time-dependent exciter are presented and discussed in detail. The applicability of the results about trapping efficiency for Hamiltonian systems to the maps considered is proven by using perturbation theory. This makes possible to determine explicit scaling laws for the trapping properties. These findings represent a generalization of previous results obtained for the case of quasi-integrable maps with parametric modulation, as well as an extension of the work by Neishtadt etal. [Regul. Chaotic Dyn. 18, 686 (2013)10.1134/S1560354713060087] on a restricted class of quasi-integrable systems with time-dependent exciters.

Effect of magnetic field ripple on parallel electron transport during microwave plasma heating in the Proto-MPEX linear plasma device

The Prototype Material Plasma Exposure eXperiment (Proto-MPEX) is a linear plasma device located at Oak Ridge National Laboratory to develop the plasma source concept for the Materials Plasma Exposure eXperiment (MPEX). Recent experiments have demonstrated the heating of electrons in a high-density deuterium plasma () via electron Bernstein waves and source plasma production via helicon waves in this linear configuration. Moreover, experimental observations suggest that the magnetic ripple adversely affects the parallel transport of the heated electrons toward the target where material samples are to be exposed to the plasma. To understand the transport process during microwave application, a test-particle Monte-Carlo (MC) code has been developed that incorporates the effects of Coulomb collisions, magnetic mirror adiabatic trapping and electron cyclotron interaction via a quasilinear RF heating operator. MC calculations indicate that the absence of 2nd turning points along the trajectory of cyclotron heated electrons significantly reduces adiabatic trapping and maximizes power transport to the Target surface. Thermalization of cyclotron heating electrons is analyzed with the MC code and it is found that for conditions relevant to Proto-MPEX, a significant fraction of the absorbed heating power is coupled to the Target surface via ballistic fast electrons; however, under certain conditions, up to 60% of the absorbed RF power can be dissipated via thermalization of the fast electrons on the background plasma. Results are compared with experimental measurements. Finally, the implications of the results are discussed in the context of the upcoming MPEX device.

Quantum bridges in phase space: interference and nonclassicality in strong-field enhanced ionisation

We perform a phase-space analysis of strong-field enhanced ionisation in molecules, with emphasis on quantum-interference effects. Using Wigner quasi-probability distributions and the quantum Liouville equation, we show that the momentum gates reported in a previous publication (Takemoto and Becker 2011 Phys. Rev. A 84 023401) may occur for static driving fields, and even for no external field at all. Their primary cause is an interference-induced bridging mechanism that occurs if both wells in the molecule are populated. In the phase-space regions for which quantum bridges occur, the Wigner functions perform a clockwise rotation whose period is intrinsic to the molecule. This evolution is essentially non-classical and non-adiabatic, as it does not follow equienergy curves or field gradients. Quasi-probability transfer via quantum bridges is favoured if the electron’s initial state is either spatially delocalised, or situated at the upfield molecular well. Enhanced ionisation results from the interplay of this cyclic motion, adiabatic tunnel ionisation and population trapping. Optimal conditions require minimising population trapping and using the bridging mechanism to feed into ionisation pathways along the field gradient.

Finite element analysis of thermomechanical behavior and residual stresses in cold flowformed Ti6Al4V alloy

Ti6Al4V alloy is very hard to flowform at room temperature due to its limited ductility. However, it retains excellent adiabatic heat trapping and thermal softening abilities, which can play an important role in improving the formability. In this paper, a 3-D finite element model of backward flowforming with three staggered rollers has been developed in Abaqus/explicit to study the thermomechanical behavior and the residual stress evolution. The model has been validated via flowforming experiments. The role of the heat generation due to plastic deformation is highlighted by comparing a thermomechanical analysis to a purely mechanical analysis without incorporating the additional heat input due to the plastic work. The maximum predicted temperature rise during cold flowforming is 911 °C, which significantly reduces the flow stress in the deformation zone. The two most important factors, which affect the temperature rise in the deformation zone, are friction coefficient and coolant heat transfer coefficient. Hence, a study has been done to assess the sensitivity of the thermomechanical behavior and the residual stresses towards these factors. The friction between the mating surfaces is helpful, but a friction coefficient higher than 0.1 causes through-thickness strain heterogeneity. An increase in the friction coefficient reduces the residual stresses, while an increase in the convective heat transfer coefficient causes a transition from compressive to tensile residual stress along the thickness of the tube.

Nonlinear coupling of kinetic Alfven waves with acoustic waves in a self-gravitating dusty plasma with adiabatic trapping

In this paper, linear and nonlinear coupling of kinetic Alfven and acoustic waves has been studied in a dusty plasma in the presence of trapping and self-gravitation effects. In this regard, we have derived the linear dispersion relations for positively and negatively coupled dust kinetic Alfven-acoustic waves. Stability analysis of the coupled dust kinetic Alfven-acoustic wave has also been presented. The formation of solitary structures has been investigated following the Sagdeev potential approach by using the two-potential theory. Numerical results show that the solitary structures can be obtained only for sub-Alfvenic regimes in the scenario of space plasmas.

Linear and nonlinear coupling of electromagnetic and electrostatic fluctuations with one dimensional trapping of electrons using product bi (r,q) distribution

In the present paper, we have investigated the ramifications of adiabatic trapping of electrons using a bi product (r,q) distribution function on obliquely propagating Alfven waves in a low β plasma. In this regard, we have analyzed the linear and nonlinear dispersion characteristics of finite amplitude coupled kinetic Alfven-acoustic solitary waves using the two-potential theory and employing Sagdeev potential approach. We have deliberated upon the results of the present inquest and highlighted its importance by citing works that have reported the simultaneous presence of electromagnetic pulses and flat-topped distribution of electrons.

Transition in electron physics of magnetic reconnection in weakly collisional plasma

Using particle-in-cell (PIC) simulations with a Monte Carlo treatment of the Coulomb collision operator, we study the transition in electron dynamics of magnetic reconnection for various levels of collisionality. The weakly collisional cases considered all fall into the so-called Hall or kinetic regime. Nevertheless, collisions may still alter the electron kinetic physics characteristic of collisionless reconnection, where adiabatic trapping energizes the electrons and leads to strong anisotropy of the electron velocity distribution and pressure. This anisotropy can support extended current sheets, associated with secondary island formation and turbulent flux rope interactions in three dimensional systems. The collisional simulations demonstrate how weak collisions may modify or eliminate these electron structures in the kinetic regimes. While the reconnection rate is not sensitive to the collisionality in the range studied, we find that increasing collisionality reduces the level of electron energization near the reconnection site. Finally, the results provide guidance for new laboratory reconnection experiments that will access the weakly collisional regimes.

Effect of adiabatic trapping on vortices and solitons in degenerate plasma in the presence of a quantizing magnetic field

The effect of adiabatic trapping as a microscopic phenomenon in an inhomogeneous degenerate plasma is investigated in the presence of a quantizing magnetic field, and a modified Hasegawa Mima equation for the drift ion-acoustic wave is obtained. The linear dispersion relation in the presence of the quantizing magnetic field is investigated. The modified Hasegawa Mima equation is investigated to obtain bounce frequencies of the trapped particles. The Korteweg–de Vries equation is derived for the two-dimensional case and finally the Sagdeev potential approach is used to obtain solitary structures. The theoretically obtained results have been analyzed numerically for different astrophysical plasma and quantizing magnetic field values.

Analysis of adiabatic trapping for quasi-integrable area-preserving maps.

Trapping phenomena involving nonlinear resonances have been considered in the past in the framework of adiabatic theory. Several results are known for continuous-time dynamical systems generated by Hamiltonian flows in which the combined effect of nonlinear resonances and slow time variation of some system parameters is considered. The focus of this paper is on discrete-time dynamical systems generated by two-dimensional symplectic maps. The possibility of extending the results of neo-adiabatic theory to quasi-integrable area-preserving maps is discussed. Scaling laws are derived, which describe the adiabatic transport as a function of the system parameters using a probabilistic point of view. These laws can be particularly relevant for physical applications. The outcome of extensive numerical simulations showing the excellent agreement with the analytical estimates and scaling laws is presented and discussed in detail.

Adiabatic trapping in coupled kinetic Alfvén-acoustic waves

In the present work, we have discussed the effects of adiabatic trapping of electrons on obliquely propagating Alfvén waves in a low β plasma. Using the two potential theory and employing the Sagdeev potential approach, we have investigated the existence of arbitrary amplitude coupled kinetic Alfvén-acoustic solitary waves in both the sub and super Alfvénic cases. The results obtained have been analyzed and presented graphically and can be applied to regions of space where the low β assumption holds true.

Step free energies at faceted solid-liquid interfaces from equilibrium molecular dynamics simulations

In this work a method is proposed for computing step free energies for faceted solid-liquid interfaces based on atomistic simulations. The method is demonstrated in an application to (111) interfaces in elemental Si, modeled with the classical Stillinger-Weber potential. The approach makes use of an adiabatic trapping procedure, and involves simulations of systems with coexisting solid and liquid phases separated by faceted interfaces containing islands with different sizes, for which the corresponding equilibrium temperatures are computed. We demonstrate that the calculated coexistence temperature is strongly affected by the geometry of the interface. We find that island radius is inversely proportional to superheating, allowing us to compute the step free energy by fitting simulation data within the formalism of classical nucleation theory. The step free energy value is computed to be γ(st) = 0.103 ± 0.005 × 10(-10) J/m. The approach outlined in this work paves the way to the calculation of step free energies relevant to the solidification of faceted crystals from liquid mixtures, as encountered in nanowire growth by the vapor-liquid-solid mechanism and in alloy casting. The present work also shows that at low undercoolings the Stillinger-Weber interatomic potential for Si tends to crystallize in the wurtzite, rather than the diamond-cubic structure.

Liquid Nucleation at Superheated Grain Boundaries

Grain boundaries with relatively low energies can be superheated above the melting temperature and eventually melt by heterogeneous nucleation of liquid droplets. We propose a thermodynamic model of this process based on the sharp-interface approximation with a disjoining potential. The distinct feature of the model is its ability to predict the shape and size of the critical nucleus by using a variational approach. The model reduces to the classical nucleation theory in the limit of large nuclei but is more general and remains valid for small nuclei. Contrary to the classical nucleation theory, the model predicts the existence of a critical temperature of superheating and offers a simple formula for its calculation. The model is tested against molecular dynamic simulations in which liquid nuclei at a superheated boundary were obtained by an adiabatic trapping procedure. The simulation results demonstrate a reassuring consistency with the model.

Adiabatic splitting, transport, and self-trapping of a Bose-Einstein condensate in a double-well potential

We show that the adiabatic dynamics of a Bose-Einstein condensate (BEC) in a double well potential can be described in terms of a dark variable resulting from the combination of the population imbalance and the spatial atomic coherence between the two wells. By means of this dark variable, we extend, to the non-linear matter wave case, the recent proposal by Vitanov and Shore [Phys. Rev. A 73, 053402 (2006)] on adiabatic passage techniques to coherently control the population of two internal levels of an atom/molecule. We investigate the conditions to adiabatically split or transport a BEC as well as to prepare an adiabatic self trapping state by the optimal delayed temporal variation of the tunneling rate via either the energy bias between the two wells or the BEC non-linearity. The emergence of non-linear eigenstates and unstable stationary solutions of the system as well as their role in the breaking down of the adiabatic dynamics is investigated in detail.

Adiabatic trapping and acceleration of the beam in the booster synchrotron of the ITEP-TWAC accelerating-storage facility

A system for adiabatic trapping of injected particles into the acceleration mode was developed and used to increase the intensity of the ion beam accelerated in the booster synchrotron of the ITEP-TWAC accelerating-storage facility at the Institute for Theoretical and Experimental Physics. Using numerical simulation, the parameters of the injected beam were optimized and the conditions for the absence of particle loss upon a changeover into the acceleration mode and subsequent acceleration to the maximum energy were determined. The effect that the characteristics of a system controlling the radio frequency of the accelerating field had on the dynamics of synchrotron motion and the particle loss was investigated. During development and adjustment of a complex of equipment that provided optimal conditions for adiabatic trapping and acceleration of C4+ ions with an initial energy of 1.3 MeV/amu, the trapping efficiency was as high as 80%, being limited only by the initial distribution of the momentum spread in the injected beam.