Bogdan Mihalcea | INFLPR - Academia.edu (original) (raw)

Papers by Bogdan Mihalcea

Research paper thumbnail of Mathieu-Hill Equation Stability Analysis for Trapped Ions. Anharmonic Corrections for Nonlinear Electrodynamic Traps

The stability properties of the Hill equation are discussed, especially those of the Mathieu equa... more The stability properties of the Hill equation are discussed, especially those of the Mathieu equation that characterize ion motion in electrodynamic traps. The solutions of the Mathieu-Hill equation for a trapped ion are characterized by employing the Floquet theory and Hill’s method solution, which yields an infinite system of linear and homogeneous equations whose coefficients are recursively determined. Stability is discussed for parameters a and q that are real. Characteristic curves are introduced naturally by the Sturm–Liouville problem for the well-known even and odd Mathieu equations cem(z,q)ce_m (z, q)cem(z,q) and sem(z,q)se_m (z, q)sem(z,q). In the case of a Paul trap, the stable solution corresponds to a superposition of harmonic motions. The maximum amplitude of stable oscillations for ideal conditions (taken into consideration) is derived. We illustrate the stability diagram for a combined (Paul and Penning) trap and represent the frontiers of the stability domains for both axial and radial motion, where the former is described by the canonical Mathieu equation. Anharmonic corrections for nonlinear Paul traps are discussed within the frame of perturbation theory, while the frontiers of the modified stability domains are determined as a function of the chosen perturbation parameter and we demonstrate they are shifted towards negative values of the a parameter. The applications of the results include but are not restricted to 2D and 3D ion traps used for different applications such as mass spectrometry (including nanoparticles), high resolution atomic spectroscopy and quantum engineering applications, among which we mention optical atomic clocks and quantum frequency metrology.

Research paper thumbnail of Mathieu–Hill Equation Stability Analysis for Trapped Ions: Anharmonic Corrections for Nonlinear Electrodynamic Traps

Photonics, Jun 11, 2024

The stability properties of the Hill equation are discussed, especially those of the Mathieu equa... more The stability properties of the Hill equation are discussed, especially those of the Mathieu equation that characterize ion motion in electrodynamic traps. The solutions of the Mathieu-Hill equation for a trapped ion are characterized by employing the Floquet theory and Hill’s method solution, which yields an infinite system of linear and homogeneous equations whose coefficients are recursively determined. Stability is discussed for parameters a and q that are real. Characteristic curves are introduced naturally by the Sturm–Liouville problem for the well-known even and odd Mathieu equations cem(z,q)ce_m (z, q)cem(z,q) and sem(z,q)se_m (z, q)sem(z,q). In the case of a Paul trap, the stable solution corresponds to a superposition of harmonic motions. The maximum amplitude of stable oscillations for ideal conditions (taken into consideration) is derived. We illustrate the stability diagram for a combined (Paul and Penning) trap and represent the frontiers of the stability domains for both axial and radial motion, where the former is described by the canonical Mathieu equation. Anharmonic corrections for nonlinear Paul traps are discussed within the frame of perturbation theory, while the frontiers of the modified stability domains are determined as a function of the chosen perturbation parameter and we demonstrate they are shifted towards negative values of the a parameter. The applications of the results include but are not restricted to 2D and 3D ion traps used for different applications such as mass spectrometry (including nanoparticles), high resolution atomic spectroscopy and quantum engineering applications, among which we mention optical atomic clocks and quantum frequency metrology.

Research paper thumbnail of Radiation dose distribution inside interaction chamber in PW laser facilities during laser-plasma proton acceleration experiments and method to increase the proton energy spectrum measurement resolution

arXiv (Cornell University), Jun 3, 2019

The paper discusses some 3D simulations to compute the ionizing radiation dose during laser-plasm... more The paper discusses some 3D simulations to compute the ionizing radiation dose during laser-plasma experiments leading to the generation of accelerated protons and electrons. Also, we suggest a new method to increase the measurement resolution of the proton energy spectrum. Monte-Carlo simulations of the radiation doses map around the laser-foil interaction point are performed using Geant4 General Particle Source code and the particular geometry chosen for the experimental setup. We obtain the map of the radiation dose distribution for high-power laser - thin solid target experiments, considering a cubic geometry of the interaction chamber. The computed radiation dose distribution shows a good agreement with various, previously obtained experimental results, and could be a step towards simulating the radiation environment inside of a spacecraft. To characterize the laser-plasma accelerated protons, we introduce a new method to enhance the measurement resolution of the proton energy spectrum by employing a stack of thin solid detectors, preferably CR-39. Each detector is thinner than the Bragg peak region on the Bragg curve that characterizes the loss of kinetic energy as a function of the particle penetration depth in the detector material. The relevance of this method for space radiation characterization and cybersecurity insurance is highlighted.

Research paper thumbnail of Quasiclassical Dynamics for Ions Confined in Axially Symmetric Electromagnetic Traps

arXiv (Cornell University), Sep 10, 2016

Quasiclassical dynamics of trapped ions is described by applying the time dependent variational p... more Quasiclassical dynamics of trapped ions is described by applying the time dependent variational principle (TDVP) on coherent state orbits, introduced as sub-manifolds of the quantum state space. The classical Hamilton functions associated to the system are obtained as the expected values of the quantum Hamiltonian on symplectic coherent states. Such formalism can be applied to Hamilton functions which are nonlinear in the infinitesimal generators of a dynamical symmetry group. We give the explicit expression of the quantum Hamilton function in case of nonlinear electromagnetic traps. Discrete quasienergy spectra result, and the corresponding quasienergy states are explicitly realized as coherent states parameterized by the stable solutions of the corresponding classical equations of motion. A dequantization algorithm is also suggested. The method is then applied to combined (Paul and Penning) and ideal Paul traps. We obtain the explicit expressions of the classical Hamilton functions for such particular traps, as well as the classical Hamilton equations of motion in complex coordinates for an octupole trap. In the pseudopotential approximation, the points of minimum of the Hamiton function define equilibrium configurations for trapped ions, of interest for quantum logic.

Research paper thumbnail of The physics and applications of strongly coupled Coulomb systems (plasmas) levitated in electrodynamic traps

Physics Reports, May 15, 2023

Charged microparticles confined in electrodynamic traps evolve into strongly coupled Coulomb syst... more Charged microparticles confined in electrodynamic traps evolve into strongly coupled Coulomb systems (SCCS) which are the subject of current investigation. Recent results with respect to particle dynamics in linear and nonlinear Paul traps are reviewed, including the case of a confined microparticle in presence of an acoustic wave. An analytical model is used to discuss dynamical stability for systems of two coupled ions confined in a Paul trap. The model is then extended to discuss quantum stability for many-body systems of trapped ions. Dynamical stability for many-body systems of identical ions confined in 3D quadrupole ion traps (QIT) is studied locally, in the neighbourhood of minimum configurations that characterize ordered structures. The analytical model is particularized to the case of a combined trap. It is demonstrated that Paul (ion) traps are versatile instruments to investigate one-component strongly coupled Coulomb systems (microplasmas). Exciting physical phenomena associated to Coulomb systems are reported, such as autowave generation, phase transitions, defect formation, system self-locking at the edges of a linear Paul trap, self-organization in layers, or pattern formation and scaling. The dynamics of ordered structures consisting of highly nonideal similarly charged solid particles with coupling parameter of the order Gamma=108\Gamma = 10^8Gamma=108 is explored. The approach used enables one to explore the interaction of microparticle structures in presence and in absence of the neutralizing plasma background, as well as to investigate various types of phenomena and physical forces experienced by these patterns. Brownian dynamics (BD) is used to characterize charged particle evolution in time and to identify regions of stable trapping. Analytical models are used to explain the experimental results. Numerical modelling considers stochastic forces of random collisions with neutral particles, viscosity of the gas medium, regular forces produced by the a.c. trapping voltage, and gravitational force. Microparticle dynamics is characterized by a stochastic Langevin differential equation. Laser plasma acceleration of charged particles is also discussed, with an emphasis on Paul traps employed to investigate collective effects in space-charge-dominated (relativistic) beams and for target micropositioning. This review paper is both an add-on as well as an update on late progress in SCCS confined in electrodynamic traps.

Research paper thumbnail of Quasienergy operators and generalized squeezed states for systems of trapped ions

Annals of Physics, 2022

Collective many-body dynamics for time-dependent quantum Hamiltonians is investigated for a dynam... more Collective many-body dynamics for time-dependent quantum Hamiltonians is investigated for a dynamical system that exhibits multiple degrees of freedom, in this case a combined (Paul and Penning) trap. Quantum stability is characterized by a discrete quasienergy spectrum, while the quasienergy states are symplectic coherent states. We introduce the generators of the Lie algebra of the symplectic group , which we use to build the coherent states (CS) associated to the system under investigation. The trapped ion is treated as a harmonic oscillator (HO) to which we associate the quantum Hamilton function. We obtain the kinetic and potential energy operators as functions of the Lie algebra generators and supply the expressions for the classical coordinate, momentum, kinetic and potential energy, along with the total energy. Moreover, we also infer the dispersions for the coordinate and momentum, together with the asymmetry and the flatness parameter for the distribution. The system interaction with laser radiation is also examined for a system of identical two-level atoms. The Hamilton function for the Dicke model is derived. The optical system is modelled as a HO (trapped ion) that undergoes interaction with an external laser field and we use it to engineer a squeezed state of the electromagnetic (EM) field. We consider coherent and squeezed states associated to both ion dynamics and to the EM field. The approach used enables one to build CS in a compact and smart manner by use of the group theory.

Research paper thumbnail of Coherent states for trapped ions. Applications in quantum optics and precision measurements

Proc. of the Ninth Meeting on CPT and Lorentz Symmetry (CPT’22), Editor: R. Lehnert, World Scientific, Jun 25, 2023

The evolution of squeezed coherent states of motion for trapped ions is investigated by applying ... more The evolution of squeezed coherent states of motion for trapped ions is investigated by applying the time-dependent variational principle for the Schrödinger equation. The method is applied in case of Paul and combined traps, for which the classical Hamiltonian and equations of motion are derived. Hence, coherent states provide a natural framework to: (a) engineer quantum correlated states for trapped ions intended for ultraprecise measurements, (b) explore the mechanisms responsible for decoherence, and (c) investigate the quantum–classical transition.

Research paper thumbnail of Radiation dose simulation during laser-plasma proton acceleration experiments and method to increase the measurement resolution of the proton energy spectrum

The paper discusses some 3D simulations to compute the ionizing radiation dose during laser-plasm... more The paper discusses some 3D simulations to compute the ionizing radiation dose during laser-plasma experiments leading to the generation of accelerated protons and electrons. Also, we suggest a new method to increase the measurement resolution of the proton energy spectrum. Monte-Carlo simulations of the radiation doses map around the laser-foil interaction point are performed using Geant4 General Particle Source code and the particular geometry chosen for the experimental setup. We obtain the map of the radiation dose distribution for high-power laser - thin solid target experiments, considering a cubic geometry of the interaction chamber. The computed radiation dose distribution shows a good agreement with various, previously obtained experimental results, and could be a step towards simulating the radiation environment inside of a spacecraft. To characterize the laser-plasma accelerated protons, we introduce a new method to enhance the measurement resolution of the proton energy ...

Research paper thumbnail of Multipole Electrodynamic Ion Trap Geometries for Microparticle Confinement under Standard Ambient Temperature and Pressure Conditions

arXiv: 1512.05503, Jan 11, 2016

Trapping of microparticles and aerosols is of great interest for physics and chemistry. We report... more Trapping of microparticles and aerosols is of great interest for physics and chemistry. We report microparticle trapping in multipole linear Paul trap geometries, operating under Standard Ambient Temperature and Pressure (SATP) conditions. An 8-electrode and a 12-electrode linear trap geometries have been designed and tested with an aim to achieve trapping for larger number of particles and to study microparticle dynamical stability in electrodynamic fields. We report emergence of planar and volume ordered structures of the microparticles, depending on the a.c. trapping frequency and particle specific charge ratio. The electric potential within the trap was mapped using the electrolytic tank method. Particle dynamics was simulated using a stochastic Langevin equation. We emphasize extended regions of stable trapping with respect to quadrupole traps, as well as good agreement between experiment and numerical simulations.

Research paper thumbnail of The physics and applications of strongly coupled Coulomb systems (plasmas) levitated in electrodynamic traps

Physics Reports, Nov 6, 2023

Charged microparticles confined in electrodynamic traps evolve into strongly coupled Coulomb syst... more Charged microparticles confined in electrodynamic traps evolve into strongly coupled Coulomb systems (SCCS) which are the subject of current investigation. Recent results with respect to particle dynamics in linear and nonlinear Paul traps are reviewed, including the case of a confined microparticle in presence of an acoustic wave. An analytical model is used to discuss dynamical stability for systems of two coupled ions confined in a Paul trap. The model is then extended to discuss quantum stability for many-body systems of trapped ions. Dynamical stability for many-body systems of identical ions confined in 3D quadrupole ion traps (QIT) is studied locally, in the neighbourhood of minimum configurations that characterize ordered structures. The analytical model is particularized to the case of a combined trap. It is demonstrated that Paul (ion) traps are versatile instruments to investigate one-component strongly coupled Coulomb systems (microplasmas). Exciting physical phenomena associated to Coulomb systems are reported, such as autowave generation, phase transitions, defect formation, system self-locking at the edges of a linear Paul trap, self-organization in layers, or pattern formation and scaling. The dynamics of ordered structures consisting of highly nonideal similarly charged solid particles with coupling parameter of the order Gamma=108\Gamma = 10^8Gamma=108 is explored. The approach used enables one to explore the interaction of microparticle structures in presence and in absence of the neutralizing plasma background, as well as to investigate various types of phenomena and physical forces experienced by these patterns. Brownian dynamics (BD) is used to characterize charged particle evolution in time and to identify regions of stable trapping. Analytical models are used to explain the experimental results. Numerical modelling considers stochastic forces of random collisions with neutral particles, viscosity of the gas medium, regular forces produced by the a.c. trapping voltage, and gravitational force. Microparticle dynamics is characterized by a stochastic Langevin differential equation. Laser plasma acceleration of charged particles is also discussed, with an emphasis on Paul traps employed to investigate collective effects in space-charge-dominated (relativistic) beams and for target micropositioning. This review paper is both an add-on as well as an update on late progress in SCCS confined in electrodynamic traps.

Research paper thumbnail of Time Dependent Variational Principle and Coherent State Orbits for a Trapped Ion

Spectral properties of the Hamiltonian function which characterizes a trapped ion are investigate... more Spectral properties of the Hamiltonian function which characterizes a trapped ion are investigated. In order to study semiclassical dynamics of trapped ions, coherent state orbits are introduced as sub-manifolds of the quantum state space, with the K\"ahler structure induced by the transition probability. The time dependent variational principle (TDVP) is applied on coherent states' orbits. The Hamilton equations of motion on K\"ahler manifolds of the type of classical phase spaces naturally arise. The associated classical Hamiltonian is obtained from the expected values on symplectic coherent states of the quantum Hamiltonian. Spectral information is thus coded within the phase portrait. We deal with the bosonic realization of the Lie algebra of the SU(1,1) group, which we particularize for the case of an ion confined in a combined, Paul and Penning trap. This formalism can be applied to Hamiltonians which are nonlinear in the infinitesimal generators of a dynamical s...

Research paper thumbnail of Multipole Traps as Tools in Environmental Studies

arXiv: Plasma Physics, 2015

Trapping of microparticles, nanoparticles and aerosols is an issue of major interest for physics ... more Trapping of microparticles, nanoparticles and aerosols is an issue of major interest for physics and chemistry. We present a setup intended for microparticle trapping in multipole linear Paul trap geometries, operating under Standard Ambient Temperature and Pressure (SATP) conditions. A 16-electrode linear trap geometry has been designed and tested, with an aim to confine a larger number of particles with respect to quadrupole traps and thus enhance the signal to noise ratio, as well as to study microparticle dynamical stability in electrodynamic fields. Experimental tests and numerical simulations suggest that multipole traps are very suited for high precision mass spectrometry measurements in case of different microparticle species or to identify the presence of certain aerosols and polluting agents in the atmosphere. Particle traps represent versatile tools for environment monitoring or for the study of many-body Coulomb systems and dusty plasmas.

Research paper thumbnail of Investigations on Dynamical Stability in 3D Quadrupole Ion Traps

Applied Sciences, 2021

We firstly discuss classical stability for a dynamical system of two ions levitated in a 3D Radio... more We firstly discuss classical stability for a dynamical system of two ions levitated in a 3D Radio-Frequency (RF) trap, assimilated with two coupled oscillators. We obtain the solutions of the coupled system of equations that characterizes the associated dynamics. In addition, we supply the modes of oscillation and demonstrate the weak coupling condition is inappropriate in practice, while for collective modes of motion (and strong coupling) only a peak of the mass can be detected. Phase portraits and power spectra are employed to illustrate how the trajectory executes quasiperiodic motion on the surface of torus, namely a Kolmogorov–Arnold–Moser (KAM) torus. In an attempt to better describe dynamical stability of the system, we introduce a model that characterizes dynamical stability and the critical points based on the Hessian matrix approach. The model is then applied to investigate quantum dynamics for many-body systems consisting of identical ions, levitated in 2D and 3D ion tra...

Research paper thumbnail of Squeezed coherent states of motion for ions confined in quadrupole and octupole ion traps

Annals of Physics, 2018

Quasiclassical dynamics of trapped ions is characterized by applying the time dependent variation... more Quasiclassical dynamics of trapped ions is characterized by applying the time dependent variational principle (TDVP) on coherent state orbits, in case of quadrupole and octupole combined (Paul and Penning) and radiofrequency (RF) traps. A dequantization algorithm is proposed, by which the classical Hamilton (energy) function associated to the system results as the expectation value of the quantum Hamiltonian on squeezed coherent states. We develop such method and particularize the quantum Hamiltonian for a combined and for a RF trap, with axial symmetry and a RF anharmonic electric potential. We also build the classical Hamiltonian functions for the particular traps we considered, and find the classical equations of motion.

Research paper thumbnail of Advances in Spectral Distribution Assessment of Laser Accelerated Protons using Multilayer CR-39 Detectors

Applied Sciences, 2019

We show that a spectral distribution of laser-accelerated protons can be extracted by analyzing t... more We show that a spectral distribution of laser-accelerated protons can be extracted by analyzing the proton track diameters observed on the front side of a second CR-39 detector arranged in a stack. The correspondence between the proton track diameter and the incident energy on the second detector is established by knowing that protons with energies only higher than 10.5 MeV can fully deposit their energy in the second CR-39 detector. The correlation between the laser-accelerated proton track diameters observed on the front side of the second CR-39 detector and the proton incident energy on the detector stack is also presented. By calculating the proton number stopped in the CR-39 stack, we find out that its dependence on the proton energy in the 1–15 MeV range presents some discontinuities at energies higher than 9 MeV. Thus, we build a calibration curve of the track diameter as a function of the proton incident energy within the 1–9 MeV range, and we infer the associated analytical...

Research paper thumbnail of Multipole electrodynamic ion trap geometries for microparticle confinement under standard ambient temperature and pressure conditions

Journal of Applied Physics, 2016

Trapping of microparticles and aerosols is of great interest for physics and chemistry. We report... more Trapping of microparticles and aerosols is of great interest for physics and chemistry. We report microparticle trapping in case of multipole linear Paul trap geometries, operating under Standard Ambient Temperature and Pressure (SATP) conditions. An 8-electrode and a 12-electrode linear trap geometries have been designed and tested with an aim to achieve trapping for larger number of particles and to study microparticle dynamical stability in electrodynamic fields. We report emergence of planar and volume ordered structures of microparticles, depending on the a.c. trapping frequency and particle specific charge ratio. The electric potential within the trap is mapped using the electrolytic tank method. Particle dynamics is simulated using a stochastic Langevin equation. We emphasize extended regions of stable trapping with respect to quadrupole traps, as well as good agreement between experiment and numerical simulations.

Research paper thumbnail of The physics and applications of strongly coupled plasmas levitated in electrodynamic traps

arXiv: Plasma Physics, 2019

Charged (nano)particles confined in electrodynamic traps can evolve into strongly correlated Coul... more Charged (nano)particles confined in electrodynamic traps can evolve into strongly correlated Coulomb systems, which are the subject of current investigation. Exciting physical phenomena associated to Coulomb systems have been reported such as autowave generation, phase transitions, system self-locking at the ends of the linear Paul trap, self-organization in layers, or pattern formation and scaling. The dynamics of ordered structures consisting of highly nonideal similarly charged nanoparticles, with coupling parameter of the order Gamma=108\Gamma = 10^8Gamma=108 is investigated. This approach enables us to study the interaction of nanoparticle structures in presence and in absence of the neutralizing plasma background, as well as to investigate various types of phenomena and physical forces these structures experience. Applications of electrodynamic levitation for mass spectrometry, including containment and study of single aerosols and nanoparticles are reviewed, with an emphasis on state of the ...

Research paper thumbnail of Gdoes and GDMS Analytical Systems, Effective Tools for Characterization of Conductive and Nonconductive Material Surfaces

In this paper we present GDOES and GDMS analytical methods, the identification and the distributi... more In this paper we present GDOES and GDMS analytical methods, the identification and the distribution along the polymer thickness of different compounds generated during the polymerization process occurred in corona discharges starting from liquid precursors. Also, analyzing by GDOES technique the metallic samples, copper and brass implanted with nitrogen we have successfully evidenced the efficiency of a new, original, processing plasma which is 10 times denser than conventional low pressure plasma.

Research paper thumbnail of Study of Quasiclassical Dynamics of Trapped Ions Using the Coherent State Formalism and Associated Algebraic Groups

The time dependent variational principle (TDVP) has been applied on coherent state orbits and the... more The time dependent variational principle (TDVP) has been applied on coherent state orbits and the Hamilton equations of motion on Kähler (symplectic) manifolds result. The classical Hamilton functions associated to the system are realized as the expected values of the quantum Hamiltonian on symplectic coherent states. The formalism applies to Hamilton functions that are nonlinear in the infinitesimal generators of a dynamical symmetry group (in case of 3D ion traps). Using symplectic coherent states, the explicit classical equations of motion on the unit disk have been obtained for any algebraic model that admits the dynamical group Sp(2,R). The corresponding quasienergy states are explicitly realized as coherent states parameterized by the stable solutions of the corresponding classical equations of motion. The explicit expression of the quantum and classical Hamilton functions, particularized for combined (Paul and Penning) and ideal Paul traps, are obtained for the first time, ta...

Research paper thumbnail of Quasienergy operators and general squeezed states for systems of trapped ions

Collective many-body dynamics for time-dependent quantum Hamiltonian functions is investigated, f... more Collective many-body dynamics for time-dependent quantum Hamiltonian functions is investigated, for a dynamical system that exhibits multiple degrees of liberty, that is a combined (Paul and Penning) trap. We introduce the generators of the Lie algebra of the symplectic group SL(2,R), which we use to build the coherent states (CS) associated to the system under investigation. The trapped ion is treated as a harmonic oscillator (HO) to which we associate the quantum Hamilton function. We obtain the kinetic and potential energy operators as functions of the Lie algebra generators, and supply the expressions for the classical coordinate, momentum, kinetic and potential energy, as well as the total energy. We also infer the dispersions for the coordinate and momentum, the asymmetry and the flatness parametre for the distribution. The system interaction with the laser radiation is also examined for a system of identical two-level atoms. The Hamilton function for the Dicke model is obtain...

Research paper thumbnail of Mathieu-Hill Equation Stability Analysis for Trapped Ions. Anharmonic Corrections for Nonlinear Electrodynamic Traps

The stability properties of the Hill equation are discussed, especially those of the Mathieu equa... more The stability properties of the Hill equation are discussed, especially those of the Mathieu equation that characterize ion motion in electrodynamic traps. The solutions of the Mathieu-Hill equation for a trapped ion are characterized by employing the Floquet theory and Hill’s method solution, which yields an infinite system of linear and homogeneous equations whose coefficients are recursively determined. Stability is discussed for parameters a and q that are real. Characteristic curves are introduced naturally by the Sturm–Liouville problem for the well-known even and odd Mathieu equations cem(z,q)ce_m (z, q)cem(z,q) and sem(z,q)se_m (z, q)sem(z,q). In the case of a Paul trap, the stable solution corresponds to a superposition of harmonic motions. The maximum amplitude of stable oscillations for ideal conditions (taken into consideration) is derived. We illustrate the stability diagram for a combined (Paul and Penning) trap and represent the frontiers of the stability domains for both axial and radial motion, where the former is described by the canonical Mathieu equation. Anharmonic corrections for nonlinear Paul traps are discussed within the frame of perturbation theory, while the frontiers of the modified stability domains are determined as a function of the chosen perturbation parameter and we demonstrate they are shifted towards negative values of the a parameter. The applications of the results include but are not restricted to 2D and 3D ion traps used for different applications such as mass spectrometry (including nanoparticles), high resolution atomic spectroscopy and quantum engineering applications, among which we mention optical atomic clocks and quantum frequency metrology.

Research paper thumbnail of Mathieu–Hill Equation Stability Analysis for Trapped Ions: Anharmonic Corrections for Nonlinear Electrodynamic Traps

Photonics, Jun 11, 2024

The stability properties of the Hill equation are discussed, especially those of the Mathieu equa... more The stability properties of the Hill equation are discussed, especially those of the Mathieu equation that characterize ion motion in electrodynamic traps. The solutions of the Mathieu-Hill equation for a trapped ion are characterized by employing the Floquet theory and Hill’s method solution, which yields an infinite system of linear and homogeneous equations whose coefficients are recursively determined. Stability is discussed for parameters a and q that are real. Characteristic curves are introduced naturally by the Sturm–Liouville problem for the well-known even and odd Mathieu equations cem(z,q)ce_m (z, q)cem(z,q) and sem(z,q)se_m (z, q)sem(z,q). In the case of a Paul trap, the stable solution corresponds to a superposition of harmonic motions. The maximum amplitude of stable oscillations for ideal conditions (taken into consideration) is derived. We illustrate the stability diagram for a combined (Paul and Penning) trap and represent the frontiers of the stability domains for both axial and radial motion, where the former is described by the canonical Mathieu equation. Anharmonic corrections for nonlinear Paul traps are discussed within the frame of perturbation theory, while the frontiers of the modified stability domains are determined as a function of the chosen perturbation parameter and we demonstrate they are shifted towards negative values of the a parameter. The applications of the results include but are not restricted to 2D and 3D ion traps used for different applications such as mass spectrometry (including nanoparticles), high resolution atomic spectroscopy and quantum engineering applications, among which we mention optical atomic clocks and quantum frequency metrology.

Research paper thumbnail of Radiation dose distribution inside interaction chamber in PW laser facilities during laser-plasma proton acceleration experiments and method to increase the proton energy spectrum measurement resolution

arXiv (Cornell University), Jun 3, 2019

The paper discusses some 3D simulations to compute the ionizing radiation dose during laser-plasm... more The paper discusses some 3D simulations to compute the ionizing radiation dose during laser-plasma experiments leading to the generation of accelerated protons and electrons. Also, we suggest a new method to increase the measurement resolution of the proton energy spectrum. Monte-Carlo simulations of the radiation doses map around the laser-foil interaction point are performed using Geant4 General Particle Source code and the particular geometry chosen for the experimental setup. We obtain the map of the radiation dose distribution for high-power laser - thin solid target experiments, considering a cubic geometry of the interaction chamber. The computed radiation dose distribution shows a good agreement with various, previously obtained experimental results, and could be a step towards simulating the radiation environment inside of a spacecraft. To characterize the laser-plasma accelerated protons, we introduce a new method to enhance the measurement resolution of the proton energy spectrum by employing a stack of thin solid detectors, preferably CR-39. Each detector is thinner than the Bragg peak region on the Bragg curve that characterizes the loss of kinetic energy as a function of the particle penetration depth in the detector material. The relevance of this method for space radiation characterization and cybersecurity insurance is highlighted.

Research paper thumbnail of Quasiclassical Dynamics for Ions Confined in Axially Symmetric Electromagnetic Traps

arXiv (Cornell University), Sep 10, 2016

Quasiclassical dynamics of trapped ions is described by applying the time dependent variational p... more Quasiclassical dynamics of trapped ions is described by applying the time dependent variational principle (TDVP) on coherent state orbits, introduced as sub-manifolds of the quantum state space. The classical Hamilton functions associated to the system are obtained as the expected values of the quantum Hamiltonian on symplectic coherent states. Such formalism can be applied to Hamilton functions which are nonlinear in the infinitesimal generators of a dynamical symmetry group. We give the explicit expression of the quantum Hamilton function in case of nonlinear electromagnetic traps. Discrete quasienergy spectra result, and the corresponding quasienergy states are explicitly realized as coherent states parameterized by the stable solutions of the corresponding classical equations of motion. A dequantization algorithm is also suggested. The method is then applied to combined (Paul and Penning) and ideal Paul traps. We obtain the explicit expressions of the classical Hamilton functions for such particular traps, as well as the classical Hamilton equations of motion in complex coordinates for an octupole trap. In the pseudopotential approximation, the points of minimum of the Hamiton function define equilibrium configurations for trapped ions, of interest for quantum logic.

Research paper thumbnail of The physics and applications of strongly coupled Coulomb systems (plasmas) levitated in electrodynamic traps

Physics Reports, May 15, 2023

Charged microparticles confined in electrodynamic traps evolve into strongly coupled Coulomb syst... more Charged microparticles confined in electrodynamic traps evolve into strongly coupled Coulomb systems (SCCS) which are the subject of current investigation. Recent results with respect to particle dynamics in linear and nonlinear Paul traps are reviewed, including the case of a confined microparticle in presence of an acoustic wave. An analytical model is used to discuss dynamical stability for systems of two coupled ions confined in a Paul trap. The model is then extended to discuss quantum stability for many-body systems of trapped ions. Dynamical stability for many-body systems of identical ions confined in 3D quadrupole ion traps (QIT) is studied locally, in the neighbourhood of minimum configurations that characterize ordered structures. The analytical model is particularized to the case of a combined trap. It is demonstrated that Paul (ion) traps are versatile instruments to investigate one-component strongly coupled Coulomb systems (microplasmas). Exciting physical phenomena associated to Coulomb systems are reported, such as autowave generation, phase transitions, defect formation, system self-locking at the edges of a linear Paul trap, self-organization in layers, or pattern formation and scaling. The dynamics of ordered structures consisting of highly nonideal similarly charged solid particles with coupling parameter of the order Gamma=108\Gamma = 10^8Gamma=108 is explored. The approach used enables one to explore the interaction of microparticle structures in presence and in absence of the neutralizing plasma background, as well as to investigate various types of phenomena and physical forces experienced by these patterns. Brownian dynamics (BD) is used to characterize charged particle evolution in time and to identify regions of stable trapping. Analytical models are used to explain the experimental results. Numerical modelling considers stochastic forces of random collisions with neutral particles, viscosity of the gas medium, regular forces produced by the a.c. trapping voltage, and gravitational force. Microparticle dynamics is characterized by a stochastic Langevin differential equation. Laser plasma acceleration of charged particles is also discussed, with an emphasis on Paul traps employed to investigate collective effects in space-charge-dominated (relativistic) beams and for target micropositioning. This review paper is both an add-on as well as an update on late progress in SCCS confined in electrodynamic traps.

Research paper thumbnail of Quasienergy operators and generalized squeezed states for systems of trapped ions

Annals of Physics, 2022

Collective many-body dynamics for time-dependent quantum Hamiltonians is investigated for a dynam... more Collective many-body dynamics for time-dependent quantum Hamiltonians is investigated for a dynamical system that exhibits multiple degrees of freedom, in this case a combined (Paul and Penning) trap. Quantum stability is characterized by a discrete quasienergy spectrum, while the quasienergy states are symplectic coherent states. We introduce the generators of the Lie algebra of the symplectic group , which we use to build the coherent states (CS) associated to the system under investigation. The trapped ion is treated as a harmonic oscillator (HO) to which we associate the quantum Hamilton function. We obtain the kinetic and potential energy operators as functions of the Lie algebra generators and supply the expressions for the classical coordinate, momentum, kinetic and potential energy, along with the total energy. Moreover, we also infer the dispersions for the coordinate and momentum, together with the asymmetry and the flatness parameter for the distribution. The system interaction with laser radiation is also examined for a system of identical two-level atoms. The Hamilton function for the Dicke model is derived. The optical system is modelled as a HO (trapped ion) that undergoes interaction with an external laser field and we use it to engineer a squeezed state of the electromagnetic (EM) field. We consider coherent and squeezed states associated to both ion dynamics and to the EM field. The approach used enables one to build CS in a compact and smart manner by use of the group theory.

Research paper thumbnail of Coherent states for trapped ions. Applications in quantum optics and precision measurements

Proc. of the Ninth Meeting on CPT and Lorentz Symmetry (CPT’22), Editor: R. Lehnert, World Scientific, Jun 25, 2023

The evolution of squeezed coherent states of motion for trapped ions is investigated by applying ... more The evolution of squeezed coherent states of motion for trapped ions is investigated by applying the time-dependent variational principle for the Schrödinger equation. The method is applied in case of Paul and combined traps, for which the classical Hamiltonian and equations of motion are derived. Hence, coherent states provide a natural framework to: (a) engineer quantum correlated states for trapped ions intended for ultraprecise measurements, (b) explore the mechanisms responsible for decoherence, and (c) investigate the quantum–classical transition.

Research paper thumbnail of Radiation dose simulation during laser-plasma proton acceleration experiments and method to increase the measurement resolution of the proton energy spectrum

The paper discusses some 3D simulations to compute the ionizing radiation dose during laser-plasm... more The paper discusses some 3D simulations to compute the ionizing radiation dose during laser-plasma experiments leading to the generation of accelerated protons and electrons. Also, we suggest a new method to increase the measurement resolution of the proton energy spectrum. Monte-Carlo simulations of the radiation doses map around the laser-foil interaction point are performed using Geant4 General Particle Source code and the particular geometry chosen for the experimental setup. We obtain the map of the radiation dose distribution for high-power laser - thin solid target experiments, considering a cubic geometry of the interaction chamber. The computed radiation dose distribution shows a good agreement with various, previously obtained experimental results, and could be a step towards simulating the radiation environment inside of a spacecraft. To characterize the laser-plasma accelerated protons, we introduce a new method to enhance the measurement resolution of the proton energy ...

Research paper thumbnail of Multipole Electrodynamic Ion Trap Geometries for Microparticle Confinement under Standard Ambient Temperature and Pressure Conditions

arXiv: 1512.05503, Jan 11, 2016

Trapping of microparticles and aerosols is of great interest for physics and chemistry. We report... more Trapping of microparticles and aerosols is of great interest for physics and chemistry. We report microparticle trapping in multipole linear Paul trap geometries, operating under Standard Ambient Temperature and Pressure (SATP) conditions. An 8-electrode and a 12-electrode linear trap geometries have been designed and tested with an aim to achieve trapping for larger number of particles and to study microparticle dynamical stability in electrodynamic fields. We report emergence of planar and volume ordered structures of the microparticles, depending on the a.c. trapping frequency and particle specific charge ratio. The electric potential within the trap was mapped using the electrolytic tank method. Particle dynamics was simulated using a stochastic Langevin equation. We emphasize extended regions of stable trapping with respect to quadrupole traps, as well as good agreement between experiment and numerical simulations.

Research paper thumbnail of The physics and applications of strongly coupled Coulomb systems (plasmas) levitated in electrodynamic traps

Physics Reports, Nov 6, 2023

Charged microparticles confined in electrodynamic traps evolve into strongly coupled Coulomb syst... more Charged microparticles confined in electrodynamic traps evolve into strongly coupled Coulomb systems (SCCS) which are the subject of current investigation. Recent results with respect to particle dynamics in linear and nonlinear Paul traps are reviewed, including the case of a confined microparticle in presence of an acoustic wave. An analytical model is used to discuss dynamical stability for systems of two coupled ions confined in a Paul trap. The model is then extended to discuss quantum stability for many-body systems of trapped ions. Dynamical stability for many-body systems of identical ions confined in 3D quadrupole ion traps (QIT) is studied locally, in the neighbourhood of minimum configurations that characterize ordered structures. The analytical model is particularized to the case of a combined trap. It is demonstrated that Paul (ion) traps are versatile instruments to investigate one-component strongly coupled Coulomb systems (microplasmas). Exciting physical phenomena associated to Coulomb systems are reported, such as autowave generation, phase transitions, defect formation, system self-locking at the edges of a linear Paul trap, self-organization in layers, or pattern formation and scaling. The dynamics of ordered structures consisting of highly nonideal similarly charged solid particles with coupling parameter of the order Gamma=108\Gamma = 10^8Gamma=108 is explored. The approach used enables one to explore the interaction of microparticle structures in presence and in absence of the neutralizing plasma background, as well as to investigate various types of phenomena and physical forces experienced by these patterns. Brownian dynamics (BD) is used to characterize charged particle evolution in time and to identify regions of stable trapping. Analytical models are used to explain the experimental results. Numerical modelling considers stochastic forces of random collisions with neutral particles, viscosity of the gas medium, regular forces produced by the a.c. trapping voltage, and gravitational force. Microparticle dynamics is characterized by a stochastic Langevin differential equation. Laser plasma acceleration of charged particles is also discussed, with an emphasis on Paul traps employed to investigate collective effects in space-charge-dominated (relativistic) beams and for target micropositioning. This review paper is both an add-on as well as an update on late progress in SCCS confined in electrodynamic traps.

Research paper thumbnail of Time Dependent Variational Principle and Coherent State Orbits for a Trapped Ion

Spectral properties of the Hamiltonian function which characterizes a trapped ion are investigate... more Spectral properties of the Hamiltonian function which characterizes a trapped ion are investigated. In order to study semiclassical dynamics of trapped ions, coherent state orbits are introduced as sub-manifolds of the quantum state space, with the K\"ahler structure induced by the transition probability. The time dependent variational principle (TDVP) is applied on coherent states' orbits. The Hamilton equations of motion on K\"ahler manifolds of the type of classical phase spaces naturally arise. The associated classical Hamiltonian is obtained from the expected values on symplectic coherent states of the quantum Hamiltonian. Spectral information is thus coded within the phase portrait. We deal with the bosonic realization of the Lie algebra of the SU(1,1) group, which we particularize for the case of an ion confined in a combined, Paul and Penning trap. This formalism can be applied to Hamiltonians which are nonlinear in the infinitesimal generators of a dynamical s...

Research paper thumbnail of Multipole Traps as Tools in Environmental Studies

arXiv: Plasma Physics, 2015

Trapping of microparticles, nanoparticles and aerosols is an issue of major interest for physics ... more Trapping of microparticles, nanoparticles and aerosols is an issue of major interest for physics and chemistry. We present a setup intended for microparticle trapping in multipole linear Paul trap geometries, operating under Standard Ambient Temperature and Pressure (SATP) conditions. A 16-electrode linear trap geometry has been designed and tested, with an aim to confine a larger number of particles with respect to quadrupole traps and thus enhance the signal to noise ratio, as well as to study microparticle dynamical stability in electrodynamic fields. Experimental tests and numerical simulations suggest that multipole traps are very suited for high precision mass spectrometry measurements in case of different microparticle species or to identify the presence of certain aerosols and polluting agents in the atmosphere. Particle traps represent versatile tools for environment monitoring or for the study of many-body Coulomb systems and dusty plasmas.

Research paper thumbnail of Investigations on Dynamical Stability in 3D Quadrupole Ion Traps

Applied Sciences, 2021

We firstly discuss classical stability for a dynamical system of two ions levitated in a 3D Radio... more We firstly discuss classical stability for a dynamical system of two ions levitated in a 3D Radio-Frequency (RF) trap, assimilated with two coupled oscillators. We obtain the solutions of the coupled system of equations that characterizes the associated dynamics. In addition, we supply the modes of oscillation and demonstrate the weak coupling condition is inappropriate in practice, while for collective modes of motion (and strong coupling) only a peak of the mass can be detected. Phase portraits and power spectra are employed to illustrate how the trajectory executes quasiperiodic motion on the surface of torus, namely a Kolmogorov–Arnold–Moser (KAM) torus. In an attempt to better describe dynamical stability of the system, we introduce a model that characterizes dynamical stability and the critical points based on the Hessian matrix approach. The model is then applied to investigate quantum dynamics for many-body systems consisting of identical ions, levitated in 2D and 3D ion tra...

Research paper thumbnail of Squeezed coherent states of motion for ions confined in quadrupole and octupole ion traps

Annals of Physics, 2018

Quasiclassical dynamics of trapped ions is characterized by applying the time dependent variation... more Quasiclassical dynamics of trapped ions is characterized by applying the time dependent variational principle (TDVP) on coherent state orbits, in case of quadrupole and octupole combined (Paul and Penning) and radiofrequency (RF) traps. A dequantization algorithm is proposed, by which the classical Hamilton (energy) function associated to the system results as the expectation value of the quantum Hamiltonian on squeezed coherent states. We develop such method and particularize the quantum Hamiltonian for a combined and for a RF trap, with axial symmetry and a RF anharmonic electric potential. We also build the classical Hamiltonian functions for the particular traps we considered, and find the classical equations of motion.

Research paper thumbnail of Advances in Spectral Distribution Assessment of Laser Accelerated Protons using Multilayer CR-39 Detectors

Applied Sciences, 2019

We show that a spectral distribution of laser-accelerated protons can be extracted by analyzing t... more We show that a spectral distribution of laser-accelerated protons can be extracted by analyzing the proton track diameters observed on the front side of a second CR-39 detector arranged in a stack. The correspondence between the proton track diameter and the incident energy on the second detector is established by knowing that protons with energies only higher than 10.5 MeV can fully deposit their energy in the second CR-39 detector. The correlation between the laser-accelerated proton track diameters observed on the front side of the second CR-39 detector and the proton incident energy on the detector stack is also presented. By calculating the proton number stopped in the CR-39 stack, we find out that its dependence on the proton energy in the 1–15 MeV range presents some discontinuities at energies higher than 9 MeV. Thus, we build a calibration curve of the track diameter as a function of the proton incident energy within the 1–9 MeV range, and we infer the associated analytical...

Research paper thumbnail of Multipole electrodynamic ion trap geometries for microparticle confinement under standard ambient temperature and pressure conditions

Journal of Applied Physics, 2016

Trapping of microparticles and aerosols is of great interest for physics and chemistry. We report... more Trapping of microparticles and aerosols is of great interest for physics and chemistry. We report microparticle trapping in case of multipole linear Paul trap geometries, operating under Standard Ambient Temperature and Pressure (SATP) conditions. An 8-electrode and a 12-electrode linear trap geometries have been designed and tested with an aim to achieve trapping for larger number of particles and to study microparticle dynamical stability in electrodynamic fields. We report emergence of planar and volume ordered structures of microparticles, depending on the a.c. trapping frequency and particle specific charge ratio. The electric potential within the trap is mapped using the electrolytic tank method. Particle dynamics is simulated using a stochastic Langevin equation. We emphasize extended regions of stable trapping with respect to quadrupole traps, as well as good agreement between experiment and numerical simulations.

Research paper thumbnail of The physics and applications of strongly coupled plasmas levitated in electrodynamic traps

arXiv: Plasma Physics, 2019

Charged (nano)particles confined in electrodynamic traps can evolve into strongly correlated Coul... more Charged (nano)particles confined in electrodynamic traps can evolve into strongly correlated Coulomb systems, which are the subject of current investigation. Exciting physical phenomena associated to Coulomb systems have been reported such as autowave generation, phase transitions, system self-locking at the ends of the linear Paul trap, self-organization in layers, or pattern formation and scaling. The dynamics of ordered structures consisting of highly nonideal similarly charged nanoparticles, with coupling parameter of the order Gamma=108\Gamma = 10^8Gamma=108 is investigated. This approach enables us to study the interaction of nanoparticle structures in presence and in absence of the neutralizing plasma background, as well as to investigate various types of phenomena and physical forces these structures experience. Applications of electrodynamic levitation for mass spectrometry, including containment and study of single aerosols and nanoparticles are reviewed, with an emphasis on state of the ...

Research paper thumbnail of Gdoes and GDMS Analytical Systems, Effective Tools for Characterization of Conductive and Nonconductive Material Surfaces

In this paper we present GDOES and GDMS analytical methods, the identification and the distributi... more In this paper we present GDOES and GDMS analytical methods, the identification and the distribution along the polymer thickness of different compounds generated during the polymerization process occurred in corona discharges starting from liquid precursors. Also, analyzing by GDOES technique the metallic samples, copper and brass implanted with nitrogen we have successfully evidenced the efficiency of a new, original, processing plasma which is 10 times denser than conventional low pressure plasma.

Research paper thumbnail of Study of Quasiclassical Dynamics of Trapped Ions Using the Coherent State Formalism and Associated Algebraic Groups

The time dependent variational principle (TDVP) has been applied on coherent state orbits and the... more The time dependent variational principle (TDVP) has been applied on coherent state orbits and the Hamilton equations of motion on Kähler (symplectic) manifolds result. The classical Hamilton functions associated to the system are realized as the expected values of the quantum Hamiltonian on symplectic coherent states. The formalism applies to Hamilton functions that are nonlinear in the infinitesimal generators of a dynamical symmetry group (in case of 3D ion traps). Using symplectic coherent states, the explicit classical equations of motion on the unit disk have been obtained for any algebraic model that admits the dynamical group Sp(2,R). The corresponding quasienergy states are explicitly realized as coherent states parameterized by the stable solutions of the corresponding classical equations of motion. The explicit expression of the quantum and classical Hamilton functions, particularized for combined (Paul and Penning) and ideal Paul traps, are obtained for the first time, ta...

Research paper thumbnail of Quasienergy operators and general squeezed states for systems of trapped ions

Collective many-body dynamics for time-dependent quantum Hamiltonian functions is investigated, f... more Collective many-body dynamics for time-dependent quantum Hamiltonian functions is investigated, for a dynamical system that exhibits multiple degrees of liberty, that is a combined (Paul and Penning) trap. We introduce the generators of the Lie algebra of the symplectic group SL(2,R), which we use to build the coherent states (CS) associated to the system under investigation. The trapped ion is treated as a harmonic oscillator (HO) to which we associate the quantum Hamilton function. We obtain the kinetic and potential energy operators as functions of the Lie algebra generators, and supply the expressions for the classical coordinate, momentum, kinetic and potential energy, as well as the total energy. We also infer the dispersions for the coordinate and momentum, the asymmetry and the flatness parametre for the distribution. The system interaction with the laser radiation is also examined for a system of identical two-level atoms. The Hamilton function for the Dicke model is obtain...