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Palmerduca E, Qin H, Cohen SA. Energizing charged particles by an orbit instability in a slowly rotating magnetic field. Phys Rev E 2022; 106:045209. [PMID: 36397595 DOI: 10.1103/physreve.106.045209] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2022] [Accepted: 09/29/2022] [Indexed: 06/16/2023]
Abstract
The stability of charged particle motion in a uniform magnetic field with an added spatially uniform transverse rotating magnetic field (RMF) is studied analytically. It is found that the stability diagram of a single particle's orbit depends critically on the chosen boundary conditions. We show that for many boundary conditions and wide regions in the parameter space, RMFs oscillating far below the cyclotron frequency can cause linear instabilities in the motion which break μ invariance and energize particles. Such energization may appear at odds with the adiabatic invariance of μ; however, adiabatic invariance is an asymptotic result and does not preclude such heating by magnetic fields oscillating at slow frequencies. This mechanism may contribute to heating in the edge plasma of field-reversed configurations (FRCs) in rotamak-FRC experiments. Furthermore, these RMF-driven instabilities may significantly enhance azimuthal current drive during the formation of FRCs in such devices.
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Affiliation(s)
- Eric Palmerduca
- Princeton Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08540, USA and Department of Astrophysical Sciences, Princeton University, Princeton, New Jersey 08544, USA
| | - Hong Qin
- Princeton Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08540, USA and Department of Astrophysical Sciences, Princeton University, Princeton, New Jersey 08544, USA
| | - Samuel A Cohen
- Princeton Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08540, USA and Department of Astrophysical Sciences, Princeton University, Princeton, New Jersey 08544, USA
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Glasser AH, Cohen SA. Simulating single-particle dynamics in magnetized plasmas: The RMF code. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2022; 93:083506. [PMID: 36050065 DOI: 10.1063/5.0101665] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2022] [Accepted: 06/30/2022] [Indexed: 06/15/2023]
Abstract
The RMF (Rotating Magnetic Field) code is designed to calculate the motion of a charged particle in a given electromagnetic field. It integrates Hamilton's equations in cylindrical coordinates using an adaptive predictor-corrector double-precision variable-coefficient ordinary differential equation solver for speed and accuracy. RMF has multiple capabilities for the field. Particle motion is initialized by specifying the position and velocity vectors. The six-dimensional state vector and derived quantities are saved as functions of time. A post-processing graphics code, XDRAW, is used on the stored output to plot up to 12 windows of any two quantities using different colors to denote successive time intervals. Multiple cases of RMF may be run in parallel and perform data mining on the results. Recent features are a synthetic diagnostic for simulating the observations of charge-exchange-neutral energy distributions and RF grids to explore a Fermi acceleration parallel to static magnetic fields.
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Affiliation(s)
- A H Glasser
- Fusion Theory & Computation, Inc., 24062 Seatter Lane Nebraska, Kingston, Washington 98346, USA
| | - S A Cohen
- Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, New Jersey 08543, USA
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Ortmann L, Pérez-Hernández JA, Ciappina MF, Schötz J, Chacón A, Zeraouli G, Kling MF, Roso L, Lewenstein M, Landsman AS. Emergence of a Higher Energy Structure in Strong Field Ionization with Inhomogeneous Electric Fields. PHYSICAL REVIEW LETTERS 2017; 119:053204. [PMID: 28949751 DOI: 10.1103/physrevlett.119.053204] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/31/2016] [Indexed: 06/07/2023]
Abstract
Studies of strong field ionization have historically relied on the strong field approximation, which neglects all spatial dependence in the forces experienced by the electron after ionization. More recently, the small spatial inhomogeneity introduced by the long-range Coulomb potential has been linked to a number of important features in the photoelectron spectrum, such as Coulomb asymmetry, Coulomb focusing, and the low energy structure. Here, we demonstrate using midinfrared laser wavelength that a time-varying spatial dependence in the laser electric field, such as that produced in the vicinity of a nanostructure, creates a prominent higher energy peak. This higher energy structure (HES) originates from direct electrons ionized near the peak of a single half-cycle of the laser pulse. The HES is separated from all other ionization events, with its location and width highly dependent on the strength of spatial inhomogeneity. Hence, the HES can be used as a sensitive tool for near-field characterization in the "intermediate regime," where the electron's quiver amplitude is comparable to the field decay length. Moreover, the large accumulation of electrons with tuneable energy suggests a promising method for creating a localized source of electron pulses of attosecond duration using tabletop laser technology.
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Affiliation(s)
- L Ortmann
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, D-01187 Dresden, Germany
| | - J A Pérez-Hernández
- Centro de Láseres Pulsados (CLPU), Parque Científico, E-37185 Villamayor, Salamanca, Spain
| | - M F Ciappina
- Max-Planck Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching, Germany
- Institute of Physics of the ASCR, ELI-Beamlines, Na Slovance 2, 182 21 Prague, Czech Republic
| | - J Schötz
- Max-Planck Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching, Germany
| | - A Chacón
- ICFO-Institut de Ciences Fotoniques, The Barcelona Institute of Science and Technology, E-08860 Castelldefels, Spain
| | - G Zeraouli
- Centro de Láseres Pulsados (CLPU), Parque Científico, E-37185 Villamayor, Salamanca, Spain
| | - M F Kling
- Max-Planck Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching, Germany
- Department für Physik, Ludwig-Maximilians-Universität München, Am Coulombwall 1, D-85748 Garching, Germany
| | - L Roso
- Centro de Láseres Pulsados (CLPU), Parque Científico, E-37185 Villamayor, Salamanca, Spain
| | - M Lewenstein
- ICFO-Institut de Ciences Fotoniques, The Barcelona Institute of Science and Technology, E-08860 Castelldefels, Spain
- ICREA, Pg. Lluis Companys 23, E-08010 Barcelona, Spain
| | - A S Landsman
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, D-01187 Dresden, Germany
- Department of Physics, Max Planck Postech, Pohang, Gyeongbuk 37673, Republic of Korea
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Zimmermann T, Mishra S, Doran BR, Gordon DF, Landsman AS. Tunneling Time and Weak Measurement in Strong Field Ionization. PHYSICAL REVIEW LETTERS 2016; 116:233603. [PMID: 27341232 DOI: 10.1103/physrevlett.116.233603] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2015] [Indexed: 06/06/2023]
Abstract
Tunneling delays represent a hotly debated topic, with many conflicting definitions and little consensus on when and if such definitions accurately describe the physical observables. Here, we relate these different definitions to distinct experimental observables in strong field ionization, finding that two definitions, Larmor time and Bohmian time, are compatible with the attoclock observable and the resonance lifetime of a bound state, respectively. Both of these definitions are closely connected to the theory of weak measurement, with Larmor time being the weak measurement value of tunneling time and Bohmian trajectory corresponding to the average particle trajectory, which has been recently reconstructed using weak measurement in a two-slit experiment [S. Kocsis, B. Braverman, S. Ravets, M. J. Stevens, R. P. Mirin, L. K. Shalm, and A. M. Steinberg, Science 332, 1170 (2011)]. We demonstrate a big discrepancy in strong field ionization between the Bohmian and weak measurement values of tunneling time, and we suggest this arises because the tunneling time is calculated for a small probability postselected ensemble of electrons. Our results have important implications for the interpretation of experiments in attosecond science, suggesting that tunneling is unlikely to be an instantaneous process.
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Affiliation(s)
- Tomáš Zimmermann
- Seminar for Applied Mathematics, ETH Zurich, CH-8093 Zurich, Switzerland
- Physics Department, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Siddhartha Mishra
- Seminar for Applied Mathematics, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Brent R Doran
- Department of Mathematics, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Daniel F Gordon
- Radiation and Acceleration Physics Section, Naval Research Laboratory, Washington, D.C. 20375, USA
| | - Alexandra S Landsman
- Seminar for Applied Mathematics, ETH Zurich, CH-8093 Zurich, Switzerland
- Physics Department, ETH Zurich, CH-8093 Zurich, Switzerland
- Max Planck Institute for the Physics of Complex Systems, D-01187 Dresden, Germany
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Landsman AS, Hofmann C, Pfeiffer AN, Cirelli C, Keller U. Unified approach to probing Coulomb effects in tunnel ionization for any ellipticity of laser light. PHYSICAL REVIEW LETTERS 2013; 111:263001. [PMID: 24483793 DOI: 10.1103/physrevlett.111.263001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/20/2013] [Indexed: 06/03/2023]
Abstract
We present experimental data that show significant deviations from theoretical predictions for the location of the center of the electron momenta distribution at low values of ellipticity ε of laser light. We show that these deviations are caused by significant Coulomb focusing along the minor axis of polarization, something that is normally neglected in the analysis of electron dynamics, even in cases where the Coulomb correction is otherwise taken into account. By investigating ellipticity-resolved electron momenta distributions in the plane of polarization, we show that Coulomb focusing predominates at lower values of ellipticity of laser light, while Coulomb asymmetry becomes important at higher values, showing that these two complementary phenomena can be used to probe long-range Coulomb interaction at all polarizations of laser light. Our results suggest that both the breakdown of Coulomb focusing and the onset of Coulomb asymmetry are linked to the disappearance of Rydberg states with increasing ellipticity.
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Affiliation(s)
- A S Landsman
- Physics Department, ETH Zurich, CH-8093 Zurich, Switzerland
| | - C Hofmann
- Physics Department, ETH Zurich, CH-8093 Zurich, Switzerland
| | - A N Pfeiffer
- Physics Department, ETH Zurich, CH-8093 Zurich, Switzerland
| | - C Cirelli
- Physics Department, ETH Zurich, CH-8093 Zurich, Switzerland
| | - U Keller
- Physics Department, ETH Zurich, CH-8093 Zurich, Switzerland
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Technical Survey of Simply Connected Compact Tori (CTs): Spheromaks, FRCs and Compression Schemes. JOURNAL OF FUSION ENERGY 2007. [DOI: 10.1007/s10894-007-9099-9] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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Cohen SA, Berlinger B, Brunkhorst C, Brooks A, Ferraro N, Lundberg DP, Roach A, Glasser AH. Formation of collisionless high-beta plasmas by odd-parity rotating magnetic fields. PHYSICAL REVIEW LETTERS 2007; 98:145002. [PMID: 17501282 DOI: 10.1103/physrevlett.98.145002] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2006] [Indexed: 05/15/2023]
Abstract
Odd-parity rotating magnetic fields (RMFo) applied to mirror-configuration plasmas have produced average electron energies exceeding 200 eV at line-averaged electron densities of approximately 10(12) cm-3. These plasmas, sustained for over 10(3)tauAlfven, have low Coulomb collisionality, vc* triple bond L/lambdaC approximately 10(-3), where lambdaC is the Coulomb scattering mean free path and L is the plasma's characteristic half length. Divertors allow reduction of the electron-neutral collision frequency to values where the RMFo coupling indicates full penetration of the RMFo to the major axis.
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Affiliation(s)
- S A Cohen
- Princeton Plasma Physics Laboratory, Princeton University, Princeton, New Jersey, USA
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