Action-angle coordinates can be constructed for so-called integrable Hamiltonian dynamical systems, for which there exists a foliation of phase space by surfaces that are invariant under the dynamical flow.
Perturbations generally destroy integrability.
However, we know that periodic orbits will survive, as will cantori, as will the “KAM” surfaces that have sufficiently irrational frequency, depending on the perturbation. There will also be irregular “chaotic” trajectories.
By “fitting” the coordinates to the invariant structures that are robust to perturbation, action-angle coordinates may be generalized to non-integrable dynamical systems. These coordinates “capture” the invariant dynamics and neatly partition the chaotic regions. These so-called chaotic coordinates are based on a construction of almost-invariant surfaces known as ghost surfaces. The theoretical definition and numerical construction of ghost surfaces and chaotic coordinates will be described and illustrated.
National Institute for Fusion Science Gyrokinetic-MHD coupled simulation of RMP plasma interaction reproduces density pump-out seen in the tokamak edge
The gyrokinetic neoclassical particle-in-cell code XGCa coupled to the MHD code M3D-C1 is applied to study the particle and heat flux caused by external 3D magnetic perturbations (RMP) in a model DIII-D H-mode plasma.
Despite the existence of KAM surfaces in the pedestal, our simulations, which so far are limited to the 0.5 to 1 ms directly after the RMP field is switched on, show the beginning of density pump-out at the pedestal top as well as a steepening of the electron temperature pedestal around the magnetic separatrix similar to experimental observations.
The basic physics is explained as a neoclassical 3D effect. Effects from plasma turbulence have been excluded and are left for future work.
Necessary and sufficient condition for the stability of linear Hamiltonian systems with periodic coefficients
Linear Hamiltonian systems with time-dependent coefficients are of importance to nonlinear Hamiltonian systems, accelerator physics, plasma physics, and quantum physics. It is shown in the paper that the solution map of a linear Hamiltonian system with time-dependent coefficients can be parameterized by an envelope matrix w, which has a clear physical meaning and satisfies a nonlinear envelope matrix equation. It is proved that a linear Hamiltonian system with periodic coefficients is stable if and only if the envelope matrix equation admits a solution with periodic w*w and a suitable initial condition. The mathematical devices utilized in this theoretical development with significant physical implications are time-dependent canonical transformations, normal forms for stable symplectic matrices, and horizontal polar decomposition of symplectic matrices. These tools systematically decompose the dynamics of linear Hamiltonian systems with time-dependent coefficients, and are expected to be effective in other studies as well, such as those on quantum algorithms for classical Hamiltonian systems.
ECP-WDMapp Advisory Board Meeting, Princeton Plasma Physics Laboratory Coupling of core and edge gyrokinetic codes
The onset and nonlinear evolution of coherent current-carrying filaments are examined using global nonlinear three-dimensional resistive MHD simulations in a spherical tokamak (ST).
We show that physical current sheets/layers develop near the tokamak edge under different circumstances, in particular as a peeling component of ELMs (due to bootstrap currents), and during vertical displacement events (associated with the scrape-off layer currents).
In all these cases, edge current sheets can become unstable to nonaxisymmetric 3-D current-sheet instabilities and nonlinearly form edge coherent current-carrying filaments.
Time-evolving edge current sheets in ST configurations are identified in our nonlinear simulations.
[F. Ebrahimi, Phys. Plasmas 23, 120705 (2016);
F. Ebrahimi, Phys. Plasmas 24, 056119 (2017)]
In the case of peeling-like edge localized modes, the longstanding problem of quasiperiodic ELM cycles is explained through the relaxation of the edge current source through direct numerical calculations of reconnecting local bi-directional fluctuation-induced electromotive force (emf) terms. Second, we examine the stability and formation of reconnecting edge peeling-driven filaments during induced vertical displacement events (VDEs) simulations. Similar to fast reconnection due to axisymmetric plasmoids,
[F. Ebrahimi & R. Raman, Phys. Rev. Lett. 114, 205003 (2015)]
we find that the growth rate of these edge filamentary structures becomes independent of Lundquist number. As well as edge reconnection physics in tokamaks, the 3-D coherent current-carrying fi lament structures and their nonlinear dynamics due to the dynamo effect presented here are also relevant to flares, which also exhibit ejection of field-aligned filamentary structures into the surrounding space.
Max Planck Princeton Center Workshop, 2018 Laboratory magnetized shock generation in laser plasmas
Collisionless shocks are ubiquitous in space and astrophysical systems, and the class of supercritical shocks is of particular importance due to their role in accelerating particles to high energies.
While these shocks have been traditionally studied by spacecraft and remote sensing observations, laboratory experiments can provide reproducible and multi-dimensional datasets that provide complementary understanding of the underlying microphysics.
We present experiments undertaken on the OMEGA and OMEGA EP laser facilities that show the formation and evolution of high-Mach number collisionless shocks created through the interaction of a laser-driven magnetic piston and magnetized ambient plasma [1,2].
Through time-resolved, 2-D imaging we observe large density and magnetic compressions that propagate at an Alfvénic Mach number $M_A\sim15$ and that occur over ion kinetic length scales.
Particle-in-cell simulations constrained by experimental data further detail the shock formation and separate dynamics of the multi-ion-species ambient plasma.
The results show that the shocks form on timescales as fast as one gyroperiod, aided by the efficient coupling of energy, and the generation of a magnetic barrier, between the piston and ambient ions.
The development of this experimental platform opens the way for controlled laboratory investigations of high-Mach-number collisionless shocks, including mechanisms of shock heating and particle acceleration.
[1] D. B. Schaeffer, W. Fox et al., Phys. Rev. Lett. 119, 025001 (2017)
[2] D. B. Schaeffer, W. Fox et al., Phys. Plasmas 24, 122702 (2017)
Max Planck Princeton Center Workshop, 2018 Intrinsic rotation mechanisms
Careful geometric analysis shows that energy transfer from the electrostatic potential to ion parallel flows breaks symmetry in the fully nonlinear toroidal momen- tum transport equation, causing countercurrent rotation peaking without applied torque. Numerical simulation with the flux-tube code GKW gives first quantitative insights.
Max Planck Princeton Center Workshop, 2018 Insights into dynamics of reconnection by comparison of scaled laboratory and space experiments
W. Fox
[#s697,
23 Apr 2018]
Max Planck Princeton Center Workshop, 2018 Magnetic reconnection experiments on DIII-D Turbulence
W. Fox
[#s698,
23 Apr 2018]
Max Planck Princeton Center Workshop, 2018 Initial simulations of tokamak edge turbulence with the Gkeyll Discontinuous Galerkin code
G. Hammett
[#s700,
23 Apr 2018]
Max Planck Princeton Center Workshop, 2018 Energetic-particle-induced geodesic acoustic modes and their role in regulating micro-turbulence
M. Schneller
[#s702,
23 Apr 2018]
Swarthmore Plasma science - From laboratory-fusion to astrophysical plasmas
Our universe is immersed in magnetized plasma, electrically conducting ionized gas.
Some of the most fundamental and long-standing astrophysical problems, such as the magnetization of the universe, collimation of astrophysical jets, the accretion process and transport in astrophysical disks (surrounding e.g. black holes) and their coronas can only be explored through plasma physics.
Our sun as a natural laboratory for plasma physics provides inspiring as well as challenging problems, including its dynamo cycles, heating, and the replication of its core reaction, fusion energy, on earth in a lab.
There is an abundance of observational/experimental data emerging from natural phenomena of space and astrophysical plasmas, as well as laboratory plasma experiments, for plasma physicists to explore.
I will review some of these topics, in particular magnetic reconnection, the rearrangement of the magnetic field topology of plasmas, which energizes many processes in nature and has been shown to also be critical in the nonlinear dynamics of many processes in toroidal fusion plasmas.
Using global simulations, I will demonstrate the instrumental role of magnetic reconnection, which enables an innovative technique for producing current in fusion plasmas.
Brookhaven National Laboratory Plasma science - From laboratory-fusion to astrophysical plasmas
Our universe is immersed in magnetized plasma, electrically conducting ionized gas.
Some of the most fundamental and long-standing astrophysical problems, such as the magnetization of the universe, collimation of astrophysical jets, the accretion process and transport in astrophysical disks (surrounding e.g. black holes) and their coronas can only be explored through plasma physics.
Our sun as a natural laboratory for plasma physics provides inspiring as well as challenging problems, including its dynamo cycles, heating, and the replication of its core reaction, fusion energy, on earth in a lab.
There is an abundance of observational/experimental data emerging from natural phenomena of space and astrophysical plasmas, as well as laboratory plasma experiments, for plasma physicists to explore.
I will review some of these topics, in particular magnetic reconnection, the rearrangement of the magnetic field topology of plasmas, which energizes many processes in nature and has been shown to also be critical in the nonlinear dynamics of many processes in toroidal fusion plasmas.
Using global simulations, I will demonstrate the instrumental role of magnetic reconnection, which enables an innovative technique for producing current in fusion plasmas.
NASA Goddard Space Flight Center Laboratory Studies of Magnetized Collisionless Shocks
Collisionless shocks are ubiquitous in space and astrophysical systems, and the class of supercritical shocks is of particular importance due to their role in accelerating particles to high energies.
While these shocks have been traditionally studied by spacecraft and remote sensing observations, laboratory experiments can provide reproducible and multi-dimensional datasets that provide complementary understanding of the underlying microphysics.
We present experiments undertaken on the OMEGA and OMEGA EP laser facilities that show the formation and evolution of high-Mach number collisionless shocks created through the interaction of a laser-driven magnetic piston and magnetized ambient plasma [1,2].
Through time-resolved, 2-D imaging we observe large density and magnetic compressions that propagate at an Alfvénic Mach number MA ~ 15 and that occur over ion kinetic length scales.
Additional shock structure and electron and ion heating are observed with optical Thomson scattering, which is also used to characterize the initial ambient plasma.
Particle-in-cell simulations constrained by experimental data further detail the shock formation and separate dynamics of the multi-ion-species ambient plasma.
The results show that the shocks form on timescales as fast as one gyroperiod, aided by the efficient coupling of energy, and the generation of a magnetic barrier, between the piston and ambient ions.
The development of this experimental platform opens the way for controlled laboratory investigations of high-Mach-number collisionless shocks, including mechanisms of shock heating and particle acceleration.
[1] D. B. Schaffer, W. Fox et al., Phys. Rev. Lett. 119, 025001 (2017)
[2] D. B. Schaffer, W. Fox et al., Phys. Plasmas 24, 122702 (2017)
Committee on a Strategic Plan for U.S. Burning Plasma Research, Princeton Trying for Upside Potential in Controlling Fusion
MIT PSFC Seminar Discontinuous Galerkin methods, positivity, exponential reconstruction, and initial simulations of gyrokinetic turbulence in a model tokamak scrape-off-layer
Many space and astrophysical plasmas are so hot and diffuse that they cannot be rigorously described as fluids.
These include the solar wind, low-luminosity black-hole accretion flows, and the intracluster medium of galaxy clusters. Currently, the lack of a rigorous theory for the plasma microphysics in these systems is a formidable obstacle to answering several fundamental questions in space and astrophysics.
Much of the difficulty arises from the freedom in a weakly collisional plasma for the particle distribution function to be anisotropic in velocity space, as well as from the shaping of such temperature anisotropy by magnetic fields.
In this talk, I will present hybrid-kinetic simulations of waves, turbulence, and magnetorotationally driven transport in collisionless, high-beta plasmas, which address how Larmor-scale kinetic instabilities are driven by and ultimately regulate temperature anisotropy, and how this regulation in turn feeds back on the macroscale dynamics.
Gyrokinetic theory will also be used to explore how temperature anisotropy affects Alfvénic turbulence and ion versus electron heating in high-beta plasmas.
Los Alamos National Laboratory (LANL) Metriplectic dynamics
Magneto-Fluid Dynamics Seminar, Courant Institute for Mathematical Sciences, New York U. Does a photon have a linear polarizability and why does it matter?
A photon (phonon, plasmon, etc) has a linear polarizability. To see this and to understand why this matters, it helps to set aside Maxwell's equations and quantum mechanics per se and start with the following basic physics. Suppose a rapidly oscillating wave field in a weakly inhomogeneous linear medium. Assuming the dispersion operator for the wave field is known, a reduced operator can be defined that governs just the wave envelope. Using the Weyl calculus, an asymptotic approximation of the reduced operator can then be constructed to any power n in the geometrical-optics (GO) parameter. The corresponding truncations yield GO (n = 0), extended GO (n = 1), and quasioptics (n = 2). Notably, an accurate formulation of the latter for inhomogeneous media has only been given recently [unpublished]. But there is even more to this approach. For waves propagating in modulated media (i.e., interacting with other waves), a reduced operator can be derived similarly for Floquet envelopes. The modulation-dependent term in this operator serves as the ponderomotive Hamiltonian of a wave, and its derivative with respect to the (loosely speaking) modulation intensity serves as the wave polarizability [Phys. Rev. A 95, 032114 (2017)]. When applied to charged particles treated as quantum waves, this gives the conventional particle polarizability. Conversely, when applied to classical waves, this defines an effective linear polarizability of a photon (phonon, plasmon, etc). Using this concept, one can interpret modulational dynamics (MD) of nonlinear electromagnetic waves as linear dispersive dynamics of a polarizable photon gas. This significantly simplifies calculations of MD and makes them less error-prone than the standard Maxwell--Vlasov approach [J. Plasma Phys. 83, 905830201 (2017)]. Even more generally, quasilinear MD of all wave ensembles are governed by Wigner--Moyal-type equations that are identical up to a (generally non-Hermitian) Hamiltonian. Then, for example, the modulational instability in the nonlinear Schrodinger equation, the zonostrophic instability of drift-wave turbulence, and the standard two-stream collisionless-plasma instability formally appear as essentially the same effect. In a broader context, elaborating on this approach seems promising for studying inhomogeneous wave turbulence.
Magneto-Fluid Dynamics Seminar, Courant Institute for Mathematical Sciences, New York U. Metriplectic dynamics -- a framework for plasma kinetic theory and numerics
In dissipationless systems, Hamiltonian mechanics, culminating in a Poisson bracket and a Hamiltonian, provides a convenient framework for both theoretical and numerical studies. In systems that obey both the First and the Second Law of Thermodynamics, the dissipationless dynamics can often be extended with a symmetric bracket and an entropy to account for the dissipation. The resulting, so-called metriplectic framework captures many interesting models, including the Navier-Stokes equations, non-isothermal kinetic polymer models, and the Vlasov-Maxwell-Landau model used in plasma physics. In this talk, we review the basic principles of metriplectic dynamics and discuss some prominent methods for time discretization. We focus on the Vlasov-Maxwell-Landau model and, especially, on the Landau collision operator for which a genuine metriplectic integrator is demonstrated. The gyrokinetic version of the Vlasov-Maxwell-Landau system is briefly visited.
ITER Organization Gyrokinetic Simulation of Pedestal and SOL Transport in Present Experiments and ITER
10th Plasma Kinetics Working Group Meeting, Wolfgang Pauli Institute, Vienna Progress in continuum gyrokinetic simulations of edge turbulence, in a helical model SOL
Magneto-Fluid Dynamics Seminar, Courant Institute for Mathematical Sciences, New York U. Variational Integration for Ideal Mhd and Formation of Current Singularity
Yao Zhou
[#s542,
14 Feb 2017]
Friday Science Meeting, General Atomics, San Diego Parasitic momentum flux in the tokamak core