Mar. 29, 2007

Dong-Hong Lee

Kyung Hee University, Korea

Invariant imbedding theory of mode conversion in MHD and plasma waves

Mar. 9, 2007

Andrew J. Schmitt

Laser Plasma Branch: Plasma Physics Division: Naval Research Lab

Progress in the physics behind direct-drive laser fusion energy

Fast Particle Interaction With Waves In Fusion Plasmas

Fluctuations and discrete particle noise in gyrokinetic simulation of drift waves

Date/Time: December 6th (Thursday) 10:45am

Location: Theory Seminar Room (T169)

Speaker: Wei-li Lee, Princeton Plasma Physics Laboratory

Title: Steady State Turbulence Simulations

Abstract:

The nonlinear physics associated steady ion temperature gradient (ITG) drift turbulence using global delta-f gyrokinetic particle simulation is the focus of this talk. The relative importance between the nonlinearly generated zonal flows and the velocity space nonlinearity is found to be dependent on the size of the simulation plasma due to the glabal nature of the flow in the presence of the velocity space nonlinearity. The simulation has also shown that profile relaxation in the simulation has negligible effect on the steady state turbulence. Instead, the nonlinear fluctuations and the ion thermal diffusivity are closely related to the zeroth-order plasma inhomogeneities. Understanding these properties of the steady state turbulence is essential for the design of the algorithms for the multiscale integrated simulation for the Fusion Simulation Project (FSP), which we will discuss.

Date/Time: Monday November 19th @ 9:30am

Location: Theory Seminar Room (T169)

Speaker: Costanza Zucca, CRPP- EPFL, Association EURATOM

Title: Effects of local ECCD driven by the optimized Equatorial and Upper EC Launchers on ITER

Abstract:
The present ITER base-line design has the EC launchers providing only co-ECCD. A variant of the EC system was recently proposed to enlarge the physics programs covered by the Upper (UL) and Equatorial (EL) Launchers. This study aims to provide the potential range of the q profile control achievable by this optimization, including the possibility to drive cnt-ECCD and central ECH. Since the EL can only drive co-ECCD, if ECH power is needed to assist the L-H transition during ramp-up, it can have detrimental effects on the final profiles, such as removing the reverse shear. Cnt-ECCD offers greater control of the plasma current density and provides, when balanced with co-ECCD, pure ECH with no net driven current. The performance of the EL in tailoring the q profile by adding co-/cnt-ECCD is analyzed. Effects of current drive and deposition width on sawtooth control by UL are also discussed. The modeling is carried out with both equilibrium and transport codes.

Date/Time: Monday November 19th @ 11:00am

Location: Theory Seminar Room (T169)

Speaker: Sebastien Jolliet, CRPP-EPFL, Association EURATOM

Title: Nonlinear global gyrokinetic PIC simulations of collisionless TEM turbulence

Abstract:
Micro-instabilities, such as Ion Temperature Gradient modes (ITG) and Collisionless Trapped Electrons Modes (CTEM), are commonly held responsible for anomalous transport observed in tokamaks. While there have been a wide range of nonlinear studies on ITG turbulence, very little is known about the nonlinear physics of CTEM. This work presents the first linear and nonlinear simulations of ITG-CTEM turbulence performed with the global PIC code ORB5 [1]. A linear benchmark of ORB5 against other gyrokinetic codes will be shown. The implementation of a nonlinear CTEM model, where special care is put on detrapped electrons, will be presented. The simulations results will focus on nonlinear phenomena including detrapping, toroidal coupling, zonal flows, profiles evolution and heat transport.

Date/Time: November 8th (Thursday) 10:45am

Location: Theory Seminar Room (T169)

Speaker: Guoyong Fu, Princeton Plasma Physics Laboratory

Title: Nonlinear Hybrid Simulations of Multiple Energetic Particle driven Alfven Modes in Toroidal Plasmas

Abstract:

Understanding of nonlinear behavior of energetic particle-driven instabilities in tokamaks is of fundamental importance for burning plasmas. Here we report recent advances in self-consistent nonlinear simulations of fast beam ion-driven Alfven modes in NSTX and DIII-D using the extended MHD code M3D[1]. In the hybrid model, the thermal electrons and ions are treated as an ideal fluid while the energetic species is described by either drift-kinetic equation or gyrokinetic equation. The effects of energetic particles are coupled to the MHD equations via the stress tensor term in the momentum equation. The hybrid code has been recently applied to study nonlinear dynamics of fishbone instability [2]. The code was also used to simulate nonlinear evolution of a single beam-driven TAE mode in NSTX. The result showed a weak frequency chirping about 20% consistent with experimental measurement [3]. In this work, we use the M3D code to simulate beam ion driven Alfven modes in NSTX plasmas with multiple unstable Alfven modes. It is found that mode saturation level of each mode can be enhanced significantly by presence of other unstable modes indicating strong nonlinear interaction between different modes. It is also found that a linearly stable n=2 mode can be nonlinearly driven by an n=1 mode at significant mode amplitude. These results together with simulation results of beam ion-driven Alfven modes in DIII-D reversed shear plasmas [4] will be presented.

Date: Thursday, Aug. 30, 2007

Time: 10:45am

Room: T169

Speaker: Bhimsen Shivamoggi,

Affliation:University of Central Florida

Title: Current-sheet Formation Near a Hyperbolic Magnetic Neutral Line in MHD

Abstract:

Current-sheet formation near a hyperbolic magnetic neutral line in
MHD is investigated by including the effects of
* sweeping
* shearing
of the magnetic field lines by the plasma flow as well as density variation
of the plasma. Exact solutions of the MHD equations appropriate for these
situations are given. This problem is shown to possess a finite-time
singularity for the incompressible plasma case and a whole new finite-time singularity for the variable-density plasma case. Theoretical results are compared with laboratory experiments.

Date: Wednesday, Aug. 1, 2007

Time: 10:45am

Room: T169

Speaker: F.M.Poli

Affliation:RPP-EPFL. Association Euratom-Confederation Suisse, CH-1015 Lausanne, Switzerland.

Title: Electrostatic instabilities and turbulence in a toroidal magnetized plasma

Abstract:

Basic plasma physics experiments in toroidal geometry offer the possibility of investigating the properties of low frequency instabilities in well-diagnosed scenarios. The development of instabilities, from a linear to a nonlinear character, and the related turbulence and its implications for anomalous particle transport, are investigated on TORPEX, a toroidal device with magnetic field ≤100 mT. Plasmas from noble gases are produced and sustained by low field side injection of microwaves (P£20 kW) with f=2.45 GHz, in the EC frequency range. Density and potential fluctuations are measured over the whole plasma cross-section, and their properties investigated for a large range of variation of control parameters, including the ion mass, the neutral gas pressure and the vertical magnetic field. For the different experimental scenarios, the maximum of fluctuations is measured where the pressure gradient and the magnetic field gradient are co-linear, indicating that the curvature of the magnetic field lines has an important role in the destabilization of the waves. The power spectrum is dominated by electrostatic fluctuations with frequencies much lower than the ion cyclotron frequency. Both drift and interchange instabilities develop and propagate on TORPEX, with the stability of both being affected by the curvature of the magnetic field. It is shown that modes of different nature are driven at separate locations over the plasma cross-section and that the wavenumber and frequency spectra, narrow at the location where the instabilities are generated, broaden during convection, suggesting an increase in the degree of turbulence. It is found that nonlinear mode-mode coupling is responsible for the redistribution of spectral energy from the dominant instabilities to other spectral components and that this mechanism is independent of the nature of the instabilities. Nonlinear interactions between the mode and its nonlinearly generated harmonics are responsible for the filling of the spectral regions between harmonics. Later in the development along the convection path, the unstable mode transfers energy to spectral components with significantly larger frequencies. This transfer of energy can be interpreted in the investigated plasma scenarios as a forward cascade in wavenumbers, with transfer of energy from large to small scales.

Date: Friday June 29
Time: 10:45 AM
Room: Theory Seminar

Speaker: Bruce Scott
Affiliation: Max-Planck-Institute for Plasma Physics (Germany)
Title: Finite Gyroradius, Flow Shear, and Trapping Effects on Edge Turbulence

Abstract:

Computations are given for low-frequency electromagnetic turbulence at
tokamak edge parameters. Both gyrofluid and delta-f gyrokinetic models
are used. Correspondence between the gyrofluid and reduced Braginskii
models is clarified: finite gyroradius (FLR) nonlinearities versus
polarization, temperature anisotropy versus viscosity, and dynamic
effects in the heat flux equations.
The basic scaling is studied with control tests against FLR effects, ExB
shear, and magnetic trapping. A comparison to an L-H scaling model is
shown, with nonlinear effects preventing the model's L-H transition
signature. Gyrofluid computations of the full flux surface with a time
dependently self consistent MHD background are used to study global
bursting. Large scale MHD events are studied in light of the ELM
phenomenon in tokamaks.

Date: Thursday June 21
Time: 10:45 AM
Room: Theory Seminar

Speaker: Bruce Scott
Affiliation: Max-Planck-Institute for Plasma Physics (Germany)
Title:

Abstract:

Date: Wednesday 6/6/2007
Time: 10:45 AM
Room: Theory Seminar

Speaker: J.D. Callen
Affiliation: University of Wisconsin
Title: Derivation of paleoclassical key hypothesis

Abstract:

The paleoclassical model of radial electron heat transport in resistive, current-carrying toroidal plasmas is based on a key hypothesis—that electron guiding centers move and diffuse with radially localized annuli of poloidal magnetic flux. This hypothesis is shown to result from transforming the drift-kinetic-equation to poloidal flux coordinates in situations where this flux is governed by a diffusion equation and analyzing the mathematical characteristic curves (guiding center trajectories) of the resultant drift-kinetic equation on the magnetic field diffusion time scale \tau_\eta=a^2/6D_\eta. These effects add a \tau_\eta time-scale Fokker-Planck-type spatial diffusion operator to the drift-kinetic equation

Date: Thursday May 31
Time: 10:45 AM
Room: Theory Seminar

Speaker: Alexey Mishchenko
Affiliation: Max-Planck-Institute for Plasma Physics (Germany)
Title: Many-particle approach to the gyrokinetic theory

Abstract:

PDF Version

Date: Friday, April 27
Time: 10:45 AM
Room: Theory Seminar

Title: Gyrokinetic Equilibrium and Self generated Flows

Speaker: Dr. Guilhem Dif-Pradalier

Affiliation: Association Euratom-CEA, Cadarache, France

Abstract:

A proper choice of the initial state of the plasma is found to be crucial in gyrokinetic simulations where the equilibrium and the fluctuations are resolved simultaneously in a full torus geometry. Recently, the generation of large scale flows has been reported in toroidal geometry whenever the initial conditions depart from an equilibrium solution of the gyrokinetic equation. In the collisionless regime, such flows remain linearly undamped and compete with the onset of turbulence. We analytically derive a precise picture at short times of the spontaneous dynamics of these flows and successfully compare it to 5D gyrokinetic simulations. Firstly, up-down asymmetric Geodesic
Acoustic Modes (GAMs) develop, linearly in time. Then, purely poloidal flows are generated with a quadratic dependance on time, and become prominent. Finally, left-right asymmetric GAMs also develop quadratically in time. The saturation time of such modes is computed analytically, allowing one to estimate the saturation level of these flows. In particular, one finds that the velocity shear induced by such modes can compete with the linear growth rate of the instability at large enough ?, potentially preventing the onset of turbulence. The magnitude of the up-down asymmetric GAMs
and poloidal flows is analytically predicted to scale like 2 ?, whereas the magnitude of the left-right asymmetric GAMs is predicted to scale like 4 ? . These dependencies are well verified in numerical simulations using the GYSELA 5D code. Conversely, when the system is initialised with an equilibrium solution of the gyrokinetic equation, any mismatch between the parallel flow and the vertical charge separation leads to the same kind of large scale electric field, although at reduced magnitude.

Date: Thursday, April 26
Time: 10:45 AM
Room: Theory Seminar

Title: Gyrokinetic Simulation Studies of Plasma Transport in NSTX Experiments

Speaker: Weixing Wang

Affiliation: PPPL

Abstract:

Global gyrokinetic simulations have been carried out to investigate both turbulent and neoclassical transport properties for experiments of axisysmmetric devices. These studies support the experimental observation that the ion transport is at the neoclassical level in the National Spherical Torus Experiment (NSTX). Nonlinear turbulence simulations using the GTC-S code have shown that ion temperature gradient (ITG) driven turbulence has significant fluctuation amplitude, but drives insignificant ion energy transport in NSTX (about the neoclassical level, sometimes even below it). This distinguished feature is in contrast to anomalous transport in other machines, such as DIIID, where ITG turbulence is shown to drive large transport (10 x neoclassical level), even though the mean turbulence fluctuation level for the two discharges are actually comparable. It is also found that self-consistent neoclassical equilibrium EXB flows, as calculated by GTC-Neo, also a global PIC code, can strongly stabilize ITG modes. Ion-ion collisions are shown to enhance ITG driven thermal transport, but not significantly. Also reported are simulations of toroidal momentum transport and anisotropic property of neoclassical equilibrium as well as the recent progress in GTC-S toward application to high-k fluctuations and the electron transport of NSTX discharges.

Date: Thursday, March 29
Time: 10:45 AM
Room: Theory Seminar

Title: Invariant imbedding theory of mode conversion in MHD and plasma waves

Speaker: Prof. Dong-Hun Lee

Affiliation: Department of Astronomy and Space Science, Kyung Hee University, Yongin, Korea

Abstract:
We present a recent study of mode conversion, which
occurs among the various wave modes in inhomogeneous plasmas.
The mode conversion in plasma waves is associated
with resonances, which often appear as singularities in the wave equation.
We suggest that a new approach called the IIM (invariant imbedding method)
enables us to solve the wave equations correctly and accurately
without any theoretical approximations, which becomes important
when the approximations such as WKB or Bremmer series are invalid
at the cutoff or singular regions. We investigate the process of
mode conversion for each resonance in MHD and multi-fluid plasma waves.

Date: Friday , March 9
Time: 10:45 AM
Room: Theory Seminar

Title: Progress in the physics behind direct-drive laser fusion energy

Speaker: Andrew J. Schmitt

Affiliation: Laser Plasma Branch: Plasma Physics Division: Naval Research
Lab

Abstract:
Since it's conception in the early 1970's, direct drive laser fusion
has made enormous progress. In the 1980's, the development of optical
smoothing techniques and the switch to shorter laser wavelengths
increased laser-target coupling and reduced the importance of
laser-plasma instabilities. The 1990's brought increased
understanding of the ablatively-driven Richtmyer-Meshkov and
Rayleigh-Taylor instabilities, and the concept of adiabat-shaping
techniques. Finally, in the last decade, the availability of
radiation hydrocodes running on massively parallel computers have
allowed us to design targets that can produce high gain in the
presence of hydrodynamic instabilities. I will review these
developments, and discuss recent advances in theoretical and
experimental physics done at NRL that brighten the prospects for
laser fusion energy.

Date: Thursday , Feb 15
Time: 10:45 AM
Room: Theory Seminar

Title: Numerical study of linear mode conversion in multi-fluid plasmas

Speaker: Eun-Hwa Kim

Affiliation: School of Physics, University of Sydney, Australia

Abstract:

The standard linear analysis of dispersion equations in homogeneous plasmas yields wave modes that are uncoupled and distinct. However, in inhomogeneous plasmas, the plasma modes are often coupled to each other and no purely single mode exists. For a certain range of frequencies and propagation angles, energy can be transferred linearly from one mode to another with constant frequency via the process of linear mode conversion (LMC). To study LMC in diverse plasma environments, a three-dimensional multi-fluid simulation code has been developed. This time dependent model can fully accommodate the effects of multi-ion species and electrons and enables us to study a wide range of fluid waves from Langmuir oscillations to Alfven waves in an arbitrarily inhomogeneous system. The LMC between two different wave modes are investigated, in the order of ascending frequencies, at the Alfven resonance, at the Buchsbaum resonance, at the perpendicular ion cyclotron resonance, and at the plasma frequency. The simulation study shows that (1) LMC from right- to left-handed polarized waves occurs at the Alfven resonance. (2) In multi-fluid plasmas, the energy of the electromagnetic wave is transferred to the electrostatic wave at the Buchsbaum resonance. (3) At the ion-ion hybrid resonance, the wave energy flows from the left- to right-handed polarized waves when the incoming wave has a small incidence angle. (4) For warm magnetized plasmas, extraordinary waves can be generated by LMC from Langmuir waves.

Date: Thursday , Feb 1
Time: 10:45 AM
Room: Theory Seminar

Speaker: Stuart Hudson

Affiliation: PPPL

Title: The effect of cantori on transport in chaotic magnetic fields

Abstract:

Cantori are the invariant sets remaining after destruction of the KAM surfaces, and it is well known that they create partial barriers to Hamiltonian transport in chaotic systems. Cantori have primarily been studied in the context of area-preserving maps. To construct cantori for continuous time, magnetic-field line flows, Lagrangian variational integration techniques are applied. Combined with an iterative Newton method, this approach leads to a numerically efficient procedure, that is relatively robust to chaos, for calculating the high-order periodic orbits that approximate cantori. Part 2 of the talk shall demonstrate that cantori have an important effect in diffusive systems. To show this, the advection-diffusion equation is solved numerically, for a chaotic flow, using a discrete-time, finite-difference method in curvilinear coordinates. There is a clear relationship between the invariant sets of the flow, such as the cantori and unstable manifolds, and the steady state solutions.

Date: Thursday , Jan 25
Time: 11:00 AM
Room: Theory Seminar

Speaker: Annick Pouquet

Affiliation: Geophysical Turbulence Program, NCAR

Title: Nonlocality of nonlinear transfer in hydrodynamic and in MHD
turbulence and the formation of small-scale structures

Abstract:

Direct numerical simulations (DNS) of three-dimensional Navier-Stokes and
magnetohydrodynamic (MHD) turbulence are analyzed to study the degree to which nonlinear terms are nonlocal, i.e. involving widely separated scales. A sharp Fourier filter is used, and both decaying and forced flows are studied, with periodic boundary conditions. In the fluid case, roughly 20% of interactions
correspond to the small scales exchanging energy with the forcing scale of
the flow, leading to a slow recovery of symmetries in the small scales and giving credence to models involving entrainment by a large-scale flow (Phys. Rev. Lett. 95, 264503, 2005; Phys. Rev. E 74, 056320, 2006). A model extending the Kolmogorov (1941) phenomenology is shown to be compatible with these results,
leading as well to a E(k)~k^(-5/3) energy spectrum. In MHD, the kinetic and magnetic energy transfer itself has strong non-local components (Phys.
Rev. E 72, 046301 and 046302, 2005), with the implication that, as soon as
one exits the linear phase of exponential growth of small scales in the form of vorticity and current sheets, a plethora of structures form, with a self-similar in time growth of the maxima of current and vorticity ~t^3, with a k^(-3) energy spectrum at those early times, and with, later on, a constant rate of energy
dissipation (Phys. Rev. Lett. 97, 244503, 2006). The transfer of magnetic
helicity, which plays a significant role in the dynamo process at the origin of planetary and stellar magnetic fields, can be similarly analyzed as well (ApJ, 640 335-343, 2006). These results will be illustrated on several flows (Taylor-Green, Beltrami (ABC), Orszag-Tang, and ABC plus random fluctuations in the small scales), up to grid resolutions of 1536^3 points in MHD. In that latter case, we also show that the current and vorticity sheets are spatially co-located and that, at the highest resolution, instabilities develop leading to roll-up of the sheets whereas at lower Reynolds numbers, the sheets simply fold after having been stretched. The nature of those structures will be discussed.

Date: Thursday, Jan 11
Time: 10:45 AM
Room: Theory Seminar

Speaker: Leonid E. Zakharov
Affiliation: PPPL
Title: Equilibrium Spline Interface (ESI) for magnetic confinement codes

Abstract:

A compact and comprehensive interface of magneto-hydrodynamic (MHD)
equilibrium codes and gyro-kinetic, particle orbit, MHD stability, and
transport codes is presented. Its irreducible set of equilibrium data
consists of four 2- or 3-D functions of coordinates and four 1-D radial profiles together with their first derivatives. The C reconstruction routines, accessible also from Fortran, allow to calculate basis functions and their first derivatives at any position inside the plasma. After this all vector fields and geometric
coefficients required for above mentioned types of codes can be calculated using only algebraic operations with no further interpolation or differentiation.

Date: Thursday, Jan 4
Time: 10:45 AM
Room: Theory Seminar

Speaker: Yas Nishimura

Affiliation: UC-Irvine

Title: Shear Alfven wave studies in global gyrokinetic simulation

Abstract:

Electromagnetic gyrokinetic simulation in toroidal geometry is developed
based on a fluid-kinetic hybrid electron model. The Alfven wave
propagation in a fully global gyrokinetic particle simulation is
investigated. In the long wave length magnetohydrodynamic (MHD) limit,
shear Alfven wave oscillation, continuum damping, and the appearance of
the frequency gap in toroidal geometries are studied. The wave propagation
across the magnetic field (the kinetic Alfven wave) is
examined by comparing the simulation results with the theoretical
dispersion relation. Finite-beta effects on the ion temperature gradient
(ITG) mode and the onset of kinetic are demonstrated.

Date: Tuesday Dec 12
Time: 10:45 AM
Room: Theory Seminar

Speaker: Boris N. Breizman

Affiliation: Institute for Fusion Studies, The University of Texas, Austin, Texas 78712
Title: Fast Particle Interaction With Waves In Fusion Plasmas

Abstract:
There are two well-known motivations for theoretical studies of fast particle interaction with waves in magnetic confinement devices. One of them is the challenge of avoiding strong collective losses of alpha particles and beam ions in future burning plasma experiments. The other one is the compelling need to quantitatively interpret the large amount of experimental data from JET, TFTR, JT-60U, DIII-D, and other machines. The second motivation involves unique diagnostic opportunities offered by MHD-spectroscopy. This talk discusses how the present theory responds to the stated challenges and what theoretical and computational advances are required to address the outstanding problems. More specifically, the talk deals with the following topics: predictive capabilities of linear theory and simulations; theory of Alfvén cascades; diagnostic opportunities based on linear and nonlinear properties of unstable modes; interplay of kinetic and fluid nonlinearities; fast chirping phenomena for non-perturbative modes; and global transport of fast particles. Recent results are presented on some of the listed topics but the main goal is to identify critical issues for future work.

Date: Thursday, Nov 30
Time: 10:45 AM
Room: Theory Seminar

Speaker: Tom Jenkins
Affiliation: Department of Astrophysical Sciences, Princeton University

Title: Fluctuations and discrete particle noise in gyrokinetic
simulation of drift waves

Abstract:
The relevance of the gyrokinetic fluctuation-dissipation theorem (FDT)
to marginally stable nonequilibrium states of the gyrokinetic plasma is
explored, with particular focus being given to the contribution of
weakly damped normal modes to the fluctuation spectrum. It is found
that the fluctuation energy carried in these normal modes exhibits the
proper scaling with particle count (as predicted by the FDT in thermal
equilibrium) even in the presence of drift waves which grow linearly and
attain a nonlinearly saturated steady state. This favorable scaling is
preserved, and the saturation amplitude of the drift wave unaffected,
for parameter regimes in which the normal modes become strongly damped and introduce a broad spectrum of discreteness-induced background noise in frequency space. The relationship of the present work to the more general issue of discrete particle noise in particle-in-cell simulations is discussed.

Date: Thursday, November 9
Time: 10:45 AM
Room: Theory Seminar

Speaker: Gianluca Spizzo

Affiliation: RFX Padova
Title: Chaos generated pinch effect

Abstract:
The pinch term describing particle transport in a toroidal plasma
confinement device is shown to result naturally from magnetic
chaos. As such, this term in the transport equation does not
describe a motion of particles in opposition to the density
gradient, but it represents a non diffusive character of the
transport. The effect is illustrated by numerical modelling of the
magnetic structure and associated particle transport. The results
are compared with data coming from the reversed field pinch
experiment at the Consorzio RFX, Padova.