September 20

 Philipp Lauber

 IPP, Garching,Germany

 Linear Gyrokinetic Calculations on the Kinetic Properties of Shear Alfven Modes in Tokamak Plasmas

 Seminar will be held on Tuesday, September 20 at 2:15 pm, T 169

September 27

Bill Nevins

 Lawrence Livermore National Lab

Discrete Particle Noise in Particle-in-Cell Simulations of
       Plasma Microturbulence

Seminar will be held on Tuesday, September 27 at 10:45 am, T 169

October 13

Allen Boozer

Columbia University

Magnetic reconnection in non-toroidal plasmas

Tuesday, September 20, 2:15 pm

Tuesday, September 27, 10:45 am

Bill Nevins, Lawrence Livermore National Lab, Livermore, CA

Title: Discrete Particle Noise in Particle-in-Cell Simulations of
       Plasma Microturbulence

Abstract: 

Allen Boozer, Columbia Univesity, New York, NY

Title: Magnetic reconnection in non-toroidal plasmas

Abstract: Magnetic reconnection is a major issue in solar and
astrophysical plasmas. The mathematical result that the evolution of a
magnetic field with only point nulls is always locally ideal limits the
nature of reconnection in non-toroidal plasmas. Here it is shown that the
exponentially increasing separation of neighboring magnetic field lines,
which is generic, tends to produce rapid magnetic reconnection if the
length of the field lines is greater than about 20 times the exponentiation,
or Lyapunov, length.

A copy of Dr. Boozer's seminar presentation is available here.   

H.C. Yee, NASA Ames Research Center, Moffett Field, CA

Title: Adaptive Flow Sensor in High Order Methods for Complex Multiscale Flows

This seminar discusses an adaptive numerical dissipation control
in high order nonlinear filter methods. This nonlinear filter
is very general and can be used in conjunction with spectral,
finite element, finite volume, and finite difference
compact and non-compact spatially central base schemes.
The nonlinear filter method consists of two steps, a divergence-free
preserving base scheme step (not involving the use of approximate
Riemann solvers or flux limiters) and a nonlinear filter step
(usually involving the use of approximate Riemann solvers
and flux limiters). The adaptive filter consists of
automatic detection of different flow features by distinct sensors
to! signal the appropriate type and amount of numerical dissipation
where needed while leaving the rest of the region free of numerical
dissipation contamination. These scheme-independent flow sensors are
capable of distinguishing shocks/shears, flame sheets, turbulent
fluctuations and spurious high-frequency oscillations. In addition,
these sensors are readily available as an improvement over existing
grid adaptation indicators. The flow sensor algorithm is based on
redundant multiresolution wavelets. One of the unique features of the
numerical method is that it is suitable for nearly incompressible to
highly compressible gas dynamics and MHD flows. It is also stable and
accurate for a wide spectrum of flow physics ranging from long time wave
propagation of smooth flows to high speed multiscale turbulent/combustion
flows including strong shock waves.

Informal Talk

Dmytro Sydorenko, University of Saskatchewan in collaboration with A.Smolyakov, I. Kaganovich, and Y. Raitses.

Title: Particle-in-cell simulation of kinetic effects in low-pressure pla smas

Several particle-in-cell codes have been developed for simulations of different plasma devices, such as dielectric wakefield accelerators, inductively coupled plasmas, Hall thrusters. The explicit and implicit schemes have been applied, including the multiscale algorithms and the parallel programming. The emphasis is made on the simulations of plasma-wall interaction in Hall thrusters. The non-Maxwellian electron velocity distribution function is obtained; it is strongly anisotropic, depleted at high energy, and non-monotonic. Secondary electrons form two counter-propagating beams; their propagation is determined by collective effects. It is shown that such modification of the electron velocity distribution function drastically changes the particles and heat losses to walls.

Nuno Loureiro, CMPD, University of Maryland and PPPL

Title: Nonlinear evolution of the tearing mode

The strongly driven (large D') tearing mode is thought to be of
relevance in connection to the sawtooth problem in tokamaks and general
reconnection phenomena in space and astrophysical plasmas.
Although some efforts have been made to analytically describe this
region of parameter space (e.g., Coppi et al. 76, Waelbroeck 89,93), the
large computational requirements for a thorough study have meant that
this regime of the tearing instability has remained largely unstudied.
In this talk, I present recent numerical results on the nonlinear
evolution of the strongly and weakly driven resistive tearing mode. Slab
geometry is adopted and the equations of reduced-MHD (RMHD) are used.
A high-resolution numerical scan of the parameter space (D',eta) shows
that, in general, the tearing mode evolves through five stages:
exponential growth, algebraic growth (Rutherford stage),
X-point collapse followed by current-sheet exponential reconnection
(Sweet--Parker stage), tearing instability of the current sheet
(generation of secondary islands), and saturation. The X-point collapse
occurs at a critical island width that scales as Wc ~ 1/D'. During the
collapse, reconnection proceeds with a rate proportional to eta^{1/2}.
The resulting current sheet becomes unstable if it has a length-to-width
ratio that exceeds a certain critical value. Secondary islands are then
formed, the evolution of which occurs in a self-similar way to the original
perturbation. At low D', the saturation amplitude is shown to be in good
agreement with recent analytic theories. At large D' we show that the saturated
amplitude depends on the existence of a previous collapse.

Norman J. Zabusky, Rutgers University

Title: Overview of Richtmyer-Meshkov flows: From the vortex paradigm to vortex double layers and baroclinic turbulence

Ilya Y. Dodin, Astrophysical Sciences Department, Princeton University

Title: Nonadiabatic Ponderomotive Barrier

A ponderomotive potential is an effective potential seen by a
particle in ac field in average over the fast oscillations. It is not
a true potential though, and, if the ac field is in resonance with
particle natural oscillations, the particle can exhibit irreversible
drift motion [1-3]. A new ponderomotive potential is found for this
case that can capture nonadiabatic dynamics [4]. The particle drift
in this new potential resembles the motion of a quantum object in a
conservative field [5]. Among other applications, these nonadiabatic
potentials can perform selective separation and cooling of plasma
species or drive electric current by asymmetrically transmitting
thermal particles in a preferential direction [1, 2, 6].

[1] N.J. Fisch, J.M. Rax, and I.Y. Dodin, Phys. Rev. Lett. 91, 205004
(2003).
[2] I.Y. Dodin, N.J. Fisch, and J.M. Rax, Phys. Plasmas 11, 5046
(2004).
[3] I.Y. Dodin and N.J. Fisch, J. Plasma Phys. 71, 289 (2005).
[4] I.Y. Dodin and N.J. Fisch, Phys. Lett. A 349, 356 (2006).
[5] I.Y. Dodin and N.J. Fisch, Phys. Rev. Lett. 95, 115001 (2005).
[6] I.Y. Dodin and N.J. Fisch, Phys. Rev. E 72, 046602 (2005).
 

Frank Cheng, National Space Organization

Title: Space Science Program in Taiwan

Taiwan's first phase space program was initiated in 1991 for a 15-year period and its goal is to establish necessary domestic infrastructure and carry out satellite programs. During this period Taiwan has established a satellite integration and test facility and launched two satellite missions (FORMOSAT-1 and FORMOSAT-2) and will launch in March, 2006 the FORMOSAT-3 mission which consists of six micro-satellites. The science objective of these missions will be described. The second phase 15-year space program started in 2004 and the goal is to establish the self-reliant capability in space science and technology for satellite mission. Presently one satellite mission is planned for every 3 to 4 years and sounding rocket experiments are planned for once or twice per year. A dual-purpose satellite mission, ARGO, is now planned for launch in late 2008. International collaboration will be a key element to achieve the second phase program goal.
 

Nuno Loureiro, CMPD, University of Maryland and PPPL

Title: Nonlinear Evolution of the Tearing Mode

The strongly driven (large D') tearing mode is thought to be of relevance in connection to the sawtooth problem in tokamaks and general reconnection phenomena in space and astrophysical plasmas. Although some efforts have been made to analytically describe this region of parameter space (e.g., Coppi et al. 76, Waelbroeck 89,93), the large computational requirements for a thorough study have meant that this regime of the tearing instability has remained largely unstudied.
In this talk, I present recent numerical results on the nonlinear evolution of the strongly and weakly driven resistive tearing mode. Slab geometry is adopted and the equations of reduced-MHD (RMHD) are used. A high-resolution numerical scan of the parameter space (D',eta) shows that, in general, the tearing mode evolves through five stages: exponential growth, algebraic growth (Rutherford stage), X-point collapse followed by current-sheet exponential reconnection (Sweet--Parker stage), tearing instability of the current sheet (generation of secondary islands), and saturation. The X-point collapse occurs at a critical island width that scales as Wc ~ 1/D'. During the collapse, reconnection proceeds with a rate proportional to eta^{1/2}. The resulting current sheet becomes unstable if it has a length-to-width ratio that exceeds a certain critical value. Secondary islands are then formed, the evolution of which occurs in a self-similar way to the original perturbation. At low D', the saturation amplitude is shown to be in good agreement with recent analytic theories. At large D' we show that the saturated amplitude depends on the existence of a previous collapse.
 

This is a repeat of the seminar presented on November 10, by request.
 

Scott Tremaine, Dept. of Astrophysical Science, Princeton University

Title: The long-term stability of planetary systems

The long-term orbital behavior of planetary orbits is the mother
of all problems in nonlinear dynamics, but remains incompletely understood
despite three centuries of study starting with Newton. Understanding this
behavior is central to many issues of planetary science: Why are the
planets so regularly spaced? How has the Earth's orbit evolved throughout
geological history? What determines the properties of the orbits of
extrasolar planets? N-body integrations allow us to follow the motion of
planets reliably for billions of years, and thereby inform us about the
evolution and current properties of planetary systems, and the ultimate
fate of the Earth and other planets.
 

Jerome Lewandowski, Theory Department, Princeton Plasma Physics Lab

Title: Particle-in-cell simulations of electromagnetic microturbulence with fully kinetic ions and electrons
 

A low-noise method suitable for PIC simulations of
electromagnetic drift wave and ITG microturbulence is presented. The
splitting scheme is based on an exact separation between adiabatic and
nonadiabatic responses for each species; such an approach allows for
noise-free, energy-conserving simulations but comes at a cost:
one must repeatedly solve coupled, nonlinear elliptic equations for the
various scalar fields. This apparent numerical difficulty is tackled using
the multigrid method. Simulation results in a simple geometry will be
presented and generalization to toroidal plasmas will be discussed.
 

Bruce Scott, Max-Planck-Institut fuer Plasmaphysik, Euratom Association, Garching, Germany

Title: Energetics in full-f and delta-f gyrokinetic equations

The derivation of the delta-f Vlasov equation starting with
the general gyrokinetic field theory is given. The total-f version with
Hamiltonian structure serves as intermediary. The main delta-f
approximation is linearisation of field polarisation and the parallel
bracket. An energy conserving form is found by applying delta-f
ordering to the spatial derivatives. The conserved quantity is the well
known delta-f free energy, related to the entropy. The conservation
properties are compared to those following from the application of the
Noether theorem to teh total-f model. Although a different energy is
conserved, the field/particle transfer terms are the same.
 

Prateek Sharma, Department of Astrophysical Sciences, Princeton University

Title: Kinetic effects in astrophysical plasmas

Many astrophysical plasmas are macroscopically collisionless,
with mean free path larger than the system size. Examples are low
luminosity accretion disks, x ray clusters, solar wind, etc. In these
cases MHD is not a good approximation. I will describe the kinetic MHD
approximation (which is valid for scales larger than the gyroradius and
frequencies smaller than the gyrofrequency, Kulsrud 1983 in Handbook of
plasma physics) for collisionless plasmas and Landau closure (Snyder et
al. Phys. Plasmas 1997, 4, 3974) for anisotropic heat fluxes. I'll discuss
the effects of anisotropic transport on MHD instabilities.
Microinstabilities (mirror, firehose, ion-cyclotron, etc.) are driven by
pressure anisotropy that arises as a natural consequence of stretching and
shearing of the field lines. I'll discuss how collisionless effects can be
important for transport in low luminosity accretion disks and x ray
clusters.
 

Roman Kolesnikov, PPPL

Title: High frequency gyrokinetic particle simulation

This presentation is a part of the ongoing OASCR/MICS research on
Multi-Scale Gyrokinetics (MSG) at PPPL. The purpose of this project is to
develop numerical algorithms for solving gyrokinetic Vlasov-Maxwell
equations which can potentially handle several orders of magnitude in both time and space and can eventually be ported into the global toroidal codes, such as GTC, to simulate kinetic effects in realistic fusion plasmas. The focus of the present talk is on the development of the algorithm which allows one to simulate high frequency dynamics based on the gyrokinetic formalism assuming only that the ion gyroradius is smaller than the scale length of the ambient magnetic field. As an example, we
will present a simple case of ion cyclotron instability simulation based on the new algorithm using a two-dimensional particle-in-cell code in simple slab geometry in the
electrostatic limit. The linear and nonlinear properties of the instabilities obtained from the high frequency gyrokinetic code will be presented. To illustrate the
nonlinear mechanisms introduced into the gyrokinetic formalism by the
gyrophase dependent part of the dynamics, and their importance for
quasi-linear ion perpendicular heating, we will make comparisons with the results from a regular Lorentz-force code. Discussions of the possible advantages this new algorithm in comparisons with other approaches used for studying RF wave-plasma interactions will be given.
 

Zhe Gao, Department of Engineering Physics Tsinghua University

Title: Multiple Eigenmodes of Geodesic Acoustic Mode in Collisionless
Plasmas
 

Both the low/zero frequency zonal flow (ZF) and higher frequency
oscillating ZF, so called the geodesic acoustic mode (GAM), first and
foremost, are plasma eigenmodes. The progress of the experimental
research on multiple GAM oscillations stimulates the research on various
types of branches in the family of ZFs. In the work, we employ a linear
gyrokinetic model in collisionless toroidal plasmas with an
electrostatic potential rigid constant around a magnetic surface, and
then the plasma response is analytically solved for plasma with circular
cross section and large aspect ratio. Besides the trivial zero frequency
solution and the standard GAM solution, a branch of low frequency mode
and a series of ISW-like modes are identified. The ISW-like modes has a
frequency spectrum roughly with a progression of sqrt(n) times the
transit frequency and strongly damped. The low frequency eigenmode has a
rigid zero frequency for low q but oscillates with a finite frequency
for higher q, and it relaxes on time scaling with the order of transit
frequency.