**Collisionless Damping of Perpendicular Magnetosonic
Waves in a Two-Ion-Species Plasma**

Daiju Dogen, Mieko Toida, and Yukiharu Ohsawa

**Abstract**

Propagation of finite-amplitude magnetosonic waves in a collisionless plasma containing two ion species is studied with a one-dimensional, fully electromagnetic code based on a three-fluid model. It is found that perpendicular magnetosonic waves are damped in a two-ion-species plasma; a magnetosonic pulse accelerates heavy ions in the direction parallel to the wave front, which results in the excitation of a longer wavelength perturbation behind the pulse. The damping due to the energy transfer from the original pulse to the longer wavelength perturbation occurs even if the plasma is collisionless and the pulse amplitude is small. The theoretically obtained damping rate is in agreement with the simulation result.

**Nonlinear m=1 mode and fast reconnection in collisional
plasmas**

A.Y. Aydemir

**Abstract**

Time evolution of the m=1 resistive kink mode is shown to be comprised of two exponential growth phases separated by a transition period during which the growth becomes temporarily algebraic. A modified Sweet-Parker model that takes into account some of the changes in the geometry of the core plasma and the growing island is offered to explain the departure from the algebraic growth of the early nonlinear phase.

**Simulation Studies of Acceleration of Heavy Ions and
their Elemental Compositions**

Mieko Toida and Yukiharu Ohsawa

**Abstract**

By using a one-dimensional, electromagnetic particle simulation code with full ion and electron dynamics, we have studied the acceleration of heavy ions by a nonlinear magnetosonic wave in a multi-ion-species plasma. First, we describe the mechanism of heavy ion acceleration by magnetosonic waves. We then investigate this by particle simulations. The simulation plasma contains four ion species: H, He, O, and Fe. The number density of He is taken to be 10% of that of H, and those of O and Fe are much lower. Simulations confirm that, as in a single-ion-species plasma, some of the hydrogens can be accelerated by the longitudinal electric field formed in the wave. Furthermore, they show that magnetosonic waves can accelerate all the particles of all the heavy species (He, O, and Fe) by a different mechanism, i.e., by the transverse electric field. The maximum speeds of the heavy species are about the same, of the order of the wave propagation speed. These are in good agreement with theoretical prediction. These results indicate that, if high-energy ions are produced in the solar corona through these mechanisms, the elemental compositions of these heavy ions can be similar to that of the background plasma, i.e., the corona.

**Collisionless electron heating in inductively coupled
discharges**

K. C. Shaing and A. Y. Aydemir

**Abstract**

A kinetic theory of collisionless electron heating is developed for inductively coupled discharges with a finite height L. The novel effect associated with the finite-length system is the resonance between the bounce motion of the electrons and the wave frequency, leading to enhanced heating. The theory is in agreement with results of particle simulations.

**Evolution of Toroidal Alfven Eigenmode Instability
in TFTR**

Wong, Majeski, Petrov, Rogers, Schilling, Wilson, Berk, Breizman, Pekker, and Wong

**Abstract**

The nonlinear behavior of the Toroidal Alfv\'en Eigenmode (TAE) driven unstable by energetic ions in the Tokamak Fusion Test Reactor (TFTR) [Phys. Plasmas 1, 1560 (1994)] is studied. The evolution of instabilities can take on several scenarios: a single mode or several modes can be driven unstable at the same time, the spectrum can be steady or pulsating and there can be negligible or anomalous loss associated with the instability. This paper presents a comparison between experimental results and recently developed nonlinear theory. Many features observed in experiment are compatible with the consequences of the nonlinear theory. Examples include the structure of the saturated pulse that emerges from the onset of instability of a single mode, and the decrease, but persistence of, TAE signals when the applied rf power is reduced or shut off.

**On the theory of magnetic field generation by relativistically
strong laser radiation**

V.I. Berezhiani, S.M. Mahajan, and N.L. Shatashvili

**Abstract**

We consider the interaction of subpicosecond relativistically strong short laser pulses with an underdense cold unmagnetized electron plasma. It is shown that the strong plasma inhomogeneity caused by laser pulses results in the generation of a low frequency (quasistatic) magnetic field. Since the electron density distribution is determined completely by the pump wave intensity, the generated magnetic field is negligibly small for nonrelativistic laser pulses but increases rapidly in the ultrarelativistic case. Due to the possibility of electron cavitation (complete expulsion of electrons from the central region) for narrow and intense beams, the increase in the generated magnetic field slows down as the beam intensity is increased. The structure of the magnetic field closely resembles that of the field produced by a solenoid; the field is maximum and uniform in the cavitation region, then it falls, changes polarity and vanishes. In extremely dense plasmas, highly intense laser pulses in the self-channeling regime can generate magnetic fields approximately 100 MG and greater.

**Turbulent Particle Transport in Tokamak Plasmas with
Impurities**

X.Y. Fu, J.Q. Dong, W. Horton, C.T. Ying, and G.J. Liu

**Abstract**

The turbulence driven by the ion temperature gradient, the mass shear-flow parallel to the magnetic field, and the impurity ion density gradient in confined plasmas is studied in a sheared slab magnetic configuration. The turbulence drive from the temperature gradient and parallel shear-flow of the majority ion component is shown to be enhanced by the shear-flow and negative density gradient of the impurity ions. The particle diffusion induced by the turbulence is obtained within the framework of quasilinear fluid theory. Optimal transport parameters for an inward `pinch' of the majority ions and the outward flow of the impurity ions are determined. The corresponding effective diffusion coefficients that include the pinch effects are computed. Correlations with tokamak experimental observations such as an isotope scaling of plasma confinement time are discussed.

**High-mode-number ballooning modes in a heliotron/torsatron
system: II. Stability**

N. Nakajima

**Abstract**

As described in the companion paper [N. Nakajima, Phys. Plasmas (1996)],
in heliotron/torsatron systems that have a large Shafranov shift, the local
magnetic shear is found to have no stabilizing effect on high-mode-number
ballooning modes at the outer side of the torus, even in the region where
the global shear is stellarator-like in nature. The disappearance of this
stabilization, in combination with the compression of the flux surfaces
at the outer side of the torus, leads at relatively low values of the plasma
pressure to significant modifications of the stabilizing effect due to
magnetic field-line bending on high-mode-number ballooning modes---specifically,
that the field-line bending stabilization can be remarkably suppressed
or enhanced. In an equilibrium that is slightly Mercier-unstable or completely
Mercier-stable due to peaked pressure profiles, such as those used in standard
stability calculations or observed in experiments on the Compact Helical
System [S. Okamura, et al., Nucl. Fusion 35, 283 (1995)], high-mode-number
ballooning modes are destabilized due to these modified stability effects,
with their eigenfunctions highly localized along the field line. Highly
localized mode structures such as these cause the ballooning mode eigenvalues
w^{2}
to have a strong field line dependence (i.e., alpha-variation) through
the strong dependence of the local magnetic curvature, such that the level
surfaces of w^{2}(y,q_{k},
a)(less
than 0) become spheroids in (y,q_{k},
a)
space, where y labels flux surfaces and q_{k}
is the radial wavenumber. Because the spheroidal level surfaces for unstable
eigenvalues are surrounded by level surfaces for stable eigenvalues of
high-mode-number toroidal Alfven eigenmodes, those high-mode-number ballooning
modes never lead to low-mode-number modes. In configuration space, these
high-mode-number modes are localized in a single toroidal pitch of the
helical coils, and hence they may experience substantial stabilization
due to finite Larmor radius effects.

**High-mode-number ballooning modes in a heliotron/torsatron
system: I. Local magnetic shear**

N. Nakajima

**Abstract**

The characteristics of the local magnetic shear, a quantity associated
with high-mode-number ballooning mode stability, are considered in heliotron/torsatron
devices that have a large Shafranov shift. The local magnetic shear is
shown to vanish even in the stellarator-like region in which the global
magnetic shear
*s~2 d*lni/*d*lny}
(i is the global rotational transform and 2py
is the toroidal flux) is positive. The reason for this is that the degree
of the local compression of the poloidal magnetic field on the outer side
of the torus, which maintains the toroidal force balance, is reduced in
the stellarator-like region of global magnetic shear because the global
rotational transform in heliotron/torsatron systems is a radially increasing
function. This vanishing of the local magnetic shear is a universal property
in heliotron/torsatron systems with a large Shafranov shift since it results
from toroidal force balance in the stellarator-like global shear regime
that is inherent to such systems.

**IFSR-748**

**An Experimental Demonstration of the Laser Wakefield
"Photon Accelerator": Longitudinal Interferometric Diagnostics for Plasma-Based
Accelerators - DISSERTATION**

Craig William Siders

**Abstract**

All-optical ultrafast time-resolved plasma diagnostics of Plasma Based
Accelerators (PBA's) are described, with emphasis on the Laser Wakefield
Accelerator (LWFA). Specifically, the diagnostic techniques involve replacing
the trailing particle bunch in the LWFA with a trailing photon bunch: a
weak ultrashort laser pulse. Since this photon pulse is derived directly
from the intense wakefield-generating laser pulse, practical difficulties
such as synchronization and dephasing are eliminated. The interaction of
the photon bunch with the plasma wake, essentially a simple time-domain
shift in optical phase, produces both "DC" phase shifts and frequency blue/red-shifting
of the probe pulse spectrum. These phase/ frequency shifts are recorded
in frequency domain interferograms, which are formally equivalent to time-domain
holograms. Experimental results of longitudinal plasma density profiling
are presented in which plasma density oscillations (Langmuir Waves) in
the wake of an intense (I_{peak} ~ 3 10^{17} W/cm^{2})
laser pulse (~ 100 fs) were measured with ultrafast time resolution. Phase
shifts consistent with large amplitude (~ 80%) density oscillations (Langmuir
waves) at the electron plasma frequency were observed in a fully tunnel-ionized
He plasma, corresponding to longitudinal electric fields of ~ 10 GV/m.
Strong radial ponderomotive forces enhance the nonlinear density oscillations.
Proposed single-shot schemes for simultaneous transverse and longitudinal
profiling are discussed. Related experiments concerning pressure-tunable
harmonic generation within and spectral modifications of phase-modulated
ultrashort laser pulses by ultrafast ionization fronts are also reported.

**Solution of the Quiet Implicit Particle-in-Cell Moment
Equations in Toroidal Geometry - Dissertation**

William David Nystrom

**Statistical Properties of the Drift Wave Fluctuations**

H. Tasso and W. Horton

**Abstract**

The nature of turbulence in macroscopically confined plasmas is reviewed and contrasted to turbulence in hydrodynamics. The statistical properties of the fluctuations are analyzed both from the Gibb's distribution for the soliton gas model of the electrostatic field and for th e Hamiltonian field theory equilibrium statistics. For that purpose, nonlinear drift wave equations are derived from two-fluid theory. From the reduced nonlinear drift wave equations we construct continuous plasma models with simple Hamiltonians, which allow canonical distributions to be defined explicitly. Partition functions and correlation functions can be calculated analytically in the one-dimensional case as functional integral averages over canonical distributions. The relation of the k-space fluctuation spectrum obtained from canonical distributions with those inferred from the electromagnetic scattering experiments is given. The open problem of saturation levels of fluctuations is discussed in the conclusions.

**Information and Correlation in Statistical Mechanical
Systems - Dissertation**

David Richard Wolf

**Abstract**

Information comes to the research or other system in untold forms. Information is carried in physical objects which interact with the observer or system that they influence. Living systems make use of information in subtle ways, to find and make use of sources of materials and energy. In this work the focus is on the reduced distribution functions and when they yield information of relevance. Information correlation functions, correlation functions, and entropy are of primary interest. The estimation of functions of the underlying distribution is examined. Several key theorems of statistical mechanics are shown to be consequences of a single theorem on counting labeled partitions, bringing together the cumulant expansion, linked cluster theorem, and Ursell development as consequences of this theorem. The information correlation functions provide a basis for the notion of the information between sets of random variables. The flow of information is closely examined, in both the classical and quantum frameworks. In the Hamiltonian context, when the unexamined part of the distribution is taken to be the maxent distribution, the information flow into the subsystem is shown to be zero. The Ising model forms the basis of a nontrivial exactly solvable system for examining the correlations and information correlation functions. The expressions for the entropies of any subset of Ising spins are given, and it is shown that the information correlation functions give the mutual information between the first and last spins considered. The quantum Heisenberg model forms the basis for a nontrivial system exhibiting dynamics. The measurement entropy and the intrinsic entropy are defined and are shown to be related by an inequality. A time-ordered mutual information that is of great interest when examining the setting and measurement of quantum states is introduced. Estimating the values of functions of the underlying distribution (i.e. entropy, mutual information, etc.) and their uncertainties forms a large portion of the key results. Closed form expressions for the moments of the entropy and the mutual information are given.

**Laser Wakefield Excitation and Measurement by Femtosecond
Longitudinal Interferometry**

C.W. Siders, S.P. LeBlanc, D. Fisher, T. Tajima, and M.C. Downer, A. Babine, A. Stepanov, and A. Sergeev

**Abstract**

Plasma density oscillations (Langmuir waves) in the wake of an intense
(I_{peak} ~ 3 10^{17} W/cm^{2}) laser pulse (100
fs) are measured with ultrafast time resolution using a longitudinal interferometric
technique. Phase shifts consistent with large amplitude (dn_{e}/n_{e}
~ 1) density waves at the electron plasma frequency were observed in a
fully tunnel-ionized He plasma, corresponding to longitudinal electric
fields of ~10 GV/m. Strong radial ponderomotive forces enhance the density
oscillations.

**Study of Micro-instabilities in Toroidal Plasmas with
Negative Magnetic Shear**

J.Q. Dong, Y.Z. Zhang, S.M. Mahajan, and P.N. Guzdar

**Abstract**

Ion temperature gradient (ITG or h_{i})
driven microinstabilities are studied, using kinetic theory, for tokamak
plasmas with very weak (positive or negative) magnetic shear (VWS). The
gradient of magnetic shear as well as the effects of parallel and perpendicular
velocity shear (v_{||}' and v_{E}') are included in the
defining equations. Two eigenmodes: the double (D) and the global (G) are
found to coexist. Parametric dependence of these instabilities, and of
the corresponding quasilinear transport is systematically analyzed. It
is shown that, in VWS plasmas, a parallel velocity shear (PVS) may stabilize
or destabilize the modes, depending on the individual as well as the relative
signs of PVS and of the gradient of magnetic shear. The quasilinear transport
induced by the instabilities may be significantly reduced with PVS in VWS
plasmas. The v_{E}' values required to completely suppress the
instabilities are much lower in VWS plasmas than they are in normal plasmas.
Possible correlations with tokamak experiments are discussed.

**Ion Acceleration and Direct Ion Heating in Three-Component
Magnetic Reconnection**

Y. Ono, M. Yamada, T. Akao, T. Tajima, and R. Matsumoto

**Abstract**

Ion acceleration and direct ion heating in magnetic reconnection are experimentally observed during counterhelicity merging of two plasma toroids. Plasma ions are accelerated up to order of the Alfven speed through contraction of the reconnected field-lines with three-components. The large increase in ion thermal energy (from 10 eV up to 200 eV) is attributed to the direct conversion of the magnetic energy into the unmagnetized ion population. This observation is consistent with the magnetohydrodynamic and macro-particle simulations.

**IFSR-741**

**Renormalization and Transition to Chaos in Area-Preserving
Maps**

D. del-Castillo-Negrete, J. M. Greene, and P. J. Morrison

**Abstract**

The problem of transition to chaos, i.e. the destruction of invariant circles or KAM (Kolmogorov-Arnold-Moser) curves, in area-preserving nontwist maps is studied within the renormalization group framework. Nontwist maps are maps for which the twist condition is violated along a curve known as the shearless curve. In renormalization language this problem is that of finding and studying the fixed points of the renormalization group operator R? that acts on the space of maps. A simple period-two fixed point? R, whose basin of attraction contains the nontwist maps for which the shearless curve exists, is found. Also, a critical period-twelve fixed point of R, with two unstable eigenvalues, is found. The basin of attraction of this critical fixed point contains the nontwist maps for which the shearless curve is at the threshold of destruction. This basic defines a new universality class for the transition to chaos in area-preserving maps.

**IFSR-740**

**Gyrokinetic Simulation of Tokamak Turbulence and Transport
in Realistic Geometry - Dissertation**

Geoffrey Mark Furnish

**Abstract**

Computational modeling of fusion plasmas is very resource-intensive, so much so that the Numerical Tokamak Project has recently been recognized as a Grand Challenge of high performance computing. In order to apply computational modeling to the analysis of fusion plasma performance and eventually to attain predictive capability, an increasing emphasis on sophisticated algorithms and computational performance is required.

In this work, an advanced three-dimensional particle simulation code was developed, supporting simulations in realistic machine geometries, including both toroidal topology and shaping in the cross-section. Gyrokinetic ions are employed in order to approach realistic tokamak parameter regimes. The code employs an object-oriented design supporting flexible, run-time selection of interchangeable components, including geometry model, particle dynamics, field strategy, grid configuration, etc. The code is designed for efficient, scalable execution on massively parallel computers, using an object-oriented wrapper over conventional message passing as the parallel technology, and supports execution on uniprocessors as a limiting case.

**Velocity shear generated Alfven waves in electron-positron
plasmas**

Andria D. Rogava, S.M. Mahajan, and Vazha I. Berezhiani

**Abstract**

Linear magnetohydrodynamics (MHD) modes in a cold, nonrelativistic electron-positron
plasma shear flow are considered. The general set of differential equations,
describing the evolution of perturbations in the framework of the nonmodal
approach is derived. It is found, that under certain circumstances, the
compressional and shear Alfven perturbations may exhibit large transient
growth fueled by the mean kinetic energy of the shear flow. The velocity
shear also induces mode coupling allowing the exchange of energy as well
as the possibility of a strong mutual transformation of these modes into
each other. The compressional Alfven mode may extract the energy of the
mean flow and transfer it to the shear Alfven mode via this coupling. The
relevance of these new physical effects to provide a better understanding
of the laboratory e^{-}-e^{+} plasmas is emphasized. It
is speculated that the shear-induced effects in the electron-positron plasmas
could also help solve some astrophysical puzzles (e.g., the generation
of pulsar radio emission). Since most astrophysical plasmas are relativistic,
it is shown that the major results of the study remain valid for weakly
sheared relativistic plasmas.

**On the Saturation of Multihelicity Modes**

H. Sugama and W. Horton

**Abstract**

Nonlinear interactions between unstable modes localized around rational magnetic surfaces with different helicities are studied by using a simple set of mode amplitude equations. Stability analyses of stationary solutions of the model equations show that, when low mode number rational surfaces corresponding to unstable modes with large radial widths are densely distributed, not all of these modes are allowed to equally contribute to the transport. In that case, some of the linear unstable modes are suppressed by nonlinear multi-helicity interactions in such a way that, in the radial profile of fluctuation amplitude, only a single peak appears within the radial width of the mode structure even if there exist other low mode number surfaces in the vicinity. These predictions are consistent with results of the resistive g turbulence simulations.

**Multiplicity of Low-Shear toroidal Alfven Eigenmodes**

J. Candy, B.N. Breizman, J.W. Van Dam, and T. Ozeki

**Abstract**

An enlarged spectrum of ideal toroidal Alfven eigenmodes is demonstrated to exist within a toroidicity-induced Alfven gap when the inverse aspect ratio is comparable to or larger than the value of the magnetic shear. This limit is appropriate for the low-shear region in most tokamaks, especially those with low aspect ratio. The new modes may be destabilized by fusion-product alpha particles more easily than the standard toroidal Alfven eigenmodes.

**Anomalous Ion Thermal Transport from Toroidal ion Temperature
Gradient Mode**

J-Y. Kim, Y. Kishimoto, W. Horton, and M. Wakatani

**Abstract**

It is shown that the observed large edge fluctuation and thermal conductivity can be explained in terms of the toroidal ion temperature gradient mode. The very weak nonlinear interaction rate due to the large radial width of the radially extended toroidal modes is found to be an essential factor. The Bohm-type diffusivity and the near-marginality in core region are also predicted by the same property.