**On the Fluctuation Spectrum of Plasma**

P. J. Morrison and B. A. Shadwick

**Abstract**

The spectrum of electron phase space density fluctuations of a plasma is calculated by a novel method that parallels conventional calculations of the partition function in statistical physics. Expressions for the electric field fluctuations and the closely related form factor agree with existing results.The method clears up ambiguous statements about equipartition and provides a new expression for the spectrum of phase space density fluctuations about stable non-Maxwellian equilibria.

**Hamiltonian Description of Fluid and Plasma
Systems with Continuous Spectra**

P. J. Morrison

**Abstract**

We show how to transform a large class of infnite degree-of-freedom Hamiltonian
systems into normal form. The energy-Casimir method that is widely used for
ascertaining stability in Hamiltonian fluid and plasma systems is only the first step. A
complete description involves changing to coordinates in which the energy is diagonal.
This amounts to a transformation to action-angle variables. Because fluid and plasma
systems typically have a continuous eigenspectrum, this transformation is nontrivial. It will be shown that a family of integral transforms, which is a generalization of the Hilbert transform, yields action-angle variables for a large class of fluid and plasma systems.

**Double tearing mode in plasmas with anomalous electron viscosity**

J. Q. Dong, S. M. Mahajan, and W. Horton

**Abstract**

The linear behavior of the double tearing mode in plasmas with a phenomenological anomalous electron viscosity is investigated within the framework of magnetohydrodynamic (MHD) theory. In the large Reynolds number R = T_{v}/T_{h} (T_{v} and T_{h} are, respectively, the viscosity penetration time of the magnetic field and the Alfvén time for a plasma sheet of width a) limit, the growth rate is found to scale as R^{-1/5} if the two resonant surfaces, at x = ±x_{s}, are close enough to satisfy x_{s}/a << (k_{y}a)^{-11/15}R^{-1/15}. For larger separation between the resonant surfaces, the growth rate transits to a R^{-1/3} scaling. The transition occurs at x_{s}/a ~ (k_{y}a)^{-11/15}R^{-1/15}. The R^{-1/5} is shown to be closely correlated with the violation of the constant-y
approximation. The linear velocity perturbations associated with the unstable double tearing mode are estimated to saturate at a level high enough to serve as a trigger for the formation of transport barriers observed in advanced tokamaks.

**A simple model of the resistive wall mode in tokamaks**

Richard Fitzpatrick

**Abstract**

A simple set of evolution equations is derived for the resistive wall mode in a large aspect-ratio, rotating, viscous, tokamak plasma. The equations take into account the non-linear deceleration of the plasma rotation generated by mode interaction with both the resistive wall and a static error-field. Furthermore, the equations are largely able to explain resistive wall mode data recently obtained from the DIII-D tokamak "Plasma physics and controlled nuclear fusion research", (International Atomic Energy Agency, Vienna, 1986), p. 159]. In particular, the role of the error-field in triggering
plasma deceleration is elucidated.

**
Modelling of Alfvén waves in JET plasmas with the CASTOR-K code
**

D. Borba, H.L. Berk, B.N. Breizman, A. Fasoli, F. Nabais, S.D. Pinches, S.E. Sharapov, D. Testa and contributors to the EFDA-JET Work Programme

**Abstract**

A hybrid magnetohydrodynamic (MHD)-gyro-kinetic model CASTOR-K developed for the study of Alfvén eigenmode (AE) stability in the presence of energetic ions has been applied to the interpretation of recent measurements of Alfvén waves in JET. These include the detailed AE damping measurements performed using the AE antenna excitation system and also the observations of Alfvén cascades in strongly reversed shear scenarios at JET. The mode conversion between the AEs and kinetic Alfvén waves and the relation to the Alfvén continuum is studied and the calculated damping is compared with the experimental data. The contribution of ion cyclotron resonant heating driven minority ions to the growth rate of the novel-type mode localized around the point of zero magnetic shear is calculated. This mode is shown to be clearly linked to the ideal MHD Alfvén continuum, computed with the CSCAS code and consistent with the observation of a quasi-periodic pattern of upward frequency sweeping Alfvén cascades in JET.

**Role of the Hall Current in Magnetohydrodynamic Dynamos**

Pablo D. Mininni, Daniel O. Gomez, and Swadesh M. Mahajan

**Abstract**

A theoretical mean field closure for Hall magnetohydrodynamics (Hall-MHD) is developed to investigate magnetic field generation through dynamo processes in low electron density astrophysical systems. We show that by modifying the dynamics of microscopic flows, the Hall currents could have a profound impact on the generation of macroscopic magnetic fields. As an illustrative example, we show how dynamo waves are modified by the inclusion of Hall currents. By dropping the usual assumption of a correlation time t for the microscopic dynamics in the mean field dynamos, we find qualitative changes in the growth rate of dynamo modes.

**Renormalization and destruction of 1/ϒ ^{2} tori in the standard nontwist map**

Amit Apte, Alexander Wurm, and P. J. Morrison

**Abstract**

Extending the work of del-Castillo-Negrete, Greene, and Morrison,
Physica D **91**, 1 (1996) and **100**, 311 (1997) on the standard nontwist
map, the breakup of an invariant torus with winding number equal to the
inverse golden mean squared is studied. Improved numerical techniques
provide the greater accuracy that is needed for this case. The new results
are interpreted within the renormalization group framework by constructing
a renormalization operator on the space of commuting map pairs, and by
studying the fixed points of the so contructed operator.

**Electron Confinement and Heating in Laser-Irradiated
Micro-Clusters**

Boris Breizman and Alex Arefiev

**Abstract**

It is shown that a two component electron distribution can emerge in
a cluster under an intense laser pulse. A bulk of internal electrons adjusts
adiabatically to the laser field whereas a smaller electron population
at the cluster edge can undergo stochastic heating. Self-consistent equilibrium
has been found and collective modes discussed for the confined electrons.

**Theoretical Studies of the VASIMR Plasma Propulsion
Concept**

Alex Arefiev

**Abstract**

This dissertation was motivated by the Variable Specific Impulse Magnetoplasma
Rocket (VASIMR) project. The VASIMR device has a magnetic mirror configuration
and consists of three main components: a low energy helicon plasma source,
which creates cold plasma via rf-discharge; an ion cyclotron-resonance
heating (ICRH) section, which is used to deposit rf-power into the plasma;
and a magnetic nozzle, which forms highly directed superalfvenic outgoing
plasma flow. The dissertation is focused on fundamental physics issues
of the helicon source operation and ICRH. A first-principle theory for
helicon sources with a self-consistent treatment of the particle balance,
power balance, and rf-field structure has been developed. The problem of
particle balance reduces to kinetic ion transport under the effect of the
ambipolar electric field and ion-neutral collisions. Power balance involves
electron heating by rf-field, heat conduction, and radiation. The rf-power
deposition is associated with the excitation of radially localized helicon
modes by an external antenna. The radial density gradient in a plasma forms
a potential well for the modes, with the resulting mode frequency being
significantly lower than that for a uniform plasma. This explains the high
efficiency of the source at low frequencies. The three key physics ingredients
have been combined into a 1D numerical model for a source with predominantly
radial flow. The code calculates the evolution of the plasma density, electron
temperature, and the rf-fields. These calculations specify the parameter
range for a stable steady-state operation of the helicon discharge. The
ICRH concept in VASIMR has two distinct features: 1) each ion passes the
resonance only once and 2) the ion motion is collisionless. The ion response
to the rf-field during single-pass ICRH can be essentially nonlinear. A
self-consistent nonlinear model for the deposition of rf-power in the ion
cyclotron frequency range into a steady-state plasma flow has been developed.
The one-dimensional fluid-type simulations confirm the theoretical picture
of the near-resonance behavior and wave energy conversion into the energy
of the directed ion flow. The regimes relevant to the VASIMR experiment
are discussed and issues such as the transition of plasma profiles and
the increase in gas pressure due to plasma production observed in the experiment
are addressed.

**Minimal Coupling and the Magnetofluid Unification**

Swadesh M. Mahajan

**Abstract**

The dynamics of a relativistic, hot charged fluid is expressed in terms
of a hybrid magnetofluid field which unifies the electromagnetic field
with an appropriately defined but analogous flow-field. In this unified
field, the fluid experiences no net force. Suitably modified (due to temperature)
minimal coupling prescription for particle dynamics may be invoked to affect
the transformation from the flow-field (or the electromagnetic) to the
magnetofluid field for the homentropic fluids. An appropriate prescription
for the general isentropic fluids is also derived. A few consequences of
the unification are worked out.

**Generation of Flows in the Solar Atmosphere Due to
Magnetofluid Coupling**

S.M. Mahajan, K.I. Nikol'skaya, N.L. Shatashvili, Z. Yoshida

**Abstract**

It is shown that a generalized magneto-Bernoulli mechanism can effectively
generate high velocity flows in the Solar subcoronal regions; sharp amplification
of the flow speed is accompanied by a significant density fall.

**Some Aspects of the Geometry of Poisson Dynamical Systems**

Vivek Narayanan

**Abstract**

The purpose of this thesis is to examine various characterizations of
nonmaximal rank in dynamical systems for which a generalization of the
Poisson bracket generates the dynamics. In particular, for systems with
symmetry, there is a connection between Goldstone modes of spontaneous
symmetry breaking induced by any G-invariant polynomial potential (G being
the symmetry group of the system), and subcasimirs that define nonmaximal
symplectic foliations. The connection is made explicit using ideas from
invariant theory, orbit space geometry, Poisson geometry, and work already
done in the area of patterns of symmetry breaking. Examples illustrating
some of these ideas are given in both finite and infinite dimensions. The
moment algebra of an ideal fluid in 2+1 dimensions is an example where
some ideas from invariant theory can be profitably used. Finally, it is
indicated how a unified bundle description might be given of all these
phenomena using the notion of principal bundle reduction, and of submaximal
distributions and their integrability. The nature of the infinite dimensional
analog of the above characterizations is also indicated in the conclusion.

**Substorm Classification with the WINDMI Model**

W. Horton, R.S. Weigel, D. Vassiliadis, and I. Doxas

**Abstract**

The results of a genetic algorithm optimization of the WINDMI model
using a substorm data set are presented. A key result obtained from a computational
search for convergence of the prediction over the database is the finding
that there are three distinct types of VB_{s}-AL wave forms.Ý Type
I and III substorms are given by the internally-triggered WINDMI model.
The WINDMI analysis identifies an additional type of event, called a type
II substorm, that requires an external trigger as in the northward turning
of the IMF model of Lyons (1995). Intrinsic database uncertainties in the
relative timing between the ground based AL electrojet signal and the arrival
time at the magnetopause of the IMF data measured by spacecraft in the
solar wind prevent a sharp division between type I and II events.Ý Within
these timing limitations we find that the fraction of events is roughly
40% type I, 40% type II, and 20% type III.

**Generalization of collisional fluid theory to long
mean-free-path and relativistic motion**

R. D. Hazeltine and S. M. Mahajan

**Abstract**

The influence of collisions on a magnetized plasma at arbitrary collisionality
is modelled by fluid equations that include the self-consistent moments
of the collision operator. A key feature of the derivation is its basis
in Lorentz-invariant equations, using the most general form of the energy-momentum
tensor in a magnetized plasma. The collisional limit of the resulting
description is shown to agree qualitatively with well-known short mean-free-path
equations. In particular it reproduces exactly the correct symmetry of
the transport matrix. Previously the long mean-free-path limit has been
shown to reproduce collisionless physics more accurately than other collisionless
fluid models.

**Density Profile Control with Current Ramping in a Transport
Simulation of Ignitor**

B. Hu, W. Horton, P. Zhu, and F. Porcelli

**Abstract**

Current ramping to achieve reversed shear (RS) confinement enhancement
and peaked density profiles are crucial in achieving ignition conditions
in Ignitor. Previous transport simulations used either fixed density profiles
or obtained flat density profiles. In this report we explore enhancement
confinement, and show a general scheme leading to density profile peaking
using the transport model JETTO in the Baldur simulations. In these simulations,
peaked density profiles result from the formation of internal transport
barrier due to reversed magnetic shear, which is produced by controlled
plasma current and volume-averaged density ramping. Such a programmed Ohmic
heating scheme is demonstrated to be an effective approach to the ignition
of a burning D-T plasma.

**Chaotic Scattering and the Magneto-Coulomb Map**

B. Hu,? W. Horton, and T. Petrosky

**Abstract**

A nonrelativistic classical electron scattering by a fixed ion in a
uniform magnetic field is discussed.The system is nonintegrable, and there
is chaotic scattering for certain class of initial conditions. A two dimensional
discrete map is derived from the equation of motion. Our map exhibits four
different types of motion by changing the parameters which characterize
the initial condition. The fractal structure for certain observables is
obtained. The width of the chaotic scattering region in the impact parameter
is estimated numerically. We suggest a certain class of plasma environments
where the chaotic scattering may have an important role.

**Dyanmo action in Hall Magnetohydrodynamics**

P. D. Mininni, D. O. Gomez, and S. M. Mahajan

**Abstract**

We show that the generally neglected Hall term in the equations for
two-fluid magnetohydrodynamics may have a profound effect on a-dynamo action.
The new calculation, in addition to subsuming the standard results from
the mean field approach, contains a contribution to the a-coefficient entirely
due to the Hall current in the microscale.

**Analytic solution for low-frequency rf sheaths in pulsed
discharges**

F. L. Waelbroeck

**Abstract**

The equations governing the evolution of rf-driven sheaths are solved
analytically in the regime where the rf frequency is small compared to
both the ionic plasma frequency and the ion transit time in the sheaths.
Poincare's map of first return is used to gain geometric insight into the
dynamics of the circuit-sheath system. The requirements of minimizing wall
bombardment while maximizing the efficiency of the coupling to the substrate
sheath are shown to lead to an optimum value for the blocking capacitance
in asymmetric discharges. This optimum value is also favorable for rapid
relaxation to steady-state in pulsed discharges. The analytic solution
is applied to the problem of negative ion extraction in afterglow plasmas.

**Geomagnetic transport in the solar wind driven nightside magnetosphere-ionosphere system **

W. Horton, C. Crabtree, I. Doxas, R. S. Weigel

**Abstract**

A spatially resolved nonlinear dynamical model of the solar wind driven geomagnetic tail plasma is developed for the purpose of space weather predictions. The model represents the fluctuating electromagnetic fields and high pressure central plasma sheet by a large number (2*N*≲200) of semiglobal coupled current loops ranging from the near-Earth geosynchronous orbit position for substorm dynamics to deep in the geotail. There is a spectrum of dynamical frequencies ranging from 1 h periods to 1 min and shorter periods. The low-frequency modes are global and lead to the dynamics of the low-dimensional (*d*=6) WINDMI model. The high-frequency dynamics are nonlinear compressional-rarefraction waves propagating up and down the geotail. The localized pulses start from sites of local reconnection set off either by the tearing mode unloading trigger or by localized solar wind disturbances acting on the nightside magnetopause. Larger unloading events lead to nonlinear steepening of the compressional pulsations which act to trigger secondary convection events under certain conditions.

**Variational principles and self-organization in two-fluid
plasmas**

Z. Yoshida and S. M. Mahajan

**Abstract**

Self-organization of an ordered structure occurs in a plasma under
rather restrictive conditions. A new framework for a variational principle
invokes a coercive form that results in a criterion for self-organizing
relaxation of a two-fluid plasma. The constraints (constants of motion
of the ideal model) are adjusted, through a weakly dissipative process,
so that the relaxed state is a stable equilibrium independent of the direct
effects of dissipation.