On the Fluctuation Spectrum of Plasma

P. J. Morrison and B. A. Shadwick


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


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


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 = Tv/Th (Tv and Th 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 = ±xs, are close enough to satisfy xs/a << (kya)-11/15R-1/15. For larger separation between the resonant surfaces, the growth rate transits to a R-1/3 scaling. The transition occurs at xs/a ~ (kya)-11/15R-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


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


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


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/ϒ2 tori in the standard nontwist map

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


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


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


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


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


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


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


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 VBs-AL wave forms. 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. 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


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


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


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


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

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


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 (2N≲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

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.