**Drift Wave Test Particle Transport in Reversed Shear
Profile**

W. Horton, H-B. Park, J-M. Kwon, D. Strozzi, P.J. Morrison, and D-I. Choi

**Abstract**

Drift wave maps, area preserving maps that describe the motion of charged particles in drift waves, are derived. The maps allow the integration of particle orbits on the long time scale needed to describe transport. Calculations using the drift wave maps show that dramatic improvement in the particle confinement, in the presence of a given level and spectrum of E x B turbulence, can occur for q(r)-profiles with reversed shear. A similar reduction in the transport, i.e. one that is independent of the turbulence, is observed in the presence of an equilibrium radial electric field with shear. The transport reduction, caused by the combined effects of radial electric field shear and both monotonic and reversed shear magnetic q-profiles, is also investigated.

**Topics in Lagrangian and Hamiltonian Fluid Dynamics:
Relabeling Symmetry and Ion-Acoustic Stability (DISSERTATION}**

Nikhil Subhash Padhye

**Abstract**

Relabeling symmetries of the Lagrangian action are found for the ideal, compressible fluid and magnetohydrodynamics (MHD). These give rise to conservation laws of potential vorticity (Ertel's theorem) and helicity in the ideal fluid, cross helicity in MHD, and a conservation law for an ideal fluid with three thermodynamic variables. The symmetry that gives rise to Ertel's theorem is generated by an infinite parameter group, and leads to a generalized Bianchi identity. The existence of a more general symmetry is also shown, with dependence on time and space derivatives of the fields, and corresponds to a family of conservation laws associated with the potential vorticity. In the Hamiltonian formalism, Casimir invariants of the noncanonical formulation are directly constructed from the symmetries of the reduction map from Lagrangian to Eulerian variables. Casimir invariants of MHD include a gauge-dependent family of invariants that incorporates magnetic helicity as a special case. Novel examples of finite dimensional, noncanonical Hamiltonian dynamics are also presented: the equations for a magnetic field line flow with a symmetry direction, and Frenet formulas that describe a curve in 3-space. In the study of Lyapunov stability of ion-acoustic waves, existence of negative energy perturbations is found at short wavelengths. The effect of adiabatic, ionic pressure on ion-acoustic waves is investigated, leading to explicit solitary and nonlinear periodic wave solutions for the adiabatic exponent = 3. In particular, solitary waves are found to exist at any wave speed above Mach number one, without an upper cutoff speed. Negative energy perturbations are found to exist despite the addition of pressure, which prevents the establishment of Lyapunov stability; however the stability of ion-acoustic waves is established in the KdV limit, in a manner far simpler than the proof of KdV soliton stability. It is also shown that the KdV free energy (Benjamin, 1972) is recovered upon evaluating (the negative of) the ion-acoustic free energy at the critical point, in the KdV approximation. Numerical study of an ion-acoustic solitary wave with a negative energy perturbation shows transients with increased perturbation amplitude. The localized perturbation moves to the left in the wave-frame, leaving the solitary wave peak intact, thus indicating that the wave may be stable.

**Effects of orbit distortion on classical transport**

K.C. Shaing, A.Y. Aydemir, and R.D. Hazeltine

**Abstract**

It is well known that electrostatic fields in tokamaks can vary on relatively short scale lengths, approaching the ion banana width. The resulting "squeezed" ion orbits are associated with significantly reduced neoclassical transport. It is shown here that an analogous process occurs, for steeper field variation, at the level of particle gyration: potentials varying on a scale comparable to the ion gyro{radius distort gyro{orbits and thus modify classical transport. The gyro{distortion can take one of three forms, depending upon the sign and size of the electric field shear; reduction in orbit width occurs only in a potential well. In this case, and assuming that the ion density and temperature vary slowly on the scale of the shrunken orbit, we compute the classical ion heat flux. It is shown that this flux is reduced by a factor of S^(-2). The sharp potential variation required for large S might result from steep electron temperature gradients near the separatrix of a spherical tokamak (with comparable poloidal and toroidal field components) or Reversed Field Pinch.

**Ion plateau transport near the tokamak magnetic axis**

K.C. Shaing and R.D. Hazeltine

**Abstract**

Conventional neoclassical transport theory does not pertain near the magnetic axis, where orbital variation of the minor radius and the poloidal field markedly change the nature of guiding-center trajectories. Instead of the conventional tokamak banana-shaped trajectories, near-axis orbits, called potato orbits, are radially wider and lead to distinctive kinetic considerations. Here it is shown that there is a plateau regime for the near-axis case; the corresponding potato-plateau ion thermal conductivity is computed.

**Test Particle Simulations for Neoclassical Transport
in a Reversed Shear Plasma**

Hyoung-Bin Park, Wendell Horton, Jae-Min Kwon, and Duk-In Choi

**Abstract**

The authors present results of test particle simulations for neocalssical transport in the core region of a reversed shear plasma by solving the guiding center equations of motion in toroidal geometry together with the Monte Carlo Coulomb collisional pitch angle scattering. The radial transport is not diffusive in the core plasma where the orbit topology is much di.erent from what is assumed in standard neoclassical theory. The results indicate that the unusual orbit topology and steep gradients in density and q profiles are not su1cient to explain the very low ion thermal conductivity observed in the ERS experiments.

**Magnetic Energy Storage and the Nightside Magnetosphere-Ionosphere
Coupling**

W. Horton, M. Pekker, and I. Doxas

**Abstract**

The change in the magnetic energy stored in the Earth's magnetotail as a function of the solar wind IMF conditions are investigated using an empirical magnetic field model. The results are used to calculate the two normal modes contained in the low-dimensional global model called WINDMI for the solar wind driven magnetosphere-ionosphere system. The coupling of the magnetosphere-ionosphere (MI) through the nightside region 1 current loop transfers power to the ionosphere through two modes: a fast (period of minutes) oscillation and a slow (period of one hour) geotail cavity mode. The solar wind drives both modes in the substorm dynamics.

**Transport theory in the collisionless limit**

R. D. Hazeltine

**Abstract**

Traditional transport theory provides a closure of fluid equations that is valid in the collisional, short mean-free-path limit. The possibility of extending an analogous closure to long mean-free-path is examined here. An appropriate kinetic equation, using a model collision operator, is solved rigorously for arbitrary collisionality but weak, Maxwellian source terms. The corresponding particle and heat flows are then expressed in terms of the density and temperature profiles. The transport matrix is found to be symmetric even at vanishing collision frequency; in the collisionless limit it takes the form of nonlocal operators. The operator corresponding to thermal conductivity agrees with one found previously by Hammett and Perkins [1]. However particle diffusion, which turns out to satisfy a local Fick's law for any finite collision frequency, becomes singular at vanishing collisionality, where the pressure gradient vanishes. We conclude that the fluxes can generally be expressed in terms of particle and energy sources, but not always in terms of pressure and temperature profiles.

**Testing Unruh Radiation with Ultra-Intense Lasers**

Pisin Chen and T. Tajima

**Abstract**

The space-charge effects of low-energy Gaussian beams in synchrotron accelerators can significantly affect the beam particle trajectories, including altering the regions of beam instability. We show that the tuneshift of a Gaussian beam is not uniform throughout the beam, but decreases as a function of particle amplitude. From the amplitude dependence of the tuneshift, we derive equations for the region of beam instability due to integer resonances and coupled resonances. We demonstrate the validity of these equations through particle simulation.

**On the Robustness of the localized spatiotemporal structures
in electron-positron-ion plasmas**

S.M. Mahajan, V.I. Berezhiani, and R. Miklaszewski

**Abstract**

It is shown that, in an electron-positron plasma with a small fraction of ions, large{amplitude localized spatiotemporal structures (light bullets) can be readily generated and sustained. These light bullets are found to be exceptionally robust: they can emerge from a large variety of initial field distributions and are remarkably stable.

**Asymptotic Persistence of collective modes in shear
flows**

Swadesh M. Mahajan and Andria D. Rogava

**Abstract**

A new nonasymptotic method is presented that reveals an unexpected richness in the spectrum of fluctuations sustained by a shear 0ow with nontrivial arbitrary mean kinematics. The prinicipal characterstic of the revealed exotic collective modes is their asymptotic persistence. "Echoeing" as well as unstable (including parametrically driven) solutions are displayed. Further areas of application, for both the method and the new physics, are outlined.

**Double Curl Beltrami Flow - Diamagnetic Structures**

S.M. Mahajan and Z. Yoshida

**Abstract**

It is shown that in an ideal coupled magnetofluid, the equilibrium magnetic (velocity) field is described by a two-parameter, double curl ( \nabla x \nabla x ) system of equations. The new system allows, amongst others, a novel, fully diamagnetic, pressure confining, minimum |B| configuration with velocity fields comparable (in appropriate units) to the magnetic fields.

**Invariants and Labels in Lie-Poisson Systems**

Jean-Luc Thiffeault and P. J. Morrison

**Abstract**

Reduction is a process that uses symmetry to lower the order of a Hamiltonian system. The new variables in the reduced picture are often not canonical: there are no clear variables representing positions and momenta, and the Poisson bracket obtained is not of the canonical type. Specifically, we give two examples that give rise to brackets of the noncanonical Lie-Poisson form: the rigid body and the two-dimensional ideal fluid. From these simple cases, we then use the semidirect product extension of algebras to describe more complex physical systems. The Casimir invariants in these systems are examined, and some are shown to be linked to the recovery of information about the configuration of the system. We discuss a case in which the extension is not a semidirect product, namely compressible reduced MHD, and find for this case that the Casimir invariants lend partial information about the configuration of the system.

**Theory of Enhanced Reversed Shear Mode in Tokamaks**

K.C. Shaing, A.Y. Aydemir, W.A. Houlberg, and M.C. Zarnstorff

**Abstract**

It is shown that toroidal magnetic field ripple induced particle flux can drive poloidal E x B speed to bifurcate over the local maximum of the non- linear poloidal (or parallel) viscosity. Here, E is the electric field and B is the magnetic field. This mechansim, together with the turbulence suppression due to the radial gradient of the E x B and diamagnetic angular velocity, is employed to explain enhanced reversed shear mode observed in the core region of tokamaks.

**Cluster Plasma and its Dispersion Relation**

T. Tajima, Y. Kishimoto, and M.C. Downer

**Abstract**

It is shown that unlike a gas plasma or an electron plasma in a metal, an ionized clustered material ("cluster plasma") permits propagation below the plasma cut-off. of electromagnetic (EM) waves whose phase velocity is close to but below the speed of light. Its unique properties allow a variety of applications, including direct acceleration of particles with its EM fields and the phase matching of waves of high harmonic generation (HHG).

**IFSR-812**

**Magnetohydrodynamics of Plasmas in the Solar, Stellar,
and Black Hole Atmospheres (Dissertation)**

Wen-Chien Chou

**Abstract**

Magnetohydrodynamics in various astrophysical systems has been investigated. In particular, the effect of rotation on the magnetic buoyancy and the general relativistic effect on the magnetohydrodynamics have been studied in detail. The analyses and the simulations are compared with the observations of the solar x-ray active regions, the spots of remote fast-rotating stars, and the jets in black hole candidates. The dynamics of magnetic flux tubes embedded in the solar or stellar atmosphere has been studied by a linear analysis and nonlinear 3D simulations.

**IFSR-811**

**Laser Driven Particle Injection (Dissertation)**

Bernhard Rudolf Rau

**Abstract**

The utilization of high-intensity, short-laser pulses may open the way not only to the possibility for next generation linear accelerators of unprecedented field gradients but also to novel particle injection methods. While much research, both theoretical as well as experimental, has been done on plasma-based linear accelerators, the idea of making use of this laser technology for the pickup and pre-acceleration of particles is relatively new and unexplored. In this dissertation, we examine possibilities of using current and future laser technology to suitably prepare plasma background particles for injection into a given (conventional or novel) particle accelerator. These possibilities pertain to novel regimes of particle injectors available by the utilization of intense, short pulse lasers. We propose setups capable of picking up electrons or ions from a plasma and show that acceleration to energies sufficient for injection can be obtained while achieving favorable injection parameters like longitudinal and transverse emittance as well as particle bunch lengths. The connected field of strong field induced ionization and its effect on the laser pulse is also investigated. Here we find a strong correspondence between our theoretical results and experimental data. In view of a next generation, laser driven linear accelerator, it will be shown that the parameters obtained for the electron injection fulfill some of the stringent requirements posed upon the injector beam which conventional electron guns cannot deliver. With respect to the ion injection, we propose a first concept of a coherent ion source. using current technology, coherent pickup and acceleration to relativistic energies may be possible for low Z ions such as hydrogen or helium. Due to the high acceleration gradient and thus short acceleration distance, this may provide new methods for both the conventional ion injection into accelerators as well as medical therapies using ion dose treatment.

**Strong Echo Effect and Nonlinear Transient Growth in
Shear Flows**

J. Vanneste, P.J. Morrison, and T. Warn

**Abstract**

The nonlinear interaction of two disturbances excited successively in a two-dimensional Couette flow is shown to lead to a transient energy growth. This phenomenon, which is called echo effect and exists in several other physical systems, is interesting because the energy growth appears long after the energy associated with the original disturbances has decayed. Here, the echo effect is studied analytically and numerically in a situation where the nonlinear response has the same order of magnitude as the two excitations. A system of amplitude equations describing the nonlinear interactions between three sheared modes is derived and employed to examine the physical mechanism of the echo. The qualitative validity of this system is confirmed by numerical simulations. The influence of viscous dissipation on the echo effect is also considered.

**Forecast of TEXT Plasma Disruptions Using Soft X-Rays
as Input Signal in a Neural Network**

A. Vannucci, K.A. Oliveira, and T. Tajima

**Abstract**

A feed-forward neural network with two hidden layers is used in this work to forecast major and minor disruptive instabilities in TEXT discharges. Using soft X-ray signals as input data, the neural net is trained with one disruptive plasma pulse, and a di.erent disruptive discharge is used for validation. After being properly trained the networks, with the same set of weights, is then used to forecast disruptions in two others di.erent plasma pulses. It is observed that the neural net is able to predict the incoming of a disruption more than 3 ms in advance. This time interval is almost three times longer than the one already obtained previously when magnetic signal from a Mirnov coil was used to feed the neural networks with. To our own eye we fail to see any indication of an upcoming disruption from the experimental data this far back from the time of disruption. Finally, from what we observe in the predictive behavior of our network, speculations are made whether the disruption triggering mechanism would be associated to an increase of the m = 2 magnetic island, that disturbs the central part of the plasma column afterwards or, in face of the results from this work, the initial perturbation would have occurred first in the central part of the plasma column, within the q = 1 magnetic surface, and then the m = 2 MHD mode would be destabilized afterwards.

**A necessary and sufficient instability condition for
inviscid shear flow**

N.J. Balmforth and P.J. Morrison

**Abstract**

We derive a condition that is necessary and sufficient for the instability of inviscid, two-dimensional, plane parallel, shear flow with equilibrium velocity profiles that are monotonic, real analytic, functions of the cross-stream coordinate. The analysis, which is based upon the Nyquist method, includes a means for delineating the possible kinds of bifurcations that involve the presence of the continuous spectrum, including those that occur at nonzero wavenumber. Several examples are given.

**Shear Flow Induced Wave Couplings in the Solar Wind**

Stefaan Poedts, Andria D. Rogava, and Swadesh M. Mahajan

**Abstract**

A sheared background flow in a plasma induces coupling between different MHD wave modes, resulting in their mutual transformations with corresponding energy redistribution between the modes (Chagelishvili, Rogava & Tsiklauri (1996)). In this way, the energy can be transfered from one wave mode to the other, but energy can also be added to or extracted from the background flow. In the present paper it is investigated whether the wave coupling and energy transfer mechanisms can operate under solar wind conditions. It is shown that this is indeed the case. Hence, the long-period waves observed in the solar wind at r > 0.3AU might be generated by much faster periodic oscillations in the photosphere of the Sun. Other possible consequences for the observable peculiar beat phenomena in the wind and acceleration of the wind particles are also discussed.

**Can a "superconductor" always expel the generalized
magnetic Field?**

S.M. Mahajan

**Abstract**

The conservation of generalized helicity in a perfectly conducting fluid may act as an electrodynamic barrier for the transition to the London (super- conducting) state when the system is immersed in a topologically nontrivial magnetic field (with a nonzero generalized helicity). An experiment is pro- posed to test whether the mechanism responsible (quantum correlations) for superconductivity respects the electrodynamic constraint.

**"Shear-Langmuir Vortexes:" New elementary mode of plasma
collective behavior**

George D. Chagelishvili, Swadesh M. Mahajan, and Andria D. Rogava

**Abstract**

Linear evolution of electrostatic perturbations in an unmagnetized, zero tempera- ture, two-component plasma shear 0ow is studied. It is shown that the velocity shear induces, due to the non-normality of linear dynamics, a new elementary mode of plasma non-periodic collective behavior - "Shear-Langmuir Vortexes" - with vortical motion of plasma species, characterized by intense energy exchange with the mean 0ow.

**Dynamics of Local Isolated Magnetic Flux Tubes in a
Fast-Rotating Stellar Atmosphere**

W. Chou, T. Tajima, R. Matsumoto, and K. Shibata

**Abstract**

Dynamics of magnetic flux tubes in the fast -rotating stellar atmosphere is studied. We focus on the effects and signatures of the instability of the flux tube emergence influenced by the Coriolis force. We present the results from a linear stability analysis and discuss its possible signatures in the course of the evolution of G-type and M-type stars. We present a 3D magnetohydrodynamical simulation of local isolated magnetic flux tubes under a magnetic buoyancy instability in co-rotating Cartesian coordinates. We find that the combination of the buoyancy instability and the Coriolis effect gives rise to a mechanism to twist the emerging magnetic flux tube into a helical structure. The tilt angle, east-west asymmetry and magnetic helicity of the twisted flux tubes in the simulations are studied in detail. The linear and nonlinear analyses provide hints as to what kind of pattern of large spots in young M-type main-sequence stars might be observed. We find that young and old G-type stars may have different distributions of spots while M-type stars may always have low latitudes spots. The size of stellar spots may decrease when a star becomes older, due to the decreasing of magnetic field. A qualitative comparison with solar observations is also presented.

**Quantum-Beamsstrahlung Laser Collider**

T. Tajima, S. Chattopadyay and M. Xie

**Abstract**

An e+e- linear collider at energies beyond a TeV runs into a problem of severe beamsstrahlung, characterized by Upsilon on the order of unity (and beyond). In the regime of extremely high Upsilon the beamsstrahlung may be largely suppressed due to the quantum e.ect. In the design of an e+e- collider there are two ways to satisfy the collider physics constraints. One is to decrease the number of particles per bunch (and thus to increase the repetition rate) and the other is to decrease the longitudinal bunch length. The former approach can limit Upsilon, while the latter boosts it. (It may be useful to reevaluate the future collider parameters in view of this.) The laser wake/eld driver for a collider in comparison with the microwave driver naturally o.ers a very short bunch length, which is appropriate for the latter collider option. We show that this choice of collider design with a short bunch length and high Upsilon has advantages and provide sample design parameters at 5 TeV. Such sample design parameters challenge us in a number of fronts, such as the preservation of high quality bunches, e1cient high repetition rate lasers, etc. The collision point physics simulated by the CAIN code shows a surprisingly well preserved luminosity spectrum.

**On the Theory of Internal Kink Oscillations**

B. N. Breizman, J. Candy, F. Porcelli, and H. L. Berk

**Abstract**

In this paper a time evolution equation for internal kink oscillations is derived. It is valid for both stable and unstable plasma regimes, and incorporates the response of an energetic particle population. A linear analysis reveals a parallel between (i) the time evolution of the spatial derivative of the internal kink radial displacement and (ii) the time evolution of the perturbed particle distribution function in the field of an electrostatic wave (Landau problem). It is shown that diamagnetic drift effects make the asymptotic decay of internal kink perturbations in a stable plasma algebraic rather than exponential. However, under certain conditions the stable root of the dispersion relation can dominate the response of the on-axis displacement for a significant period of time. The form of the evolution equation naturally allows one to include a nonlinear, fully toroidal treatment of energetic particles into the theory of internal kink oscillations.

**Plasma Near the Horizon of a Schwarzschild Black Hole**

W. Chou and T. Tajima

**Abstract**

Very close to the horizon of a black hole, the gravitational acceleration
becomes so large that vacuum can begin to radiate (the Hawking radiation).
The temperature of this radiation can exceed (twice of) the rest mass of
electrons and positrons at the distance to the horizon on the order of
the Compton wavelength. In this vicinity, even with 3R_{s} (R_{s}
is the Schwarzschild radius), an electron-positron plasma is realized and
self-sustained. Using the 3+1 paradigm of general relativistic hydrodynamics,
we find a steady equilibrium solution and that there is an opaque layer
around the horizon so that the apparent temperature of a black hole may
be lower than the Hawking temperature. We find that this plasma (in the
"QED sea") is hydrodynamically marginally stable. Away from this vicinity,
we also find several nontrivial hydrodynamic equilibrium solutions of plasma
on the equatorial plane. The plasma above the "QED sea" may be unstable
under certain conditions giving rise to such salient phenomena as (general
and special) relativistic jets. These equilibrium solutions provide a good
starting point to study the dynamics of plasma around a black hole.

**Outbursts from a Black Hole via Alfven Wave to EM Wave
Mode Conversion**

J. Daniel and T. Tajima

**Abstract**

A new mechanism for outbursts from a black hole is proposed. A recent
work on general relativistic plasma equilibria around a black hole has
shown the possibility of equilibrium presence of matter and magnetic fields
in the neighborhood of the event horizon even where the corpuscular equilibrium
is not allowed (R < 3R_{s}, where R_{s} is the Schwarzschild
radius). A large amplitude Alfven pulse in the black-hole electron-positron
atmosphere that propagates away from the hole into lower magnetic field
regions can experience resonance and mode-convert itself into a large amplitude
electromagnetic (EM) pulse. It is shown theoretically and computationally
that through this process a large amount of mass can be picked up by the
solitary EM pulse capable of traveling in vacuum, with which particles
are accelerated to relativistic energies. Photon spectra are obtained not
inconsistent with observation, which follow a multiple power law with log-log
slopes of approximately -1, before a "knee" in the spectrum at energies
slightly greater than 1 MeV. it is suggested that this may be a possible
mechanism for the outbursts of the black-hole binary GRO J1655-40.

**Growth and saturation of TAE modes destabilized by
ICRF produced tails**

H. Vernon Wong and H.L. Berk

**Abstract**

The linear growth rates of TAE (Toroidal Alfv6en Eigenmode) modes destabilised by ICRF (Ion Cyclotron Range of Frequency) heating are calculated over a range of plasma parameters. Nonlinear saturation of a single unstable mode is investigated both analytically and numerically when wave-particle trapping is the dominant satura- tion mechanism. A numerical code has been developed based on a reduced resonance description of the wave-particle interaction (using a Hamiltonian formalism). A delta- f algorithm was incorporated to allow a low-noise description of mode evolution with particle sources and sinks present. The numerically observed saturation amplitudes cor- relate well with theoretical predictions to within 20%. Self-excited frequency sweeping resulting from the excitation of many simultaneous wave-particle resonances at dif- ferent energies is demonstrated and explained as an extension of previous published theory [Berk et al., to be published in Phys. Lett].

**Drift Waves and Transport**

W. Horton

**Abstract**

The role of a variety of drift waves in inhomogeneous plasma for producing transport is reviewed. The physical mechanisms for the growth of drift waves, and the processes that establish the states of vortex and wave turbulence are analyzed. The role of drift wave phenomena in magnetic confinement systems is critically examined.

**IFSR-797**

**Strongly Nonlinear Magnetosonic Waves and Ion Acceleration**

B. Rau and T. Tajima

**Abstract**

The electromagnetic fields associated with a nonlinear compressional
Alfven wave propagating perpendicular to an arbitrarily strong external
magnetic field are derived. While recovering the known properties of nonlinear
Alfven waves in the weakly magnetized regime, new scaling laws are found
for the strongly magnetized case. We show that the electric field increases
only with the first power of the external magnetic for the strongly magnetized
and high phase velocity case relevant for ion acceleration to high energies.
We sketch an experimental setup capable of ion pickup and acceleration
that is not subjected to detrapping of ions due to a *v* x *B*
acceleration.

**Symmetries and Entropy Production of Transport in Toroidal
Confinement Systems**

H. Sugama and W. Horton

**Abstract**

A synthesized formulation of the classical, neoclassical, and anomalous transport in toroidal confinement systems with electromagnetic fluctuations and large mean flows is presented. The positive definite entropy production rate and the conjugate flux-force pairs are rigorously defined for each transport process. The Onsager symmetries of the classical and neoclassical transport matrices are derived from the self-adjointness of the linearized collision operator. The linear gyrokinetic equation with given electromagnetic fluctuations determines the anomalous fluxes with the quasilinear anomalous transport matrix which satisfies the Onsager symmetry.

**A Low-Dimensional Dynamical Model for the Solar Wind
Driven Geotail-Ionosphere System**

C.W. Horton and I. Doxas

**Abstract**

A six-dimensional nonlinear dynamics model is derived for the basic energy components of the night-side magnetotail coupled to the ionosphere by the region 1 currents. In the absence of solar wind driving and ionospheric dissipation the system is a three-degree-of-freedom Hamiltonian system. The large ion gyroradius conductance of the quasineutral sheet produces the energization of the central plasma sheet (CPS) while the unloading is triggered when the net geotail current or current density exceeds a critical value. For a steady southward IMF the model predicts an irregular sequence of substorms with a mean recurrence period of about 1~hr as in the Klimas \etal\ (1992) Faraday loop model. Here we use the new model as a nonlinear prediction filter on the Bargatze \etal\ (1985) database. Starting with physics calculations of the 13 physical parameters of the model we show that the average relative variance (ARV) is comparable to that obtained with data-based prediction filters. To obtain agreement between the predicted AL and the database AL it is essential to include the nonlinear increase of the ionospheric conductance with power deposited in the ionosphere.