**Fast magnetic reconnection via jets and current micro-sheets**

P. G. Watson and I. J. D. Craig

**Abstract**

Numerical simulations of highly nonlinear magnetic reconnection provide evidence of ultrathin current micro-sheets. These small-scale sheets are formed by strong exhaust jets from a
primary, large-scale, current layer. The overall size of the secondary micro-sheet is determined
by the thickness of the primary sheet. Preliminary scalings show that the thickness of the microsheet varies linearly with the plasma resistivity. This scaling suggests that micro-sheets may
provide fast reconnection sites in magnetically complex plasmas such as the solar corona and
planetary magnetospheres.

**Wave driven magnetic reconnection in the Taylor problem**

Richard Fitzpatrick, Amitava Bhattacharjee, Zhi-Wei Ma, and Timur Linde

**Abstract**

An improved Laplace transform theory is developed in order to investigate the initial response of a stable slab plasma equilibrium enclosed by conducting walls to a suddenly applied wall perturbation in the so-called Taylor problem. The novel feature of this theory is that it does not employ asymptotic matching. If the wall perturbation is switched on slowly compared to the Alfvén time then the plasma response eventually asymptotes to that predicted by conventional asymptotic matching theory. However, at early times there is a compressible Alfvén wave driven contribution to the magnetic reconnection rate which is not captured by asymptotic matching theory, and leads to a significant increase in the reconnection rate. If the wall perturbation is switched on rapidly compared to the Alfvén time then strongly localized compressible Alfvén wave-pulses are generated which bounce backward and forward between the walls many times. Each instance these wave-pulses cross the resonant surface they generate a transient surge in the reconnection rate. The maximum pulse driven reconnection rate can be much larger than that predicted by conventional asymptotic matching theory.

**Hall current effects in dynamic magnetic reconnection solutions**

P. G. Watson, I. J. D. Craig and J. Heerikhuisen

**Abstract**

The impact of Hall current contributions on flow driven planar magnetic merging solutions is discussed. The Hall current is important if the dimensionsless Hall parameter (or normalized ion skin depth) satisfies *c _{H}* >

**A numerical study of forced magnetic reconnection in the viscous Taylor problem**

Richard Fitzpatrick

**Abstract**

Two-dimensional, nonlinear magnetohydrodynamical simulations are used to investigate the
so-called Taylor problem, in which a small amplitude boundary perturbation is suddenly applied to
a tearing stable, slab plasma equilibrium‹the perturbation being such as to drive magnetic
reconnection within the plasma. This type of reconnection, which is not due to an intrinsic plasma
instability, is generally known as "forced reconnection." For numerical reasons, the investigation is
restricted to the large magnetic Prandtl number limit. The simulation results are highly consistent
with the analysis of Hahm and Kulsrud [Phys. Fluids **28**, 2412 (1985)] (modified by strong plasma viscosity). At high perturbation amplitudes, the system exhibits a phase of SweetParker
reconnection, as predicted by Wang and Bhattacharjee [Phys. Fluids B **4**, 1795 (1992)]. An
expression for the threshold perturbation amplitude required to trigger SweetParker reconnection is derived, and successfully benchmarked against numerical simulations. This expression suggests that a SweetParker phase is only likely to occur during forced reconnection in tokamaks when the plasma is extremely hot and perturbation amplitude relatively large.

**Shielding of resonant magnetic perturbations in the long mean-free path regime**

F. L. Waelbroeck

**Abstract**

The effect of diamagnetic drifts and of long electron mean free path on the shielding of resonant magnetic perturbations by plasma rotation is investigated. The nature of the force exerted on a moving plasma by a resonant perturbation is qualitatively altered by both drift and long mean-free-path effects. The force is found to have three minima, each of which is a possible locus for discontinuous transitions in plasma velocity. Between these minima are two points where the force exerted by the perturbation is resonant. These points describe locked states where shielding is ineffective and a magnetic island will grow. They correspond to rotation velocities such that either the electrons or the ions are at rest in the frame of the perturbation. The ion root, however, is unstable.

**Equilibrium of a rotating mirror plasma**

R. D. Hazeltine, S. M. Mahajan, P. M. Valanju, and H. Quevedo

**Abstract**

The theory of axisymmetric equilibrium in a rotating mirror device is studied and compared with experimental data. In contrast to earlier studies that assumed constant along the magnetic field, the present formalism determines the two-dimensional structure of the electrostatic potential, which is nonlinearly coupled to the rotation. It is shown that parallel variation of the potential plays an important role in the resulting confinement. The limits of validity and possible applications of these results to centrifugally confined fusion plasmas and ion mass filters are considered.

**Plasma parameter scaling of the error-field penetration threshold
in tokamaks**

Richard Fitzpatrick

**Abstract**

A previously published analytical formula for the error-field penetration threshold in rotating
tokamak plasmas is successfully benchmarked against nonlinear magnetohydrodynamical
simulations in slab geometry. Moreover, the fundamental assumption underlying the derivation of
this formula, namely, that the response of a flowing plasma to a low amplitude, quasistatic, resonant
magnetic perturbation is governed by *linear, constant*-ψ layer physics, is verified over a wide range
of plasma parameters, which includes the parameter range relevant to Ohmic and neutral beam
injection start-up discharges in modern-day tokamaks. It is concluded that the formula in question
can be used to estimate error-field penetration thresholds in such plasmas.

**Magnetic Reconnection solutions based on a Generalized OHM's Law
**

P. G. Watson and I. J. D. Craig

**Abstract**

It is known that exact magnetic reconnection solutions can be constructed
for collisionally dominated resistive plasmas. In this paper we refine the
collisional resistive description by invoking an Ohm¹s law that includes Hall current
and plasma inertial contributions.
We first demonstrate the surprising fact that the analytic treatment of both
two and three dimensional current sheet reconnection remains valid for the generalized
Ohm¹s law description. A discussion of planar reconnection shows that while
the influence of inertial effects is generally small, the Hall current is likely to be
important in most physically realistic plasma regimes, even for turbulent current
sheet models. In particular, by influencing the magnetic and electric fields within
the current sheet, the Hall current can be expected to have a strong influence on
the particle acceleration capabilities of magnetic merging solutions. We also address
the extent to which the new solutions alleviate the need for enhanced, anomalous
resistivities to moderate the large current densities that arise in collisional resistive
merging.

**Frequency Sweeping in Plasmas due to Phase Space Structures**

H. L. Berk

**Abstract**

This review examines the nonlinear dynamics of a plasma near marginal stability when there is a balance between a destabilizing resonant kinetic drive and stabilizing dissipation that is present in the background plasma. A reduced cubic nonlinear integral equation in time that describes the self-consistent evolution of the resonant wave-particle system near marginal stability has been derived. Included in this description is extrinsic stochastic phenomena (such as collisions) on the kinetic component, which allows for a single control parameter. The nonlinear solutions exhibit different saturation scenarios depending on the value of this parameter. When it is sufficiently small, the solution does not reach a saturated value but instead explodes in accordance with a self-similar solution. Just after the phase space explosion, the integral equation breaks down. The description of the subsequent evolution required a numerical simulation of the Vlasov equation (or of a particle code) with the addition of velocity diffusion (or particle annihilation). A different type of saturation mechanism arises from the one where the distribution flattens in a fixed region of phase space. Instead, phase space structures form as either holes or clumps. To balance the background plasma dissipation, a hole moves "up" and a clump moves "down" in the momentum coordinate of phase space. A self-consistent particle-wave adiabatic theory, where the time scale for evolution is much larger than a particle trapping time, has been developed to understand the evolution of a phase space structures. In some cases this adiabatic theory predicts that the phase space structure evolves to a state where the theory can no longer make a prediction. Analysis shows that this is just the point where the phase space structure is marginally stable to the onset of non-adiabatic oscillations. Several experiments involving energetic particle excitation of Alfvén waves have produced frequency sweeping signatures that are compatible with the theory for the formation of phase space structures. The observation of the time scale of the frequency shift may allow a determination of internal field amplitudes.

**Instability of Phase Space Structures**

D. Yu. Eremin and H. L. Berk

**Abstract**

Adiabatic analysis of self-consistent dynamics of a phase space structure surrounded by passing particles under the assumption of a slowly changing amplitude and frequency has revealed that the system can reach a point where adiabatic theory breaks down. Linear perturbative analysis shows that an instability is triggered at precisely these points. Numerical runs were performed to test the adiabatic theory and the instability analysis of a BGK mode for the bump-on-tail problem. First a passing particle distribution function was used that has a constant slope with respect to the action variable. Then a flat passing particle distribution function, which has nearly the same instability criterion and growth rate as the first case was studied and it produces a precise comparison with the results from numerical simulation until instability sets in. Afterwards smaller phase space structures still persist and frequency sweeping continues at a lower rate.

**Scaling of Driven Magnetic Reconnection Rates**

A. Y. Aydemir and A. B. Gott

**Abstract**

Computational experiments in various collisionality regimes show that, when the drive is unambiguously separated from the reconnection region, driven magnetic reconnection, in its idealized and extensively studied two dimensional form, proceeds at a rate determined only by the boundary
conditions. Within certain bounds, details of the physics model used in studying this ubiquitous phenomenon play only a peripheral role: they determine the structure of the reconnection layer but not the overall reconnection rate. Therefore, scaling laws for models where this separation is absent will tend to be problem specific features, not universal laws of driven magnetic reconnection.

**Firehose Driven Magnetic Fluctuations in the Magnetosphere**

W. Horton, B.-Y. Xu, and H. Vernon Wong

**Abstract**

The nonlinear saturation of the firehose instability in the high plasma pressure central plasma sheet is shown to produce a wide spectrum of Alfvénic fluctuations in the range of Pi-2 geomagnetic pulsations. The wave energy sources are the small p||/p⊥ > 1 + B^{2}µ0p⊥ anisotropies which are created by Earthward ion convection at constant first and second adiabatic invariants. In the nonlinear state, the fieldline curvature force is weaker than the linear force. This weakening of the driving force limits the amplitude of the Alfvénic fluctuations. Away from the equatorial plane, the plasma is firehose stable, but carries large magnetic fluctuations.

**Theoretical components of the VASIMR plasma propulsion concept**

Alexey V. Arefiev and Boris N. Breizman

**Abstract**

The ongoing development of the Variable Specific Impulse Magnetoplasma Rocket (VASIMR) involves basic physics analysis of its three major components: helicon plasma source, ion cyclotronresonance heating (ICRH) module, and magnetic nozzle. This paper presents an overview of recent theoretical efforts associated with the project. It includes: 1) a first-principle model for helicon plasma source, 2) a nonlinear theory for the deposition of rf-power at the ion cyclotron frequency into plasma flow, and 3) a discussion of the plasma detachment mechanism relevant to VASIMR.

**Forced magnetic reconnection in the inviscid Taylor problem**

Andrew Cole and Richard Fitzpatrick

**Abstract**

The equation of incompressible inviscid 2-D MHD (magnetohydrodynamics) are numerically evolved in order to study a well-known model of forced magnetic reconnection. This problem, known as the Taylor problem, considers the response of a tearing-stable slab plasma equilibrium to a sudden, small amplitude boundary perturbation. The applied perturbation is such as to force magnetic reconnection and subsequent magnetic island formation within the plasma. The early dynamical phases of the reconnection process are investigated and found to be in good agreement with the analytic predictions of Hahm & Kulsrud [Phys. Fluids, **28**, 2412 (1985)]. Recent criticisms of this analysis by Ishizawa & Tokuda [Phys. Plasmas, **8**, 376, (2001)] are shown to be unwarranted.

**Harmonic generation in clusters**

Mykhailo V. Fomyts'kyi, Boris N. Breizman, Alexey V. Arefiev, and Charles Chiu

**Abstract**

A model is presented for the nonlinear response of a small cluster, with a size much smaller than the wavelength, at the third harmonic of the laser frequency. The model involves collective modes of a cold electron core confined within a positively charged ion background. The response
of the electron core to the laser field is similar to that of a weakly nonlinear oscillator driven by an external force. In particular, there is a resonant enhancement of the third harmonic when the frequency of the applied field is close to one third of the core eigenfrequency. It is shown that density nonuniformity or nonspherical shape of the ion background is necessary for harmonic generation. Particle-in-cell simulations have been performed to model the time evolution of the third harmonic response as the ion density profile changes due to cluster expansion. The simulation results are consistent with the predictions of the cold electron core model. In addition, the code
quantifies the role of stochastic electron heating, an alternative harmonic generation mechanism.

**Radiation Reaction and Relativistic Hydrodynamics**

V.I. Berezhiani, R.D. Hazeltine, and S.M. Mahajan

**Abstract**

By invoking the radiation reaction force, first perturbatively derived by Landau and Lifschitz, and later shown by Rohrlich to be exact for a single particle, we construct a set of fluid equations obeyed by a relativistic plasma interacting with the radiation field. After showing that this approach reproduced the known results for a locally Maxwellian plasma, we derive and display the basic dynamical equations for a general magnetized plasma in which the radiation reaction force augments the direct Lorentz force.

**Hall Current and Alfvén Wave**

Shuichi Ohsaki, and Swadesh M. Mahajan

**Abstract**

In ideal inhomogeneous magnetohydrodynamics (MHD), the Alfvén wave (the dominant low frequency mode of a magnetized plasmas) displays a continuous spectrum associated with singular eigenfunctions. It is shown that the coupling of the Hall term with the sound wave induces higher (fourth) order derivative in the Alfvén mode equation, and by resolving the singularity replaces the MHD continuum by a discrete spectrum. The mode structure resulting from the Hall resolution of the singularity is compared with the standard electron-inertia approach.

**Study of internal transport barrier triggering mechanism in tokamak plasmas**

J.Q. Dong, Z.Z. Mou, Y.X. Long, and S.M. Mahajan

**Abstract**

The sheared flow layers driven by the magnetic energy, released in tearing-reconnection processes inherent in dissipative magneto-hydrodynamics (MHD), are proposed as triggering mechanism for the creation of internal transport barrier (ITB) in tokamak plasmas. The double tearing mode, mediated by anomalous electron viscosity in configurations with non-monotonic safety factor, is investigated as an example. Particular emphasis is placed on the formation of sheared poloidal flow layers in the vicinity of the magnetic islands. A quasilinear simulation demonstrates that the sheared flows induced by the mode have desirable characteristics (lying just outside the magnetic islands), and sufficient levels required for ITB formation. A possible explanation is also proffered for the experimental observation that the transport barriers are preferentially formed in the proximity of low order rational surfaces.

**Laser Z-Pinch Dipole-Target Experiments to Simulate Space Physics Acceleration Processes**

W. Horton and C. Chiu

**Abstract**

Laboratory experiments using a plasma wind generated by laser-target interaction are proposed and analyzed to investigate the creation of shock in front of the magnetosphere and the dynamo mechanism. Magnetic dipoles are placed in the plasma wind and measurements of the electron fluxes bombarding the spheres surrounding the dipoles are recorded. The experiments are to be analyzed with the methods used in theoretical simulation of the solar-wind-driven magnetosphere interactions. The proposed experiments, which involve measurements on the creation of the shock front due to the impact of the supersonic plasma wind on the magnetosphere, and the subsequent generation of energetic electrons, are thought to be relevant to understanding the acceleration mechanisms at work in shock-driven magnetic dipole confined plasma.

**Theory of Alfvén eigenmodes in shear reversed plasmas**

B. N. Breizman, H. L. Berk, M. S. Pekker, S. D. Pinches, and S. E. Sharapov

**Abstract**

Plasma configurations with shear reversal are prone to the excitation of unusual Alfvén eigenmodes by energetic particles. These modes exhibit a quasi-periodic pattern of predominantly upward frequency sweeping (Alfvén Cascades) as the safety factor *q* changes in time. This work presents a theory that employs two complementary mechanisms for establishing Alfvén Cascades: (1) a nonstandard adiabatic response of energetic particles with large orbits and (2) toroidal magnetohydrodynamic (MHD) effects that are second-order in inverse aspect ratio. The developed theory explains the transition from Alfvén Cascades to the Toroidicity Induced Alfvén Eigenmodes (TAEs), including modifications of the TAEs themselves near the shear reversal point.

**Multi-Wave Model for Plasma-Wave Interaction**

E.G. Evstatiev, W. Horton, and P.J. Morrison

**Abstract**

A model is presented that describes the interaction of electrons with both longitudinal and transverse waves in a cold plasma. Starting from the Lagrangian for the system of fields, background plasma, and particles, a finite dimensional self-consistent model is derived using the envelope approximation for the waves. The (squared) wave amplitudes and phases form action-angle variables in the closed system of waves and particles. The system conserves energy and momentum, and thus is natural for solving the beam-loading problem. Numerical simulations are performed to compare with earlier electrostatic problems.

**Theory of Magnetized Rossby Waves in the Ionospheric E-layer**

T.D. Kaladze, G.D. Aburjania, O.A. Kharshiladze, I. Vekua, W. Horton, and O. Sharia

**Abstract**

For the weakly-ionized E-layer plasma, a generalized Charney-Obukhov equation for the magnetized Rossby waves is derived. This magnetized Rossby wave is produced by the dynamo electric field and represents the ionoshperic generalization of the tropospheric Rossby waves in a rotating atmosphere by the spatially inhomogeneous geomagnetic field. The basic characteristics of the wave are given. The modified Rossby velocity and Rossby-Obukhov radius are introduced. The mechanism of self-organization into solitary vortical nonlinear structures is examined. The mechanism of a self-organization of solitary structures is the result of the mutual compensation of wave dispersion and interaction through the scalar and Poisson bracket convective nonlinearities in the nonlinear wave equation. As a result, the solitary structures are anisotropic containing a circular vortex superimposed on a dipole perturbation. The degree of anisotropy sharply increases when the vortex size approached the so-called intermediate geostrophic size.

**Ballooning Stability of the Earth's Magnetosphere**

Christopher Eugene Crabtree

**Abstract**

A substorm is a frequently occurring ordered sequence of global energetic
events in the magnetosphere and ionosphere. The most obvious manifestation
of a substorm is auroral brightening, due to an increase in the number
of electrons precipitating into the ionosphere. During a substorm, quiet auroral
arcs suddenly intensify. Electrojets are produced in the ionosphere, and
magnetic disturbances are observed on the surface of the Earth with magnetometers.
Plasma instabilities in the inner magnetosphere, in the region where
the nightside auroral magnetic field lines cross the magnetic equator, are a candidate
to explain the triggering mechanism of these substorms. This region is
at a distance of about ten times the radius of the Earth in the midnight sector.
In this region the plasma thermal pressure gradient reaches its highest value
and the plasma is susceptible to unstable motions.
We have investigated the linear stability of the inner magnetosphere
against fast interchange-ballooning dynamics as a possible candidate for the magnetospheric substorm trigger, using different models of the quiet-time magnetospheric magnetic field. The region most likely unstable to these dynamics
is found to map to the lower edge of stable auroral arcs. We then extend
the ideal fast-MHD analysis to include local gyrokinetic effects such as waveparticle
resonances, in order to explain the low-frequency oscillations that are
observed prior to and during the onset of substorms. We generalize the local
kinetic analysis to include non-local orbital effects due to the mirroring
motion of the particles between the Earth's magnetic poles. We developed a
new numerical technique to solve the resulting non-linear integral eigenvalue
equations. We also investigated a magnetic compressional trapped particle
instability in detail and obtained the conditions for instability as well as the
growth rates and mode structures. We invoke this low-frequency drift wave
instability to explain compressional Pi2 oscillations observed throughout the
substorm onset period and argue that they play an important role in substorm
dynamics.

**Charged Particle Energization from Solar Winds**

Wei-Tai Lin

**Abstract**

This thesis researches on the energy gain mechanism of charged particles in the Earth's magnetosphere. Particles coming from solar wind pass by
the nose of the magnetosphere. When particles arrive in the tail region along
the magnetopause they enter the Earth's magnetosphere through reconnection
and generate the tail current. The solar wind leads to produce the electric field
across the magnetic field in the geotail of the Earth. According to Faraday's
law under steady state there exists an electric field *E _{y}* and

Protons acquire around *50keV* as they drift toward the Earth from
the Earth's magnetotail. These protons typically release the energies around
*10keV* into the ring current area under constant electric field *1mV=m* when particles are close to the Earth. Ions spend around 30 minutes drifting to
around *5R _{E}* under the constant electric field

**Bounds on dissipation in Magnetohydrodynamic Couette and
Hartmann shear flows**

A. Alexakis, F. Pétrélis, P. J. Morrison, and Charles R. Doering

**Abstract**

Shear flow with an applied cross-stream magnetic field is studied using dissipative incompressible magnetohydrodynamics. The study incorporates exact solutions, the energy stability method, and exact bounds on the total energy dissipation rate. Two physical configurations are examined: magnetic Couette flow and Hartmann flow, the latter being Poiseuille flow with the existence of a perpendicular magnetic field. Explicit expressions are derived for energy stability regions in the parameter space and these expressions are compared with numerically obtained results. For large enough Reynolds numbers the energy dissipation rate is shown to be bounded by a function of the magnetic Prandtl number. The bounds we obtain on the dissipation rate are compared with
experimental results.

**Landau Damping**

W. E. Drummond

**Abstract**

The damping of a longitudinal plasma wave of finite amplitude is considered. It is shown that the Landau result is the first in a systematic expansion in a small parameter, and the corrections for finite wave amplitude are shown to be 5th order in the small parameter. The contributions to the damping from particles with different velocities near the phase velocity are explicitly calculated and this leads to a simple physical picture of the dampling process.

**Swirling astrophysical flows - efficient amplifiers of Alfvén waves!?**

A. D. Rogava, S. M. Mahajan, G. Bodo, and S. Massaglia

**Abstract**

We show that a *helical *shear flow of a magnetized plasma may serve as an efficient amplifier of Alfvén waves. We find that even when the flow is purely ejectional (i.e., when no rotation is present) Alfvén waves are amplified through the transient, shear-induced, algebraic amplification process. Series of transient amplifications, taking place sequentially along the flow, may result in a *cascade amplification*of these waves. However, when a flow is swirling or *helical*(i.e., some rotation is imposed on the plasma motion), Alfvén waves become subject to new, much more powerful shear instabilities. In this case, depending on the type of differential rotation, both usual and parametric instabilities may appear. We claim that these phenomena may lead to the generation of large amplitude Alfvén waves and the mechanism may account for the appearance of such waves in the solar atmosphere, in accretion-ejection flows and in accretion columns. These processes may also serve as an important initial (linear and nonmodal) phase in the ultimate subcritical transition to MHD Alfvénic turbulence in various kinds of astrophysical shear flows.

**IFSR-962**

**Kelvin-Helmholtz instability in Beltrami fields**

A. Ito, Z. Yoshida, T. Tatsuno, and S. Ohsaki, and S. M. Mahajan

**Abstract**

The stability of Beltrami flows has been analyzed. The model equation represents the coupling of the Kelvin-Helmholtz (KH) instability with Alfvén waves. In a single Beltrami flow that parallels a force-free magnetic field, the magnetic field reduces the growth rate of the KH instability, while the marginally stable wave number is unchanged. Calculating the marginally stable eigenfunction of a magnetohydrodynamic flow, the necessary and sufficient condition for the exponential stability has been derived. The stability of double Beltrami flows has also been analyzed, which is represented by linear combinations of two Beltrami flows. Coupling of two vortices yields both stabilizing and destabilizing effects depending on the amplitudes and the eigenvalues of two Beltrami functions.

**IFSR-961**

**The Coronal Hole Creation: Theory and Simulation**

S. M. Mahajan, R. Miklaszewski, K. I. Nikol'skaya, and N. L. Shatashvili

**Abstract**

The possibility, that sufficiently fast plasma flows may be able to create channels (coronal holes, hereafter - CH) for their escape from the solar magnetic field network is investigated. Using a dissipative two-fluid code in which the flows are treated at par with the currents, we have studied the expected CH formation for representative test cases. We give the simulation results for: 1) the interaction of primary flows with 2 neighboring arcade-like ambient magnetic field structures, and 2) the primary flow interaction with 4 neighboring arcade-like structures. For the former case, though there is some dissipation of flow energy, the coronal hole is cold and practically empty compared to the closed coronal structures. In the latter case, the combined effect, of the structure-structure and flow-structure interaction creates a highly divergent, and multiple looped stretched 2-dimensional coronal hole with a hot base: the velocity field is maximum in the central region of CH at some distance away from the base unlike the coronal hole formed out of the two arcade structures.

**Bounds on dissipation in MHD problems in plane shear geometry**

F. Pétrélis, A. Alexakis, Charles R. Doering, P. J. Morrison

**Abstract**

The total dissipation rate for magnetohydrodynamic (MHD) flows in plane geometry with both velocity and magnetic shear is studied. For some boundary conditions it is shown that the lower bound on the dissipation rate is achieved by the equivalent of Stokes flow for MHD. Using the 'background method' (Doering & Constantin, Phys. Rev. Lett. **69**, 1648 -1651 (1992)) upper bounds for the dissipation rate are calculated. For a shear layer, with both velocity and magnetic shear, parameter dependence of the upper bound is obtained. As a by-product of this calculation, an 'energy stability' domain is calculated. A sheet pinch is also studied, and it is shown that the upper bound tends to zero as the resistivity tends to zero. Thus, an antiturbulence result is obtained.

**MHD spectroscopy**

A Fasoli, D Testa, S Sharapov, H L Berk, B Breizman, A Gondhalekar, R F Heeter, M Mantsinen and contributors to the EFDA-JET Workprogramme

**Abstract**

Experiments are conducted on the JET tokamak to demonstrate the diagnostic
potential of Magneto-Hydro-Dynamics (MHD) spectroscopy, for the plasma
bulk and its suprathermal components, using Alfvén eigenmodes (AEs) excited
by external antennas and by energetic particles. The measurements of AE
frequencies and mode numbers give information on the bulk plasma. Improved
equilibrium reconstruction, in particular in terms of radial profiles of density
and safety factor, is possible from the comparison between the antenna driven
spectrum and that calculated theoretically. Details of the time evolution of the
non-monotonic safety factor profile in advanced scenarios are reconstructed
from the frequency behaviour of ICRH-driven energetic particle modes. The
plasma effective mass is inferred from the resonant frequency of externally
driven AEs in discharges with similar equilibrium profiles. The stability
thresholds and the nonlinear development of the instabilities give clues on
energy and spatial distribution of the fast particle population. The presence
of unstable AEs provides lower limits in the energy of ICRH generated fast
ion tails. Fast ion pressure gradients and their evolution are inferred from the
stability of AEs at different plasma radial positions. Finally, the details of the
AE spectrum in the nonlinear stage are used to obtain information about the fast
particle velocity space diffusion.

**Turbulent electron thermal transport in tokamaks**

W. Horton, B. Hu, J. Q. Dong and P. Zhu

**Abstract**

The origin of anomalous electron thermal turbulence from spatial gradients in magnetized plasmas is described. Laboratory experiments demonstrating key features of drift waves are reviewed. The turbulent electromagnetic fields produce an anomalous transport that scales with both the gradient parameters and microscopic plasma scale length parameters. The change from the micro-scale dominated gyro-Bohm to the macro-scale dominated Bohm scaling laws is discussed. The close correlations between the electron turbulent transport theory and the confinement properties measured in the steady state hot electron plasmas produced in tokamak devices are presented.