**Laboratory simulations of bow shocks and magnetospheres **

W. Horton, C. Chiu, T. Ditmire

ASTROPHYSICS AND SPACE SCIENCE 298 (1-2): 395-401 JUN 2005

**Abstract **

Laboratory experiments using a plasma wind generated by laser-target interaction are proposed and analyzed to investigate the creation of a shock in front of the magnetosphere and the dynamo mechanism. The proposed experiments and simulations are thought to be relevant to understanding the electron acceleration mechanisms at work in shock-driven magnetic dipole confined plasma in compact magnetized stars. ©* 2005 Springer*

DOI: 10.1007/s10509-005-3981-6

**IFSR-1059**

**Laboratory simulation of magnetospheric plasma shocks **

W. Horton, C. Chiu, T. Ditmire, P. Valanju, R. Presura, V. V. Ivanovb, Y. Sentoku, V. I. Sotnikov, A. Esaulov, N. Le Galloudec, T. E. Cowan, I. Doxas

ASTROPHYSICS AND SPACE SCIENCE 298 (1-2): 299-303 Jun 2005

**Abstract **

Laboratory experiments using a plasma wind generated by laser-target interaction are developed to investigate the creation of a shock in front of the magnetosphere and the dynamo mechanism. Magnetic obstacles are placed in the plasma wind and measurements of the electron density gradients surrounding the obstacles are recorded. The experiments are analyzed with the methods used in theoretical simulation of the solar-wind-driven magnetosphere interactions. The proposed experiments are thought to be relevant to understanding the electron acceleration mechanisms at work in shock-driven magnetic dipole confined plasma surrounding compact magnetized stars and planets. Electron shock acceleration mechanisms are discussed in some detail. ©* 2005 COSPAR Published by Elsevier, Inc. *

DOI: 10.1016/j.asr.2005.01.087

**Beam anisotropy effect on Alfvén eigenmode stability in ITER-like plasmas **

N. N. Gorelenkov, H. L. Berk, R. V. Budny

**Abstract**

This work studies the stability of the toroidicity-induced Alfvén eigenmodes (TAE) in the proposed ITER burning plasma experiment, which can be driven unstable by two groups of energetic particles, the 3.5 MeV α-particle fusion products and the tangentially injected 1 MeV beam ions. Both species are super-Alfvénic but they have different pitch angle distributions and the drive for the same pressure gradients is typically stronger from co-injected beam ions as compared with the isotropically distributed α-particles. This study includes the effect of anisotropy of the beam ion distribution function on TAE growth rate directly via the additional velocity space drive and indirectly in terms of the enhanced effect of the resonant particle phase space density. For near parallel injection TAEs are marginally unstable if the injection aims at the plasma centre, where the ion Landau damping is strong, whereas with the off-axis neutral beam injection the instability is stronger with the growth rate near 0.5% of the TAE mode frequency. In contrast, for perpendicular beam injection TAEs are predicted to be stabilized in nominal ITER discharges.

In addition, the effect of TAEs on the fast ion beta profiles is evaluated by introducing a fast ion redistribution toy model based on a quasi-linear diffusion theory, which uses analytic expressions for the local growth and damping rates. These results illustrate the parameter window that is available for plasma burn when TAE modes are excited. ©*2005 IAEA* (www.iop.org/)

DOI: 10.1088/0029-5515/45/4/002

**Two-fluid magnetic island dynamics in slab geometr****y**.** II. Islands interacting with resistive walls or resonant magnetic perturbations **

R. Fitzpatrick, F. L. Waelbroeck

**Abstract **

The dynamics of a propagating magnetic island interacting with a resistive wall or an externally generated, resonant magnetic perturbation is investigated using two-fluid, drift-(magnetohydrodynamical) (MHD) theory in slab geometry. In both cases, the island equation of motion is found to take exactly the same form as that predicted by single-fluid MHD theory. Three ion polarization terms are found in the Rutherford island width evolution equation. The first is the drift-MHD polarization term for an isolated island, and is unaffected by the interaction with a wall or magnetic perturbation. Next, there is the polarization term due to interaction with a wall or magnetic perturbation which is predicted by single-fluid MHD theory. This term is always destabilizing. Finally, there is a hybrid of the other two polarization terms. The sign of this term depends on many factors. However, under normal circumstances, it is stabilizing if the noninteracting island propagates in the ion diamagnetic direction (with respect to the wall or magnetic perturbation) and destabilizing if it propagates in the electron diamagnetic direction. ©2005 *American Institute of Physics*

DOI: 10.1063/1.1833391

**Two-fluid magnetic island dynamics in slab geometr****y. I. Isolated islands **

R. Fitzpatrick, F. L. Waelbroeck

**Abstract**

A set of reduced, two-dimensional, two-fluid, drift-MHD (magnetohydrodynamical) equations is derived. Using these equations, a complete and fully self-consistent solution is obtained for an isolated magnetic island propagating through a slab plasma with uniform but different ion and electron fluid velocities. The ion and electron fluid flow profiles around the island are uniquely determined, and are everywhere continuous. Moreover, the island phase velocity is uniquely specified by the condition that the island-induced modifications to the ion and electron velocity profiles remain localized in the vicinity of the island. Finally, the ion polarization current correction to the Rutherford island width evolution equation is evaluated and found to be stabilizing provided that the anomalous perpendicular ion viscosity significantly exceeds the anomalous perpendicular electron viscosity.
©2005 *American Institute of Physics*

DOI: 10.1063/1.1833375

**Shielding of error field by liquid metal wall in tokamaks**

L-J Zheng, M. Kotschenreuther, F. Waelbroeck

**Abstract**

It is shown that the error field in a tokamak can be shielded by a flowing liquid metal wall. In particular, a flowing liquid metal wall can prevent resonance amplification of the error field by the plasma near its no-wall stability limit. ©*2006 IAEA *(www.iop.org/)

DOI: 10.1088/0029-5515/46/8/L03

**Nonlinear finite-Larmor-radius drift-kinetic equation**

H. V. Wong

**Abstract**

An efficient method is described for deriving the drift-kinetic equation. A maximal ordering is invoked: the ordering parameter ε≪1 is formally taken to be proportional to *m/e*, subject to the proviso that the parallel electric field E_{||}~ε. Electric drifts can be of the order of particle thermal velocities. The drift-kinetic equation is derived up to second order in ε, and is in a form such that the phase-space volume following the particle phase-space trajectories is preserved. The mean density, mean velocity, momentum flow tensor, and the presure tensor are evaluated in terms of the electromagnetic fields and the velocity moments of the drift-kinetic distribution function (‾G). The moments of the drift-kinetic equation reproduce the corresponding moments of the Vlasov equation up to order ε^{2}. A consistent set of fluid-kinetic equations is formulated, with the fluid-like perpendicular motion described by the perpendicular component of the momentum equation. The drift-kinetic equation describes the parallel motion, and the solution (‾G) is required to evaluate the velocity moments necessary to close the set of equations. ©*2005 American Institute of Physics*

DOI: 10.1063/1.2116867

**Kinetic damping of toroidal Alfvén eigenmodes **

G. Y. Fu, H. L. Berk, A. Pletzer

**Abstract**

The damping of Toroidal Alfvén Eigenmodes in Joint European Torus (JET) [P. H. Rebut and B. E. Kenn, Fusion Technol.**11**, 13 (1987)] plasmas is investigated by using a reduced kinetic model. Typically no significant damping is found to occur near the center of the plasma due to mode conversion to kinetic Alfvén waves. In contrast, continuum damping from resonance near the plasma edge may be significant, and when it is, it gives rise to damping rates that are compatible with the experimental observations. ©2005 *American Institute of Physics *

DOI: 10.1063/1.1995007

**Two-fluid magnetic island dynamics in slab geometry: Determination of the island phase velocity **

R. Fitzpatrick, P. G. Watson, F. L. Waelbroeck

**Abstract**

The physics which determines the phase-velocity of a comparatively wide, isolated, magnetic island, formed as a result of a nonlinear tearing instability in a magnetic confinement device relying on the existence of nested magnetic flux surfaces, is investigated using a two-fluid model in slab geometry. It is found that the phase velocity is fixed by *momentum transport* across the magnetic flux surfaces in the region immediately surrounding the magnetic separatrix. Analytic predictions for the phase velocity are obtained, and are successfully benchmarked against the results of two-dimensional, drift-magnetohydrodynamical simulations.
©2005 *American Institute of Physics*

DOI: 10.1063/1.2001644

**Femtosecond pump-probe study of preformed plasma channels**

R. Zgadzaj, E. W. Gaul, N. H. Matlis, G. Shvets, M. C. Downer

**Abstract**

We report femtosecond pump-probe experiments in He plasma waveguides using 800-nm, 80-fs pump pulses of 0.2×10^{18} W/cm^{2} peak guided intensity and single orthogonally polarized 800-nm probe pulses ~0.1% as intense as the pump. Single-shot spectra and spatial profiles of the probe pulses exiting the channels are measured through a crossed-polarization analyzer at various pump-probe time delays Δt. At |Δt| ≳ 100 fs, we observe frequency-domain interference between the probe and a weak component of the exiting pump created by hybridization of its polarization state through interaction with the channel. Frequency-domain interference measurements show this ''depolarized'' component differs substantially in mode structure from the injected pump pulse. This component is nearly undetectable by direct measurements of pump leakage without the probe. We analyze possible causes of depolarization within the channel and near its entrance and exit regions. At Δt ≲ 0, i.e., the probe pulse propagates in the leading edge of the pump pulse, we observe spectral blueshifts in the transmitted-probe spectrum that are not evident in the transmitted pump. The evidence indicates that pump depolarization and probe blueshifts both originate primarily near the channel entrance. ©*2004 Optical Society of America*

**Energetic ion transport due to Alfvén eigenmode bursts **

Y. Todo, H. L. Berk, B. N. Breizman

**Abstract**

Recurrent bursts of toroidicity-induced Alfvén eigenmodes (TAE) are studied using a self-consistent simulation model. Bursts of beam ion losses observed in the neutral beam injection experiment at the Toakamak Fusion Test Reactor are reproduced using experimental parameters. Only co-injected beam ions build up to a significant stored energy even though their distribution is flattened in the plasma center. They are not directly lost as their orbits extend beyond the outer plasma edge when the core plasma leans on a high field side limiter. The time evolution of the beam ion density during a burst and the particle loss mechanism are presented. In the simulation, the distance to the limiter is decreased after the stored beam energy saturates. We show that the co-passing beam particles may not readily reach the limiter even if the orbit width of edge-located particles is larger than outer edge spacing between the limiter and plasma. For the parameters of this run the stored energy of the co-injected beam density only drops rapidly, after the gap width from the plasma edge to the limiter becomes less than 0.3 of the minor radius. The existence of KAM (Kolmogorov-Arnold-Moser) surfaces of the edge mode even at large field amplitudes apparently inhibits energetic co-passing particles from being lost to the limiter at larger gap widths. ©*2004 The Japan Society of Plasma Science and Nuclear Fusion Research *

**IFSR-1049**

**Application of detuned laser beatwave for generation of few-cycle electromagnetic pulses**

S. Kalmykov, G. Shvets

AIP Conference Proceedings, v. 737, 552 (2004)

An approach to compressing high-power laser beams in plasmas via coherent Raman sideband generation is described. The technique requires two beams: a pump and a probe detuned by a near-resonant frequency Ømega<ømega_p. The two laser beams drive a high-amplitude electron plasma wave (EPW) which modifies the refractive index of plasma so as to produce a periodic phase modulation of the incident laser with the laser beat period 2\pi/Ømega. Thus, a train of chirped laser beatnotes (each of duration 2\pi/Ømega) is formed in plasma. The chirp is positive (the longer-wavelength sidebands are advanced in time) when Ømega<ømega_p and negative otherwise. Finite group velocity dispersion (GVD) of radiation in plasma can compress the positively chirped beatnotes to a few-laser-cycle duration thus creating in plasma a sequence of sharp electromagnetic spikes separated in time by 2\pi/Ømega. Driven EPW locks the phase of laser sidebands and thus reduces the effect of GVD. Compression of the chirped beatnotes can be implemented in a separate plasma of higher density, where the laser sidebands become uncoupled.

**The resistive wall mode and feedback control physics design in NSTX**

S. A. Sabbagh, J. M. Bialek, R. E. Bell, A. H. Glasser, B. P. LeBlanc, J. E. Menard, F. Paoletti, M. G. Bell, R. Fitzpatrick, E. D. Fredrickson, A.M. Garofalo, D. A. Gates, S. M. Kaye, L. L. Lao, R. Maingi, D. Mueller, G. A. Navratil, D. Stutman, W. Zhu

**Abstract **

One of the goals of the National Spherical Torus Experiment (NSTX) is to investigate the physics of global mode stabilization in a low aspect ratio device. NSTX has a major radius R_{0} = 0.86 m, a midplane half-width of 0.7 m, and an on-axis vacuum toroidal field B_{0} ≤ 0.6 T and has reached a plasma current I_{p} = 1.5 MA. Experiments have established the wall-stabilized MHD operating space of the machine. The maximum β_{t} and β_{N} have reached 35% and 6.5%, respectively, with β_{N} reaching 9.5l_{i}. Collapses in plasma toroidal rotation and β_{t} have been correlated with violation of the n = 1 ideal MHD beta limit, β_{N no-wall}, computed by the DCON stability code using time-evolving EFIT reconstructions of experimental discharges. The resistive wall mode (RWM) was observed over a wide range of β_{N} when β_{N no-wall} was exceeded. Plasma toroidal rotation damping during the RWM was rapid and global. Damping rates were more than five times larger than caused by low toroidal mode number rotating modes alone, which displayed a slower, diffusive rotation damping away from the rational surface. The rotation damping rate and dynamics depend on the applied toroidal field and the computed minimum value of the safety factor. The computed RWM perturbed field structure from experimental plasma reconstructions has been input to the VALEN feedback analysis code for quantitative comparison of experimental and theoretical RWM growth rates and to analyse the effectiveness of various active feedback stabilization designs. The computed RWM *n* = 1 mode growth rate, which depends on plasma equilibrium parameters such as β_{N} and pressure profile peaking, agrees well with experimental growth rates in different operating regimes. Increasing β_{N} in the ST initially improves mode coupling to the stabilizing wall; however, at the highest β_{N} values reached, the ideal with-wall beta limit, β_{N wall}, is approached, the effectiveness of the passive stabilizing plates is reduced, and the computed RWM growth rate approaches ideal MHD growth rates. Several active mode control designs were considered and evaluated. The most effective configuration is computed to provide stabilization at β_{N} up to 94% of the ideal with-wall limit .©*2004 IAEA* (www.iop.org/)

DOI: 10.1088/0029-5515/44/4/001

**The role of energetic particles in fusion plasmas**

S. D. Pinches, H. L. Berk, D. N. Borba, B. N. Breizman, S. Briguglio, A. Fasoli, G. Fogaccia, M. P. Gryaznevich, V. Kiptily, M. J. Mantsinen, S. E. Sharapov, D. Testa, R. G. L. Vann, G. Vlad, F. Zonca

**Abstract**

In the burning fusion plasmas of next step devices such as ITER (2001 ITER-FEAT *Outline Design Report* IAEA/ITER EDA/DS/18 (Vienna: IAEA) p 21), the majority of the heating of the fusing fuel will come from the plasma self-heating by fusion born α -particles. Recent advances in theoretical understanding, together with the development of new diagnostic techniques, make this a timely opportunity to survey the role of energetic particles in fusion plasmas and how it projects to future burning plasma devices. ©*2004 IAEA* (www.iop.org/)

DOI: 10.1088/0741-3335/46/12B/017

**The legacy of Masahiro Wakatani**

J. W. Van Dam, W. C. Horton

**Abstract**

As a memorial to Masahiro Wakatani, late professor of plasma physics at Kyoto University, a review is given of his legacy of achievements in scientific research, international collaborations, university administration, student guidance, and personal life. ©*2004 The Japan Society of Plasma Science and Nuclear Fusion Research *

**Response to comment on "Forced magnetic reconnection in the inviscid Taylor problem"**

A. Cole, R. Fitzpatrick

**Abstract**

We agree with the Comment that the final result obtained by Ishizawa and Tokuda is extremely implausible. However, Ishizawa and Tokuda's central claim-that Hahm and Kulsrud improperly used the constant -ψ approximation to obtain their results-cannot be lightly dismissed, since in their calculation Hahm and Kulsrud do not make a proper distinction between the reconnected magnetic flux at the center of the layer ψ_{in} and the asymptotic flux for the external solution ψ_{out}. Hence, it seems to us that a publication redoing Hahm and Kulsrud's analysis but retaining the vitally important distinction between ψ_{in} and ψ_{out}, and then verifying the analysis by careful comparison with numerical simualtions, is warranted. *©2004 American Institute of Physics *

DOI: 10.1063/1.1814118

**Erratum: "Observation of tearing mode deceleration and locking due to eddy currents induced in a conducting shell"**

B. E. Chapman, R. Fitzpatrick, D. Craig, P. Martin, G. Spizzo

DOI: 10.1063/1.1792614

**Exact steady state reconnection solutions in weakly collisional plasmas **

P. G. Watson, F. Porcelli

**Abstract**

We consider the problem of reconnection in weakly collisional plasmas in the strong guide field limit. In this regime the standard resistive Ohm's law is modified to include electron compressibility and electron inertia effects. Despite the increased complexity of the governing equations, we show that analytic steady state solutions, like those discovered by Craig and Henton for the purely resistive case, can be developed for this new system. The resulting solutions are somewhat richer than those of Craig and Henton, and there are various different regimes in parameter space to consider that exhibit multiple length scales, boundary layer effects, and other features. We also examine the dynamical behavior of these new solutions by solving the time-dependent problem numerically. ©*2004 The American Astronomical Society*

DOI: 10.1086/425646

**Anomalous skin effect for anisotropic electron velocity distribution function **

I. Kaganovich, E. Startsev, G. Shvets

**Abstract**

The anomalous skin effect in a plasma with a highly anisotropic electron velocity distribution function (EVDF) is very different from the skin effect in a plasma with isotropic EVDF. An analytical solution was derived for the electric field penetrated into plasma with the EVDF described as a Maxwellian with two temperatures T_{x}>>T_{z}, where x is the direction along the plasma boundary and z is the direction perpendicular to the plasma boundary. The skin layer was found to consist of two distinct regions of width of order v_{T[sub }_{x]}/ω and v_{T[sub z]}/ω, where v_{T[sub }_{x,z]} = the square root of (T_{ x,z}/*m*) is the thermal electron velocity and ω is the incident wave frequency. ©*2004 American Institute of Physics*

DOI: 10.1063/1.1723461

**Scale hierarchy created in plasma flow **

Z. Yoshida, S. M. Mahajan, S. Ohsaki

**Abstract**

The cooperation of nonlinearity (producing collapsed characteristics) and dispersion (unfolding singularities) underlies a robust mechanism that imparts two distinct scales (*L* measuring the system size, and δ_{i} typically of the order of the ion skin depth) to the double Beltrami states of a two-fluid plasma. It is shown that the conventional single-fluid model [magnetohydrodynamic (MHD)] seemingly valid for a large system (δ_{i}/*L*≈0), fails to capture the small scale that is created by the singular perturbation of the two-fluid effect (dispersion). The small-scale component plays an important role in various plasma phenomena, such as coronal heating. The double Beltrami model is compared and contrasted with the standard MHD pathway (Parker's model of current sheet, for instance).
©2004 *American Institute of Physics*

DOI: 10.1063/1.1762877

**IFSR-1039**

**Formation of large scale structures in dusty magnetoplasmas **

P. K. Shukla, S. M. Mahajan

PHYSICS LETTERS A 328 (2-3): 185-188 JUL 26 2004

**Abstract **

We discuss possibility of the formation of large scale structures in a dusty magnetoplasma composed of electrons, ions and charged dust grains. By using the multifluid equations as well as Ampére's law, we derive a pair of equations that describes a robust nonlinear coupling between the dust fluid and the magnetic field. In the steady state, the governing equations for the macroscopic dusty plasma state follow the Beltrami pair, which dictates the formation of structures on a spatial scale comparable to the dust skin depth *c*/*ω*_{pd}; where *c* is speed of light in vacuum and *ω*_{pd} is the dust plasma frequency. The relevance of our investigation to large scale self-organized structures in astrophysical dusty magnetofluids is discussed.
©2004 *Elsevier *

DOI: 10.1016/j.physleta.2004.06.019

**Beat-Wave Excitation of Plasma Waves Based on Relativistic Bistability **

G. Shvets

**Abstract**

A nonlinear beat-wave regime of plasma wave excitation is considered. Two beat-wave drivers are considered: intensity-modulated laser pulse and density-modulated (microbunched) electron beam. It is shown that a long beat-wave pulse can excite strong plasma waves in its wake even when the beat-wave frequency is detuned from the electron plasma frequency. The wake is caused by the dynamic bistability of the nonlinear plasma wave if the beat-wave amplitude exceeds the analytically calculated threshold. In the context of a microbunched beam driven plasma wakefield accelerator, this excitation regime can be applied to developing a femtosecond electron injector. ©2004 *The American Physical Society*

DOI: 10.1103/PhysRevLett.93.195004

**Dynamical plasma response of resistive wall modes to changing external magnetic perturbations**

M. Shilov, C. Cates, R. James, A. Klein, O. Katsuro-Hopkins, Y. Liu, M. E. Mauel, D. A. Maurer, G. A. Navratil, T. S. Pedersen, N. Stillits, R. Fitzpatric, S. F. Paul

**Abstract**

The plasma response to external resonant magnetic perturbations is measured as a function of stability of the resistive wall mode (RWM). The magnetic perturbations are produced with a flexible, high-speed waveform generator that is preprogrammed to drive an in-vessel array of 30 independent control coils and to produce an *m/n* = 3/1 helical field. Both quasi-static and "phase-flip" magnetic perturbations are applied to time-evolving discharges in order to observe the dynamical response of the plasma as a function of RWM stability. The evolving stability of the RWM is estimated using equilibrium reconstructions and ideal stability computations, facilitating comparison with theory. The plasma resonant response depends upon the evolution of the edge safety factor, q*, and the plasma rotation. For discharges adjusted to maintain relatively constant edge safety factor, q*<3, the amplitude of the plasma response to a quasistatic field perturbation does not vary strongly near marginal stability and is consistent with the Fitzpatrick–Aydemir equations with high viscous dissipation. Applying "phase-flip" magnetic perturbations that rapidly change toroidal phase by 180° allows observation of the time scale for the plasma response to realign with the applied perturbation. This phase realignment time increases at marginal stability, as predicted by theory. This effect is easily measured and suggests that the response to time-varying external field perturbations may be used to detect the approach to RWM instability. *©2004 American Institute of Physics
*DOI: 10.1063/1.1688793

**The resistive wall mode and feedback control physics design in NSTX**

S. A. Sabbagh, J. M. Bialek, R. E. Bell, A .H. Glasser, B. P. LeBlanc, J. E. Menard, F. Paoletti, M. G. Bell, R. Fitzpatrick, E. D. Fredrickson, A. M. Garofalo, D. A. Gates, S. M. Kaye, L. L. Lao, R. Maingi, D. Mueller, G. A. Navratil, D. Stutman, W. Zhu, NSTX Research Team

**Abstract**

One of the goals of the National Spherical Torus Experiment (NSTX) is to investigate the physics of global mode stabilization in a low aspect ratio device. NSTX has a major radius R0 = 0.86 m, a midplane half-width of 0.7 m, and an on-axis vacuum toroidal field B0 ≤ 0.6 T and has reached a plasma current Ip = 1.5 MA. Experiments have established the wall-stabilized MHD operating space of the machine. The maximum βt and βN have reached 35% and 6.5%, respectively, with βN reaching 9.5li. Collapses in plasma toroidal rotation and βt have been correlated with violation of the n = 1 ideal MHD beta limit, βN no-wall, computed by the DCON stability code using time-evolving EFIT reconstructions of experimental discharges. The resistive wall mode (RWM) was observed over a wide range of βN when βN no-wall was exceeded. Plasma toroidal rotation damping during the RWM was rapid and global. Damping rates were more than five times larger than caused by low toroidal mode number rotating modes alone, which displayed a slower, diffusive rotation damping away from the rational surface. The rotation damping rate and dynamics depend on the applied toroidal field and the computed minimum value of the safety factor. The computed RWM perturbed field structure from experimental plasma reconstructions has been input to the VALEN feedback analysis code for quantitative comparison of experimental and theoretical RWM growth rates and to analyse the effectiveness of various active feedback stabilization designs. The computed RWM n = 1 mode growth rate, which depends on plasma equilibrium parameters such as βN and pressure profile peaking, agrees well with experimental growth rates in different operating regimes. Increasing βN in the ST initially improves mode coupling to the stabilizing wall; however, at the highest βN values reached, the ideal with-wall beta limit, βN wall, is approached, the effectiveness of the passive stabilizing plates is reduced, and the computed RWM growth rate approaches ideal MHD growth rates. Several active mode control designs were considered and evaluated. The most effective configuration is computed to provide stabilization at βN up to 94% of the ideal with-wall limit. *© 2004 IAEA, Vienna *(www.iop.org/)

DOI: 10.1088/0029-5515/44/4/011

**The role of energetic particles in fusion plasmas**

S. D. Pinches, H. L. Berk, D. N. Borba, B. N. Breizman, S. Briguglio, A. Fasoli, G. Fogaccia, M. P. Gryaznevich, V. Kiptily, M. J. Mantsinen, S. E. Sharapov, D. Testa, R. G. L. Vann, G. Vlad, F. Zonca, JET-EFDA Contributors

**Abstract**

In the burning fusion plasmas of next step devices such as ITER (2001 ITER-FEAT Outline Design Report IAEA/ITER EDA/DS/18 (Vienna: IAEA) p 21), the majority of the heating of the fusing fuel will come from the plasma self-heating by fusion born α -particles. Recent advances in theoretical understanding, together with the development of new diagnostic techniques, make this a timely opportunity to survey the role of energetic particles in fusion plasmas and how it projects to future burning plasma devices. *© 2004 IOP Publishing Ltd. *(www.iop.org/)

DOI: 10.1088/0741-3335/46/12B/017

**Spectroscopic determination of the internal amplitude of frequency sweeping TAE**

S. D. Pinches, H. L. Berk, M. P. Gryaznevich, S. E. Sharapov, JET-EFDA Contributors

**Abstract**

From an understanding of the processes that cause a marginally unstable eigenmode of the system to sweep in frequency, it is shown how the absolute peak amplitude of the mode can be determined from the spectroscopic measurements of the frequency sweeping rate, e.g. with Mirnov coils outside the plasma. In a first attempt to implement such a diagnostic calculation, the MISHKA code (Mikhailovskii A B et al 1997 Plasma Phys. Rep. 23 844) is used to determine the global mode structure of toroidal Alfvén eigenmodes (TAEs) (Cheng C Z et al 1985 Ann. Phys. (NY) 161 21) observed in the MAST spherical tokamak (Sykes A et al 2001 Nucl. Fusion 41 1423). Simulations using the HAGIS code (Pinches S D 1996 PhD Thesis The University of Nottingham, Pinches S D et al 1998 Comput. Phys. Commun. 111 131) are then made, replicating the experimentally observed sweeping phenomena. The fundamental theory is then used together with these simulation results to predict the internal field amplitude from the observed frequency sweeping. The calculated mode amplitude is shown to agree with that obtained from Mirnov coil measurements. *©* *2004 IOP Publishing Ltd. *(www.iop.org/)

DOI: 10.1088/0741-3335/46/7/S04

**The role of laser-pulse duration in the neutron yield of deuterium cluster targets**

K. W. Madison, P. K. Patel, M. Allen, D. Price, R. Fitzpatrick, and T. Ditmire

**Abstract**

We present an experimental and computational study of the ion and fusion neutron yields from explosions of deuterium clusters irradiated with 100-TW laser pulses. We find that the cluster explosion energy and resultant fusion yield are sensitive to the laser pulse rise time as determined by the pulse duration for a fixed envelope shape. Our experimental observations are consistent with the results of particle simulations of the laser-cluster interaction which show that the explosion energies of the clusters are determined by a single parameter: the ratio of the cluster ionization time to its intrinsic expansion time. This competition of time scales sets a fundamental constraint on the ion emission and resultant neutron yield performance of these targets as a function of laser-pulse duration. *© 2004 The American Physical Society *

DOI: 10.1103/PhysRevA.70.053201

**Scrape Off Layer Physics for Burning Plasmas and Innovative Divertor Solutions **

M. Kotschenreuther, P. Valanju, J. Wiley, T. Rognlein, S. M. Mahajan, M. Pekker

**Abstract **

Two distinct topics concerning SOL physics are examined. First, a novel magnetic divertor geometry is presented: 1) inducing a *second* axi-symmetric x-point downstream of main plasma x-point. For reactor relevant coils, field line lengths from the core x-point to the wall can be increased ~2-3 times, and flux expansion can be increased ~5 times. 2) the potential reactor consequences of large SOL convection from “blob-like” transport are examined for the first time. ARIES RS geometries have been simulated using UEDGE, including large convection in the far SOL similar to what is seen in experiments. The hot CX neutral spectrum at the wall is computed using the kinetic neutral code NUT. The high edge plasma temperature plus large recycling from blob like SOL transport give highly enhanced sputtering for a tungsten wall from CX neutrals. Numerical simulations of 2-D nonlinear fluid equations describing blob turbulence from SOL resistive ballooning nodes finds that impurities generated at the wall are rapidly convected inward toward the separatrix. Blob turbulence also greatly reduces the impurity screening of the SOL, leading to the potential for core radiation collapse in a tungsten wall reactor.

**IFSR-1031**

**Hall MHD solitons and the acceleration of reflected electrons **

C. Chiu, W. Horton

Published in *Proceeding of the 5th annual International Conference on High Energy Density Laboratory Astrophysics*, Tucson, Arizona, March 10-13, 2004. (www.hedla.org/)

**IFSR-1030**

**Implications of convective scr ape-off layer transport for fusion reactors with solid and liquid walls**

M. Kotschenreuther, T. Rognlien, P. Valanju

FUSION ENGINEERING AND DESIGN 72 (1-3): 169-180 NOV 2004

**Abstract **

Recent experimental observations in tokamaks indicate enhanced convection of plasma blobs toward the main chamber wall. Potential implications of these observations for reactors are examined here. Two-dimensional plasma edge calculations are performed with UEDGE, including convective transport consistent with present experiments. This is coupled to a kinetic neutral calculation using the code NUT, to compute the hot neutral flux to the wall. The inclusion of convection increases sputtering of the wall by roughly an order of magnitude. For tungsten walls, erosion (neglecting re-deposition) is estimated to be ~.6mm year^{-1}. The enhanced source of impurities for high Z walls requires an enhanced plasma screening factor to allow ignition. Low Z liquid materials enable acceptable plasma contamination with much lower screening factors. Rough estimates of dust generation from erosion rates with convection imply significant safety issues. Plasma transport via blobs can also strongly modify models of impurity screening and redeposition, and represents a potential feasibility issue in need of further research. ©2004 *Elsevier*

DOI: 10.1016/j.fusengdes.2004.07.016

**Driven reconnection in a quadrupole cusp field**

A. Y. Aydemir

**Abstract **

Driven magnetic reconnection in a quadrupole cusp field is examined numerically in various collisionality regimes. Quasi-steady-state reconnection rates far in excess of often-quoted limits are observed. As expected, the rate is determined by external boundary conditions and appears to be limited only by computational concerns; thus, in this configuration the slow reconnection is differentiated from the fast one only by changes in the reconnection-layer geometry. Collisional reconnection exhibits the typical extended current layer of the Sweet-Parker model, whereas the collisionless reconnection mediated by kinetic-Alvén or whistler waves has the Petschek-type "*X*-layer" configuration. The current density at the *X* point is reduced in the collisionless cases, in qualitative agreement with the results from the Versatile Toroidal Facility experiment.

DOI: 10.10.1063/1.2032647

**Convective transport in the scrape-off layer of tokamaks **

A. Y. Aydemir

**Abstract**

A detailed study of blob formation, dynamics, and the associated convective transport in the scrape-off layer (SOL) of tokamak plasmas is presented. Dissipation level in the system, in addition to the blob size, is shown to play an important role in determining whether a blob propagates as a coherent object. Nonlinear SOL interchange/ballooning modes are shown to be capable of creating blobs near the separatrix without relying on the core or edge-plasma dynamics. Finally, the SOL density profiles under diffusive and convective transport assumptions are compared. In the convective regime, here assumed to be driven by the SOL interchange modes, two different scaling with the machine size *R* is found for the characteristic density “*e*-folding” length λ_{n}. When the dominant loss mechanism for the blobs is diffusive, the scale length becomes independent of machine size as the connection length increases. In the less typical case where the parallel losses along the open field lines dominate, λ_{n}∼ R^{1/2}.

DOI: 10.1063/1.1927539

**Statistical mechanics of two-dimensional turbulence **

S. Jung, P.J. Morrison, and H. Swinney

**Abstract**

A statistical mechanical description is proposed for two-dimensional inviscid fluid turbulence. Using this description, we make predictions for turbulent flow in a rapidly rotating laboratory annulus. Measurements on this system reveal coherent vortices in a mean zonal flow. The flow is anisotropic and inhomogeneous but has low dissipation and forcing. In statistical mechanics two crucial requirements for equilibrium are statistical independence of macro-cells (subsystems) and additivity of invariants of the macro-cells. One of these invariants is energy, an extensive quantity, which should be additive; i.e. the interaction energy between a macro-cell and the rest of the system (reservoir) should be small. We use additivity to select the appropriate Casimir invariants from the infinite set available in vortex dynamics. Exchange of micro-cells within a macro-cell should not alter an invariant of a macro-cell. Statistical analyses of turbulence for several decades have considered macro-cells without explicitly considering their statistical independence. A novel feature of the present study is our choice of the macro-cells, which are continuous phase space surfaces based on mean values of the streamfunction; the surfaces can be used to define a canonical distribution. We show that this approach can describe anisotropic and inhomogeneous properties of a flow. Quantities such as energy and enstrophy can be defined on each surface. Our approach leads to the prediction that on a surface there should be a linear relation between the ensemble-averaged potential vorticity and the time-averaged streamfunction; our laboratory data are in good accord with this prediction. Further, the approach predicts that although the probability distribution function for potential vorticity in the entire system is non-Gaussian, the distribution function of micro-cells should be Gaussian on the macro-cells, i.e., for surfaces defined by mean values of the streamfunction. This prediction is also supported by the turbulence data. While our statistical mechanics approach was motivated by and applied to experiments on turbulence in a rotating annulus, the approach is quite general and is applicable to a large class of Hamiltonian systems, including drift-wave plasma models, Vlasov-Poisson dynamics, and kinetic theories of stellar dynamics.

**A relativistic beam-plasma system with electromagnetic waves**

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

**Abstract**

A nonlinear multi-wave model that describes the interaction of an electron beam, plasma waves,
and electromagnetic waves in a cold plasma is derived and studied. The derivation, which is based
on slow amplitude and phase change approximations, begins with the electromagnetic Lagrangian
coupled to an electron beam, a background plasma, and electrostatic and electromagnetic waves.
The model obtained is finite dimensional, and allows for efficient computational and analytical
study. Numerical computations demonstrate that with the inclusion of an electromagnetic wave
with the plasma wave, the beam-plasma instability is suppressed. If two electromagnetic waves
that satisfy a beat-wave matching condition are included, the plasma wave is seen to be amplified
provided the beat-wave amplitude exceeds a certain threshold.

**Hamiltonian and action principle formulations of plasma physics**

P. J. Morrison

**Abstract**

Hamiltonian and action principle formulations of the basic equations of plasma physics are reviewed.
Various types of Lagrangian and Poisson bracket formulations for kinetic and fluid theories
are discussed, and it is described how such formulations can be used to derive and approximate
physical models. Additional uses are also described. Two applications are treated in greater detail:
an algorithm based on Dirac brackets for the calculation of V-states of contour dynamics and
the calculation of fluctuation spectra of Vlasov theory and shear flow dynamics by methods of
statistical mechanics.

**Self-organization phenomena and decaying self-similar state in two-dimensional incompressible viscous fluids **

Y. Kondoh, S. Serizawa, A. Nakano, T. Takahashi, J.W. Van Dam

**Abstract **

The final self-similar state of decaying two-dimensional (2D) turbulence in 2D incompressible viscous flow is analytically and numerically investigated for the case with periodic boundaries. It is proved by theoretical analysis and simulations that the sinh-Poisson state comega=-sinh(betapsi) is not realized in the dynamical system of interest. It is shown by an eigenfunction spectrum analysis that a sufficient explanation for the self-organization to the decaying self-similar state is the faster energy decay of higher eigenmodes and the energy accumulation to the lowest eigenmode for given boundary conditions due to simultaneous normal and inverse cascading by nonlinear mode couplings. The theoretical prediction is demonstrated to be correct by simulations leading to the lowest eigenmode of {(1,0)+(0,1)} of the dissipative operator for the periodic boundaries. It is also clarified that an important process during nonlinear self-organization is an interchange between the dominant operators, which leads to the final decaying self-similar state.

DOI: 10.1103/PhysRevE.70.066312

**IFSR-1023**

**Non-Invariance of Both Magnetic Fluxes within Flux Tubes and Global Helicities in an Ideal Plasma and Numerical Demonstrations of a Generalized Self-Organization Theory **

Y. Kondoh, S. Serizawa, T. Takahashi, J. W. Van Dam

J. Plasma Fusion Res. SERIES, Vol.6 (2004) 601-604 (pdf)

**Abstract **

It is analytically proved that the magnetic flux within a flux tube, the generalized vorticity flux within a vortex flux tube, the magnetic helicity, and the self-helicity are not conserved in the ideally conducting, fully ionized plasma confined by perfectly conducting walls. Self-organization theories based on helicities is clarified to lose their theoretical and physical basis. Numerical demonstrations are presented to show the usefulness of a generalized theory of self-organization based on minimizing the rate of change of global auto-correlations for multiple dynamical field quantities.

**Stimulated Raman backscattering of laser radiation in deep plasma channels **

S. Yu. Kalmykov, G. Shvets

**Abstract **

Stimulated Raman backscattering (RBS) of intense radiation confined by a single-mode plasma channel with a radial variation of plasma frequency greater than a homogeneous-plasma RBS bandwidth is characterized by a strong transverse localization of resonantly driven electron plasma waves (EPW). The EPW localization reduces the peak growth rate of RBS and increases the amplification bandwidth. The continuum of nonbound modes of backscattered radiation shrinks the transverse field profile in a channel and increases the RBS growth rate. Solution of the initial-value problem shows that an electromagnetic pulse amplified by the RBS in the single-mode deep plasma channel has a group velocity higher than in the case of homogeneous-plasma Raman amplification. Implications to the design of a RBS pulse compressor in plasma channel are discussed.

[DOI: 10.1063/1.1778743]

**Remarks on the discrete Alfvén wave spectrum induced by the Hall current**

A. Ito, A. Hirose, S. M. Mahajan, S. Ohsaki

**Abstract**

It is shown that the discrete Alfvén wave induced by the Hall current [S. Ohsaki and S. M. Mahajan, Phys. Plasmas **11**, 898 (2004)] is equivalent to the kinetic Alfvén wave (KAW). The KAW is, thus, accessible in a fluid description. It is further shown that the dispersion relation for the Hall magnetohydrodynamic waves can be reproduced from the kinetic theory only if the ion temperature is negligible compared with the electron temperature.

DOI: 10.1063.1.1804979

**Engineering the Electromagnetic Properties of Periodic Nanostructures Using Electrostatic Resonances**

G. Shvets, Y. A. Urzhumov

**Abstract**

Electromagnetic properties of periodic two-dimensional subwavelength structures consisting of closely packed inclusions of materials with negative dielectric permittivity ε in a dielectric host with positive ε_{h} can be engineered using the concept of multiple electrostatic resonances. Fully electromagnetic solutions of Maxwell's equations reveal multiple wave propagation bands, with the wavelengths much longer than the nanostructure period. Some of these bands are described using the quasistatic theory of the effective dielectric permittivity ε_{qs}. Those bands exhibit multiple cutoffs and resonances which are found to be related to each other through a duality condition. An additional propagation band characterized by a negative magnetic permeability is found. Imaging with subwavelength resolution in that band is demonstrated.

DOI: 10.1103/PhysRevLett.93.243902

**IFSR-1019**

**Temperature gradiant driven electron transport in NSTX and Tore Supra**

W. Horton, H. V. Wong, P. J. Morrison, A. Wurm, J. H. Kim, J. C. Perez, J. Pratt, G. T. Hoang, B. P. LeBlanc, R. Ball

NUCLEAR FUSION 45 (8): 976-985 Aug 2005

**Abstract **

Electron thermal fluxes are derived from the power balance for Tore Supra (TS) and NSTX discharges with centrally deposited fast wave electron heating. Measurements of the electron temperature and density profiles, combined with ray tracing computations of the power absorption profiles, allow detailed interpretation of the thermal flux versus temperature gradient. Evidence supporting the occurrence of electron temperature gradient turbulent transport in the two confinement devices is found. With control of the magnetic rotational transform profile and the heating power, internal transport barriers are created in TS and NSTX discharges. These partial transport barriers are argued to be a universal feature of transport equations in the presence of invariant tori that are intrinsic to non-monotonic rotational transforms in dynamical systems.

DOI: 10.1088/0029-5515/45/8/025

**Nonlinear dynamics of the firehose instability in a magnetic dipole geotail geometry **

H. Vernon Wong, B.-Y. Xu, W. Horton, J. Pratt, J. W. Van Dam

**Abstract **

The nonlinear dynamics of the firehose instability provides a possible explanation for the onset of the magnetic fluctuations associated with bursty bulk flows and substorms. Magnetic fluctuations called Pi2 geomagnetic pulsations are associated with bursty flows in the geotail plasma, where the plasma pressure exceeds the magnetic pressure. These strong magnetic fluctuations are often associated with substorms and start a few minutes before the arrival of the dipolarization pulse. Motivated by these observations, we have derived a nonlinear partial differential equation and developed an initial value code to investigate the firehose anisotropy-driven turbulence in the Earth's geotail. We show that Hall MHD and dispersive ion kinetic effects limit the range of unstable parallel wavenumbers and determine the frequency spectrum of the turbulence. Nonlinear saturation is caused by the nonlinear weakening at large magnetic field line distortions of the destabilizing magnetic curvature force driven by the pressure anisotropy.

DOI: 10.1029/2003JA010288

**Beam ion driven instabilities in the National Spherical Tokamak Experiment**

N. N. Gorelenkov, E. Belova, H. L. Berk, C. Z. Cheng, E. Fredrickson, W. W. Heidbrink, S. Kaye, G. J. Kramer

**Abstract**

Recent progress in the analysis of the low and high frequency beam ion driven instabilities in the National Spherical Tokamak Experiment (NSTX) [S. Kaye et al., Fusion Technol. **36**, 16 (1999)] plasma is reported. The low Alfvén speed with respect to the beam ion injection velocity in NSTX offers a window in the plasma parameter space to study instabilities driven by super-Alfvénic fusion alphas, which are expected in the International Tokamak Experimental Reactor—ITER [D. J. Campbell, Phys. Plasmas **8**, 2041 (2001)]. Low frequency magnetic field activities identified as an instability of toroidicity-induced Alfvén eigenmodes (TAEs) have been observed in NSTX and analyzed with the linear hybrid kinetic magnetohydrodynamic stability code NOVA-K [C. Z. Cheng, Phys. Rep. **1**, 211 (1992)]. The comparison between the TAE analysis and observations in NSTX and DIII–D [J. L. Luxon, Nucl. Fusion **42**, 614 (2002)] similarity experiments confirms that the toroidal mode number of the most unstable TAE modes scales with *q ^{-2}* and is independent of plasma major radius, where

**IFSR-1016**

**Relation between Hall-magnetohydrodynamics and
the kinetic Alfvén wave **

Akira Hirose, Atsushi Ito, Swadesh M. Mahajan, Shuichi Ohsaki

Physics Letters A Volume 330 Issue 6 (2004) 474-480

**Abstract**

Effects of a finite ion temperature on the Hall magnetohydrodynamics (MHD), which breaks down for a finite ion temperature, are clarified in terms of a rigorous three-field kinetic dispersion relation. The MHD mode equation becomes anisotropic with respect to the ion pressure because of the double adiabaticity in ion dynamics.

**IFSR-1015**

**A dynamical model for the coupled inner magnetosphere and tail **

I. Doxas, W. Horton, W. T. Lin, S. Seibert, and M. Mithaiwala

PLASMA SCIENCE, IEEE TRANSACTIONS on Volume 32, Issue 4, Aug. 2004 Page(s):1443 - 1448

**Abstract**

WINDMI-RC is a family of physics-based models that range in dimensionality from low-order models of dimension *d = 8*, which model the flow of energy between the eight highest global energy components of the tail, to high-order models with dimension *d* ~ 100 or more, for models that resolve the nonlinear dynamics of the system into different latitude zones. The models are intrinsically three dimensional in configuration space and use the basic geometry of the Tsyganenko magnetic field model to define the geometrical quantities. The models satisfy the constraints of the conservations laws of energy and electrical charge in their network of nodes and branches that follow from the structure of the system. These models describe the injection of plasma from the plasma sheet and across the Alfvén layer into the inner ring current. The transport uses the storm-time solar wind dynamo electric field as the driver for the network model coupled to the inner magnetospheric corotation electric field.