**Optical magnetism and negative refraction in plasmonic metamaterials**

Y. A. Urzhumov, G. Shvets

**Abstract**

In this review we describe the challenges and opportunities for creating magnetically active metamaterials in the optical part of the spectrum. The emphasis is on the sub-wavelength periodic metamaterials whose unit cell is much smaller than the optical wavelength. The conceptual differences between microwave and optical metamaterials are demonstrated. We also describe several theoretical techniques used for calculating the effective parameters of plasmonic metamaterials: the effective dielectric permittivity View the MathML source and magnetic permeability View the MathML source. Several examples of negative permittivity and negative permeability plasmonic metamaterials are used to illustrate the theory. © *2008 Elsevier Ltd. All rights reserved*.

DOI:10.1016/j.ssc.2007.08.047

**Fluid model for relativistic, magnetized plasmas**

J. M. TenBarge, R. D. Hazeltine, S. M. Mahajan

**Abstract**

Many astrophysical plasmas and some laboratory plasmas are relativistic: Either the thermal speed or the local bulk flow in some frame approaches the speed of light. Often, such plasmas are magnetized in the sense that the Larmor radius is smaller than any gradient scale length of interest. Conventionally, relativistic magnetohydrodynamics (MHD) is employed to treat relativistic, magnetized plasmas. However, MHD requires the collision time to be shorter than any other time scale in the system. Thus, MHD employs the thermodynamic equilibrium form of the stress tensor, neglecting pressure anisotropy and heat flow parallel to the magnetic field. Recent work has attempted to remedy these shortcomings. This paper re-examines the closure question and finds a more complete theory, which yields a more physical and self-consistent closure. Beginning with exact moments of the kinetic equation, we derive a closed set of Lorentz-covariant fluid equations for a magnetized plasma allowing for pressure and heat flow anisotropy. Basic predictions of the model, especially of the dispersion relation's dependence upon relativistic temperature, are examined. ©*2008 American Institute of Physics*

DOI: 10.1063/1.2839286

**Excitation of Alfvén eigenmodes by low energy beam ions in the DIII-D and JET tokamaks**

R. Nazikian, N. N. Gorelenkov, B. Alper, H. L. Berk, D. Borba, R. V. Budny, G. Y. Fu, W. W. Heidbrink, G. J. Kramer, M. A. Makowski, S. D. Pinches, S. E. Sharapov, W. M. Solomon, E. J. Strait, R. B. White, M. A. Van Zeeland

**Abstract**

Core localized Alfvén eigenmodes in DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] and Joint European Torus (JET) [P. H. Rebut and B. E. Keen, Fusion Technol. 11, 13 (1987)] plasmas are driven by deuterium neutral beam ions traveling well below the Alfvén speed. Modes are observed in reverse magnetic shear discharges with deuterium ion velocities as low as 0.23 and 0.16 of the Alfvén speed parallel to the magnetic field in DIII-D and JET plasmas, respectively. Ellipticity-induced Alfvén eigenmodes in DIII-D and toroidicity-induced Alfvén eigenmodes in JET are excited by deuterium ions traveling well below the fundamental passing ion resonance condition, indicating the role of high-order resonances in driving these modes. NOVA-K analysis reveals many high-order resonances as contributing to the mode drive at high central safety factor due to the correspondingly large poloidal orbit width and the decrease in the perpendicular scale length of the modes. ©*2008 American Institute of Physics*

DOI: 10.1063/1.2839286

**Intense geodesic acousticlike modes driven by suprathermal ions in a tokamak plasma **

T. Nazikian, GY Fu, ME Austin, HL Berk, RV Budny, NN Forelenkov, WW Heidbrink, CT Holcomb, GJ Kramer, GR McKee, MA Makowski, WM Solomon, M. Shafer, EJ Strait, MA Zeeland

**Abstract**

Intense axisymmetric oscillations driven by suprathermal ions injected in the direction counter to the toroidal plasma current are observed in the DIII-D tokamak. The modes appear at nearly half the ideal geodesic acoustic mode frequency, in plasmas with comparable electron and ion temperatures and elevated magnetic safety factor (q_{min}>=2). Strong bursting and frequency chirping are observed, concomitant with large (10%–15%) drops in the neutron emission. Large electron density fluctuations (ñ_{e}/n_{e}~=1.5%) are observed with no detectable electron temperature fluctuations, confirming a dominant compressional contribution to the pressure perturbation as predicted by kinetic theory. The observed mode frequency is consistent with a recent theoretical prediction for the energetic-particle-driven geodesic acoustic mode. *©2008 The American Physical Society*

DOI:10.1103/PhysRevLett.101.185001

**A sharp boundary model for the vertical and kink stability of large aspect-ratio vertically elongated tokamak plasmas **

R. Fitzpatrick

**Abstract**

A relatively straightforward version of the well-known sharp boundary model is developed in order to investigate the ideal n=0 and n=1 stability of large aspect-ratio, high-beta, tokamak plasmas with vertically elongated poloidal cross sections which are surrounded by either ideal, resistive, or partial conducting walls. All calculations made using the model reduce to comparatively simple matrix eigenvalue problems. Various example calculations are described. ©2008 *American Institute of Physics*

DOI:10.1063/1.2975359

**Drift-tearing magnetic islands in tokamak plasmas **

R. Fitzpatrick, F.L. Waelbroeck

**Abstract**

A systematic fluid theory of nonlinear magnetic island dynamics in conventional low-beta, large aspect-ratio, circular cross-section tokamak plasmas is developed using an extended magnetohydrodynamics model that incorporates diamagnetic flows, ion gyroviscosity, fast parallel electron heat transport, the ion sound wave, the drift wave, and average magnetic field-line curvature. The model excludes the compressible Alfvén wave, geodesic field-line curvature, neoclassical effects, and ion Landau damping. A collisional closure is used for plasma dynamics parallel to the magnetic field. Two distinct branches of island solutions are found, namely the “sonic” and “hypersonic” branches. Both branches are investigated analytically, using suitable ordering schemes, and in each case the problem is reduced to a relatively simple set of nonlinear differential equations that can be solved numerically via iteration. The solution determines the island phase velocity, relative to the plasma, and the effect of local currents on the island stability. Sonic islands are relatively wide, flatten both the temperature and density profiles, and tend to propagate close to the local ion fluid velocity. Hypersonic islands, on the other hand, are relatively narrow, only flatten the temperature profile, radiate drift-acoustic waves, and tend to propagate close to the local electron fluid velocity. The hypersonic solution branch ceases to exist above a critical island width. Under normal circumstances, both types of island are stabilized by local ion polarization currents. © 2008 *American Institute of Physics*

DOI:10.1063/1.2829757

**Observation of simultaneous fast and slow light**

P. Bianucci, C. Fietz, J. Robertson, G. Shvets, C. Shih

**Abstract**

We present a microresonator-based system capable of simultaneously producing time-advanced and time-delayed pulses. The effect is based on the combination of a sharp spectral feature with two orthogonally-polarized propagating waveguide modes. We include an experimental proof-of-concept implementation using a silica microsphere coupled to a tapered optical fiber and use a time-domain picture to interpret the observed delays. We also discuss potential applications for future all-optical networks. *©2008 The American Physical Society *

DOI: 10.1103/PhysRevA.77.053816

**Scientists protest professor's dismissal**

H. L. Berk, N. J. Fisch, A. Burdakov, G. I. Dimov, A. A. Ivanov, E. P. Kruglyakov, V. Moiseenko, K. Noack, V. P. Pastukhov, S. Tanaka, O. Agren

**Electron thermal transport analysis in Tokamak a Configuration variable**

E. Asp, J-H Kim, W. Horton, L. Porte, S. Alberti, A. Karpushov, Y. Martin, O. Sauter, G. Turri, the TCV Team

**Abstract**

A Tokamak à Configuration Variable (TCV) [G. Tonetti, A. Heym, F. Hofmann et al., in Proceedings of the 16th Symposium on Fusion Technology, London, U.K., edited by R. Hemsworth (North-Holland, Amsterdam, 1991), p. 587] plasma with high power density (up to 8 MW/m3) core deposited electron cyclotron resonance heating at significant plasma densities (<=7×1019 m-3) is analyzed for the electron thermal transport. The discharge distinguishes itself as it has four distinct high confinement mode (H-mode) phases. An Ohmic H-mode with type III edge localized modes (ELMs), which turns into a type I ELMy H-mode when the ECRH is switched on. The ELMs then vanish, which gives rise to a quasistationary ELM-free H-mode. This ELM-free phase can be divided into two, one without magnetohydrodynamics (MHD) and one with. The MHD mode in the latter case causes the confinement to drop by ~15%. For all four phases both large-scale trapped electron (TEM) and ion temperature gradient (ITG) modes and small-scale electron temperature gradient (ETG) modes are analyzed. The analytical TEM formulas have difficulty in explaining both the magnitude and the radial profile of the electron thermal flux. Collisionality governs the drive of the TEM, which for the discharge in question implies it can be driven by either the temperature or density gradient. The TEM response function is derived and it is shown to be relatively small and to have sharp resonances in its energy dependence. The ETG turbulence, predicted by the Institute for Fusion Studies electron gyrofluid code, is on the other hand driven solely by the electron temperature gradient. Both trapped and passing electrons add to the ETG instability and turbulent thermal flux. For easy comparison of the results of the above approaches and also with the Weiland model, a dimensionless error measure, the so-called average relative variance is introduced. According to this method the ETG model explains 70% of the variation in the electron heat diffusivity whereas the predictive capabilities of the TEM-ITG models are poor. These results for TCV support the conclusion that the ETG model is able to explain a wide range of anomalous electron transport data, in addition to existing evidence from ASDEX [F. Ryter, F. Leuterer, G. Pereverzev, H.-U. Fahrbach, J. Stober, W. Suttrop, and the ASDEX Upgrade Team, Phys. Rev. Lett. 86, 2325 (2001)], Tore Supra [G. T. Hoang, W. Horton, C. Bourdelle, B. Hu, X. Garbet, and M. Ottaviani, Phys. Plasmas 10, 405 (2003)] and the Frascati Tokamak Upgrade [A. Jacchia, F. D. Luca, S. Cirant, C. Sozzi, G. Bracco, A. Brushi, P. Buratti, S. Podda, and O. Tudisco, Nucl. Fusion 42, 1116 (2002)]. *©2008 American Institute of Physics*

DOI: 10.1063/1.2965828

**Benchmark tests of fusion plasma simulation codes for studying microturbulence and energetic-particle dynamics**

T. Watanabe, Y. Todo, W. Horton

**Abstract**

Benchmark tests of two simulation codes used for studying microturbulence and energetic-particle dynamics in magnetic fusion plasmas are conducted on present-day parallel supercomputer systems. Both the codes achieved high efficiency on the Earth Simulator with vector processors, and showed good performance scaling on massively parallel supercomputers with more than 10,000 commodity processors. The benchmark results obtained indicated high adaptability of fusion plasma simulation codes to state-of-the-art supercomputer systems. *©2008 The Japan Society of Plasma Science and Nuclear Fusion Research*

DOI: 10.1585/pfr.3.061

**IFSR-1260**

**A method for the intensification of atomic oxygen green line emission by internal gravity waves **

T. Kaladze, W. Horton, T. Garner, J. Van Dam, M. Mays

**Abstract**

Low-frequency internal gravity waves, such as may be generated by seismic activity and nonlinearly propagated through the stably stratified atmosphere to the E layer of the ionosphere, are shown to cause intensification of atomic oxygen green line emission when their amplitude is sufficiently large. The nonlinear equations for the internal gravity waves are derived with the interaction of the induced currents with the geomagnetic field taken into account. When the source of the internal gravity waves is sufficiently strong, nonlinear vortex structures are predicted to be formed in the upper stratosphere and lower ionosphere. These nonlinear vortex structures are damped owing to Joule losses. The vortices provide a mechanism for increasing the concentration of atomic oxygen in the E layer and hence the associated intensity of the green light radiation at 557.7 nm. Data are discussed that report the observation of enhanced green light emission prior to earthquakes; this could lead to a forecasting model if the connection with seismic activity can be established. *An edited version of this paper was published by AGU. ©* *2008 American Geophysical Union*

DOI: 10.1029/2008JA013425

**Reduction of chaotic particle transport driven by drift waves in sheared flows**

Marcus, Caldas, Guimaraes-Filho, Morrison, Horton, Kuznetsov, Nascimento

**Abstract**

Investigations of chaotic particle transport by drift waves propagating in the edge plasma of tokamaks with poloidal zonal flow are described. For large aspect ratio tokamaks, the influence of radial electric field profiles on convective cells and transport barriers, created by the nonlinear interaction between the poloidal flow and resonant waves, is investigated. For equilibria with edge shear flow, particle transport is seen to be reduced when the electric field shear is reversed. The transport reduction is attributed to the robust invariant tori that occur in nontwist Hamiltonian systems. This mechanism is proposed as an explanation for the transport reduction in Tokamak Chauffage Alfvén Brésilien [R. M. O. Galva~o et al., Plasma Phys. Controlled Fusion 43, 1181 (2001)] for discharges with a biased electrode at the plasma edge. *©2008 American Institute of Physics*

DOI: 10.1063/1.3009532

**Plasma acceleration and cooling by strong laser field due to the action of radiation reaction force**

V. Berezhiani, S. Mahajan, Z. Yoshida

**Abstract**

It is shown that for super intense laser pulses propagating in a hot plasma, the action of the radiation reaction force (appropriately incorporated into the equations of motion) causes strong bulk plasma motion with the kinetic energy raised even to relativistic values; the increase in bulk energy is accompanied by a corresponding cooling (intense cooling) of the plasma. The effects are demonstrated through explicit analytical calculations. *©2008 The American Physical Society *

DOI: 10.1103/PhysRevE.78.066403

**Three-dimensional filamentary structures of a relativistic electron beam in fast ignition plasmas**

A. Karmakar, N. Kumar, A. Pukhov, O. Polomarov, G. Shvets

**Abstract**

The filamentary structures and associated electromagnetic fields of a relativistic electron beam have been studied by three-dimensional particle-in-cell simulations in the context of fast ignition fusion. The simulations explicitly include collisions in return plasma current and distinctly examine the effects of beam temperature and collisions on the growth of filamentary structures generated. *©2008 American Institute of Physics*

DOI: 10.1063/1.3042208

**From Scattering Parameters to Snell's Law: A Subwavelength Near-Infrared Negative-Index Metameterial**

X. Zhang, M. Davanco, Y. Uzhumov, G. Shvets, S. Forrest

**Abstract**

A general relation is derived between the band structure of an arbitrary low-loss unit cell and its effective index of refraction. In addition, we determine the maximum unit cell size that defines the "metamaterial regime" [D. R. Smith, Phys. Rev. E 71, 036617 (2005)10.1103/PhysRevE.71.036617]. Furthermore, these general rules allow for the design of a subwavelength near-infrared negative-index material, where the negative refractive index is verified by band calculations to be a bulk property. Full-wavelength simulations of prisms consisting of these unit cells suggest behavior consistent with Snell's law in the negative-index regime. *©2008 The American Physical Society *

DOI: 10.1103/PhysRevLett.101.267401

**Collision-Driven Negative-Energy Waves and the Weibel Instability of a Relativistic Electron Beam in a Quasineutral Plasma**

A. Karmakar, N. Kumar, G. Shvets, O. Polomarov, A. Pukhov

**Abstract**

A new model describing the Weibel instability of a relativistic electron beam propagating through a resistive plasma is developed. For finite-temperature beams, a new class of negative-energy magnetosound waves is identified, whose growth due to collisional dissipation destabilizes the beam-plasma system even for high beam temperatures. We perform 2D and 3D particle-in-cell simulations and show that in 3D geometry the Weibel instability persists even for collisionless background plasma. The anomalous plasma resistivity in 3D is caused by the two-stream instability. *©2008 The American Physical Society *

DOI: 10.1103/PhysRevLett.101.255001

**IFSR-1254**

**Linear superposition of nonlinear waves**

S. Mahajan, Hideakimiura

**Abstract**

Exact nonlinear (arbitrary amplitude) wave-like solutions of an incompressible, magnetized, non-dissipative two-fluid system are found. It is shown that, in 1-D propagation, these fully nonlinear solutions display a rare property; they can be linearly superposed. *©2008 Cambridge University Press*

DOI: 10.1017/S0022377808007770

**All-optical control of nonlinear focusing of laser beams in plasma beat wave accelerator **

S. Kalmykov, S. Yi, G. Shvets

**Abstract**

Nonlinear focusing of a bi-color laser in plasma can be controlled by varying the difference frequency Ω. The driven electron density perturbation forms a co-moving periodic focusing (de-focusing) channel if Ω is below (above) the electron Langmuir frequency ωp. Hence, the beam focusing is enhanced for Ω < ωp and is suppressed otherwise. In particular, a catastrophic relativistic self-focusing of a high-power laser beam can be prevented all-optically by a second, much weaker, co-propagating beam shifted in frequency by Ω > ωp. A bi-envelope equation describing the early stage of the mutual de-focusing is derived and analyzed. Later stages, characterized by a well-developed electromagnetic cascade, are investigated numerically. Stable propagation of the over-critical laser pulse over several Rayleigh lengths is predicted. The non-resonant plasma beat wave (Ω ≠ ωp) can accelerate pre-injected electrons above 100 MeV with low energy spread. *©2008 Institute of Physics and IOP Publishing Limited*

DOI: 10.1088/0741-3335/51/2/024011

**IFSR-1252**

**Fusion-Fission Transmutation Scheme-Efficient destruction of nuclear waste **

M. Kotschenreuther, P.M. Valanju, S.M. Mahajan, E.A. Schneider

**Abstract**

A fusion-assisted transmutation system for the destruction of transuranic nuclear waste is developed by combining a subcritical fusion-fission hybrid assembly uniquely equipped to burn the worst thermal nonfissile transuranic isotopes with a new fuel cycle that uses cheaper light water reactors for most of the transmutation. The center piece of this fuel cycle, the high power density compact fusion neutron source (100 MW, outer radius <3 m), is made possible by the new divertor with the a heat-handling capacity five times that of the standard alternative. The number of hybrids needed to destroy a given amount of waste is an order of magnitude below the corresponding number of critical fast-spectrum reactors (FRs) as the latter cannot fully exploit the new fuel cycle. Also, the time needed for 99% transuranic waste destruction reduces from centuries (with FR) to decades. *© 2008 Elsevier B.V.*

DOI: 10.1016/j.fusengdes.2008.11.019

**Collisionless plasma expansion into vacuum: two new twists on an old problem**

A.V Arefiev, B.N. Breizman

**Abstract**

The paper deals with a generic problem of collisionless plasma expansion into vacuum in the regimes where the expanding plasma consists of hot electrons and cold ions. The expansion is caused by electron pressure and serves as an energy transfer mechanism from electrons to ions. This process is often described under the assumption of Maxwellian electrons, which easily fails in the absence of collisions. The paper discusses two systems with a naturally occurring non-Maxwellian distribution: an expanding laser-irradiated nanoplasma and a supersonic jet coming out of a magnetic nozzle. The presented rigorous kinetic description demonstrates how the deviation from the Maxwellian distribution fundamentally alters the process of ion acceleration during plasma expansion. This result points to the critical importance of a fully kinetic treatment in problems with collisionless plasma expansion.

**All-optical suppression of relativistic self-focusing of laser beams in plasmas **

S. Kalmykov, S. Yi, G. Shvets

**Abstract**

It is demonstrated that a catastrophic relativistic self-focusing (RSF) of a high-power laser pulse can be prevented all-optically by a second, much weaker, copropagating pulse. RSF suppression occurs when the difference frequency of the pulses slightly exceeds the electron plasma frequency. The mutual defocusing is caused by the three-dimensional electron density perturbation driven by the laser beat wave slightly above the plasma resonance. A bienvelope model describing the early stage of the mutual defocusing is derived and analyzed. Later stages, characterized by the presence of a strong electromagnetic cascade, are investigated numerically. Stable propagation of the laser pulse with weakly varying spot size and peak amplitude over several Rayleigh lengths is predicted. *©2008 The American Physical Society *

DOI: 10.1103/PhysRevE.78.057401

**Merging of Super-Alfvenic Current Filaments during Collisionless Weibel Instability of Relativistic Electrong Beams **

O. Polomarov, I. Kaganovich, G. Shvets

**Abstract**

The theoretical framework predicting the long-term evolution, structure, and coalescence energetics of current filaments during the Weibel instability of an electron beam in a collisionless plasma is developed. We emphasize the nonlinear stage of the instability, during which the beam density of filaments increases to the background ion density, and the ambient plasma electrons are fully expelled from the filaments. Our analytic and numerical results demonstrate that the beam filaments can carry super-Alfvénic currents and develop hollow-current density profiles. This explains why the initially increasing magnetic field energy eventually decreases during the late stage of the instability. *©2008 The American Physical Society *

DOI: 10.1103/PhysRevLett.101.175001

**Wave localization and density bunching in pair ion plasmas**

S. Mahajan, N. Shatashvili

**Abstract**

By investigating the nonlinear propagation of high intensity electromagnetic (EM) waves in a pair ion plasma, whose symmetry is broken via contamination by a small fraction of high mass immobile ions, it is shown that this new and interesting state of (laboratory created) matter is capable of supporting structures that strongly localize and bunch the EM radiation with density excess in the region of localization. Testing of this prediction in controlled laboratory experiments can lend credence, inter alia, to conjectures on structure formation (via the same mechanism) in the MEV era of the early universe. *©2008 American Institute of Physics*

DOI: 10.1063/1.3005382

**Hall magnetohydrodynamics in a strong magnetic field **

D. Gomez, S. Mahajan, P. Dmitruk

**Abstract**

For a plasma embedded in a strong external magnetic field, the spatial structures tend to develop fine scales preferentially across the field, rather than along the parallel direction. This feature, which allowed a major simplification in the theoretical structure of one-fluid magnetohydrodynamics (leading to reduced magnetohydrodynamics), is exploited here to derive what may be called the reduced Hall magnetohydrodynamic equations (RHMHD) reflecting two-fluid effects such as the Hall current and the electron pressure. These physical effects, which can be relevant in astrophysical environments and also in fusion plasmas, allow for the propagation of circularly polarized normal modes such as whistlers and shear/ion-cyclotron waves. In this paper, the RHMHD system of equations is integrated numerically, to investigate externally driven turbulence. *©2008 American Institute of Physics*

DOI: 10.1063/1.2991395

**Existence of the Magnetorotational Instability **

S.M. Mahajan, V. Krishan

**Abstract**

By posing and solving a global axisymmetric eigenvalue problem on an infinite domain with modes vanishing at zero and infinity for a differentially rotating MHD plasma, the conditions for the occurrence of a purely growing low-frequency mode known as the magnetorotational instability (MRI) are mapped. It is shown that the MRI criterion drawn from the "local dispersion relation" is at best inadequate and may even be misleading. The physics of the MRI is rather nuanced. It is dictated by the details of the radial profile of the rotation velocity Ω (r) and not just by the sign and the magnitude of its gradient, Ω'. The salient features of the class of profiles for which the MRI-like eigenmodes may occur are given along with the eigenspectrum. For a variety of other profiles, it is shown that an unstable magnetorotational mode is not a valid eigensolution. *©* *2008 The American Astronomical Society *

DOI: 10.1086/589321

**IFSR-1245**

**Zonal flow generation by internal gravity waves in the atmosphere **

W. Horton, T.D. Kaladze, J.W. Van Dam, T.W. Garner

**Abstract**

A novel mechanism for the generation of low-frequency large-scale zonal flows by higher-frequency, small-scale, finite-amplitude internal gravity (IG) waves is analyzed in the atmosphere from the troposphere to the ionosphere E layer. The nonlinear generation mechanism is based on the parametric excitation of convective cells by finite-amplitude IG waves. A set of coupled equations describing the nonlinear interaction of IG waves and zonal flows is derived. The generation of zonal flows is due to the Reynolds stress and mean stratification forces produced by finite-amplitude IG waves. The onset mechanism for the instability is governed by a generalized Lighthill instability criterion. Explicit expressions for the maximum growth rate as well as for the optimal spatial dimensions of the zonal flows are derived. The growth rates of zonal flow instabilities and the conditions for driving them are determined. A comparison with existing results is carried out. The present theory can be used for the interpretation of IG wave observations in the Earth's atmosphere and laboratory experiments. Some earthquake-related phenomena are briefly discussed. *An edited version of this paper was published by AGU. ©* *2008 American Geophysical Union*

DOI: 10.1029/2007JA012952

**John Morgan Greene **

P.J. Morrison, V. Chan

**Neoclassical tearing mode saturation in periodic current sheets**

F. Militello, M. Ottaviana, F. Porcelli

**Abstract**

The saturation of Neoclassical Tearing Mode islands in a periodic slab configuration is investigated. Several theoretical models, all based on a generalization of Rutherford's procedure, that aim at reducing the complete system to a single equation of the magnetic island width, are compared against numerical simulations. When the effects of the bootstrap current and of the second derivative of the equilibrium current profile are included, the numerical saturation levels are well matched with the predictions of this equation in a wide region of the stability diagram. However, the numerical results diverge from the standard theory when evaluating the threshold for nonlinear destabilization, since the theoretical value appears to be strongly conservative. In other words, the standard generalization of Rutherford's equation is not able to capture the minimum value of the linear stability parameter and of the island width such that below them the Neoclassical Tearing Mode is always suppressed. To correct this discrepancy, a new theoretical model in which the transverse propagation of the island affects the bootstrap current term is proposed. ©*2008 American Institute of Physics*

DOI: 10.1063/1.2901193

**Interaction between turbulence and a nonlinear tearing mode in the low β regime**

F. Militello, F.L. Waelbroeck, R. Fitzpatrick, W. Horton

**Abstract**

The interaction between turbulence and a nonlinear tearing mode is investigated numerically using a 2D electrostatic model. Turbulence is found to cause transitions between the different roots for the propagation velocity of the mode. The transitions take the mode towards roots with slower propagation that are characterized by a locally flattened density profile. For sufficiently large islands the transition reduces the drive for the tearing mode. ©*2008 American Institute of Physics*

DOI: 10.1063/1.2917915

**IFSR-1241**

**Feasibility of achieving gain in transition to the ground state of C VI at 3.4 nm**

Y. Avitzour, S. Suckewer

JOSA B, Vol. 24, Issue 4, pp. 819-828

**Abstract**

We present numerical studies of recombination gain in the transition to the ground state of H-like C (2→1 transition at λ=3.4 nm). It is shown that high gain (up to about 180 cm^{−1}) can be achieved using currently available, relatively compact, laser technology. The model includes the ionization of the plasma by an ultraintense, ultrashort laser pulse, followed by plasma expansion, cooling, and recombination. Transient population inversion is generated during the recombination process. We investigate the behavior of the gain with respect to different plasma parameters and pump pulse parameters and explain how the different properties of the plasma and the pump pulse affect the gain. *©2007 Optical Society of America *

**Optical properties of sub-wavelength hole arrays in SiC membranes**

Y.A. Urzhumov, D. Korobkin, B. Neuner III, C. Zorman, G. Shvets

**Abstract**

It is shown that perforated SiC membranes can be used for engineering optical properties of metamaterials in the infrared. The complex-valued frequency-dependent effective dielectric permittivity ε_{eff}(ω) of a single membrane can be controlled by the size and spacing between the holes. Regions of the anomalous dispersion and strong absorption described by ε_{eff}(ω) have been identified and related to the excitation of even-parity surface phonon polaritons of a smooth SiC film. The effective permittivity description has been validated by comparing the transmittance and absorbance of the film obtained from ε_{eff}(ω) with that calculated using first principles electromagnetic simulations. Theoretical predictions of the enhanced transmission and absorption in the perforated film have been verified experimentally using FTIR micro-spectroscopy. For the first time, the dependence of enhanced transmission and absorption on the incidence plane of the incoming radiation has been studied. ©*2008 Institute of Physics and IOP Publishing Limited*

DOI: 10.1088/1464-4258/9/9/S07

**IFSR-1239**

D. Korobkin, Y.A. Urzhumov, B.Neuner III, C. Zorman, Z. Zhang, I.D. Mayergoyz, G. Shvets

**Abstract**

We theoretically and experimentally study electromagnetic properties of a novel mid-infrared metamaterial: optically thin silicon carbide (SiC) membrane perforated by an array of sub-wavelength holes. Giant absorption and transmission is found using Fourier transformed infrared (FTIR) microscopy and explained by introducing a frequency-dependent effective permittivity ε_{eff}(ω) of the perforated film. The value of ε_{eff}(ω) is determined by the excitation of two distinct types of hole resonances: delocalized slow surface polaritons (SSPs) whose frequencies are largely determined by the array period, and a localized surface polariton (LSP) corresponding to the resonance of an isolated hole. Only SSPs are shown to modify ε_{eff}(ω) strongly enough to cause giant transmission and absorption. Because of the sub-wavelength period of the hole array, anomalous optical properties can be directly traced to surface polaritons, and their interpretation is not obscured by diffractive effects. Giant absorbance of this metamaterial can be utilized in designing highly efficient thermal radiation sources. *©2008 Springer *

DOI: 10.1007/s00339-007-4084-8

** Strongly Driven Frequency-Sweeping Events in Plasmas**

R.G.L. Vann, H.L. Berk, A.R. Soto-Chavez

**Abstract**

A generic model of a kinetic plasma formed from a source and sink is presented which without instability would form a strongly unstable state due to a single mode. Instead, the resulting wave-particle resonant interaction maintains the distribution near a marginally stable state through the continual production of fast frequency-sweeping modes that sweep unidirectionally (upward in our case) throughout the energy-inverted region of the distribution function. The energy of these modes can be channeled to the background plasma through wave dissipation and, in our particular example, one quarter of the injected energy is available to be channeled. *©2008 The American Physical Society *

DOI: 10.1103/PhysRevLett.99.025003

**Reversed shear Alfvén eigenmode stabilization by localized electron cyclotron heating**

M.A. Van Zeeland, W.W. Heidbrink, R. Nazikian, W.M. Soloman, M.E. Austin, H.L. Berk, N.N. Gorelenkov, C.T. Holcomb, A.W. Hyatt, G.J. Kramer, J. Lohr, M.A. Makowski, G.R. McKee, C.C. Petty, S.E. Sharapov, T.L. Rhodes

**Abstract**

Reversed shear Alfvén eigenmode (RSAE) activity in DIII-D is stabilized by electron cyclotron heating (ECH) applied near the minimum of the magnetic safety factor (*q*_{min}) in neutral beam heated discharges with reversed-magnetic shear. The degree of RSAE stabilization, fast ion density and the volume averaged neutron production (*S*_{n}) are highly dependent on ECH deposition location relative to *q*_{min}. While discharges with ECH stabilization of RSAEs have higher *S*_{n} and more peaked fast ion profiles than discharges with significant RSAE activity, neutron production remains strongly reduced (up to 60% relative to TRANSP predictions assuming classical fast ion transport) even when RSAEs are stabilized. ©*2008 Institute of Physics and IOP Publishing Limited*

DOI: 10.1088/0741-3335/50/3/035009

**Chapter 5: Physics of energetic ions**

A. Fasoli, C. Gormenzano, H.L. Berk, B. Breizman, S. Briguglio, D. S. Darrow, N. Gorelenkov, W. W. Heidbrink, A. Jaun, S.V. Konovalov, R. Nazikian, J.-M. Noterdaeme, S. Sharapov, K. Shinehara, D. Testa, K. Tobita, T. Todo, G. Vlad, F. Zonca

**Abstract**

This chapter reviews the progress accomplished since the redaction of the first ITER Physics Basis (1999 Nucl. Fusion 39 2137–664) in the field of energetic ion physics and its possible impact on burning plasma regimes. New schemes to create energetic ions simulating the fusion-produced alphas are introduced, accessing experimental conditions of direct relevance for burning plasmas, in terms of the Alfvénic Mach number and of the normalised pressure gradient of the energetic ions, though orbit characteristics and size cannot always match those of ITER. Based on the experimental and theoretical knowledge of the effects of the toroidal magnetic field ripple on direct fast ion losses, ferritic inserts in ITER are expected to provide a significant reduction of ripple alpha losses in reversed shear configurations. The nonlinear fast ion interaction with kink and tearing modes is qualitatively understood, but quantitative predictions are missing, particularly for the stabilisation of sawteeth by fast particles that can trigger neoclassical tearing modes. A large database on the linear stability properties of the modes interacting with energetic ions, such as the Alfvén eigenmode has been constructed. Comparisons between theoretical predictions and experimental measurements of mode structures and drive/damping rates approach a satisfactory degree of consistency, though systematic measurements and theory comparisons of damping and drive of intermediate and high mode numbers, the most relevant for ITER, still need to be performed. The nonlinear behaviour of Alfvén eigenmodes close to marginal stability is well characterized theoretically and experimentally, which gives the opportunity to extract some information on the particle phase space distribution from the measured instability spectral features. Much less data exists for strongly unstable scenarios, characterised by nonlinear dynamical processes leading to energetic ion redistribution and losses, and identified in nonlinear numerical simulations of Alfvén eigenmodes and energetic particle modes. Comparisons with theoretical and numerical analyses are needed to assess the potential implications of these regimes on burning plasma scenarios, including in the presence of a large number of modes simultaneously driven unstable by the fast ions. ©*2007 Institute of Physics and IOP Publishing Limited*

DOI: 10.1088/0029-5515/47/6/S05

**IFSR-1235**

**Predictions and observations of low-shear beta-induced shear Alfvén–acoustic eigenmodes in toroidal plasmas**

N.N. Gorelenkov, H.L. Berk, E. Fredrickson, S. E. Sharapov

Physics Letters A Volume 370, Issue 1, 8 October 2007, Pages 70-77

**Abstract**

New global MHD eigenmode solutions arising in gaps in the low frequency Alfvén–acoustic continuum below the geodesic acoustic mode (GAM) frequency have been found numerically and have been used to explain relatively low frequency experimental signals seen in NSTX and JET tokamaks. These global eigenmodes, referred to here as Beta-induced Alfvén–Acoustic Eigenmodes (BAAE), exist in the low magnetic safety factor region near the extrema of the Alfvén–acoustic continuum. In accordance to the linear dispersion relations, the frequency of these modes shifts as the safety factor, q, decreases. We show that BAAEs can be responsible for observations in JET plasmas at relatively low beta <2% as well as in NSTX plasmas at relatively high-beta >20%. In contrast to the mostly electrostatic character of GAMs the new global modes also contain an electromagnetic (magnetic field line bending) component due to the Alfvén coupling, leading to wave phase velocities along the field line that are large compared to the sonic speed. Qualitative agreement between theoretical predictions and observations are found. *©2007 Elsevier B.V.*

DOI: 10.1016/j.physleta.2007.05.113

**Evidence for anomalous effects on the current evolution in the tokamak hybrid operating scenarios**

T.A. Casper, R.J. Jayakumar, S.L. Allen, C.T. Holcomb, L.L. LoDestro, M.A. Makowski, L.D. Pearlstein, H.L. Berk, C.M. Greenfield, T.C. Luce, C.C. Petty, P.A. Politzer, M. R. Wade

**Abstract**

Alternatives to the usual picture of advanced tokamak (AT) discharges are those that form when anomalous thermal conductivity and/or resistivity alter plasma current and pressure profiles to achieve stationary characteristics through self-organizing mechanisms where a measure of desired AT features is maintained without external current-profile control. Regimes exhibiting these characteristics are those where the safety factor (*q*) evolves to a stationary profile with the on-axis and minimum *q*~ 1. Operating scenarios with fusion performance exceeding H-mode at the same plasma current and where the inductively driven current density achieves a stationary configuration with either small or nonexisting sawteeth should enhance the performance of ITER and future burning plasma experiments. We present simulation results of anomalous current-profile formation and evolution using theory-based hyper-resistive models. These simulations are stimulated by experimental observations with which we compare and contrast the simulated evolution. We find that the hyper-resistivity is sufficiently strong to modify the current-profile evolution to achieve conditions consistent with experimental observations. Modelling these anomalous effects is important for developing a capability to scale current experiments to future burning plasmas. ©*2007 Institute of Physics and IOP Publishing Limited*

DOI: 10.1088/0029-5515/47/8/013

**IFSR-1233**

**Energy Confinement Scaling Predictions for the Stabilized Tandem Mirror**

J. Pratt, W. Horton, H.L. Berk

**Abstract**

The absence of toroidal curvature and the relatively weak internal parallel currents in a tandem mirror gives the system favorable stability and transport properties. GAMMA-10 experiments demonstrate that sheared plasma rotation suppresses turbulent radial losses through control of the radial potential profiles. Recent achievements of the GAMMA-10 include 3 keV ion confinement potentials and *T* _{e} ≥ 800 eV. Total energy confinement times for the GAMMA-10 experiment exceed by an order of magnitude the corresponding empirical confinement times in toroidal devices. At the temperatures achieved in the GAMMA-10, the end loss rate τ_{p}≅ 100 ms so that radial losses determine τ_{E}, as intended in tandem mirror reactor designs. Drift-wave results on radial confinement times developed using Bohm, gyro-Bohm, and electron temperature gradient (ETG) scalings imply that the tandem mirror has a qualitatively different form of drift-wave radial transport from that in toroidal devices. Drift-wave eigenmodes for the GAMMA-10 are analyzed for the fluctuating electrostatic potential and magnetic perturbations. *©2008 Springer *

DOI: 10.1007/s10894-007-9113-2

**Scaling of the peak magnetic reconnection rate in the inviscid Taylor problem**

R. Fitzpatrick

**Abstract**

A dispute regarding the scaling of the peak magnetic reconnection rate in the inviscid Taylor problem for ka<<1 is resolved. *©2008 American Institute of Physics *

DOI: 10.1063/1.2839768

**IFSR-1231**

T. Cho, V.P. Pastukhov, W. Horton, T. Numakura, M. Hirata, J. Kohagura, N.V. Chudin, J. Pratt

**Abstract**

Although space weather is modeled after tropospheric weather, both in its conception as a weather system and in our efforts to forecast it, no capability exists today for assimilating magnetospheric data into space weather simulations. In this paper a scheme is proposed for assimilating magnetospheric data into a global MHD code. The scheme is similar to ensemble Kalman filters, but it is less reliant on dense data coverage and allows numerical models easier adherence to conservation laws. Three different estimates of the computational cost of the proposed scheme indicate that it is easily achievable with current computational resources. *An edited version of this paper was published by AGU. ©* *2007 American Geophysical Union*

DOI: 10.1029/2006SW000236

**Study of thermonuclear Alfven instabilities in next step burning plasma proposals **

N.N. Gorelenkov, H.L. Berk, R. Budny, C.Z. Zheng, G.-Y. Fu, W.W. Heidbrink, G.J. Kramer, D. Meade, R. Nazikian

**Abstract**

The stability of α-particle driven shear Alfvén eigenmodes (AE) for nominal burning plasma (BP) parameters in the proposed international tokamak experimental reactor (ITER), fusion ignition research experiment (FIRE) and IGNITOR tokamaks is studied. JET plasma, where fusion αs were generated in tritium experiments, is also studied to compare the numerical predictions with the existing experiments. An analytic assessment of toroidal AE (TAE) stability is first presented, where the α-particle β due to the fusion reaction rate and electron drag is simply and accurately estimated in plasmas with central temperature in the range of 7–20 keV. In this assessment the hot particle drive is balanced against ion-Landau damping of the background deuterons, and electron collision effects and stability boundaries are determined. Then two numerical studies of AE instability are presented. In one, the HIgh-*n* STability (HINST) code is used to predict the instabilities of low and moderately high frequency Alfvén modes. HINST computes the non-perturbative solutions of the AE including effects of ion finite Larmor radius, orbit width, trapped electrons etc. The stability calculations are repeated using the global code NOVAK. We show that for these plasmas the spectrum of the least stable AE modes is at medium-/high-n numbers. In HINST, TAEs are locally unstable due to the α pressure gradient in all the devices under consideration except IGNITOR. However, NOVAK calculations show that the global mode structure enhances the damping mechanisms and produces stability for the nominal FIRE proposal and near-marginal stability for the nominal ITER proposal. NBI ions produce a strong stabilizing effect for JET. However, in ITER, the beam energies needed to penetrate to the core must be high (~1 MeV) so that a diamagnetic drift frequency comparable to that of α-particles is produced by the beam ions which induces a destabilizing effect. A serious question remains whether the perturbation theory used in NOVAK overestimates the stability predictions, so that it is premature to conclude that the nominal operation of all three BP proposals without neutral beam injection are stable (or marginally stable) to AEs. ©*2003 Institute of Physics and IOP Publishing Limited*

DOI: 10.1088/0029-5515/43/7/313

**Edge-localized modes explained as the amplification of scrape-off-layer current coupling **

L.J. Zheng, H. Takahashi, E.D. Fredrickson

**Abstract**

It is shown that the edge-localized modes (ELMs) observed in tokamak H mode discharges can be explained as external magnetohydrodynamic (MHD) mode amplification due to coupling with scrape-off-layer current. The proposed model offers a new ELM mechanism that produces a sharp onset and initial fast growth of magnetic perturbations even when the underlying equilibrium is only marginally unstable for a MHD mode and also a quick quenching after the bursting peak. The theory also reproduces various other ELM features. *©2008 American Physical Society *

DOI: 10.1103/PhysRevLett.100.115001

**Summary: Third IAEA technical meeting on theory of plasma instabilities **

H.R. Wilson, B.N. Breizman, A.G. Peeters

©*2007 Institute of Physics and IOP Publishing Limited*

DOI: 10.1088/0029-5515/47/12/010

**Hamiltonian formulation and analysis of a collisionless fluid reconnection model**

E. Tassi, P. J. Morrison, F. L. Waelbroeck, and D. Grasso

**Abstract**

The Hamiltonian formulation of a plasma four-field fluid model that describes collisionless reconnection is presented. The formulation is noncanonical with a corresponding Lie–Poisson bracket. The bracket is used to obtain new independent families of invariants, so-called Casimir invariants, three of which are directly related to Lagrangian invariants of the system. The Casimirs are used to obtain a variational principle for equilibrium equations that generalize the Grad–Shafranov equation to include flow. Dipole and homogeneous equilibria are constructed. The linear dynamics of the latter is treated in detail in a Hamiltonian context: canonically conjugate variables are obtained; the dispersion relation is analyzed and exact thresholds for spectral stability are obtained; the canonical transformation to normal form is described; an unambiguous definition of negative energy modes is given; and thresholds sufficient for energy-Casimir stability are obtained. The Hamiltonian formulation is also used to obtain an expression for the collisionless conductivity and it is further used to describe the linear growth and nonlinear saturation of the collisionless tearing mode. ©*2007 Institute of Physics and IOP Publishing Limited
*DOI: 10.1088/0741-3335/50/8/085014

**Hypersonic drift-tearing magnetic islands in tokamak plasmas **

R. Fitzpatrick, F.L. Waelbroeck

**Abstract**

A two-fluid theory of long wavelength, hypersonic, drift-tearing magnetic islands in low-collisionality, low-beta plasmas possessing relatively weak magnetic shear is developed. The model assumes both slab geometry and cold ions, and neglects electron temperature and equilibrium current gradient effects. The problem is solved in three asymptotically matched regions. The “inner region” contains the island. However, the island emits electrostatic drift-acoustic waves that propagate into the surrounding “intermediate region,” where they are absorbed by the plasma. Since the waves carry momentum, the inner region exerts a net force on the intermediate region, and vice versa, giving rise to strong velocity shear in the region immediately surrounding the island. The intermediate region is matched to the surrounding “outer region,” in which ideal magnetohydrodynamic holds. Isolated hypersonic islands propagate with a velocity that lies between those of the unperturbed local ion and electron fluids, but is much closer to the latter. The ion polarization current is stabilizing, and increases with increasing island width. Finally, the hypersonic branch of isolated island solutions ceases to exist above a certain critical island width. Hypersonic islands whose widths exceed the critical width are hypothesized to bifurcate to the so-called “sonic” solution branch. ©*2007 American Institute of Physics*

DOI: 10.1063/1.2811928

E. A. Lazarus, T. C. Luce, M. E. Austin, D. P. Brennan, K. H. Burrell, M. S. Chu, J. R. Ferron, A. W. Hyatt, R. J. Jayakumar, L. L. Lao, J. Lohr, M. A. Makowski, T. H. Osborne, C. C. Petty, P. A. Politzer, R. Prater, T. L. Rhodes, J. T. Scoville, W. M. Solomon, E. J. Strait, A. D. Turnbull, F. L. Waelbroeck, and C. Zhang

**Abstract**

The role of interchange and internal kink modes in the sawtooth oscillations is explored by comparing bean- and oval-shaped plasmas. The n=1 instability that results in the collapse of the sawtooth has been identified as a quasi-interchange in the oval cases and the internal kink in the bean shape. The ion and electron temperature profiles are followed in detail through the sawtooth ramp. It is found that electron energy transport rates are very high in the oval and quite low in the bean shape. Ion energy confinement in the oval is excellent and the sawtooth amplitude (deltaT/T) in the ion temperature is much larger than that of the electrons. The sawtooth amplitudes for ions and electrons are comparable in the bean shape. The measured q profiles in the bean and oval shapes are found to be consistent with neoclassical current diffusion of the toroidal current, and the observed differences in q largely result from the severe differences in electron energy transport. For both shapes the collapse flattens the q profile and after the collapse return to q0>~1. Recent results on intermediate shapes are reported. These shapes show that the electron energy transport improves gradually as the plasma triangularity is increased. © 2007 *American Institute of Physics*

DOI: 10.1063/1.2436849

**IFSR-1220**

**Bifurcated states of the error-field-induced magnetic islands **

L.-J. Zheng, B. Li, R.D. Hazeltine

Physics Letters A Volume 372, Issue 12, 17 March 2008, Pages 2056-2060

**Abstract**

We find that the formation of the magnetic islands due to error fields shows bifurcation when neoclassical effects are included. The bifurcation, which follows from including bootstrap current terms in a description of island growth in the presence of error fields, provides a path to avoid the island-width pole in the classical description. The theory offers possible theoretical explanations for the recent DIII-D and JT-60 experimental observations concerning confinement deterioration with increasing error field.* ©2008 Elsevier B.V.*

DOI: 10.1016/j.physleta.2007.11.017

**Comment on "Derivation of paleoclassical key hypothesis" [Phys. Plasmas 14, 040701 (2007)] **

A. Thyagaraja, C.M. Roach, R.D. Hazeltine

**Abstract**

The paleoclassical hypothesis, derived in Callen [Phys. Plasmas 14, 040701 (2007)], proposes that electron guiding centers experience additional diffusion which is absent from neoclassical theory. This is claimed to be associated with the diffusion of poloidal magnetic flux, and to be most significant in cold resistive plasmas. In this comment we explain why the paleoclassical hypothesis contradicts electrodynamics. © *2008 American Institute of Physics *

DOI: 10.1063/1.2828096

**Plasma fluctuations as Markovian noise **

B. Li, R.D. Hazeltine, K.W. Gentle

**Abstract**

Noise theory is used to study the correlations of stationary Markovian fluctuations that are homogeneous and isotropic in space. The relaxation of the fluctuations is modeled by the diffusion equation. The spatial correlations of random fluctuations are modeled by the exponential decay. Based on these models, the temporal correlations of random fluctuations, such as the correlation function and the power spectrum, are calculated. We find that the diffusion process can give rise to the decay of the correlation function and a broad frequency spectrum of random fluctuations. We also find that the transport coefficients may be estimated by the correlation length and the correlation time. The theoretical results are compared with the observed plasma density fluctuations from the tokamak and helimak experiments. *©2007 The American Physical Society*

DOI: 10.1103/PhysRevE.76.066402

**Fluid Model for Relativistic, Magnetized Plasmas**

J. TenBarge, S.M. Mahajan, R.D. Hazeltine

**Abstract**

Many astrophysical plasmas and some laboratory plasmas are relativistic: either the thermal speed or the local bulk flow in some frame approaches the speed of light. Often, such plasmas are magnetized in the sense that the Larmor radius is smaller than the gradient scale length of interest. Conventionally, relativistic MHD is employed to treat relativistic, magnetized plasmas; however, MHD requires the collision time to be shorter than any other time scale in the system. Thus, MHD employs the thermodynamic equilibrium form of the stress tensor, neglecting pressure anisotropy and heat flow parallel to the magnetic field. Recent work has attempted to remedy these shortcomings. This paper re-examines the closure question and finds a more complete theory, which yields a more physical and self-consistent closure. Beginning with exact moments of the kinetic equation, we derive a closed set of Lorentz-covariant fluid equations for a magnetized plasma allowing for pressure and heat flow anisotropy. Basic predictions of the model, especially of the dispersion relation’s dependence upon relativistic temperature, are examined.

**Global Axisymmetric Magnetorotational Instability with Density Gradients**

Jesse Pino, S.M. Mahajan

**Abstract**

We examine global incompressible axisymmetric perturbations of a differentially rotating MHD plasma with radial density gradients. It is shown that the standard magnetorotational instability (MRI) criterion drawn from the local dispersion relation is often misleading. If the equilibrium magnetic field is either purely axial or purely toroidal, the problem reduces to finding the global radial eigenvalues of an effective potential. The standard Keplerian profile including the origin is mathematically ill-posed, and thus any solution will depend strongly on the inner boundary. We find a class of unstable modes localized by the form of the rotation and density profiles, with reduced dependence on boundary conditions. *© 2008 The American Astronomical Society*

**Active control of internal transport barrier formation due to off-axis electron-cyclotron heating in GAMMA 10 experiments**

T. Cho, V.P. Pastukhov, W. Horton, T. Numakura, M. Hirata, J. Kohagura, N.V. Chudin, J. Pratt

**Abstract**

The controlled formation of an internal transport barrier (ITB) is observed in GAMMA 10 [T. Cho *et al*., Nucl. Fusion **45**, 1650 (2005)]. The barrier is localized within a layer of a strongly sheared **E _{r}×B **plasma rotation (5.5<r

DOI: 10.1063/1.2906262

**Ambipolar acceleration of ions in a magnetic nozzle**

A.V. Arefiev, B.N. Breizman

**Abstract**

This paper describes a magnetic nozzle with a magnetic mirror configuration that transforms a collisionless subsonic plasma flow into a supersonic jet expanding into the vacuum. The nozzle converts electron thermal energy into the ion kinetic energy via an ambipolar electric field. The ambipolar potential in the expanding plume involves a time-dependent rarefaction wave. Travelling through the rarefaction wave, electrons lose some kinetic energy and can become trapped downstream from the mirror throat. This work presents a rigorous adiabatic description of the trapped electron population. It examines the impact of the adiabatic cooling of the trapped electrons on the ambipolar potential and the ensuing ion acceleration. The problem is formulated for an arbitrary incoming electron distribution and then a “water-bag” electron distribution is used to obtain a closed-form analytical solution. *©2008 American Institute of Physics *

DOI:10.1063/1.2907786

**Magnetic nozzle and plasma detachment model for a steady-state flow**

B.N. Breizman, M.R. Tushentsov, A.V. Arefiev

**Abstract**

Plasma propulsion concepts that employ a guiding magnetic field raise the question of how the magnetically controlled plasma can detach from the spacecraft. This paper presents a detachment scenario relevant to high-power thrusters in which the plasma can stretch the magnetic field lines to infinity, similar to the solar wind. In previous work, the corresponding ideal magnetohydrodynamics equations have been solved analytically for a plasma flow in a slowly diverging nozzle. That solution indicates that efficient detachment is feasible if the nozzle is sufficiently long. In order to extend the previous model beyond the idealizations of analytical theory, a Lagrangian code is developed in this work to simulate steady-state kinetic plasma flows and to evaluate nozzle efficiency. The code is benchmarked against the analytical results and then used to examine situations that are not analytically tractable, including plasma behavior in the recent Detachment Demonstration Experiment at the National Aeronautics and Space Administration. *©2008 American Institute of Physics*

DOI:10.1063/1.2903844

**"Maximum" entropy production in self-organized plasma boundary layer: A thermodynamic discussion about turbulent heat transport **

Z. Yoshida, S.M. Mahajan

**Abstract**

A thermodynamic model of a plasma boundary layer, characterized by enhanced temperature contrasts and “maximum entropy production,” is proposed. The system shows bifurcation if the heat flux entering through the inner boundary exceeds a critical value. The state with a larger temperature contrast (larger entropy production) sustains a self-organized flow. An inverse cascade of energy is proposed as the underlying physical mechanism for the realization of such a heat engine.* ©2008 American Institute of Physics *

DOI: 10.1063/1.2890189

**Studies of laser wakefield structures and electron acceleration in underdense plasmas**

A. Maksimchuk, S. Reed, S. S. Bulanov, V. Chvykov, G. Kalintchenko, T. Matsuoka, C. McGuffey, G. Mourou, N. Naumova, J. Nees, P. Rousseau, V. Yanovsky, K. Krushelnick, N. H. Matlis, S. Kalmykov, G. Shvets, M. C. Downer, C. R. Vane, J. R. Beene, D. Stracener, D. R. Schultz

**Abstract**

Experiments on electron acceleration and optical diagnostics of laser wakes were performed on the HERCULES facility in a wide range of laser and plasma parameters. Using frequency domain holography we demonstrated single shot visualization of individual plasma waves, produced by 40 TW, 30 fs laser pulses focused to the intensity of 10^{19} W/cm^{2} onto a supersonic He gas jet with plasma densities n_{e}<10^{19} cm^{−3}. These holographic “snapshots” capture the variation in shape of the plasma wave with distance behind the driver, and resolve wave front curvature seen previously only in simulations. High-energy quasimonoenergetic electron beams were generated using plasma density in the range 1.5×10^{19}≤n_{e}≤3.5×10^{19} cm^{−3}. These experiments demonstrated that the energy, charge, divergence, and pointing stability of the beam can be controlled by changing n_{e}, and that higher electron energies and more stable beams are produced for lower densities. An optimized quasimonoenergetic beam of over 300 MeV and 10 mrad angular divergence is demonstrated at a plasma density of n_{e}≅1.5×10^{19} cm^{−3}. The resultant relativistic electron beams have been used to perform photo-fission of ^{238}U with a record high reaction yields of ~3×10^{5}/J. The results of initial experiments on electron acceleration at 70 TW are discussed. *©2008 American Institute of Physics*

DOI:10.1063/1.2856373

**Classical Perfect Diamagnetism: Expulsion of Current from the Plasma Interior **

S.M. Mahajan

**Abstract**

The vanishing of generalized helicity is shown to be the necessary and sufficient condition for a perfect conductor to display perfect diamagnetism, considered to be the defining attribute of a conventional superconductor. Although conventional superconductivity is brought about by quantum correlations in classical systems, prepared in the state of zero initial helicity (helicity is a constant of the motion for a perfect conductor), it can mimic the superconductor's behavior. *©2008 The American Physical Society *

DOI:10.1103/PhysRevLett.100.075001

**Manipulating Electromagnetic Waves in Magnetized Plasmas: Compression, Frequency Shifting, and Release **

Yoav Avitzour, G Shvets

**Abstract**

A new approach to manipulating the duration and frequency of microwave pulses using magnetized plasmas is demonstrated. The plasma accomplishes two functions: (i) slowing down and spatially compressing the incident wave, and (ii) modifying the propagation properties (group velocity and frequency) of the wave in the plasma during a uniform in space adiabatic in time variation of the magnitude and/or direction of the magnetic field. The increase in the group velocity results in the shortening of the temporal pulse duration. Depending on the plasma parameters, the frequency of the outgoing compressed pulse can either change or remain unchanged. Such dynamic manipulation of radiation in plasma opens new avenues for manipulating high power microwave pulses. *©2008 The American Physical Society*

DOI:10.1103?PhysRevLett.100.065006

**Metamaterials add an extra dimension**

G. Shvets

**Abstract **

In a major departure from their humble origins as ultrathin monolayers, optical metamaterials have now advanced to three-dimensional bulk media exhibiting both electric and magnetic activity. *© 2008 Nature Publishing Group *

DOI:10.1038/nmat2088

**The complex Bloch bands of a 2D plasmonic crystal displaying isotropic negative refraction **

M Davanco, Y Urzhumov, G Shvets

**Abstract**

The propagation characteristics of a subwavelength plasmonic crystal are studied based on its complex Bloch band structure. Photonic crystal bands are generated with an alternative 2D Finite Element Method formulation in which the Bloch wave problem is reduced to a quadratic eigenvalue system for the Bloch wavevector amplitude k. This method constitutes an efficient and convenient alternative to nonlinear search methods normally employed in the calculation of photonic bands when dispersive materials are involved. The method yields complex wavevector Bloch modes that determine the wave-scattering characteristics of finite crystals. This is evidenced in a comparison between the band structure of the square-lattice plasmonic crystal and scattering transfer-functions from a corresponding finite crystal slab. We report on a wave interference effect that leads to transmission resonances similar to Fano resonances, as well as on the isotropy of the crystal’s negative index band. Our results indicate that effective propagation constants obtained from scattering simulations may not always be directly related to individual crystal Bloch bands. *© 2007 Optical Society of America *

**Spectral Gap of Shear Alfvén Waves in a Periodic array of Magnetic Mirrors **

Yang Zhang, W.W. Heidbrink, H. Boehmer, R. McWilliams, Guangye Chen, B.N. Breizman, S. Vincena, T. Carter, D. Leneman, W. Gekelman, P. Pribyl, B. Bru

**Abstract**

A multiple magnetic mirror array is formed at the Large Plasma Device (LAPD) [W. Gekelman, H. Pfister, Z. Lucky, J. Bamber, D. Leneman, and J. Maggs, Rev. Sci. Instrum. 62, 2875 (1991)] to study axial periodicity-influenced Alfvén spectra. Shear Alfvén waves (SAW) are launched by antennas inserted in the LAPD plasma and diagnosed by B-dot probes at many axial locations. Alfvén wave spectral gaps and continua are formed similar to wave propagation in other periodic media due to the Bragg effect. The measured width of the propagation gap increases with the modulation amplitude as predicted by the solutions to Mathieu's equation. A two-dimensional finite-difference code modeling SAW in a mirror array configuration shows similar spectral features. Machine end-reflection conditions and damping mechanisms including electron-ion Coulomb collision and electron Landau damping are important for simulation. *© 2008 American Institute of Physics *

DOI: 10.1063/1.2827518